id	sid	tid	token	lemma	pos
esrj-31288	1	1	geofisica	geofisica	PROPN
esrj-31288	1	2	colombiana	colombiana	PROPN
esrj-31288	1	3	p	p	PROPN
esrj-31288	1	4	p	p	PROPN
esrj-31288	1	5	5	5	NUM
esrj-31288	1	6	-1	-1	SYM
esrj-31288	1	7	1	1	NUM
esrj-31288	1	8	0121	0121	NUM
esrj-31288	1	9	2974n	2974n	NOUN
esrj-31288	1	10	°	°	ADP
esrj-31288	1	11	5	5	NUM
esrj-31288	1	12	d	d	NOUN
esrj-31288	1	13	l	l	NOUN
esrj-31288	1	14	c	c	NOUN
esrj-31288	2	1	i	i	PRON
esrj-31288	2	2	e	e	VERB
esrj-31288	2	3	mb	mb	ADP
esrj-31288	2	4	r	r	PROPN
esrj-31288	2	5	e	e	PROPN
esrj-31288	2	6	de	de	X
esrj-31288	2	7	2001	2001	NUM
esrj-31288	2	8	bogota	bogota	PROPN
esrj-31288	2	9	0	0	NUM
esrj-31288	3	1	c.	c.	PROPN
esrj-31288	3	2	iss	iss	PROPN
esrj-31288	3	3	n	n	CCONJ
esrj-31288	3	4	interval	interval	NOUN
esrj-31288	3	5	velocity	velocity	NOUN
esrj-31288	3	6	determination	determination	NOUN
esrj-31288	3	7	by	by	ADP
esrj-31288	3	8	downward	downward	ADJ
esrj-31288	3	9	continuation	continuation	NOUN
esrj-31288	3	10	of	of	ADP
esrj-31288	3	11	the	the	DET
esrj-31288	3	12	traveltime	traveltime	NOUN
esrj-31288	3	13	function	function	NOUN
esrj-31288	3	14	:	:	PUNCT
esrj-31288	3	15	paraxial	paraxial	ADJ
esrj-31288	3	16	ray	ray	NOUN
esrj-31288	3	17	approximation	approximation	NOUN
esrj-31288	3	18	luis	luis	PROPN
esrj-31288	3	19	montes	montes	PROPN
esrj-31288	3	20	v	v	PROPN
esrj-31288	3	21	,	,	PUNCT
esrj-31288	3	22	des	des	PROPN
esrj-31288	3	23	profesor	profesor	NOUN
esrj-31288	3	24	asociado	asociado	PROPN
esrj-31288	3	25	departamento	departamento	PROPN
esrj-31288	3	26	de	de	PROPN
esrj-31288	3	27	geociencias	geociencias	PROPN
esrj-31288	3	28	facultad	facultad	PROPN
esrj-31288	3	29	de	de	PROPN
esrj-31288	3	30	ciencias	ciencias	PROPN
esrj-31288	3	31	universidad	universidad	PROPN
esrj-31288	3	32	nacional	nacional	PROPN
esrj-31288	3	33	de	de	PROPN
esrj-31288	3	34	colombia	colombia	PROPN
esrj-31288	3	35	.	.	PUNCT
esrj-31288	4	1	resumen	resumen	PROPN
esrj-31288	4	2	present	present	PROPN
esrj-31288	4	3	amos	amos	PROPN
esrj-31288	4	4	un	un	PROPN
esrj-31288	4	5	rnetodo	rnetodo	PROPN
esrj-31288	4	6	para	para	PROPN
esrj-31288	4	7	estirnar	estirnar	PROPN
esrj-31288	4	8	las	las	PROPN
esrj-31288	4	9	velocidades	velocidades	PROPN
esrj-31288	4	10	de	de	X
esrj-31288	4	11	intervalo	intervalo	PROPN
esrj-31288	4	12	,	,	PUNCT
esrj-31288	4	13	la	la	PROPN
esrj-31288	4	14	profundidad	profundidad	PROPN
esrj-31288	4	15	y	y	PROPN
esrj-31288	4	16	la	la	PROPN
esrj-31288	4	17	geometrfa	geometrfa	PROPN
esrj-31288	4	18	de	de	X
esrj-31288	4	19	los	los	PROPN
esrj-31288	4	20	reflectores	reflectore	NOUN
esrj-31288	4	21	en	en	PROPN
esrj-31288	4	22	modelos	modelos	PROPN
esrj-31288	4	23	3d	3d	PROPN
esrj-31288	4	24	que	que	PROPN
esrj-31288	4	25	constan	constan	PROPN
esrj-31288	4	26	de	de	PROPN
esrj-31288	4	27	un	un	PROPN
esrj-31288	4	28	apilado	apilado	PROPN
esrj-31288	4	29	de	de	PROPN
esrj-31288	4	30	capas	capas	PROPN
esrj-31288	4	31	hornogeneas	hornogeneas	PROPN
esrj-31288	4	32	e	e	PROPN
esrj-31288	4	33	isotr6picas	isotr6picas	PROPN
esrj-31288	4	34	con	con	PROPN
esrj-31288	4	35	velocidades	velocidades	PROPN
esrj-31288	4	36	y	y	PROPN
esrj-31288	4	37	densidades	densidades	PROPN
esrj-31288	4	38	arbitrarias	arbitrarias	PROPN
esrj-31288	4	39	,	,	PUNCT
esrj-31288	4	40	separadas	separadas	PROPN
esrj-31288	4	41	por	por	NOUN
esrj-31288	4	42	interfaces	interface	NOUN
esrj-31288	4	43	suaves	suave	VERB
esrj-31288	4	44	.	.	PUNCT
esrj-31288	5	1	el	el	PROPN
esrj-31288	5	2	tiempo	tiempo	PROPN
esrj-31288	5	3	de	de	X
esrj-31288	5	4	transite	transite	ADJ
esrj-31288	5	5	de	de	X
esrj-31288	5	6	cualquier	cualquier	NOUN
esrj-31288	5	7	rayo	rayo	NOUN
esrj-31288	5	8	reflejado	reflejado	VERB
esrj-31288	5	9	en	en	PROPN
esrj-31288	5	10	una	una	X
esrj-31288	5	11	interfaz	interfaz	X
esrj-31288	5	12	particular	particular	PROPN
esrj-31288	5	13	y	y	PROPN
esrj-31288	5	14	registrado	registrado	VERB
esrj-31288	5	15	en	en	X
esrj-31288	5	16	la	la	X
esrj-31288	5	17	vecindad	vecindad	PROPN
esrj-31288	5	18	de	de	PROPN
esrj-31288	5	19	un	un	PROPN
esrj-31288	5	20	rayo	rayo	PROPN
esrj-31288	5	21	zero	zero	NUM
esrj-31288	5	22	-	-	PUNCT
esrj-31288	5	23	offset	offset	NOUN
esrj-31288	5	24	se	se	PROPN
esrj-31288	5	25	expresa	expresa	PROPN
esrj-31288	5	26	mediante	mediante	PROPN
esrj-31288	6	1	una	una	PROPN
esrj-31288	7	1	funci6n	funci6n	PROPN
esrj-31288	8	1	referida	referida	PROPN
esrj-31288	9	1	a	a	DET
esrj-31288	9	2	un	un	PROPN
esrj-31288	9	3	sistema	sistema	PROPN
esrj-31288	9	4	de	de	PROPN
esrj-31288	9	5	coordenadas	coordenadas	PROPN
esrj-31288	9	6	centrado	centrado	PROPN
esrj-31288	9	7	en	en	PROPN
esrj-31288	9	8	el	el	PROPN
esrj-31288	9	9	rayo	rayo	PROPN
esrj-31288	9	10	;	;	PUNCT
esrj-31288	9	11	tal	tal	PROPN
esrj-31288	9	12	funci6n	funci6n	PROPN
esrj-31288	9	13	se	se	PROPN
esrj-31288	9	14	estima	estima	PROPN
esrj-31288	9	15	en	en	PROPN
esrj-31288	9	16	la	la	PROPN
esrj-31288	9	17	superficie	superficie	PROPN
esrj-31288	9	18	superior	superior	PROPN
esrj-31288	9	19	del	del	PROPN
esrj-31288	9	20	modelo	modelo	PROPN
esrj-31288	9	21	.	.	PUNCT
esrj-31288	10	1	la	la	PROPN
esrj-31288	10	2	funci6n	funci6n	ADJ
esrj-31288	10	3	tiempo	tiempo	X
esrj-31288	10	4	de	de	X
esrj-31288	10	5	transite	transite	ADJ
esrj-31288	10	6	de	de	X
esrj-31288	10	7	reflexi6n	reflexi6n	PROPN
esrj-31288	10	8	asociada	asociada	PROPN
esrj-31288	10	9	a	a	DET
esrj-31288	10	10	cada	cada	PROPN
esrj-31288	10	11	superficie	superficie	PROPN
esrj-31288	10	12	reflectora	reflectora	PROPN
esrj-31288	10	13	se	se	PROPN
esrj-31288	10	14	deterrnina	deterrnina	PROPN
esrj-31288	10	15	en	en	PROPN
esrj-31288	10	16	la	la	PROPN
esrj-31288	10	17	superficie	superficie	PROPN
esrj-31288	10	18	superior	superior	PROPN
esrj-31288	10	19	en	en	X
esrj-31288	10	20	la	la	PROPN
esrj-31288	10	21	vecindad	vecindad	PROPN
esrj-31288	10	22	del	del	PROPN
esrj-31288	10	23	rayo	rayo	PROPN
esrj-31288	10	24	central	central	ADJ
esrj-31288	10	25	.	.	PUNCT
esrj-31288	11	1	la	la	PROPN
esrj-31288	11	2	geometria	geometria	PROPN
esrj-31288	11	3	de	de	PROPN
esrj-31288	11	4	la	la	PROPN
esrj-31288	11	5	superficie	superficie	PROPN
esrj-31288	11	6	limitante	limitante	PROPN
esrj-31288	11	7	superior	superior	PROPN
esrj-31288	11	8	de	de	X
esrj-31288	11	9	una	una	PROPN
esrj-31288	11	10	capa	capa	VERB
esrj-31288	11	11	particular	particular	ADJ
esrj-31288	11	12	y	y	PROPN
esrj-31288	11	13	el	el	PROPN
esrj-31288	11	14	tiernpo	tiernpo	PROPN
esrj-31288	11	15	de	de	X
esrj-31288	11	16	transite	transite	PROPN
esrj-31288	11	17	estirnado	estirnado	NOUN
esrj-31288	11	18	sobre	sobre	PROPN
esrj-31288	11	19	la	la	PROPN
esrj-31288	11	20	misma	misma	PROPN
esrj-31288	11	21	permite	permite	PROPN
esrj-31288	11	22	calcular	calcular	PROPN
esrj-31288	11	23	la	la	PROPN
esrj-31288	11	24	velocidad	velocidad	PROPN
esrj-31288	11	25	de	de	PROPN
esrj-31288	11	26	intervalo	intervalo	PROPN
esrj-31288	11	27	de	de	PROPN
esrj-31288	11	28	la	la	PROPN
esrj-31288	11	29	capa	capa	VERB
esrj-31288	11	30	en	en	X
esrj-31288	11	31	cuesti6n	cuesti6n	PROPN
esrj-31288	11	32	y	y	PROPN
esrj-31288	11	33	la	la	PROPN
esrj-31288	11	34	geometria	geometria	PROPN
esrj-31288	11	35	de	de	X
esrj-31288	11	36	la	la	X
esrj-31288	11	37	interfaz	interfaz	PROPN
esrj-31288	11	38	limitante	limitante	PROPN
esrj-31288	11	39	inferior	inferior	PROPN
esrj-31288	11	40	.	.	PUNCT
esrj-31288	12	1	con	con	PROPN
esrj-31288	12	2	la	la	PROPN
esrj-31288	12	3	velocidad	velocidad	PROPN
esrj-31288	12	4	de	de	PROPN
esrj-31288	12	5	intervale	intervale	PROPN
esrj-31288	12	6	y	y	PROPN
esrj-31288	12	7	la	la	PROPN
esrj-31288	12	8	geometrfa	geometrfa	PROPN
esrj-31288	12	9	de	de	PROPN
esrj-31288	12	10	las	las	PROPN
esrj-31288	12	11	interfaces	interface	NOUN
esrj-31288	12	12	limitantes	limitante	NOUN
esrj-31288	12	13	,	,	PUNCT
esrj-31288	12	14	se	se	X
esrj-31288	12	15	estima	estima	PROPN
esrj-31288	12	16	la	la	PROPN
esrj-31288	12	17	funci6n	funci6n	PROPN
esrj-31288	12	18	de	de	X
esrj-31288	12	19	tiempo	tiempo	X
esrj-31288	12	20	de	de	X
esrj-31288	12	21	transite	transite	PROPN
esrj-31288	12	22	del	del	PROPN
esrj-31288	12	23	siguiente	siguiente	PROPN
esrj-31288	12	24	reflector	reflector	PROPN
esrj-31288	12	25	sobre	sobre	PROPN
esrj-31288	12	26	la	la	PROPN
esrj-31288	12	27	interfaz	interfaz	PROPN
esrj-31288	12	28	limitante	limitante	PROPN
esrj-31288	12	29	inferior	inferior	PROPN
esrj-31288	12	30	.	.	PUNCT
esrj-31288	13	1	en	en	ADP
esrj-31288	13	2	este	este	X
esrj-31288	13	3	paso	paso	PROPN
esrj-31288	13	4	se	se	PROPN
esrj-31288	13	5	simula	simula	PROPN
esrj-31288	13	6	el	el	PROPN
esrj-31288	13	7	posicionamiento	posicionamiento	PROPN
esrj-31288	13	8	de	de	AUX
esrj-31288	13	9	las	las	PROPN
esrj-31288	13	10	fuentes	fuentes	PROPN
esrj-31288	13	11	y	y	PROPN
esrj-31288	13	12	los	los	PROPN
esrj-31288	13	13	detectores	detectore	VERB
esrj-31288	13	14	sobre	sobre	PROPN
esrj-31288	13	15	la	la	PROPN
esrj-31288	13	16	superficie	superficie	PROPN
esrj-31288	13	17	anterior	anterior	PROPN
esrj-31288	13	18	de	de	X
esrj-31288	13	19	la	la	PROPN
esrj-31288	13	20	pr6xima	pr6xima	PROPN
esrj-31288	13	21	capa	capa	PROPN
esrj-31288	13	22	subyacente	subyacente	PROPN
esrj-31288	13	23	.	.	PUNCT
esrj-31288	14	1	el	el	PROPN
esrj-31288	14	2	proceso	proceso	PROPN
esrj-31288	14	3	se	se	PROPN
esrj-31288	14	4	repite	repite	PROPN
esrj-31288	14	5	recursivamente	recursivamente	PROPN
esrj-31288	14	6	en	en	PROPN
esrj-31288	14	7	las	las	PROPN
esrj-31288	14	8	capas	capas	PROPN
esrj-31288	14	9	mas	mas	PROPN
esrj-31288	14	10	profundas	profundas	PROPN
esrj-31288	14	11	hasta	hasta	PROPN
esrj-31288	14	12	obtener	obtener	PROPN
esrj-31288	14	13	la	la	PROPN
esrj-31288	14	14	soluci6n	soluci6n	PROPN
esrj-31288	14	15	completa	completa	PROPN
esrj-31288	14	16	sin	sin	PROPN
esrj-31288	14	17	conocimiento	conocimiento	NOUN
esrj-31288	14	18	previo	previo	NOUN
esrj-31288	14	19	,	,	PUNCT
esrj-31288	14	20	excepto	excepto	PROPN
esrj-31288	14	21	el	el	PROPN
esrj-31288	14	22	obtenido	obtenido	PROPN
esrj-31288	14	23	en	en	PROPN
esrj-31288	14	24	las	las	X
esrj-31288	14	25	capas	capas	PROPN
esrj-31288	14	26	superiores	superiore	VERB
esrj-31288	14	27	y	y	PROPN
esrj-31288	14	28	la	la	PROPN
esrj-31288	14	29	funci6n	funci6n	PROPN
esrj-31288	14	30	tiempos	tiempos	NOUN
esrj-31288	14	31	de	de	ADP
esrj-31288	14	32	transite	transite	PROPN
esrj-31288	14	33	de	de	PROPN
esrj-31288	14	34	cada	cada	PROPN
esrj-31288	14	35	superficie	superficie	PROPN
esrj-31288	14	36	reflectora	reflectora	PROPN
esrj-31288	14	37	.	.	PUNCT
esrj-31288	15	1	se	se	PROPN
esrj-31288	15	2	desarrollaron	desarrollaron	PROPN
esrj-31288	15	3	programas	programas	PROPN
esrj-31288	15	4	de	de	PROPN
esrj-31288	15	5	computador	computador	PROPN
esrj-31288	15	6	que	que	PROPN
esrj-31288	15	7	expresan	expresan	PROPN
esrj-31288	15	8	el	el	PROPN
esrj-31288	15	9	algoritmo	algoritmo	PROPN
esrj-31288	15	10	del	del	PROPN
esrj-31288	15	11	metodo	metodo	PROPN
esrj-31288	15	12	y	y	PROPN
esrj-31288	15	13	,	,	PUNCT
esrj-31288	15	14	posteriorrnente	posteriorrnente	NOUN
esrj-31288	15	15	,	,	PUNCT
esrj-31288	15	16	se	se	X
esrj-31288	15	17	probaron	probaron	PROPN
esrj-31288	15	18	con	con	PROPN
esrj-31288	15	19	datos	datos	PROPN
esrj-31288	15	20	sinteticos	sintetico	NOUN
esrj-31288	15	21	,	,	PUNCT
esrj-31288	15	22	suministrando	suministrando	PROPN
esrj-31288	15	23	velocidades	velocidades	PROPN
esrj-31288	15	24	de	de	PROPN
esrj-31288	15	25	intervalo	intervalo	PROPN
esrj-31288	15	26	y	y	PROPN
esrj-31288	15	27	profundidades	profundidade	VERB
esrj-31288	15	28	de	de	X
esrj-31288	15	29	los	los	PROPN
esrj-31288	15	30	reflectores	reflectores	PROPN
esrj-31288	15	31	con	con	PROPN
esrj-31288	15	32	errores	errore	NOUN
esrj-31288	15	33	considerados	considerado	NOUN
esrj-31288	15	34	aceptables	aceptable	NOUN
esrj-31288	15	35	.	.	PUNCT
esrj-31288	16	1	palabras	palabras	PROPN
esrj-31288	16	2	clave	clave	PROPN
esrj-31288	16	3	:	:	PUNCT
esrj-31288	16	4	trazamiento	trazamiento	PROPN
esrj-31288	16	5	de	de	X
esrj-31288	16	6	rayos	rayos	PROPN
esrj-31288	16	7	,	,	PUNCT
esrj-31288	16	8	teoria	teoria	PROPN
esrj-31288	16	9	del	del	X
esrj-31288	16	10	ravo	ravo	NOUN
esrj-31288	16	11	,	,	PUNCT
esrj-31288	16	12	problema	problema	PROPN
esrj-31288	16	13	inverso	inverso	PROPN
esrj-31288	16	14	,	,	PUNCT
esrj-31288	16	15	continuacion	continuacion	NOUN
esrj-31288	16	16	hacia	hacia	PROPN
esrj-31288	16	17	abajo	abajo	PROPN
esrj-31288	16	18	,	,	PUNCT
esrj-31288	16	19	velocidad	velocidad	PROPN
esrj-31288	16	20	de	de	PROPN
esrj-31288	16	21	intervalo	intervalo	PROPN
esrj-31288	16	22	abstract	abstract	PROPN
esrj-31288	16	23	we	we	PRON
esrj-31288	16	24	present	present	VERB
esrj-31288	16	25	a	a	DET
esrj-31288	16	26	method	method	NOUN
esrj-31288	16	27	to	to	PART
esrj-31288	16	28	estimate	estimate	VERB
esrj-31288	16	29	interval	interval	NOUN
esrj-31288	16	30	velocities	velocity	NOUN
esrj-31288	16	31	,	,	PUNCT
esrj-31288	16	32	reflector	reflector	NOUN
esrj-31288	16	33	depths	depth	NOUN
esrj-31288	16	34	and	and	CCONJ
esrj-31288	16	35	geometries	geometry	NOUN
esrj-31288	16	36	in	in	ADP
esrj-31288	16	37	3d	3d	PROPN
esrj-31288	16	38	models	model	NOUN
esrj-31288	16	39	consisting	consist	VERB
esrj-31288	16	40	of	of	ADP
esrj-31288	16	41	a	a	DET
esrj-31288	16	42	pile	pile	NOUN
esrj-31288	16	43	of	of	ADP
esrj-31288	16	44	isotropic	isotropic	ADJ
esrj-31288	16	45	and	and	CCONJ
esrj-31288	16	46	homogeneous	homogeneous	ADJ
esrj-31288	16	47	layers	layer	NOUN
esrj-31288	16	48	of	of	ADP
esrj-31288	16	49	any	any	DET
esrj-31288	16	50	velocities	velocity	NOUN
esrj-31288	16	51	and	and	CCONJ
esrj-31288	16	52	densities	density	NOUN
esrj-31288	16	53	separated	separate	VERB
esrj-31288	16	54	by	by	ADP
esrj-31288	16	55	smooth	smooth	ADJ
esrj-31288	16	56	interfaces	interface	NOUN
esrj-31288	16	57	.	.	PUNCT
esrj-31288	17	1	the	the	DET
esrj-31288	17	2	travel	travel	NOUN
esrj-31288	17	3	time	time	NOUN
esrj-31288	17	4	of	of	ADP
esrj-31288	17	5	a	a	DET
esrj-31288	17	6	ray	ray	NOUN
esrj-31288	17	7	reflecting	reflect	VERB
esrj-31288	17	8	on	on	ADP
esrj-31288	17	9	a	a	DET
esrj-31288	17	10	particular	particular	ADJ
esrj-31288	17	11	interface	interface	NOUN
esrj-31288	17	12	and	and	CCONJ
esrj-31288	17	13	registered	register	VERB
esrj-31288	17	14	in	in	ADP
esrj-31288	17	15	the	the	DET
esrj-31288	17	16	vicinity	vicinity	NOUN
esrj-31288	17	17	of	of	ADP
esrj-31288	17	18	a	a	DET
esrj-31288	17	19	zero	zero	NUM
esrj-31288	17	20	-	-	PUNCT
esrj-31288	17	21	offset	offset	VERB
esrj-31288	17	22	ray	ray	NOUN
esrj-31288	17	23	is	be	AUX
esrj-31288	17	24	expressed	express	VERB
esrj-31288	17	25	by	by	ADP
esrj-31288	17	26	a	a	DET
esrj-31288	17	27	function	function	NOUN
esrj-31288	17	28	referred	refer	VERB
esrj-31288	17	29	to	to	ADP
esrj-31288	17	30	a	a	DET
esrj-31288	17	31	ray	ray	NOUN
esrj-31288	17	32	-	-	PUNCT
esrj-31288	17	33	centered	center	VERB
esrj-31288	17	34	coordinated	coordinated	ADJ
esrj-31288	17	35	system	system	NOUN
esrj-31288	17	36	,	,	PUNCT
esrj-31288	17	37	fnnction	fnnction	NOUN
esrj-31288	17	38	which	which	PRON
esrj-31288	17	39	is	be	AUX
esrj-31288	17	40	estimated	estimate	VERB
esrj-31288	17	41	at	at	ADP
esrj-31288	17	42	the	the	DET
esrj-31288	17	43	uppermost	uppermost	ADJ
esrj-31288	17	44	surface	surface	NOUN
esrj-31288	17	45	of	of	ADP
esrj-31288	17	46	the	the	DET
esrj-31288	17	47	model	model	NOUN
esrj-31288	17	48	.	.	PUNCT
esrj-31288	18	1	the	the	DET
esrj-31288	18	2	reflection	reflection	NOUN
esrj-31288	18	3	travel	travel	NOUN
esrj-31288	18	4	time	time	NOUN
esrj-31288	18	5	function	function	NOUN
esrj-31288	18	6	associated	associate	VERB
esrj-31288	18	7	to	to	ADP
esrj-31288	18	8	each	each	DET
esrj-31288	18	9	reflecting	reflect	VERB
esrj-31288	18	10	surface	surface	NOUN
esrj-31288	18	11	is	be	AUX
esrj-31288	18	12	determined	determine	VERB
esrj-31288	18	13	at	at	ADP
esrj-31288	18	14	the	the	DET
esrj-31288	18	15	superior	superior	ADJ
esrj-31288	18	16	surface	surface	NOUN
esrj-31288	18	17	in	in	ADP
esrj-31288	18	18	the	the	DET
esrj-31288	18	19	neighborhood	neighborhood	NOUN
esrj-31288	18	20	of	of	ADP
esrj-31288	18	21	the	the	DET
esrj-31288	18	22	reference	reference	NOUN
esrj-31288	18	23	ray	ray	NOUN
esrj-31288	18	24	.	.	PUNCT
esrj-31288	19	1	the	the	DET
esrj-31288	19	2	geometry	geometry	NOUN
esrj-31288	19	3	of	of	ADP
esrj-31288	19	4	the	the	DET
esrj-31288	19	5	upper	upper	ADJ
esrj-31288	19	6	limiting	limit	VERB
esrj-31288	19	7	surface	surface	NOUN
esrj-31288	19	8	of	of	ADP
esrj-31288	19	9	a	a	DET
esrj-31288	19	10	particular	particular	ADJ
esrj-31288	19	11	layer	layer	NOUN
esrj-31288	19	12	and	and	CCONJ
esrj-31288	19	13	the	the	DET
esrj-31288	19	14	travel	travel	NOUN
esrj-31288	19	15	time	time	NOUN
esrj-31288	19	16	function	function	NOUN
esrj-31288	19	17	estimated	estimate	VERB
esrj-31288	19	18	on	on	ADP
esrj-31288	19	19	this	this	DET
esrj-31288	19	20	interface	interface	NOUN
esrj-31288	19	21	allow	allow	VERB
esrj-31288	19	22	to	to	PART
esrj-31288	19	23	calculate	calculate	VERB
esrj-31288	19	24	the	the	DET
esrj-31288	19	25	interval	interval	NOUN
esrj-31288	19	26	velocity	velocity	NOUN
esrj-31288	19	27	of	of	ADP
esrj-31288	19	28	the	the	DET
esrj-31288	19	29	layer	layer	NOUN
esrj-31288	19	30	and	and	CCONJ
esrj-31288	19	31	the	the	DET
esrj-31288	19	32	geometry	geometry	NOUN
esrj-31288	19	33	of	of	ADP
esrj-31288	19	34	the	the	DET
esrj-31288	19	35	bottom	bottom	ADJ
esrj-31288	19	36	limiting	limit	VERB
esrj-31288	19	37	interface	interface	NOUN
esrj-31288	19	38	.	.	PUNCT
esrj-31288	20	1	with	with	ADP
esrj-31288	20	2	the	the	DET
esrj-31288	20	3	interval	interval	NOUN
esrj-31288	20	4	velocity	velocity	NOUN
esrj-31288	20	5	and	and	CCONJ
esrj-31288	20	6	geometry	geometry	NOUN
esrj-31288	20	7	of	of	ADP
esrj-31288	20	8	the	the	DET
esrj-31288	20	9	two	two	NUM
esrj-31288	20	10	limiting	limit	VERB
esrj-31288	20	11	interfaces	interface	NOUN
esrj-31288	20	12	of	of	ADP
esrj-31288	20	13	the	the	DET
esrj-31288	20	14	layer	layer	NOUN
esrj-31288	20	15	,	,	PUNCT
esrj-31288	20	16	the	the	DET
esrj-31288	20	17	travel	travel	NOUN
esrj-31288	20	18	time	time	NOUN
esrj-31288	20	19	function	function	NOUN
esrj-31288	20	20	of	of	ADP
esrj-31288	20	21	the	the	DET
esrj-31288	20	22	following	follow	VERB
esrj-31288	20	23	reflector	reflector	NOUN
esrj-31288	20	24	is	be	AUX
esrj-31288	20	25	estimated	estimate	VERB
esrj-31288	20	26	at	at	ADP
esrj-31288	20	27	the	the	DET
esrj-31288	20	28	bottom	bottom	ADJ
esrj-31288	20	29	interface	interface	NOUN
esrj-31288	20	30	.	.	PUNCT
esrj-31288	21	1	this	this	DET
esrj-31288	21	2	step	step	NOUN
esrj-31288	21	3	simulates	simulate	NOUN
esrj-31288	21	4	positioning	position	VERB
esrj-31288	21	5	the	the	DET
esrj-31288	21	6	sources	source	NOUN
esrj-31288	21	7	and	and	CCONJ
esrj-31288	21	8	detectors	detector	NOUN
esrj-31288	21	9	on	on	ADP
esrj-31288	21	10	the	the	DET
esrj-31288	21	11	anterior	anterior	ADJ
esrj-31288	21	12	surface	surface	NOUN
esrj-31288	21	13	of	of	ADP
esrj-31288	21	14	the	the	DET
esrj-31288	21	15	next	next	ADJ
esrj-31288	21	16	subjacent	subjacent	NOUN
esrj-31288	21	17	layer	layer	NOUN
esrj-31288	21	18	.	.	PUNCT
esrj-31288	22	1	the	the	DET
esrj-31288	22	2	procedure	procedure	NOUN
esrj-31288	22	3	is	be	AUX
esrj-31288	22	4	repeated	repeat	VERB
esrj-31288	22	5	recursively	recursively	ADV
esrj-31288	22	6	at	at	ADP
esrj-31288	22	7	deeper	deep	ADJ
esrj-31288	22	8	layers	layer	NOUN
esrj-31288	22	9	getting	get	VERB
esrj-31288	22	10	the	the	DET
esrj-31288	22	11	complete	complete	ADJ
esrj-31288	22	12	solution	solution	NOUN
esrj-31288	22	13	without	without	ADP
esrj-31288	22	14	a	a	DET
esrj-31288	22	15	priori	priori	ADJ
esrj-31288	22	16	knowledge	knowledge	NOUN
esrj-31288	22	17	but	but	CCONJ
esrj-31288	22	18	the	the	DET
esrj-31288	22	19	upper	upper	ADJ
esrj-31288	22	20	determined	determined	ADJ
esrj-31288	22	21	layers	layer	NOUN
esrj-31288	22	22	and	and	CCONJ
esrj-31288	22	23	the	the	DET
esrj-31288	22	24	estimated	estimate	VERB
esrj-31288	22	25	travel	travel	NOUN
esrj-31288	22	26	time	time	NOUN
esrj-31288	22	27	functions	function	NOUN
esrj-31288	22	28	of	of	ADP
esrj-31288	22	29	each	each	DET
esrj-31288	22	30	reflecting	reflect	VERB
esrj-31288	22	31	surface	surface	NOUN
esrj-31288	22	32	.	.	PUNCT
esrj-31288	23	1	computer	computer	NOUN
esrj-31288	23	2	's	's	PART
esrj-31288	23	3	programs	program	NOUN
esrj-31288	23	4	expressing	express	VERB
esrj-31288	23	5	the	the	DET
esrj-31288	23	6	algorithm	algorithm	NOUN
esrj-31288	23	7	of	of	ADP
esrj-31288	23	8	the	the	DET
esrj-31288	23	9	method	method	NOUN
esrj-31288	23	10	were	be	AUX
esrj-31288	23	11	developed	develop	VERB
esrj-31288	23	12	and	and	CCONJ
esrj-31288	23	13	tested	test	VERB
esrj-31288	23	14	with	with	ADP
esrj-31288	23	15	synthetic	synthetic	ADJ
esrj-31288	23	16	data	datum	NOUN
esrj-31288	23	17	,	,	PUNCT
esrj-31288	23	18	providing	provide	VERB
esrj-31288	23	19	the	the	DET
esrj-31288	23	20	interval	interval	NOUN
esrj-31288	23	21	velocities	velocity	NOUN
esrj-31288	23	22	and	and	CCONJ
esrj-31288	23	23	reflector	reflector	NOUN
esrj-31288	23	24	's	's	PART
esrj-31288	23	25	depths	depth	NOUN
esrj-31288	23	26	with	with	ADP
esrj-31288	23	27	errors	error	NOUN
esrj-31288	23	28	considered	consider	VERB
esrj-31288	23	29	acceptable	acceptable	ADJ
esrj-31288	23	30	.	.	PUNCT
esrj-31288	24	1	key	key	ADJ
esrj-31288	24	2	words	word	NOUN
esrj-31288	24	3	:	:	PUNCT
esrj-31288	24	4	ray	ray	NOUN
esrj-31288	24	5	tracing	tracing	PROPN
esrj-31288	24	6	,	,	PUNCT
esrj-31288	24	7	ray	ray	NOUN
esrj-31288	24	8	theory	theory	NOUN
esrj-31288	24	9	,	,	PUNCT
esrj-31288	24	10	inverse	inverse	NOUN
esrj-31288	24	11	problem	problem	NOUN
esrj-31288	24	12	,	,	PUNCT
esrj-31288	24	13	downward	downward	ADJ
esrj-31288	24	14	continuation	continuation	NOUN
esrj-31288	24	15	,	,	PUNCT
esrj-31288	24	16	interval	interval	NOUN
esrj-31288	24	17	velocity	velocity	NOUN
esrj-31288	24	18	introduction	introduction	NOUN
esrj-31288	24	19	the	the	DET
esrj-31288	24	20	interval	interval	NOUN
esrj-31288	24	21	velocity	velocity	NOUN
esrj-31288	24	22	is	be	AUX
esrj-31288	24	23	a	a	DET
esrj-31288	24	24	basic	basic	ADJ
esrj-31288	24	25	parameter	parameter	NOUN
esrj-31288	24	26	in	in	ADP
esrj-31288	24	27	seismic	seismic	ADJ
esrj-31288	24	28	data	datum	NOUN
esrj-31288	24	29	processing	processing	NOUN
esrj-31288	24	30	,	,	PUNCT
esrj-31288	24	31	specially	specially	ADV
esrj-31288	24	32	in	in	ADP
esrj-31288	24	33	depth	depth	NOUN
esrj-31288	24	34	migration	migration	NOUN
esrj-31288	24	35	and	and	CCONJ
esrj-31288	24	36	interpretation	interpretation	NOUN
esrj-31288	24	37	of	of	ADP
esrj-31288	24	38	seismic	seismic	ADJ
esrj-31288	24	39	sections	section	NOUN
esrj-31288	24	40	.	.	PUNCT
esrj-31288	25	1	in	in	ADP
esrj-31288	25	2	the	the	DET
esrj-31288	25	3	high	high	ADJ
esrj-31288	25	4	-	-	PUNCT
esrj-31288	25	5	frequency	frequency	NOUN
esrj-31288	25	6	range	range	NOUN
esrj-31288	25	7	the	the	DET
esrj-31288	25	8	propagation	propagation	NOUN
esrj-31288	25	9	of	of	ADP
esrj-31288	25	10	seismic	seismic	ADJ
esrj-31288	25	11	wave	wave	NOUN
esrj-31288	25	12	is	be	AUX
esrj-31288	25	13	well	well	ADV
esrj-31288	25	14	described	describe	VERB
esrj-31288	25	15	by	by	ADP
esrj-31288	25	16	paraxial	paraxial	ADJ
esrj-31288	25	17	ray	ray	NOUN
esrj-31288	25	18	theory	theory	NOUN
esrj-31288	25	19	.	.	PUNCT
esrj-31288	26	1	in	in	ADP
esrj-31288	26	2	order	order	NOUN
esrj-31288	26	3	to	to	PART
esrj-31288	26	4	estimate	estimate	VERB
esrj-31288	26	5	the	the	DET
esrj-31288	26	6	interval	interval	NOUN
esrj-31288	26	7	velocity	velocity	NOUN
esrj-31288	26	8	using	use	VERB
esrj-31288	26	9	a	a	DET
esrj-31288	26	10	travel	travel	NOUN
esrj-31288	26	11	time	time	NOUN
esrj-31288	26	12	inversion	inversion	NOUN
esrj-31288	26	13	method	method	NOUN
esrj-31288	26	14	we	we	PRON
esrj-31288	26	15	recourse	recourse	VERB
esrj-31288	26	16	to	to	ADP
esrj-31288	26	17	the	the	DET
esrj-31288	26	18	mathematical	mathematical	ADJ
esrj-31288	26	19	formalism	formalism	NOUN
esrj-31288	26	20	developed	develop	VERB
esrj-31288	26	21	by	by	ADP
esrj-31288	26	22	bortfeld	bortfeld	NOUN
esrj-31288	26	23	(	(	PUNCT
esrj-31288	26	24	1989	1989	NUM
esrj-31288	26	25	)	)	PUNCT
esrj-31288	26	26	.	.	PUNCT
esrj-31288	27	1	the	the	DET
esrj-31288	27	2	bortfeldss	bortfeldss	NOUN
esrj-31288	27	3	originally	originally	ADV
esrj-31288	27	4	ideas	idea	NOUN
esrj-31288	27	5	were	be	AUX
esrj-31288	27	6	presented	present	VERB
esrj-31288	27	7	for	for	ADP
esrj-31288	27	8	earth	earth	NOUN
esrj-31288	27	9	models	model	NOUN
esrj-31288	27	10	consisting	consist	VERB
esrj-31288	27	11	of	of	ADP
esrj-31288	27	12	homogeneous	homogeneous	ADJ
esrj-31288	27	13	layers	layer	NOUN
esrj-31288	27	14	.	.	PUNCT
esrj-31288	28	1	using	use	VERB
esrj-31288	28	2	dynamic	dynamic	ADJ
esrj-31288	28	3	ray	ray	NOUN
esrj-31288	28	4	tracing	tracing	NOUN
esrj-31288	28	5	,	,	PUNCT
esrj-31288	28	6	hubral	hubral	ADJ
esrj-31288	28	7	et	et	PROPN
esrj-31288	28	8	al	al	PROPN
esrj-31288	28	9	.	.	PROPN
esrj-31288	29	1	(	(	PUNCT
esrj-31288	29	2	1992	1992	NUM
esrj-31288	29	3	)	)	PUNCT
esrj-31288	29	4	extended	extend	VERB
esrj-31288	29	5	posteriorly	posteriorly	NOUN
esrj-31288	29	6	the	the	DET
esrj-31288	29	7	validity	validity	NOUN
esrj-31288	29	8	of	of	ADP
esrj-31288	29	9	the	the	DET
esrj-31288	29	10	formalism	formalism	NOUN
esrj-31288	29	11	to	to	ADP
esrj-31288	29	12	layered	layered	ADJ
esrj-31288	29	13	media	medium	NOUN
esrj-31288	29	14	with	with	ADP
esrj-31288	29	15	lateral	lateral	ADJ
esrj-31288	29	16	inhomogeneity	inhomogeneity	NOUN
esrj-31288	29	17	.	.	PUNCT
esrj-31288	30	1	the	the	DET
esrj-31288	30	2	parameter	parameter	NOUN
esrj-31288	30	3	describing	describe	VERB
esrj-31288	30	4	a	a	DET
esrj-31288	30	5	paraxial	paraxial	ADJ
esrj-31288	30	6	ray	ray	NOUN
esrj-31288	30	7	are	be	AUX
esrj-31288	30	8	its	its	PRON
esrj-31288	30	9	distance	distance	NOUN
esrj-31288	30	10	to	to	ADP
esrj-31288	30	11	geofislca	geofislca	PROPN
esrj-31288	30	12	colombiana	colombiana	PROPN
esrj-31288	30	13	,	,	PUNCT
esrj-31288	30	14	5	5	NUM
esrj-31288	30	15	,	,	PUNCT
esrj-31288	30	16	diciembre	diciembre	PROPN
esrj-31288	30	17	de	de	X
esrj-31288	30	18	2001	2001	NUM
esrj-31288	30	19	the	the	DET
esrj-31288	30	20	central	central	ADJ
esrj-31288	30	21	ray	ray	NOUN
esrj-31288	30	22	and	and	CCONJ
esrj-31288	30	23	the	the	DET
esrj-31288	30	24	deviation	deviation	NOUN
esrj-31288	30	25	of	of	ADP
esrj-31288	30	26	its	its	PRON
esrj-31288	30	27	slowness	slowness	NOUN
esrj-31288	30	28	vector	vector	NOUN
esrj-31288	30	29	from	from	ADP
esrj-31288	30	30	that	that	PRON
esrj-31288	30	31	of	of	ADP
esrj-31288	30	32	the	the	DET
esrj-31288	30	33	central	central	ADJ
esrj-31288	30	34	ray	ray	NOUN
esrj-31288	30	35	.	.	PUNCT
esrj-31288	31	1	at	at	ADP
esrj-31288	31	2	any	any	DET
esrj-31288	31	3	point	point	NOUN
esrj-31288	31	4	of	of	ADP
esrj-31288	31	5	a	a	DET
esrj-31288	31	6	paraxial	paraxial	ADJ
esrj-31288	31	7	ray	ray	NOUN
esrj-31288	31	8	,	,	PUNCT
esrj-31288	31	9	the	the	DET
esrj-31288	31	10	parameters	parameter	NOUN
esrj-31288	31	11	are	be	AUX
esrj-31288	31	12	linearly	linearly	ADV
esrj-31288	31	13	dependent	dependent	ADJ
esrj-31288	31	14	on	on	ADP
esrj-31288	31	15	those	those	PRON
esrj-31288	31	16	at	at	ADP
esrj-31288	31	17	its	its	PRON
esrj-31288	31	18	initial	initial	ADJ
esrj-31288	31	19	point	point	NOUN
esrj-31288	31	20	.	.	PUNCT
esrj-31288	32	1	the	the	DET
esrj-31288	32	2	dependency	dependency	NOUN
esrj-31288	32	3	is	be	AUX
esrj-31288	32	4	described	describe	VERB
esrj-31288	32	5	by	by	ADP
esrj-31288	32	6	the	the	DET
esrj-31288	32	7	propagator	propagator	NOUN
esrj-31288	32	8	matrix	matrix	NOUN
esrj-31288	32	9	,	,	PUNCT
esrj-31288	32	10	which	which	PRON
esrj-31288	32	11	is	be	AUX
esrj-31288	32	12	written	write	VERB
esrj-31288	32	13	as	as	ADP
esrj-31288	32	14	a	a	DET
esrj-31288	32	15	product	product	NOUN
esrj-31288	32	16	of	of	ADP
esrj-31288	32	17	many	many	ADJ
esrj-31288	32	18	ray	ray	NOUN
esrj-31288	32	19	-	-	PUNCT
esrj-31288	32	20	segment	segment	NOUN
esrj-31288	32	21	propagator	propagator	NOUN
esrj-31288	32	22	matrices	matrix	NOUN
esrj-31288	32	23	,	,	PUNCT
esrj-31288	32	24	each	each	DET
esrj-31288	32	25	one	one	NUM
esrj-31288	32	26	associated	associate	VERB
esrj-31288	32	27	to	to	ADP
esrj-31288	32	28	each	each	DET
esrj-31288	32	29	layer	layer	NOUN
esrj-31288	32	30	.	.	PUNCT
esrj-31288	33	1	after	after	ADP
esrj-31288	33	2	kahn	kahn	PROPN
esrj-31288	33	3	(	(	PUNCT
esrj-31288	33	4	1987	1987	NUM
esrj-31288	33	5	)	)	PUNCT
esrj-31288	33	6	the	the	DET
esrj-31288	33	7	ray	ray	NOUN
esrj-31288	33	8	-	-	PUNCT
esrj-31288	33	9	segment	segment	NOUN
esrj-31288	33	10	propagator	propagator	NOUN
esrj-31288	33	11	matrix	matrix	NOUN
esrj-31288	33	12	through	through	ADP
esrj-31288	33	13	one	one	NUM
esrj-31288	33	14	layer	layer	NOUN
esrj-31288	33	15	is	be	AUX
esrj-31288	33	16	decomposed	decompose	VERB
esrj-31288	33	17	in	in	ADP
esrj-31288	33	18	a	a	DET
esrj-31288	33	19	product	product	NOUN
esrj-31288	33	20	of	of	ADP
esrj-31288	33	21	matrix	matrix	NOUN
esrj-31288	33	22	operators	operator	NOUN
esrj-31288	33	23	containing	contain	VERB
esrj-31288	33	24	the	the	DET
esrj-31288	33	25	parameters	parameter	NOUN
esrj-31288	33	26	of	of	ADP
esrj-31288	33	27	the	the	DET
esrj-31288	33	28	layer	layer	NOUN
esrj-31288	33	29	,	,	PUNCT
esrj-31288	33	30	and	and	CCONJ
esrj-31288	33	31	to	to	PART
esrj-31288	33	32	determine	determine	VERB
esrj-31288	33	33	the	the	DET
esrj-31288	33	34	parameters	parameter	NOUN
esrj-31288	33	35	of	of	ADP
esrj-31288	33	36	that	that	DET
esrj-31288	33	37	layer	layer	NOUN
esrj-31288	33	38	is	be	AUX
esrj-31288	33	39	necessary	necessary	ADJ
esrj-31288	33	40	to	to	PART
esrj-31288	33	41	know	know	VERB
esrj-31288	33	42	the	the	DET
esrj-31288	33	43	travel	travel	NOUN
esrj-31288	33	44	time	time	NOUN
esrj-31288	33	45	function	function	NOUN
esrj-31288	33	46	on	on	ADP
esrj-31288	33	47	its	its	PRON
esrj-31288	33	48	anterior	anterior	ADJ
esrj-31288	33	49	surface	surface	NOUN
esrj-31288	33	50	.	.	PUNCT
esrj-31288	34	1	at	at	ADP
esrj-31288	34	2	the	the	DET
esrj-31288	34	3	uppermost	uppermost	ADJ
esrj-31288	34	4	surface	surface	NOUN
esrj-31288	34	5	the	the	DET
esrj-31288	34	6	travel	travel	NOUN
esrj-31288	34	7	time	time	NOUN
esrj-31288	34	8	function	function	NOUN
esrj-31288	34	9	of	of	ADP
esrj-31288	34	10	each	each	DET
esrj-31288	34	11	reflecting	reflect	VERB
esrj-31288	34	12	interface	interface	NOUN
esrj-31288	34	13	can	can	AUX
esrj-31288	34	14	be	be	AUX
esrj-31288	34	15	estimated	estimate	VERB
esrj-31288	34	16	measuring	measure	VERB
esrj-31288	34	17	the	the	DET
esrj-31288	34	18	travel	travel	NOUN
esrj-31288	34	19	times	time	NOUN
esrj-31288	34	20	of	of	ADP
esrj-31288	34	21	several	several	ADJ
esrj-31288	34	22	rays	ray	NOUN
esrj-31288	34	23	in	in	ADP
esrj-31288	34	24	the	the	DET
esrj-31288	34	25	neighborhood	neighborhood	NOUN
esrj-31288	34	26	luis	luis	PROPN
esrj-31288	34	27	montes	montes	PROPN
esrj-31288	34	28	vides	vide	NOUN
esrj-31288	34	29	of	of	ADP
esrj-31288	34	30	the	the	DET
esrj-31288	34	31	central	central	ADJ
esrj-31288	34	32	ray	ray	NOUN
esrj-31288	34	33	.	.	PUNCT
esrj-31288	35	1	based	base	VERB
esrj-31288	35	2	on	on	ADP
esrj-31288	35	3	the	the	DET
esrj-31288	35	4	anterior	anterior	ADJ
esrj-31288	35	5	ideas	idea	NOUN
esrj-31288	35	6	a	a	DET
esrj-31288	35	7	method	method	NOUN
esrj-31288	35	8	to	to	PART
esrj-31288	35	9	estimate	estimate	VERB
esrj-31288	35	10	the	the	DET
esrj-31288	35	11	interval	interval	NOUN
esrj-31288	35	12	velocities	velocity	NOUN
esrj-31288	35	13	and	and	CCONJ
esrj-31288	35	14	reflector	reflector	NOUN
esrj-31288	35	15	's	's	PART
esrj-31288	35	16	depth	depth	NOUN
esrj-31288	35	17	was	be	AUX
esrj-31288	35	18	developed	develop	VERB
esrj-31288	35	19	.	.	PUNCT
esrj-31288	36	1	test	test	NOUN
esrj-31288	36	2	on	on	ADP
esrj-31288	36	3	synthetic	synthetic	ADJ
esrj-31288	36	4	data	datum	NOUN
esrj-31288	36	5	showed	show	VERB
esrj-31288	36	6	that	that	SCONJ
esrj-31288	36	7	the	the	DET
esrj-31288	36	8	algorithm	algorithm	NOUN
esrj-31288	36	9	representing	represent	VERB
esrj-31288	36	10	the	the	DET
esrj-31288	36	11	method	method	NOUN
esrj-31288	36	12	provides	provide	VERB
esrj-31288	36	13	results	result	NOUN
esrj-31288	36	14	with	with	ADP
esrj-31288	36	15	errors	error	NOUN
esrj-31288	36	16	considered	consider	VERB
esrj-31288	36	17	acceptables	acceptable	NOUN
esrj-31288	36	18	.	.	PUNCT
esrj-31288	37	1	the	the	DET
esrj-31288	37	2	solutions	solution	NOUN
esrj-31288	37	3	obtained	obtain	VERB
esrj-31288	37	4	are	be	AUX
esrj-31288	37	5	valid	valid	ADJ
esrj-31288	37	6	only	only	ADV
esrj-31288	37	7	in	in	ADP
esrj-31288	37	8	the	the	DET
esrj-31288	37	9	second	second	ADJ
esrj-31288	37	10	order	order	NOUN
esrj-31288	37	11	approximation	approximation	NOUN
esrj-31288	37	12	of	of	ADP
esrj-31288	37	13	the	the	DET
esrj-31288	37	14	travel	travel	NOUN
esrj-31288	37	15	times	time	NOUN
esrj-31288	37	16	function	function	NOUN
esrj-31288	37	17	and	and	CCONJ
esrj-31288	37	18	its	its	PRON
esrj-31288	37	19	range	range	NOUN
esrj-31288	37	20	of	of	ADP
esrj-31288	37	21	applicability	applicability	NOUN
esrj-31288	37	22	corresponds	correspond	VERB
esrj-31288	37	23	to	to	ADP
esrj-31288	37	24	the	the	DET
esrj-31288	37	25	hyperbolic	hyperbolic	ADJ
esrj-31288	37	26	dynamic	dynamic	ADJ
esrj-31288	37	27	correction	correction	NOUN
esrj-31288	37	28	.	.	PUNCT
esrj-31288	38	1	traveltime	traveltime	PROPN
esrj-31288	38	2	function	function	NOUN
esrj-31288	38	3	according	accord	VERB
esrj-31288	38	4	the	the	DET
esrj-31288	38	5	formalism	formalism	NOUN
esrj-31288	38	6	developed	develop	VERB
esrj-31288	38	7	by	by	ADP
esrj-31288	38	8	bortfeld	bortfeld	NOUN
esrj-31288	38	9	(	(	PUNCT
esrj-31288	38	10	1989	1989	NUM
esrj-31288	38	11	)	)	PUNCT
esrj-31288	38	12	,	,	PUNCT
esrj-31288	38	13	the	the	DET
esrj-31288	38	14	earth	earth	NOUN
esrj-31288	38	15	model	model	NOUN
esrj-31288	38	16	consists	consist	VERB
esrj-31288	38	17	of	of	ADP
esrj-31288	38	18	a	a	DET
esrj-31288	38	19	pile	pile	NOUN
esrj-31288	38	20	of	of	ADP
esrj-31288	38	21	homogeneous	homogeneous	ADJ
esrj-31288	38	22	layers	layer	NOUN
esrj-31288	38	23	of	of	ADP
esrj-31288	38	24	any	any	DET
esrj-31288	38	25	velocities	velocity	NOUN
esrj-31288	38	26	and	and	CCONJ
esrj-31288	38	27	densities	density	NOUN
esrj-31288	38	28	.	.	PUNCT
esrj-31288	39	1	the	the	DET
esrj-31288	39	2	layers	layer	NOUN
esrj-31288	39	3	are	be	AUX
esrj-31288	39	4	separated	separate	VERB
esrj-31288	39	5	by	by	ADP
esrj-31288	39	6	arbitrarily	arbitrarily	ADV
esrj-31288	39	7	curved	curved	ADJ
esrj-31288	39	8	but	but	CCONJ
esrj-31288	39	9	smooth	smooth	ADJ
esrj-31288	39	10	interfaces	interface	NOUN
esrj-31288	39	11	.	.	PUNCT
esrj-31288	40	1	the	the	DET
esrj-31288	40	2	uppermost	uppermost	ADJ
esrj-31288	40	3	interface	interface	NOUN
esrj-31288	40	4	,	,	PUNCT
esrj-31288	40	5	called	call	VERB
esrj-31288	40	6	anterior	anterior	ADJ
esrj-31288	40	7	surface	surface	NOUN
esrj-31288	40	8	,	,	PUNCT
esrj-31288	40	9	is	be	AUX
esrj-31288	40	10	assumed	assume	VERB
esrj-31288	40	11	to	to	PART
esrj-31288	40	12	be	be	AUX
esrj-31288	40	13	plane	plane	NOUN
esrj-31288	40	14	and	and	CCONJ
esrj-31288	40	15	contains	contain	VERB
esrj-31288	40	16	sources	source	NOUN
esrj-31288	40	17	and	and	CCONJ
esrj-31288	40	18	detectors	detector	NOUN
esrj-31288	40	19	.	.	PUNCT
esrj-31288	41	1	the	the	DET
esrj-31288	41	2	reflecting	reflect	VERB
esrj-31288	41	3	interface	interface	NOUN
esrj-31288	41	4	is	be	AUX
esrj-31288	41	5	called	call	VERB
esrj-31288	41	6	the	the	DET
esrj-31288	41	7	posterior	posterior	ADJ
esrj-31288	41	8	surface	surface	NOUN
esrj-31288	41	9	.	.	PUNCT
esrj-31288	42	1	one	one	NUM
esrj-31288	42	2	normal	normal	ADJ
esrj-31288	42	3	ray	ray	NOUN
esrj-31288	42	4	to	to	ADP
esrj-31288	42	5	the	the	DET
esrj-31288	42	6	reflecting	reflect	VERB
esrj-31288	42	7	interface	interface	NOUN
esrj-31288	42	8	,	,	PUNCT
esrj-31288	42	9	called	call	VERB
esrj-31288	42	10	central	central	ADJ
esrj-31288	42	11	ray	ray	NOUN
esrj-31288	42	12	,	,	PUNCT
esrj-31288	42	13	intersects	intersect	VERB
esrj-31288	42	14	the	the	DET
esrj-31288	42	15	anterior	anterior	ADJ
esrj-31288	42	16	surface	surface	NOUN
esrj-31288	42	17	at	at	ADP
esrj-31288	42	18	the	the	DET
esrj-31288	42	19	origin	origin	NOUN
esrj-31288	42	20	of	of	ADP
esrj-31288	42	21	the	the	DET
esrj-31288	42	22	xyz	xyz	PROPN
esrj-31288	42	23	coordinate	coordinate	NOUN
esrj-31288	42	24	system	system	NOUN
esrj-31288	42	25	and	and	CCONJ
esrj-31288	42	26	the	the	DET
esrj-31288	42	27	posterior	posterior	ADJ
esrj-31288	42	28	surface	surface	NOUN
esrj-31288	42	29	at	at	ADP
esrj-31288	42	30	the	the	DET
esrj-31288	42	31	origin	origin	NOUN
esrj-31288	42	32	of	of	ADP
esrj-31288	42	33	the	the	DET
esrj-31288	42	34	x'y'z	x'y'z	PROPN
esrj-31288	42	35	'	'	PUNCT
esrj-31288	42	36	coordinate	coordinate	NOUN
esrj-31288	42	37	system	system	NOUN
esrj-31288	42	38	.	.	PUNCT
esrj-31288	43	1	in	in	ADP
esrj-31288	43	2	the	the	DET
esrj-31288	43	3	vicinity	vicinity	NOUN
esrj-31288	43	4	of	of	ADP
esrj-31288	43	5	the	the	DET
esrj-31288	43	6	central	central	ADJ
esrj-31288	43	7	ray	ray	NOUN
esrj-31288	43	8	,	,	PUNCT
esrj-31288	43	9	any	any	DET
esrj-31288	43	10	transmitted	transmit	VERB
esrj-31288	43	11	ray	ray	NOUN
esrj-31288	43	12	is	be	AUX
esrj-31288	43	13	described	describe	VERB
esrj-31288	43	14	by	by	ADP
esrj-31288	43	15	its	its	PRON
esrj-31288	43	16	initial	initial	ADJ
esrj-31288	43	17	position	position	NOUN
esrj-31288	43	18	x	x	PUNCT
esrj-31288	43	19	and	and	CCONJ
esrj-31288	43	20	slowness	slowness	NOUN
esrj-31288	43	21	13	13	NUM
esrj-31288	43	22	vectors	vector	NOUN
esrj-31288	43	23	,	,	PUNCT
esrj-31288	43	24	and	and	CCONJ
esrj-31288	43	25	by	by	ADP
esrj-31288	43	26	its	its	PRON
esrj-31288	43	27	final	final	ADJ
esrj-31288	43	28	position	position	NOUN
esrj-31288	43	29	x	x	NOUN
esrj-31288	43	30	'	'	PUNCT
esrj-31288	43	31	and	and	CCONJ
esrj-31288	43	32	slowness	slowness	NOUN
esrj-31288	43	33	p	p	X
esrj-31288	43	34	'	'	PUNCT
esrj-31288	43	35	vectors	vector	NOUN
esrj-31288	43	36	.	.	PUNCT
esrj-31288	44	1	representation	representation	NOUN
esrj-31288	44	2	is	be	AUX
esrj-31288	44	3	by	by	ADP
esrj-31288	44	4	twocomponent	twocomponent	NOUN
esrj-31288	44	5	vectors	vector	NOUN
esrj-31288	44	6	.	.	PUNCT
esrj-31288	45	1	the	the	DET
esrj-31288	45	2	two	two	NUM
esrj-31288	45	3	-	-	PUNCT
esrj-31288	45	4	component	component	NOUN
esrj-31288	45	5	position	position	NOUN
esrj-31288	45	6	and	and	CCONJ
esrj-31288	45	7	slowness	slowness	NOUN
esrj-31288	45	8	vectors	vector	NOUN
esrj-31288	45	9	are	be	AUX
esrj-31288	45	10	obtained	obtain	VERB
esrj-31288	45	11	by	by	ADP
esrj-31288	45	12	projecting	project	VERB
esrj-31288	45	13	the	the	DET
esrj-31288	45	14	three	three	NUM
esrj-31288	45	15	-	-	PUNCT
esrj-31288	45	16	component	component	NOUN
esrj-31288	45	17	vectors	vector	NOUN
esrj-31288	45	18	into	into	ADP
esrj-31288	45	19	the	the	DET
esrj-31288	45	20	tangent	tangent	ADJ
esrj-31288	45	21	plane	plane	NOUN
esrj-31288	45	22	to	to	ADP
esrj-31288	45	23	the	the	DET
esrj-31288	45	24	anterior	anterior	ADJ
esrj-31288	45	25	and	and	CCONJ
esrj-31288	45	26	posterior	posterior	ADJ
esrj-31288	45	27	surface	surface	NOUN
esrj-31288	45	28	at	at	ADP
esrj-31288	45	29	the	the	DET
esrj-31288	45	30	intersection	intersection	NOUN
esrj-31288	45	31	point	point	NOUN
esrj-31288	45	32	with	with	ADP
esrj-31288	45	33	the	the	DET
esrj-31288	45	34	central	central	ADJ
esrj-31288	45	35	ray	ray	NOUN
esrj-31288	45	36	.	.	PUNCT
esrj-31288	46	1	the	the	DET
esrj-31288	46	2	vectors	vector	NOUN
esrj-31288	46	3	x	x	PUNCT
esrj-31288	46	4	and	and	CCONJ
esrj-31288	46	5	13	13	NUM
esrj-31288	46	6	of	of	ADP
esrj-31288	46	7	any	any	DET
esrj-31288	46	8	transmitted	transmit	VERB
esrj-31288	46	9	ray	ray	NOUN
esrj-31288	46	10	determine	determine	VERB
esrj-31288	46	11	the	the	DET
esrj-31288	46	12	vectors	vector	NOUN
esrj-31288	46	13	x	x	PRON
esrj-31288	46	14	'	'	PUNCT
esrj-31288	46	15	and	and	CCONJ
esrj-31288	46	16	p	p	X
esrj-31288	46	17	'	'	PUNCT
esrj-31288	46	18	.	.	PUNCT
esrj-31288	47	1	the	the	DET
esrj-31288	47	2	first	first	ADJ
esrj-31288	47	3	-	-	PUNCT
esrj-31288	47	4	order	order	NOUN
esrj-31288	47	5	approximation	approximation	NOUN
esrj-31288	47	6	of	of	ADP
esrj-31288	47	7	x	x	SYM
esrj-31288	47	8	and	and	CCONJ
esrj-31288	47	9	13	13	NUM
esrj-31288	47	10	sets	set	VERB
esrj-31288	47	11	a	a	DET
esrj-31288	47	12	linear	linear	ADJ
esrj-31288	47	13	relationship	relationship	NOUN
esrj-31288	47	14	:	:	PUNCT
esrj-31288	47	15	a	a	X
esrj-31288	47	16	,	,	PUNCT
esrj-31288	47	17	fl	fl	PROPN
esrj-31288	47	18	,	,	PUNCT
esrj-31288	47	19	~	~	PUNCT
esrj-31288	47	20	and	and	CCONJ
esrj-31288	47	21	d	d	NOUN
esrj-31288	47	22	are	be	AUX
esrj-31288	47	23	2x2	2x2	NUM
esrj-31288	47	24	jacobian	jacobian	ADJ
esrj-31288	47	25	matrices	matrix	NOUN
esrj-31288	47	26	and	and	CCONJ
esrj-31288	47	27	po	po	NOUN
esrj-31288	47	28	is	be	AUX
esrj-31288	47	29	the	the	DET
esrj-31288	47	30	slowness	slowness	ADJ
esrj-31288	47	31	vector	vector	NOUN
esrj-31288	47	32	of	of	ADP
esrj-31288	47	33	the	the	DET
esrj-31288	47	34	central	central	ADJ
esrj-31288	47	35	ray	ray	NOUN
esrj-31288	47	36	.	.	PUNCT
esrj-31288	48	1	similar	similar	ADJ
esrj-31288	48	2	equations	equation	NOUN
esrj-31288	48	3	apply	apply	VERB
esrj-31288	48	4	for	for	ADP
esrj-31288	48	5	reflected	reflect	VERB
esrj-31288	48	6	events	event	NOUN
esrj-31288	48	7	.	.	PUNCT
esrj-31288	49	1	according	accord	VERB
esrj-31288	49	2	bortfeld	bortfeld	NOUN
esrj-31288	49	3	,	,	PUNCT
esrj-31288	49	4	in	in	ADP
esrj-31288	49	5	the	the	DET
esrj-31288	49	6	second	second	ADJ
esrj-31288	49	7	-	-	PUNCT
esrj-31288	49	8	order	order	NOUN
esrj-31288	49	9	approximation	approximation	NOUN
esrj-31288	49	10	,	,	PUNCT
esrj-31288	49	11	the	the	DET
esrj-31288	49	12	travel	travel	NOUN
esrj-31288	49	13	time	time	NOUN
esrj-31288	49	14	of	of	ADP
esrj-31288	49	15	a	a	DET
esrj-31288	49	16	transmitted	transmit	VERB
esrj-31288	49	17	ray	ray	NOUN
esrj-31288	49	18	from	from	ADP
esrj-31288	49	19	any	any	DET
esrj-31288	49	20	source	source	NOUN
esrj-31288	49	21	position	position	NOUN
esrj-31288	49	22	at	at	ADP
esrj-31288	49	23	the	the	DET
esrj-31288	49	24	anterior	anterior	ADJ
esrj-31288	49	25	surface	surface	NOUN
esrj-31288	49	26	x	x	X
esrj-31288	49	27	to	to	ADP
esrj-31288	49	28	any	any	DET
esrj-31288	49	29	receiver	receiver	ADJ
esrj-31288	49	30	position	position	NOUN
esrj-31288	49	31	x	x	NOUN
esrj-31288	49	32	'	'	PUNCT
esrj-31288	49	33	at	at	ADP
esrj-31288	49	34	the	the	DET
esrj-31288	49	35	reflecting	reflect	VERB
esrj-31288	49	36	interface	interface	NOUN
esrj-31288	49	37	is	be	AUX
esrj-31288	49	38	given	give	VERB
esrj-31288	49	39	by	by	ADP
esrj-31288	49	40	:	:	PUNCT
esrj-31288	49	41	t(x	t(x	PROPN
esrj-31288	49	42	,	,	PUNCT
esrj-31288	49	43	x	x	NOUN
esrj-31288	49	44	'	'	PUNCT
esrj-31288	49	45	)	)	PUNCT
esrj-31288	49	46	=	=	PUNCT
esrj-31288	49	47	to	to	PART
esrj-31288	49	48	po	po	X
esrj-31288	49	49	·	·	SYM
esrj-31288	49	50	x++x	x++x	PROPN
esrj-31288	49	51	'	'	PUNCT
esrj-31288	49	52	·	·	PUNCT
esrj-31288	49	53	dfl	dfl	PROPN
esrj-31288	49	54	-	-	PUNCT
esrj-31288	49	55	iy	iy	PROPN
esrj-31288	49	56	'	'	PUNCT
esrj-31288	49	57	+1	+1	PROPN
esrj-31288	49	58	..	..	PUNCT
esrj-31288	49	59	i	i	PRON
esrj-31288	49	60	·	·	PUNCT
esrj-31288	49	61	b-1	b-1	PROPN
esrj-31288	49	62	ax	ax	NOUN
esrj-31288	49	63	-i	-i	PROPN
esrj-31288	49	64	·	·	PUNCT
esrj-31288	49	65	b-1i	b-1i	NOUN
esrj-31288	49	66	'	'	PART
esrj-31288	49	67	2	2	NUM
esrj-31288	49	68	two	two	NUM
esrj-31288	49	69	transmitted	transmit	VERB
esrj-31288	49	70	paraxial	paraxial	ADJ
esrj-31288	49	71	rays	ray	NOUN
esrj-31288	49	72	(	(	PUNCT
esrj-31288	49	73	one	one	NUM
esrj-31288	49	74	starting	start	VERB
esrj-31288	49	75	at	at	ADP
esrj-31288	49	76	x	x	X
esrj-31288	49	77	and	and	CCONJ
esrj-31288	49	78	x	x	NOUN
esrj-31288	49	79	"	"	PUNCT
esrj-31288	49	80	other	other	ADJ
esrj-31288	49	81	at	at	ADP
esrj-31288	49	82	)	)	PUNCT
esrj-31288	49	83	combine	combine	VERB
esrj-31288	49	84	into	into	ADP
esrj-31288	49	85	a	a	DET
esrj-31288	49	86	reflected	reflect	VERB
esrj-31288	49	87	one	one	NUM
esrj-31288	49	88	,	,	PUNCT
esrj-31288	49	89	with	with	ADP
esrj-31288	49	90	the	the	DET
esrj-31288	49	91	travel	travel	NOUN
esrj-31288	49	92	time	time	NOUN
esrj-31288	49	93	function	function	VERB
esrj-31288	49	94	t(x	t(x	PROPN
esrj-31288	49	95	,	,	PUNCT
esrj-31288	49	96	x	x	NOUN
esrj-31288	49	97	"	"	PUNCT
esrj-31288	49	98	)	)	PUNCT
esrj-31288	49	99	given	give	VERB
esrj-31288	49	100	by	by	ADP
esrj-31288	49	101	the	the	DET
esrj-31288	49	102	sum	sum	NOUN
esrj-31288	49	103	of	of	ADP
esrj-31288	49	104	the	the	DET
esrj-31288	49	105	travel	travel	NOUN
esrj-31288	49	106	times	time	NOUN
esrj-31288	49	107	-	-	PUNCT
esrj-31288	49	108	of	of	ADP
esrj-31288	49	109	the	the	DET
esrj-31288	49	110	two	two	NUM
esrj-31288	49	111	transmitted	transmit	VERB
esrj-31288	49	112	rays	ray	NOUN
esrj-31288	49	113	:	:	PUNCT
esrj-31288	49	114	t(x	t(x	PROPN
esrj-31288	49	115	,	,	PUNCT
esrj-31288	49	116	x	x	NOUN
esrj-31288	49	117	"	"	PUNCT
esrj-31288	49	118	)	)	PUNCT
esrj-31288	49	119	=	=	PUNCT
esrj-31288	49	120	to	to	ADP
esrj-31288	49	121	2po	2po	NOUN
esrj-31288	49	122	+	+	CCONJ
esrj-31288	49	123	(	(	PUNCT
esrj-31288	49	124	x	x	X
esrj-31288	49	125	+	+	NUM
esrj-31288	49	126	x	x	NOUN
esrj-31288	49	127	"	"	PUNCT
esrj-31288	49	128	)	)	PUNCT
esrj-31288	50	1	+	+	PUNCT
esrj-31288	51	1	+	+	CCONJ
esrj-31288	51	2	(	(	PUNCT
esrj-31288	51	3	x	x	X
esrj-31288	51	4	+	+	NUM
esrj-31288	51	5	x	x	NOUN
esrj-31288	51	6	"	"	PUNCT
esrj-31288	51	7	)	)	PUNCT
esrj-31288	51	8	.	.	PUNCT
esrj-31288	52	1	d	d	X
esrj-31288	52	2	-i	-i	PUNCT
esrj-31288	52	3	c	c	PROPN
esrj-31288	52	4	1	1	NUM
esrj-31288	52	5	..	..	PUNCT
esrj-31288	52	6	(	(	PUNCT
esrj-31288	52	7	x	x	X
esrj-31288	52	8	+	+	NUM
esrj-31288	52	9	x	x	X
esrj-31288	52	10	"	"	PUNCT
esrj-31288	52	11	)	)	PUNCT
esrj-31288	53	1	+	+	CCONJ
esrj-31288	53	2	1	1	X
esrj-31288	53	3	..	..	PUNCT
esrj-31288	53	4	(	(	PUNCT
esrj-31288	53	5	x	x	X
esrj-31288	53	6	"	"	PUNCT
esrj-31288	53	7	x	x	NOUN
esrj-31288	53	8	)	)	PUNCT
esrj-31288	53	9	.	.	PUNCT
esrj-31288	54	1	b-1	b-1	PROPN
esrj-31288	54	2	a	a	DET
esrj-31288	54	3	1	1	NUM
esrj-31288	54	4	..	..	PUNCT
esrj-31288	54	5	(	(	PUNCT
esrj-31288	54	6	x	x	X
esrj-31288	54	7	"	"	PUNCT
esrj-31288	54	8	x	x	NOUN
esrj-31288	54	9	)	)	PUNCT
esrj-31288	54	10	-2	-2	NOUN
esrj-31288	55	1	2	2	NUM
esrj-31288	55	2	-2	-2	INTJ
esrj-31288	55	3	where	where	SCONJ
esrj-31288	55	4	to	to	PART
esrj-31288	55	5	is	be	AUX
esrj-31288	55	6	the	the	DET
esrj-31288	55	7	two	two	NUM
esrj-31288	55	8	way	way	NOUN
esrj-31288	55	9	travel	travel	NOUN
esrj-31288	55	10	time	time	NOUN
esrj-31288	55	11	of	of	ADP
esrj-31288	55	12	the	the	DET
esrj-31288	55	13	central	central	ADJ
esrj-31288	55	14	ray	ray	NOUN
esrj-31288	55	15	.	.	PUNCT
esrj-31288	56	1	expression	expression	NOUN
esrj-31288	56	2	(	(	PUNCT
esrj-31288	56	3	3	3	X
esrj-31288	56	4	)	)	PUNCT
esrj-31288	56	5	is	be	AUX
esrj-31288	56	6	called	call	VERB
esrj-31288	56	7	the	the	DET
esrj-31288	56	8	parabolic	parabolic	ADJ
esrj-31288	56	9	approximation	approximation	NOUN
esrj-31288	56	10	of	of	ADP
esrj-31288	56	11	the	the	DET
esrj-31288	56	12	travel	travel	NOUN
esrj-31288	56	13	time	time	NOUN
esrj-31288	56	14	along	along	ADP
esrj-31288	56	15	the	the	DET
esrj-31288	56	16	paraxial	paraxial	ADJ
esrj-31288	56	17	ray	ray	NOUN
esrj-31288	56	18	,	,	PUNCT
esrj-31288	56	19	and	and	CCONJ
esrj-31288	56	20	is	be	AUX
esrj-31288	56	21	not	not	PART
esrj-31288	56	22	the	the	DET
esrj-31288	56	23	best	good	ADJ
esrj-31288	56	24	approximation	approximation	NOUN
esrj-31288	56	25	.	.	PUNCT
esrj-31288	57	1	it	it	PRON
esrj-31288	57	2	is	be	AUX
esrj-31288	57	3	known	know	VERB
esrj-31288	57	4	a	a	DET
esrj-31288	57	5	long	long	ADJ
esrj-31288	57	6	time	time	NOUN
esrj-31288	57	7	ago	ago	ADV
esrj-31288	57	8	that	that	SCONJ
esrj-31288	57	9	in	in	ADP
esrj-31288	57	10	simple	simple	ADJ
esrj-31288	57	11	layered	layered	ADJ
esrj-31288	57	12	media	medium	NOUN
esrj-31288	57	13	,	,	PUNCT
esrj-31288	57	14	seismic	seismic	ADJ
esrj-31288	57	15	nearvertical	nearvertical	ADJ
esrj-31288	57	16	reflections	reflection	NOUN
esrj-31288	57	17	are	be	AUX
esrj-31288	57	18	better	well	ADV
esrj-31288	57	19	approximated	approximate	VERB
esrj-31288	57	20	by	by	ADP
esrj-31288	57	21	hyperbolic	hyperbolic	ADJ
esrj-31288	57	22	rather	rather	ADV
esrj-31288	57	23	than	than	ADP
esrj-31288	57	24	parabolic	parabolic	ADJ
esrj-31288	57	25	travel	travel	NOUN
esrj-31288	57	26	times	time	NOUN
esrj-31288	57	27	curves	curve	NOUN
esrj-31288	57	28	.	.	PUNCT
esrj-31288	58	1	ifwe	ifwe	NOUN
esrj-31288	58	2	square	square	PROPN
esrj-31288	58	3	(	(	PUNCT
esrj-31288	58	4	3	3	NUM
esrj-31288	58	5	)	)	PUNCT
esrj-31288	58	6	and	and	CCONJ
esrj-31288	58	7	retain	retain	VERB
esrj-31288	58	8	only	only	ADV
esrj-31288	58	9	its	its	PRON
esrj-31288	58	10	terms	term	NOUN
esrj-31288	58	11	up	up	ADP
esrj-31288	58	12	to	to	ADP
esrj-31288	58	13	the	the	DET
esrj-31288	58	14	second	second	ADJ
esrj-31288	58	15	-	-	PUNCT
esrj-31288	58	16	order	order	NOUN
esrj-31288	58	17	in	in	ADP
esrj-31288	58	18	x	x	X
esrj-31288	58	19	and	and	CCONJ
esrj-31288	58	20	x	x	X
esrj-31288	58	21	'	'	X
esrj-31288	58	22	,	,	PUNCT
esrj-31288	58	23	the	the	DET
esrj-31288	58	24	hyperbolic	hyperbolic	ADJ
esrj-31288	58	25	approximation	approximation	NOUN
esrj-31288	58	26	of	of	ADP
esrj-31288	58	27	the	the	DET
esrj-31288	58	28	travel	travel	NOUN
esrj-31288	58	29	time	time	NOUN
esrj-31288	58	30	for	for	ADP
esrj-31288	58	31	the	the	DET
esrj-31288	58	32	paraxial	paraxial	ADJ
esrj-31288	58	33	ray	ray	NOUN
esrj-31288	58	34	is	be	AUX
esrj-31288	58	35	obtained	obtain	VERB
esrj-31288	58	36	(	(	PUNCT
esrj-31288	58	37	ursin	ursin	NOUN
esrj-31288	58	38	,	,	PUNCT
esrj-31288	58	39	1982	1982	NUM
esrj-31288	58	40	)	)	PUNCT
esrj-31288	58	41	.	.	PUNCT
esrj-31288	59	1	(	(	PUNCT
esrj-31288	59	2	"	"	PUNCT
esrj-31288	59	3	)	)	PUNCT
esrj-31288	59	4	2	2	NUM
esrj-31288	59	5	_	_	PUNCT
esrj-31288	59	6	i	i	PRON
esrj-31288	59	7	"	"	PUNCT
esrj-31288	59	8	2	2	NUM
esrj-31288	59	9	t	t	NOUN
esrj-31288	59	10	x	x	NOUN
esrj-31288	59	11	,	,	PUNCT
esrj-31288	59	12	x	x	SYM
esrj-31288	59	13	-(to-2po'z(x+x	-(to-2po'z(x+x	NUM
esrj-31288	59	14	)	)	PUNCT
esrj-31288	59	15	)	)	PUNCT
esrj-31288	60	1	+	+	CCONJ
esrj-31288	60	2	2to(1(x	2to(1(x	NUM
esrj-31288	60	3	+	+	CCONJ
esrj-31288	60	4	x	x	NOUN
esrj-31288	60	5	"	"	PUNCT
esrj-31288	60	6	)	)	PUNCT
esrj-31288	60	7	·	·	PUNCT
esrj-31288	61	1	o	o	X
esrj-31288	61	2	'	'	X
esrj-31288	61	3	c	c	PROPN
esrj-31288	61	4	t	t	PROPN
esrj-31288	61	5	(	(	PUNCT
esrj-31288	61	6	x	x	PROPN
esrj-31288	61	7	+	+	NUM
esrj-31288	61	8	x	x	NOUN
esrj-31288	61	9	"	"	PUNCT
esrj-31288	61	10	)	)	PUNCT
esrj-31288	62	1	+	+	CCONJ
esrj-31288	62	2	t	t	X
esrj-31288	62	3	(	(	PUNCT
esrj-31288	62	4	x	x	NOUN
esrj-31288	62	5	"	"	PUNCT
esrj-31288	62	6	x	x	NOUN
esrj-31288	62	7	)	)	PUNCT
esrj-31288	62	8	·	·	PUNCT
esrj-31288	62	9	b-1	b-1	PROPN
esrj-31288	62	10	a	a	DET
esrj-31288	62	11	t	t	PROPN
esrj-31288	62	12	(	(	PUNCT
esrj-31288	62	13	x	x	X
esrj-31288	62	14	"	"	PUNCT
esrj-31288	62	15	x)/	x)/	NOUN
esrj-31288	62	16	(	(	PUNCT
esrj-31288	62	17	4	4	NUM
esrj-31288	62	18	)	)	PUNCT
esrj-31288	62	19	equations	equation	NOUN
esrj-31288	62	20	(	(	PUNCT
esrj-31288	62	21	3	3	NUM
esrj-31288	62	22	)	)	PUNCT
esrj-31288	62	23	and	and	CCONJ
esrj-31288	62	24	(	(	PUNCT
esrj-31288	62	25	4	4	X
esrj-31288	62	26	)	)	PUNCT
esrj-31288	62	27	contains	contain	VERB
esrj-31288	62	28	the	the	DET
esrj-31288	62	29	same	same	ADJ
esrj-31288	62	30	nine	nine	NUM
esrj-31288	62	31	unknown	unknown	ADJ
esrj-31288	62	32	parameters	parameter	NOUN
esrj-31288	62	33	:	:	PUNCT
esrj-31288	62	34	one	one	NUM
esrj-31288	62	35	in	in	ADP
esrj-31288	62	36	to	to	ADP
esrj-31288	62	37	'	'	PUNCT
esrj-31288	62	38	two	two	NUM
esrj-31288	62	39	in	in	ADP
esrj-31288	62	40	po	po	NOUN
esrj-31288	62	41	'	'	PUNCT
esrj-31288	62	42	three	three	NUM
esrj-31288	62	43	in	in	ADP
esrj-31288	62	44	ll	ll	NOUN
esrj-31288	62	45	-	-	PUNCT
esrj-31288	62	46	ia	ia	NOUN
esrj-31288	62	47	and	and	CCONJ
esrj-31288	62	48	three	three	NUM
esrj-31288	62	49	in	in	ADP
esrj-31288	62	50	d	d	PROPN
esrj-31288	62	51	-i	-i	PUNCT
esrj-31288	62	52	~	~	PUNCT
esrj-31288	62	53	(	(	PUNCT
esrj-31288	62	54	because	because	SCONJ
esrj-31288	62	55	the	the	DET
esrj-31288	62	56	matrices	matrix	NOUN
esrj-31288	62	57	are	be	AUX
esrj-31288	62	58	symmetric	symmetric	ADJ
esrj-31288	62	59	)	)	PUNCT
esrj-31288	62	60	,	,	PUNCT
esrj-31288	62	61	in	in	ADP
esrj-31288	62	62	consequence	consequence	NOUN
esrj-31288	62	63	(	(	PUNCT
esrj-31288	62	64	3	3	NUM
esrj-31288	62	65	)	)	PUNCT
esrj-31288	62	66	and	and	CCONJ
esrj-31288	62	67	(	(	PUNCT
esrj-31288	62	68	4	4	X
esrj-31288	62	69	)	)	PUNCT
esrj-31288	62	70	can	can	AUX
esrj-31288	62	71	be	be	AUX
esrj-31288	62	72	determined	determine	VERB
esrj-31288	62	73	registering	register	VERB
esrj-31288	62	74	at	at	ADP
esrj-31288	62	75	least	least	ADV
esrj-31288	62	76	nine	nine	NUM
esrj-31288	62	77	travel	travel	NOUN
esrj-31288	62	78	times	time	NOUN
esrj-31288	62	79	for	for	ADP
esrj-31288	62	80	rays	ray	NOUN
esrj-31288	62	81	in	in	ADP
esrj-31288	62	82	the	the	DET
esrj-31288	62	83	vicinity	vicinity	NOUN
esrj-31288	62	84	of	of	ADP
esrj-31288	62	85	a	a	DET
esrj-31288	62	86	central	central	ADJ
esrj-31288	62	87	ray	ray	NOUN
esrj-31288	62	88	at	at	ADP
esrj-31288	62	89	uppermost	uppermost	ADJ
esrj-31288	62	90	surface	surface	NOUN
esrj-31288	62	91	.	.	PUNCT
esrj-31288	63	1	for	for	ADP
esrj-31288	63	2	each	each	DET
esrj-31288	63	3	reflector	reflector	NOUN
esrj-31288	63	4	interface	interface	NOUN
esrj-31288	63	5	in	in	ADP
esrj-31288	63	6	the	the	DET
esrj-31288	63	7	model	model	NOUN
esrj-31288	63	8	,	,	PUNCT
esrj-31288	63	9	a	a	DET
esrj-31288	63	10	travel	travel	NOUN
esrj-31288	63	11	time	time	NOUN
esrj-31288	63	12	function	function	NOUN
esrj-31288	63	13	like	like	ADP
esrj-31288	63	14	equation	equation	NOUN
esrj-31288	63	15	(	(	PUNCT
esrj-31288	63	16	4	4	X
esrj-31288	63	17	)	)	PUNCT
esrj-31288	63	18	will	will	AUX
esrj-31288	63	19	be	be	AUX
esrj-31288	63	20	estimated	estimate	VERB
esrj-31288	63	21	at	at	ADP
esrj-31288	63	22	the	the	DET
esrj-31288	63	23	uppermost	uppermost	ADJ
esrj-31288	63	24	surface	surface	NOUN
esrj-31288	63	25	.	.	PUNCT
esrj-31288	64	1	interval	interval	NOUN
esrj-31288	64	2	velocity	velocity	NOUN
esrj-31288	64	3	considering	consider	VERB
esrj-31288	64	4	the	the	DET
esrj-31288	64	5	travel	travel	NOUN
esrj-31288	64	6	time	time	NOUN
esrj-31288	64	7	function	function	NOUN
esrj-31288	64	8	determined	determine	VERB
esrj-31288	64	9	at	at	ADP
esrj-31288	64	10	the	the	DET
esrj-31288	64	11	anterior	anterior	ADJ
esrj-31288	64	12	surface	surface	NOUN
esrj-31288	64	13	of	of	ADP
esrj-31288	64	14	a	a	DET
esrj-31288	64	15	layer	layer	NOUN
esrj-31288	64	16	and	and	CCONJ
esrj-31288	64	17	known	know	VERB
esrj-31288	64	18	the	the	DET
esrj-31288	64	19	geometry	geometry	NOUN
esrj-31288	64	20	of	of	ADP
esrj-31288	64	21	that	that	DET
esrj-31288	64	22	interface	interface	NOUN
esrj-31288	64	23	(	(	PUNCT
esrj-31288	64	24	k	k	NOUN
esrj-31288	64	25	n	n	CCONJ
esrj-31288	64	26	-	-	PUNCT
esrj-31288	64	27	i	i	NOUN
esrj-31288	64	28	)	)	PUNCT
esrj-31288	64	29	'	'	PUNCT
esrj-31288	64	30	we	we	PRON
esrj-31288	64	31	will	will	AUX
esrj-31288	64	32	show	show	VERB
esrj-31288	64	33	how	how	SCONJ
esrj-31288	64	34	the	the	DET
esrj-31288	64	35	interval	interval	NOUN
esrj-31288	64	36	velocity	velocity	NOUN
esrj-31288	64	37	of	of	ADP
esrj-31288	64	38	the	the	DET
esrj-31288	64	39	layer	layer	NOUN
esrj-31288	64	40	can	can	AUX
esrj-31288	64	41	be	be	AUX
esrj-31288	64	42	determined	determine	VERB
esrj-31288	64	43	,	,	PUNCT
esrj-31288	64	44	uniquely	uniquely	ADV
esrj-31288	64	45	.	.	PUNCT
esrj-31288	65	1	the	the	DET
esrj-31288	65	2	total	total	ADJ
esrj-31288	65	3	transfer	transfer	NOUN
esrj-31288	65	4	matrix	matrix	NOUN
esrj-31288	65	5	,	,	PUNCT
esrj-31288	65	6	which	which	PRON
esrj-31288	65	7	describes	describe	VERB
esrj-31288	65	8	the	the	DET
esrj-31288	65	9	ray	ray	NOUN
esrj-31288	65	10	propagation	propagation	NOUN
esrj-31288	65	11	in	in	ADP
esrj-31288	65	12	the	the	DET
esrj-31288	65	13	n	n	CCONJ
esrj-31288	65	14	"	"	PUNCT
esrj-31288	65	15	layer	layer	NOUN
esrj-31288	65	16	,	,	PUNCT
esrj-31288	65	17	can	can	AUX
esrj-31288	65	18	be	be	AUX
esrj-31288	65	19	decomposed	decompose	VERB
esrj-31288	65	20	after	after	ADP
esrj-31288	65	21	kahn	kahn	PROPN
esrj-31288	65	22	(	(	PUNCT
esrj-31288	65	23	1987	1987	NUM
esrj-31288	65	24	)	)	PUNCT
esrj-31288	65	25	in	in	ADP
esrj-31288	65	26	a	a	DET
esrj-31288	65	27	product	product	NOUN
esrj-31288	65	28	of	of	ADP
esrj-31288	65	29	matrices	matrix	NOUN
esrj-31288	65	30	:	:	PUNCT
esrj-31288	65	31	(	(	PUNCT
esrj-31288	65	32	i	i	NOUN
esrj-31288	65	33	)	)	PUNCT
esrj-31288	66	1	[	[	X
esrj-31288	66	2	an	an	DET
esrj-31288	66	3	bn	bn	NOUN
esrj-31288	66	4	]	]	X
esrj-31288	66	5	[	[	PUNCT
esrj-31288	66	6	i	i	PRON
esrj-31288	66	7	a	a	DET
esrj-31288	66	8	~	~	NOUN
esrj-31288	66	9	vnsni	vnsni	NOUN
esrj-31288	66	10	]	]	PUNCT
esrj-31288	66	11	en	en	ADP
esrj-31288	66	12	dn	dn	PROPN
esrj-31288	66	13	v;;ikn	v;;ikn	NOUN
esrj-31288	66	14	1	1	NUM
esrj-31288	67	1	[	[	X
esrj-31288	67	2	~	~	PUNCT
esrj-31288	67	3	o	o	X
esrj-31288	67	4	]	]	X
esrj-31288	67	5	[	[	PUNCT
esrj-31288	67	6	l	l	X
esrj-31288	67	7	~	~	PUNCT
esrj-31288	67	8	]	]	X
esrj-31288	67	9	(	(	PUNCT
esrj-31288	67	10	5	5	NUM
esrj-31288	67	11	)	)	PUNCT
esrj-31288	67	12	-i	-i	NUM
esrj-31288	67	13	1	1	NUM
esrj-31288	67	14	-il	-il	NOUN
esrj-31288	67	15	-cos({3n)v	-cos({3n)v	PUNCT
esrj-31288	67	16	;	;	PUNCT
esrj-31288	67	17	;	;	PUNCT
esrj-31288	67	18	kn	kn	PROPN
esrj-31288	67	19	-	-	PROPN
esrj-31288	67	20	i	i	PRON
esrj-31288	68	1	[	[	X
esrj-31288	68	2	cos({3n	cos({3n	NOUN
esrj-31288	68	3	)	)	PUNCT
esrj-31288	68	4	~]with	~]with	NOUN
esrj-31288	68	5	l	l	NOUN
esrj-31288	69	1	=	=	PUNCT
esrj-31288	69	2	'	'	PUNCT
esrj-31288	69	3	l({3n	l({3n	X
esrj-31288	69	4	)	)	PUNCT
esrj-31288	69	5	=	=	SYM
esrj-31288	69	6	0	0	PUNCT
esrj-31288	69	7	(	(	PUNCT
esrj-31288	69	8	6	6	NUM
esrj-31288	69	9	)	)	PUNCT
esrj-31288	69	10	(	(	PUNCT
esrj-31288	69	11	2	2	X
esrj-31288	69	12	)	)	PUNCT
esrj-31288	69	13	the	the	DET
esrj-31288	69	14	capital	capital	NOUN
esrj-31288	69	15	letters	letter	NOUN
esrj-31288	69	16	in	in	ADP
esrj-31288	69	17	the	the	DET
esrj-31288	69	18	matrix	matrix	NOUN
esrj-31288	69	19	relation	relation	NOUN
esrj-31288	69	20	(	(	PUNCT
esrj-31288	69	21	6	6	NUM
esrj-31288	69	22	)	)	PUNCT
esrj-31288	69	23	are	be	AUX
esrj-31288	69	24	2x2	2x2	NUM
esrj-31288	69	25	matrices	matrix	NOUN
esrj-31288	69	26	:	:	PUNCT
esrj-31288	69	27	e.g.	e.g.	ADV
esrj-31288	69	28	,	,	PUNCT
esrj-31288	69	29	1	1	NUM
esrj-31288	69	30	is	be	AUX
esrj-31288	69	31	the	the	DET
esrj-31288	69	32	unity	unity	NOUN
esrj-31288	69	33	matrix	matrix	NOUN
esrj-31288	69	34	,	,	PUNCT
esrj-31288	69	35	q	q	PUNCT
esrj-31288	69	36	is	be	AUX
esrj-31288	69	37	the	the	DET
esrj-31288	69	38	zero	zero	NUM
esrj-31288	69	39	matrix	matrix	NOUN
esrj-31288	69	40	and	and	CCONJ
esrj-31288	69	41	k	k	PROPN
esrj-31288	69	42	n	n	PRON
esrj-31288	69	43	is	be	AUX
esrj-31288	69	44	the	the	DET
esrj-31288	69	45	matrix	matrix	NOUN
esrj-31288	69	46	of	of	ADP
esrj-31288	69	47	curvature	curvature	NOUN
esrj-31288	69	48	of	of	ADP
esrj-31288	69	49	the	the	DET
esrj-31288	69	50	n	n	CCONJ
esrj-31288	69	51	"	"	PUNCT
esrj-31288	69	52	interface	interface	NOUN
esrj-31288	69	53	.	.	PUNCT
esrj-31288	70	1	the	the	DET
esrj-31288	70	2	n	n	CCONJ
esrj-31288	70	3	"	"	PUNCT
esrj-31288	70	4	interval	interval	NOUN
esrj-31288	70	5	velocity	velocity	NOUN
esrj-31288	70	6	is	be	AUX
esrj-31288	70	7	vn	vn	PROPN
esrj-31288	70	8	'	'	PUNCT
esrj-31288	70	9	and	and	CCONJ
esrj-31288	70	10	sn	sn	VERB
esrj-31288	70	11	the	the	DET
esrj-31288	70	12	path	path	NOUN
esrj-31288	70	13	length	length	NOUN
esrj-31288	70	14	of	of	ADP
esrj-31288	70	15	the	the	DET
esrj-31288	70	16	central	central	ADJ
esrj-31288	70	17	ray	ray	NOUN
esrj-31288	70	18	in	in	ADP
esrj-31288	70	19	the	the	DET
esrj-31288	70	20	layer	layer	NOUN
esrj-31288	70	21	.	.	PUNCT
esrj-31288	71	1	the	the	DET
esrj-31288	71	2	angle	angle	NOUN
esrj-31288	71	3	between	between	ADP
esrj-31288	71	4	the	the	DET
esrj-31288	71	5	normal	normal	ADJ
esrj-31288	71	6	vector	vector	NOUN
esrj-31288	71	7	of	of	ADP
esrj-31288	71	8	the	the	DET
esrj-31288	71	9	(	(	PUNCT
esrj-31288	71	10	n	n	NOUN
esrj-31288	71	11	i	i	PRON
esrj-31288	71	12	)	)	PUNCT
esrj-31288	71	13	th	th	PROPN
esrj-31288	71	14	interface	interface	NOUN
esrj-31288	71	15	at	at	ADP
esrj-31288	71	16	the	the	DET
esrj-31288	71	17	intersection	intersection	NOUN
esrj-31288	71	18	point	point	NOUN
esrj-31288	71	19	with	with	ADP
esrj-31288	71	20	the	the	DET
esrj-31288	71	21	central	central	ADJ
esrj-31288	71	22	ray	ray	NOUN
esrj-31288	71	23	and	and	CCONJ
esrj-31288	71	24	the	the	DET
esrj-31288	71	25	slowness	slowness	NOUN
esrj-31288	71	26	vector	vector	NOUN
esrj-31288	71	27	of	of	ADP
esrj-31288	71	28	the	the	DET
esrj-31288	71	29	central	central	ADJ
esrj-31288	71	30	ray	ray	NOUN
esrj-31288	71	31	is	be	AUX
esrj-31288	71	32	f3	f3	ADJ
esrj-31288	71	33	n	n	ADV
esrj-31288	71	34	.	.	PUNCT
esrj-31288	72	1	the	the	DET
esrj-31288	72	2	matrices	matrix	NOUN
esrj-31288	72	3	on	on	ADP
esrj-31288	72	4	the	the	DET
esrj-31288	72	5	right	right	ADJ
esrj-31288	72	6	side	side	NOUN
esrj-31288	72	7	of	of	ADP
esrj-31288	72	8	the	the	DET
esrj-31288	72	9	transfer	transfer	NOUN
esrj-31288	72	10	matrix	matrix	NOUN
esrj-31288	72	11	are	be	AUX
esrj-31288	72	12	responsible	responsible	ADJ
esrj-31288	72	13	for	for	ADP
esrj-31288	72	14	the	the	DET
esrj-31288	72	15	following	follow	VERB
esrj-31288	72	16	transfers	transfer	NOUN
esrj-31288	72	17	of	of	ADP
esrj-31288	72	18	positions	position	NOUN
esrj-31288	72	19	and	and	CCONJ
esrj-31288	72	20	slowness	slowness	NOUN
esrj-31288	72	21	vectors	vector	NOUN
esrj-31288	72	22	,	,	PUNCT
esrj-31288	72	23	from	from	ADP
esrj-31288	72	24	right	right	ADJ
esrj-31288	72	25	to	to	ADP
esrj-31288	72	26	left	left	ADV
esrj-31288	72	27	:	:	PUNCT
esrj-31288	72	28	(	(	PUNCT
esrj-31288	72	29	i	i	NOUN
esrj-31288	72	30	)	)	PUNCT
esrj-31288	72	31	from	from	ADP
esrj-31288	72	32	the	the	DET
esrj-31288	72	33	(	(	PUNCT
esrj-31288	72	34	n	n	NOUN
esrj-31288	72	35	i	i	PRON
esrj-31288	72	36	)	)	PUNCT
esrj-31288	72	37	th	th	PROPN
esrj-31288	72	38	interface	interface	NOUN
esrj-31288	72	39	into	into	ADP
esrj-31288	72	40	the	the	DET
esrj-31288	72	41	tangent	tangent	NOUN
esrj-31288	72	42	plane	plane	NOUN
esrj-31288	72	43	,	,	PUNCT
esrj-31288	72	44	(	(	PUNCT
esrj-31288	72	45	2	2	NUM
esrj-31288	72	46	)	)	PUNCT
esrj-31288	72	47	from	from	ADP
esrj-31288	72	48	the	the	DET
esrj-31288	72	49	tangent	tangent	ADJ
esrj-31288	72	50	plane	plane	NOUN
esrj-31288	72	51	into	into	ADP
esrj-31288	72	52	the	the	DET
esrj-31288	72	53	plane	plane	NOUN
esrj-31288	72	54	perpendicular	perpendicular	NOUN
esrj-31288	72	55	to	to	ADP
esrj-31288	72	56	the	the	DET
esrj-31288	72	57	central	central	ADJ
esrj-31288	72	58	ray	ray	NOUN
esrj-31288	72	59	,	,	PUNCT
esrj-31288	72	60	(	(	PUNCT
esrj-31288	72	61	3	3	NUM
esrj-31288	72	62	)	)	PUNCT
esrj-31288	72	63	from	from	ADP
esrj-31288	72	64	the	the	DET
esrj-31288	72	65	plane	plane	NOUN
esrj-31288	72	66	perpendicular	perpendicular	NOUN
esrj-31288	72	67	to	to	ADP
esrj-31288	72	68	the	the	DET
esrj-31288	72	69	central	central	ADJ
esrj-31288	72	70	ray	ray	NOUN
esrj-31288	72	71	at	at	ADP
esrj-31288	72	72	the	the	DET
esrj-31288	72	73	(	(	PUNCT
esrj-31288	72	74	n	n	NOUN
esrj-31288	72	75	i	i	PRON
esrj-31288	72	76	)	)	PUNCT
esrj-31288	72	77	th	th	PROPN
esrj-31288	72	78	interface	interface	NOUN
esrj-31288	72	79	into	into	ADP
esrj-31288	72	80	a	a	DET
esrj-31288	72	81	perpendicular	perpendicular	ADJ
esrj-31288	72	82	plane	plane	NOUN
esrj-31288	72	83	to	to	ADP
esrj-31288	72	84	the	the	DET
esrj-31288	72	85	central	central	ADJ
esrj-31288	72	86	ray	ray	NOUN
esrj-31288	72	87	at	at	ADP
esrj-31288	72	88	the	the	DET
esrj-31288	72	89	n	n	CCONJ
esrj-31288	72	90	'	'	CCONJ
esrj-31288	72	91	"	"	PUNCT
esrj-31288	72	92	interface	interface	NOUN
esrj-31288	72	93	,	,	PUNCT
esrj-31288	72	94	and	and	CCONJ
esrj-31288	72	95	finally	finally	ADV
esrj-31288	72	96	from	from	ADP
esrj-31288	72	97	the	the	DET
esrj-31288	72	98	tangent	tangent	ADJ
esrj-31288	72	99	plane	plane	NOUN
esrj-31288	72	100	into	into	ADP
esrj-31288	72	101	the	the	DET
esrj-31288	72	102	n	n	CCONJ
esrj-31288	72	103	"	"	PUNCT
esrj-31288	72	104	interface	interface	NOUN
esrj-31288	72	105	,	,	PUNCT
esrj-31288	72	106	i.e.	i.e.	X
esrj-31288	72	107	into	into	ADP
esrj-31288	72	108	the	the	DET
esrj-31288	72	109	reflector	reflector	NOUN
esrj-31288	72	110	.	.	PUNCT
esrj-31288	72	111	!	!	PUNCT
esrj-31288	73	1	1	1	NUM
esrj-31288	73	2	t	t	NOUN
esrj-31288	73	3	n	n	VERB
esrj-31288	73	4	is	be	AUX
esrj-31288	73	5	the	the	DET
esrj-31288	73	6	one	one	NUM
esrj-31288	73	7	way	way	NOUN
esrj-31288	73	8	travel	travel	NOUN
esrj-31288	73	9	time	time	NOUN
esrj-31288	73	10	of	of	ADP
esrj-31288	73	11	the	the	DET
esrj-31288	73	12	central	central	ADJ
esrj-31288	73	13	ray	ray	NOUN
esrj-31288	73	14	through	through	ADP
esrj-31288	73	15	the	the	DET
esrj-31288	73	16	n	n	CCONJ
esrj-31288	73	17	"	"	PUNCT
esrj-31288	73	18	layer	layer	NOUN
esrj-31288	73	19	.	.	PUNCT
esrj-31288	74	1	in	in	ADP
esrj-31288	74	2	this	this	DET
esrj-31288	74	3	step	step	NOUN
esrj-31288	74	4	,	,	PUNCT
esrj-31288	74	5	besides	besides	SCONJ
esrj-31288	74	6	k	k	PROPN
esrj-31288	74	7	n	n	X
esrj-31288	74	8	-	-	PUNCT
esrj-31288	74	9	i	i	PRON
esrj-31288	74	10	'	'	PUNCT
esrj-31288	74	11	we	we	PRON
esrj-31288	74	12	assume	assume	VERB
esrj-31288	74	13	to	to	PART
esrj-31288	74	14	know	know	VERB
esrj-31288	74	15	the	the	DET
esrj-31288	74	16	interval	interval	NOUN
esrj-31288	74	17	velocity	velocity	NOUN
esrj-31288	74	18	of	of	ADP
esrj-31288	74	19	the	the	DET
esrj-31288	74	20	superior	superior	ADJ
esrj-31288	74	21	layer	layer	NOUN
esrj-31288	74	22	vn	vn	PROPN
esrj-31288	74	23	-	-	PUNCT
esrj-31288	74	24	i	i	PRON
esrj-31288	74	25	and	and	CCONJ
esrj-31288	74	26	the	the	DET
esrj-31288	74	27	angle	angle	NOUN
esrj-31288	74	28	of	of	ADP
esrj-31288	74	29	incidence	incidence	NOUN
esrj-31288	74	30	of	of	ADP
esrj-31288	74	31	the	the	DET
esrj-31288	74	32	paraxial	paraxial	ADJ
esrj-31288	74	33	ray	ray	NOUN
esrj-31288	75	1	an	an	DET
esrj-31288	75	2	_	_	NOUN
esrj-31288	75	3	i	i	PRON
esrj-31288	75	4	at	at	ADP
esrj-31288	75	5	the	the	DET
esrj-31288	75	6	anterior	anterior	ADJ
esrj-31288	75	7	surface	surface	NOUN
esrj-31288	75	8	.	.	PUNCT
esrj-31288	76	1	multiplying	multiply	VERB
esrj-31288	76	2	the	the	DET
esrj-31288	76	3	matrices	matrix	NOUN
esrj-31288	76	4	in	in	ADP
esrj-31288	76	5	expression	expression	NOUN
esrj-31288	76	6	(	(	PUNCT
esrj-31288	76	7	5	5	NUM
esrj-31288	76	8	)	)	PUNCT
esrj-31288	76	9	,	,	PUNCT
esrj-31288	76	10	we	we	PRON
esrj-31288	76	11	obtain	obtain	VERB
esrj-31288	76	12	the	the	DET
esrj-31288	76	13	following	follow	VERB
esrj-31288	76	14	equations	equation	NOUN
esrj-31288	76	15	:	:	PUNCT
esrj-31288	76	16	(	(	PUNCT
esrj-31288	76	17	3	3	X
esrj-31288	76	18	)	)	PUNCT
esrj-31288	76	19	geofislca	geofislca	PROPN
esrj-31288	76	20	colombiana	colombiana	PROPN
esrj-31288	76	21	,	,	PUNCT
esrj-31288	76	22	5	5	NUM
esrj-31288	76	23	,	,	PUNCT
esrj-31288	76	24	diciembre	diciembre	PROPN
esrj-31288	76	25	de	de	X
esrj-31288	76	26	2001	2001	NUM
esrj-31288	76	27	interval	interval	NOUN
esrj-31288	76	28	velocity	velocity	NOUN
esrj-31288	76	29	determination	determination	NOUN
esrj-31288	76	30	by	by	ADP
esrj-31288	76	31	downward	downward	ADJ
esrj-31288	76	32	continuation	continuation	NOUN
esrj-31288	76	33	of	of	ADP
esrj-31288	76	34	the	the	DET
esrj-31288	76	35	traveltime	traveltime	NOUN
esrj-31288	76	36	function	function	NOUN
esrj-31288	76	37	,	,	PUNCT
esrj-31288	76	38	i'araxial	i'araxial	PROPN
esrj-31288	76	39	ray	ray	NOUN
esrj-31288	76	40	approximation	approximation	NOUN
esrj-31288	76	41	an	an	DET
esrj-31288	76	42	=	=	NOUN
esrj-31288	76	43	'	'	PRON
esrj-31288	76	44	l({3n)-cos({3n)sn'l-1({3n)kn-1	l({3n)-cos({3n)sn'l-1({3n)kn-1	PROPN
esrj-31288	76	45	en	en	X
esrj-31288	76	46	=	=	PROPN
esrj-31288	76	47	vnsn'l-'({3n	vnsn'l-'({3n	PROPN
esrj-31288	76	48	)	)	PUNCT
esrj-31288	76	49	c	c	NOUN
esrj-31288	76	50	,	,	PUNCT
esrj-31288	76	51	=	=	NOUN
esrj-31288	76	52	v;/kn'l({3n)-v;;'cos({3n	v;/kn'l({3n)-v;;'cos({3n	ADJ
esrj-31288	76	53	)	)	PUNCT
esrj-31288	77	1	[	[	X
esrj-31288	77	2	snkn	snkn	NOUN
esrj-31288	77	3	+	+	CCONJ
esrj-31288	77	4	l]'l-	l]'l-	PROPN
esrj-31288	77	5	'	'	PUNCT
esrj-31288	77	6	(	(	PUNCT
esrj-31288	77	7	{	{	PUNCT
esrj-31288	77	8	3	3	NUM
esrj-31288	77	9	n	n	NOUN
esrj-31288	77	10	)	)	PUNCT
esrj-31288	77	11	kn-	kn-	PROPN
esrj-31288	77	12	'	'	PUNCT
esrj-31288	77	13	dn	dn	PROPN
esrj-31288	77	14	=[	=[	PROPN
esrj-31288	77	15	snk	snk	PROPN
esrj-31288	77	16	n	n	PROPN
esrj-31288	77	17	+	+	PROPN
esrj-31288	77	18	!	!	PUNCT
esrj-31288	77	19	ji	ji	PROPN
esrj-31288	77	20	-	-	PUNCT
esrj-31288	77	21	i({3n	i({3n	NOUN
esrj-31288	77	22	)	)	PUNCT
esrj-31288	77	23	determining	determine	VERB
esrj-31288	77	24	the	the	DET
esrj-31288	77	25	inverse	inverse	NOUN
esrj-31288	77	26	of	of	ADP
esrj-31288	77	27	!	!	PUNCT
esrj-31288	77	28	l	l	NOUN
esrj-31288	77	29	n	n	ADV
esrj-31288	77	30	from	from	ADP
esrj-31288	77	31	(	(	PUNCT
esrj-31288	77	32	8)	8)	NUM
esrj-31288	77	33	and	and	CCONJ
esrj-31288	77	34	multiplying	multiplying	NOUN
esrj-31288	77	35	by	by	ADP
esrj-31288	77	36	(	(	PUNCT
esrj-31288	77	37	7	7	X
esrj-31288	77	38	)	)	PUNCT
esrj-31288	77	39	we	we	PRON
esrj-31288	77	40	obtain	obtain	VERB
esrj-31288	77	41	!	!	PUNCT
esrj-31288	78	1	1~'an	1~'an	ADJ
esrj-31288	78	2	'	'	PUNCT
esrj-31288	78	3	that	that	SCONJ
esrj-31288	78	4	we	we	PRON
esrj-31288	78	5	recalled	recall	VERB
esrj-31288	78	6	u	u	NOUN
esrj-31288	78	7	:	:	PUNCT
esrj-31288	78	8	equation	equation	NOUN
esrj-31288	78	9	(	(	PUNCT
esrj-31288	78	10	12	12	NUM
esrj-31288	78	11	)	)	PUNCT
esrj-31288	78	12	is	be	AUX
esrj-31288	78	13	equivalent	equivalent	ADJ
esrj-31288	78	14	to	to	ADP
esrj-31288	78	15	the	the	DET
esrj-31288	78	16	following	follow	VERB
esrj-31288	78	17	three	three	NUM
esrj-31288	78	18	equations	equation	NOUN
esrj-31288	78	19	:	:	PUNCT
esrj-31288	78	20	1	1	NUM
esrj-31288	78	21	1	1	NUM
esrj-31288	78	22	u22	u22	PROPN
esrj-31288	78	23	=	=	SYM
esrj-31288	78	24	--cos({3n	--cos({3n	PROPN
esrj-31288	78	25	)	)	PUNCT
esrj-31288	79	1	kn	kn	PROPN
esrj-31288	79	2	_	_	PROPN
esrj-31288	79	3	,	,	PUNCT
esrj-31288	79	4	22	22	NUM
esrj-31288	79	5	vnsn	vnsn	NOUN
esrj-31288	79	6	vn	vn	INTJ
esrj-31288	79	7	'	'	PUNCT
esrj-31288	79	8	at	at	ADP
esrj-31288	79	9	the	the	DET
esrj-31288	79	10	anterior	anterior	ADJ
esrj-31288	79	11	surface	surface	NOUN
esrj-31288	79	12	of	of	ADP
esrj-31288	79	13	the	the	DET
esrj-31288	79	14	layer	layer	NOUN
esrj-31288	79	15	the	the	DET
esrj-31288	79	16	snell	snell	NOUN
esrj-31288	79	17	's	's	PART
esrj-31288	79	18	law	law	NOUN
esrj-31288	79	19	is	be	AUX
esrj-31288	79	20	used	use	VERB
esrj-31288	79	21	:	:	PUNCT
esrj-31288	79	22	cos\{3n)=	cos\{3n)=	ADV
esrj-31288	79	23	1	1	NUM
esrj-31288	79	24	-	-	PUNCT
esrj-31288	79	25	sin2(an_1	sin2(an_1	NOUN
esrj-31288	79	26	)	)	PUNCT
esrj-31288	79	27	{	{	PUNCT
esrj-31288	79	28	vn	vn	X
esrj-31288	79	29	}	}	PUNCT
esrj-31288	79	30	2	2	NUM
esrj-31288	79	31	vn_1	vn_1	NOUN
esrj-31288	79	32	where	where	SCONJ
esrj-31288	79	33	an_i	an_i	NOUN
esrj-31288	79	34	is	be	AUX
esrj-31288	79	35	the	the	DET
esrj-31288	79	36	angle	angle	NOUN
esrj-31288	79	37	of	of	ADP
esrj-31288	79	38	incidence	incidence	NOUN
esrj-31288	79	39	and	and	CCONJ
esrj-31288	79	40	{	{	PUNCT
esrj-31288	79	41	3n	3n	NOUN
esrj-31288	79	42	is	be	AUX
esrj-31288	79	43	the	the	DET
esrj-31288	79	44	angle	angle	NOUN
esrj-31288	79	45	of	of	ADP
esrj-31288	79	46	transmission	transmission	NOUN
esrj-31288	79	47	of	of	ADP
esrj-31288	79	48	the	the	DET
esrj-31288	79	49	central	central	ADJ
esrj-31288	79	50	ray	ray	NOUN
esrj-31288	79	51	,	,	PUNCT
esrj-31288	79	52	see	see	VERB
esrj-31288	79	53	figure	figure	NOUN
esrj-31288	79	54	i.	i.	NOUN
esrj-31288	79	55	by	by	ADP
esrj-31288	79	56	definition	definition	NOUN
esrj-31288	79	57	the	the	DET
esrj-31288	79	58	interval	interval	NOUN
esrj-31288	79	59	velocity	velocity	NOUN
esrj-31288	79	60	is	be	AUX
esrj-31288	79	61	:	:	PUNCT
esrj-31288	79	62	v	v	NUM
esrj-31288	79	63	2sn	2sn	ADJ
esrj-31288	79	64	n	n	CCONJ
esrj-31288	79	65	(	(	PUNCT
esrj-31288	79	66	17	17	NUM
esrj-31288	79	67	)	)	PUNCT
esrj-31288	79	68	/)"t	/)"t	PUNCT
esrj-31288	80	1	n	n	CCONJ
esrj-31288	80	2	solving	solve	VERB
esrj-31288	80	3	simultaneously	simultaneously	ADV
esrj-31288	80	4	the	the	DET
esrj-31288	80	5	equations	equation	NOUN
esrj-31288	80	6	(	(	PUNCT
esrj-31288	80	7	13	13	NUM
esrj-31288	80	8	)	)	PUNCT
esrj-31288	80	9	,	,	PUNCT
esrj-31288	80	10	(	(	PUNCT
esrj-31288	80	11	14	14	NUM
esrj-31288	80	12	)	)	PUNCT
esrj-31288	80	13	,	,	PUNCT
esrj-31288	80	14	(	(	PUNCT
esrj-31288	80	15	15	15	NUM
esrj-31288	80	16	)	)	PUNCT
esrj-31288	80	17	,	,	PUNCT
esrj-31288	80	18	(	(	PUNCT
esrj-31288	80	19	16	16	NUM
esrj-31288	80	20	)	)	PUNCT
esrj-31288	80	21	and	and	CCONJ
esrj-31288	80	22	(	(	PUNCT
esrj-31288	80	23	17	17	NUM
esrj-31288	80	24	)	)	PUNCT
esrj-31288	80	25	,	,	PUNCT
esrj-31288	80	26	see	see	VERB
esrj-31288	80	27	appendix	appendix	NOUN
esrj-31288	80	28	a	a	PRON
esrj-31288	80	29	,	,	PUNCT
esrj-31288	80	30	the	the	DET
esrj-31288	80	31	interval	interval	NOUN
esrj-31288	80	32	velocity	velocity	NOUN
esrj-31288	80	33	of	of	ADP
esrj-31288	80	34	the	the	DET
esrj-31288	80	35	layer	layer	NOUN
esrj-31288	80	36	vn	vn	PROPN
esrj-31288	80	37	is	be	AUX
esrj-31288	80	38	determined	determine	VERB
esrj-31288	80	39	,	,	PUNCT
esrj-31288	80	40	except	except	SCONJ
esrj-31288	80	41	in	in	ADP
esrj-31288	80	42	case	case	NOUN
esrj-31288	80	43	of	of	ADP
esrj-31288	80	44	a	a	DET
esrj-31288	80	45	spherical	spherical	ADJ
esrj-31288	80	46	reflector	reflector	NOUN
esrj-31288	80	47	as	as	SCONJ
esrj-31288	80	48	was	be	AUX
esrj-31288	80	49	pointed	point	VERB
esrj-31288	80	50	by	by	ADP
esrj-31288	80	51	krey	krey	PROPN
esrj-31288	80	52	(	(	PUNCT
esrj-31288	80	53	1989).this	1989).this	NUM
esrj-31288	80	54	step	step	NOUN
esrj-31288	80	55	permits	permit	VERB
esrj-31288	80	56	to	to	PART
esrj-31288	80	57	know	know	VERB
esrj-31288	80	58	also	also	ADV
esrj-31288	80	59	the	the	DET
esrj-31288	80	60	three	three	NUM
esrj-31288	80	61	others	other	NOUN
esrj-31288	80	62	unknowns	unknown	VERB
esrj-31288	80	63	sn	sn	PROPN
esrj-31288	80	64	'	'	PUNCT
esrj-31288	80	65	/)"t	/)"t	PUNCT
esrj-31288	80	66	n	n	CCONJ
esrj-31288	80	67	'	'	CCONJ
esrj-31288	80	68	fj	fj	PROPN
esrj-31288	80	69	n	n	NOUN
esrj-31288	80	70	'	'	PUNCT
esrj-31288	80	71	and	and	CCONJ
esrj-31288	80	72	in	in	ADP
esrj-31288	80	73	con	con	NOUN
esrj-31288	80	74	sequence	sequence	NOUN
esrj-31288	80	75	to	to	PART
esrj-31288	80	76	determine	determine	VERB
esrj-31288	80	77	a	a	DET
esrj-31288	80	78	nand	nand	NOUN
esrj-31288	80	79	!	!	PUNCT
esrj-31288	81	1	l	l	NOUN
esrj-31288	81	2	n	n	X
esrj-31288	81	3	.	.	PUNCT
esrj-31288	82	1	geometry	geometry	NOUN
esrj-31288	82	2	of	of	ADP
esrj-31288	82	3	posterior	posterior	ADJ
esrj-31288	82	4	surface	surface	NOUN
esrj-31288	82	5	to	to	PART
esrj-31288	82	6	determine	determine	VERB
esrj-31288	82	7	the	the	DET
esrj-31288	82	8	geometry	geometry	NOUN
esrj-31288	82	9	of	of	ADP
esrj-31288	82	10	the	the	DET
esrj-31288	82	11	posterior	posterior	ADJ
esrj-31288	82	12	surface	surface	NOUN
esrj-31288	82	13	is	be	AUX
esrj-31288	82	14	necessary	necessary	ADJ
esrj-31288	82	15	to	to	PART
esrj-31288	82	16	know	know	VERB
esrj-31288	82	17	sn	sn	NOUN
esrj-31288	82	18	'	'	PUNCT
esrj-31288	82	19	/)"t	/)"t	PUNCT
esrj-31288	82	20	n	n	CCONJ
esrj-31288	82	21	'	'	CCONJ
esrj-31288	82	22	fj	fj	NUM
esrj-31288	82	23	n	n	PROPN
esrj-31288	82	24	and	and	CCONJ
esrj-31288	82	25	vn	vn	X
esrj-31288	82	26	'	'	PUNCT
esrj-31288	82	27	i.e.	i.e.	X
esrj-31288	82	28	,	,	PUNCT
esrj-31288	82	29	which	which	PRON
esrj-31288	82	30	were	be	AUX
esrj-31288	82	31	solved	solve	VERB
esrj-31288	82	32	the	the	DET
esrj-31288	82	33	anterior	anterior	ADJ
esrj-31288	82	34	step	step	NOUN
esrj-31288	82	35	.	.	PUNCT
esrj-31288	83	1	to	to	PART
esrj-31288	83	2	calculate	calculate	VERB
esrj-31288	83	3	the	the	DET
esrj-31288	83	4	inverse	inverse	NOUN
esrj-31288	83	5	of	of	ADP
esrj-31288	83	6	d	d	NOUN
esrj-31288	83	7	n	n	PRON
esrj-31288	83	8	equation	equation	NOUN
esrj-31288	83	9	(	(	PUNCT
esrj-31288	83	10	10	10	NUM
esrj-31288	83	11	)	)	PUNCT
esrj-31288	83	12	is	be	AUX
esrj-31288	83	13	used	use	VERB
esrj-31288	83	14	:	:	PUNCT
esrj-31288	83	15	d~	d~	NUM
esrj-31288	83	16	'	'	PART
esrj-31288	83	17	=	=	ADJ
esrj-31288	83	18	i({3n)[snkn	i({3n)[snkn	NOUN
esrj-31288	83	19	-rr	-rr	NOUN
esrj-31288	83	20	'	'	PUNCT
esrj-31288	83	21	the	the	DET
esrj-31288	83	22	product	product	NOUN
esrj-31288	83	23	of	of	ADP
esrj-31288	83	24	(	(	PUNCT
esrj-31288	83	25	18	18	NUM
esrj-31288	83	26	)	)	PUNCT
esrj-31288	83	27	by	by	ADP
esrj-31288	83	28	(	(	PUNCT
esrj-31288	83	29	9	9	X
esrj-31288	83	30	)	)	PUNCT
esrj-31288	83	31	gives	give	VERB
esrj-31288	83	32	the	the	DET
esrj-31288	83	33	matrix	matrix	NOUN
esrj-31288	83	34	geofisica	geofisica	PROPN
esrj-31288	83	35	colombiana	colombiana	PROPN
esrj-31288	83	36	,	,	PUNCT
esrj-31288	83	37	5	5	NUM
esrj-31288	83	38	,	,	PUNCT
esrj-31288	83	39	diciembre	diciembre	PROPN
esrj-31288	83	40	de	de	X
esrj-31288	83	41	2001	2001	NUM
esrj-31288	83	42	(	(	PUNCT
esrj-31288	83	43	7	7	NUM
esrj-31288	83	44	)	)	PUNCT
esrj-31288	83	45	(	(	PUNCT
esrj-31288	83	46	8)	8)	NUM
esrj-31288	83	47	t(sn	t(sn	NOUN
esrj-31288	83	48	,	,	PUNCT
esrj-31288	83	49	gn	gn	PROPN
esrj-31288	83	50	)	)	PUNCT
esrj-31288	83	51	~n.j	~n.j	X
esrj-31288	83	52	(	(	PUNCT
esrj-31288	83	53	9	9	X
esrj-31288	83	54	)	)	PUNCT
esrj-31288	83	55	anterior	anterior	ADJ
esrj-31288	83	56	surface	surface	NOUN
esrj-31288	83	57	l-----i--~	l-----i--~	NOUN
esrj-31288	83	58	(	(	PUNCT
esrj-31288	83	59	10	10	NUM
esrj-31288	83	60	)	)	PUNCT
esrj-31288	83	61	(	(	PUNCT
esrj-31288	83	62	12	12	NUM
esrj-31288	83	63	)	)	PUNCT
esrj-31288	83	64	posterior	posterior	ADJ
esrj-31288	83	65	surface	surface	NOUN
esrj-31288	83	66	(	(	PUNCT
esrj-31288	83	67	13	13	NUM
esrj-31288	83	68	)	)	PUNCT
esrj-31288	83	69	(	(	PUNCT
esrj-31288	83	70	14	14	X
esrj-31288	83	71	)	)	PUNCT
esrj-31288	83	72	figure	figure	NOUN
esrj-31288	83	73	j.	j.	PROPN
esrj-31288	83	74	left	leave	VERB
esrj-31288	83	75	:	:	PUNCT
esrj-31288	83	76	a	a	DET
esrj-31288	83	77	seismic	seismic	ADJ
esrj-31288	83	78	system	system	NOUN
esrj-31288	83	79	and	and	CCONJ
esrj-31288	83	80	the	the	DET
esrj-31288	83	81	travel	travel	NOUN
esrj-31288	83	82	lime	lime	NOUN
esrj-31288	83	83	function	function	NOUN
esrj-31288	83	84	of	of	ADP
esrj-31288	83	85	rays	ray	NOUN
esrj-31288	83	86	reflected	reflect	VERB
esrj-31288	83	87	on	on	ADP
esrj-31288	83	88	the	the	DET
esrj-31288	83	89	posterior	posterior	ADJ
esrj-31288	83	90	surface	surface	NOUN
esrj-31288	83	91	,	,	PUNCT
esrj-31288	83	92	sources	source	NOUN
esrj-31288	83	93	and	and	CCONJ
esrj-31288	83	94	detectors	detector	NOUN
esrj-31288	83	95	on	on	ADP
esrj-31288	83	96	the	the	DET
esrj-31288	83	97	anterior	anterior	ADJ
esrj-31288	83	98	surface	surface	NOUN
esrj-31288	83	99	.	.	PUNCT
esrj-31288	84	1	right	right	ADV
esrj-31288	84	2	:	:	PUNCT
esrj-31288	84	3	the	the	DET
esrj-31288	84	4	central	central	PROPN
esrj-31288	84	5	ray	ray	PROPN
esrj-31288	84	6	cross	cross	VERB
esrj-31288	84	7	the	the	DET
esrj-31288	84	8	anterior	anterior	ADJ
esrj-31288	84	9	surface	surface	NOUN
esrj-31288	84	10	with	with	ADP
esrj-31288	84	11	angles	angle	NOUN
esrj-31288	84	12	of	of	ADP
esrj-31288	84	13	incidence	incidence	NOUN
esrj-31288	84	14	and	and	CCONJ
esrj-31288	84	15	transmission	transmission	NOUN
esrj-31288	84	16	.	.	PUNCT
esrj-31288	85	1	(	(	PUNCT
esrj-31288	85	2	15	15	NUM
esrj-31288	85	3	)	)	PUNCT
esrj-31288	85	4	(	(	PUNCT
esrj-31288	85	5	16	16	NUM
esrj-31288	85	6	)	)	PUNCT
esrj-31288	85	7	(	(	PUNCT
esrj-31288	85	8	19	19	NUM
esrj-31288	85	9	)	)	PUNCT
esrj-31288	85	10	reorganizing	reorganize	VERB
esrj-31288	85	11	terms	term	NOUN
esrj-31288	85	12	in	in	ADP
esrj-31288	85	13	(	(	PUNCT
esrj-31288	85	14	19	19	NUM
esrj-31288	85	15	)	)	PUNCT
esrj-31288	85	16	vn	vn	NOUN
esrj-31288	85	17	d-	d-	X
esrj-31288	85	18	;	;	PUNCT
esrj-31288	85	19	"	"	PUNCT
esrj-31288	85	20	cn	cn	PROPN
esrj-31288	85	21	=	=	NOUN
esrj-31288	85	22	'	'	NUM
esrj-31288	85	23	l({3	l({3	NUM
esrj-31288	85	24	n	n	NOUN
esrj-31288	85	25	)	)	PUNCT
esrj-31288	86	1	[	[	X
esrj-31288	86	2	s	s	X
esrj-31288	86	3	n	n	PRON
esrj-31288	86	4	kn	kn	NOUN
esrj-31288	86	5	+	+	CCONJ
esrj-31288	86	6	ir	ir	PROPN
esrj-31288	86	7	'	'	PUNCT
esrj-31288	86	8	{	{	PUNCT
esrj-31288	86	9	kn	kn	PROPN
esrj-31288	86	10	'	'	NUM
esrj-31288	86	11	l({3	l({3	NUM
esrj-31288	86	12	n	n	CCONJ
esrj-31288	86	13	)	)	PUNCT
esrj-31288	86	14	cos({3n)[s	cos({3n)[s	NOUN
esrj-31288	86	15	n	n	PRON
esrj-31288	86	16	kn	kn	PROPN
esrj-31288	86	17	+	+	PROPN
esrj-31288	86	18	i]'l-	i]'l-	PROPN
esrj-31288	86	19	'	'	PART
esrj-31288	86	20	(	(	PUNCT
esrj-31288	86	21	{	{	PUNCT
esrj-31288	86	22	3	3	NUM
esrj-31288	86	23	n)kn	n)kn	PROPN
esrj-31288	86	24	-	-	PUNCT
esrj-31288	86	25	d	d	PROPN
esrj-31288	86	26	(	(	PUNCT
esrj-31288	86	27	20	20	NUM
esrj-31288	86	28	)	)	PUNCT
esrj-31288	86	29	then	then	ADV
esrj-31288	86	30	'	'	PUNCT
esrj-31288	86	31	l({3n	l({3n	X
esrj-31288	86	32	)	)	PUNCT
esrj-31288	87	1	[	[	X
esrj-31288	87	2	s	s	X
esrj-31288	87	3	nkn	nkn	NOUN
esrj-31288	87	4	+	+	CCONJ
esrj-31288	87	5	ir	ir	PROPN
esrj-31288	87	6	'	'	PUNCT
esrj-31288	87	7	kn	kn	PROPN
esrj-31288	87	8	'	'	PUNCT
esrj-31288	87	9	l({3n	l({3n	NUM
esrj-31288	87	10	)	)	PUNCT
esrj-31288	87	11	=	=	PRON
esrj-31288	87	12	vndn'cn	vndn'cn	ADJ
esrj-31288	87	13	+	+	SYM
esrj-31288	87	14	cos({3n)kn-1	cos({3n)kn-1	PROPN
esrj-31288	87	15	(	(	PUNCT
esrj-31288	87	16	21	21	NUM
esrj-31288	87	17	)	)	PUNCT
esrj-31288	87	18	to	to	PART
esrj-31288	87	19	find	find	VERB
esrj-31288	87	20	:	:	PUNCT
esrj-31288	88	1	[	[	X
esrj-31288	88	2	snkn	snkn	NOUN
esrj-31288	88	3	+	+	NOUN
esrj-31288	88	4	ir'kn	ir'kn	NOUN
esrj-31288	88	5	=	=	SYM
esrj-31288	88	6	'	'	PUNCT
esrj-31288	88	7	l-1{({3n)vndn1c.n	l-1{({3n)vndn1c.n	NOUN
esrj-31288	88	8	+	+	CCONJ
esrj-31288	88	9	cos({3n)kn	cos({3n)kn	PROPN
esrj-31288	88	10	-	-	PUNCT
esrj-31288	88	11	i	i	NOUN
esrj-31288	88	12	}	}	PUNCT
esrj-31288	88	13	'	'	NUM
esrj-31288	88	14	l-	l-	X
esrj-31288	88	15	'	'	PUNCT
esrj-31288	88	16	(	(	PUNCT
esrj-31288	88	17	{	{	PUNCT
esrj-31288	88	18	3n	3n	NUM
esrj-31288	88	19	)	)	PUNCT
esrj-31288	88	20	(	(	PUNCT
esrj-31288	88	21	22	22	NUM
esrj-31288	88	22	)	)	PUNCT
esrj-31288	88	23	term	term	NOUN
esrj-31288	88	24	simplified	simplify	VERB
esrj-31288	88	25	by	by	ADP
esrj-31288	88	26	recalling	recall	VERB
esrj-31288	88	27	(	(	PUNCT
esrj-31288	88	28	i	i	PROPN
esrj-31288	88	29	8)	8)	NUM
esrj-31288	88	30	q	q	NOUN
esrj-31288	88	31	=	=	SYM
esrj-31288	88	32	i.-	i.-	NOUN
esrj-31288	88	33	'	'	PUNCT
esrj-31288	88	34	(	(	PUNCT
esrj-31288	88	35	{	{	PUNCT
esrj-31288	88	36	3n	3n	NUM
esrj-31288	88	37	)	)	PUNCT
esrj-31288	88	38	{	{	PUNCT
esrj-31288	88	39	v	v	NOUN
esrj-31288	88	40	n	n	DET
esrj-31288	88	41	d'n	d'n	NOUN
esrj-31288	88	42	'	'	PART
esrj-31288	88	43	c	c	NOUN
esrj-31288	88	44	,	,	PUNCT
esrj-31288	88	45	+	+	CCONJ
esrj-31288	88	46	cos({3	cos({3	NUM
esrj-31288	88	47	n)kn-	n)kn-	NOUN
esrj-31288	88	48	'	'	PUNCT
esrj-31288	88	49	}	}	PUNCT
esrj-31288	88	50	i.-1	i.-1	NOUN
esrj-31288	88	51	(	(	PUNCT
esrj-31288	88	52	{	{	PUNCT
esrj-31288	88	53	3n	3n	NOUN
esrj-31288	88	54	)	)	PUNCT
esrj-31288	88	55	to	to	PART
esrj-31288	88	56	get	get	VERB
esrj-31288	88	57	:	:	PUNCT
esrj-31288	88	58	(	(	PUNCT
esrj-31288	88	59	23	23	NUM
esrj-31288	88	60	)	)	PUNCT
esrj-31288	88	61	luis	luis	PROPN
esrj-31288	88	62	montes	montes	PROPN
esrj-31288	88	63	vides	vide	VERB
esrj-31288	88	64	~---i------7	~---i------7	PROPN
esrj-31288	88	65	t3	t3	NOUN
esrj-31288	88	66	~	~	PUNCT
esrj-31288	89	1	_	_	PUNCT
esrj-31288	89	2	_	_	PUNCT
esrj-31288	90	1	-+-	-+-	NOUN
esrj-31288	91	1	_	_	PUNCT
esrj-31288	91	2	_	_	PUNCT
esrj-31288	92	1	-	-	PUNCT
esrj-31288	92	2	;	;	PUNCT
esrj-31288	92	3	?	?	PUNCT
esrj-31288	93	1	t2	t2	PROPN
esrj-31288	93	2	~----t-----	~----t-----	PUNCT
esrj-31288	93	3	?	?	PUNCT
esrj-31288	94	1	t1	t1	NOUN
esrj-31288	94	2	r	r	NOUN
esrj-31288	94	3	3	3	NUM
esrj-31288	94	4	v	v	NUM
esrj-31288	94	5	3	3	NUM
esrj-31288	94	6	figure	figure	NOUN
esrj-31288	94	7	2	2	NUM
esrj-31288	94	8	.	.	PUNCT
esrj-31288	95	1	the	the	DET
esrj-31288	95	2	model	model	NOUN
esrj-31288	95	3	is	be	AUX
esrj-31288	95	4	analyzed	analyze	VERB
esrj-31288	95	5	like	like	ADP
esrj-31288	95	6	three	three	NUM
esrj-31288	95	7	seismic	seismic	ADJ
esrj-31288	95	8	systems	system	NOUN
esrj-31288	95	9	,	,	PUNCT
esrj-31288	95	10	each	each	DET
esrj-31288	95	11	one	one	NUM
esrj-31288	95	12	with	with	ADP
esrj-31288	95	13	its	its	PRON
esrj-31288	95	14	own	own	ADJ
esrj-31288	95	15	central	central	ADJ
esrj-31288	95	16	ray	ray	NOUN
esrj-31288	95	17	and	and	CCONJ
esrj-31288	95	18	each	each	DET
esrj-31288	95	19	reflector	reflector	NOUN
esrj-31288	95	20	like	like	ADP
esrj-31288	95	21	its	its	PRON
esrj-31288	95	22	posterior	posterior	ADJ
esrj-31288	95	23	surface	surface	NOUN
esrj-31288	95	24	.	.	PUNCT
esrj-31288	96	1	there	there	PRON
esrj-31288	96	2	are	be	VERB
esrj-31288	96	3	travel	travel	NOUN
esrj-31288	96	4	time	time	NOUN
esrj-31288	96	5	functions	function	NOUN
esrj-31288	96	6	associated	associate	VERB
esrj-31288	96	7	to	to	ADP
esrj-31288	96	8	each	each	DET
esrj-31288	96	9	system	system	NOUN
esrj-31288	96	10	and	and	CCONJ
esrj-31288	96	11	estimated	estimate	VERB
esrj-31288	96	12	on	on	ADP
esrj-31288	96	13	the	the	DET
esrj-31288	96	14	anterior	anterior	ADJ
esrj-31288	96	15	surface	surface	NOUN
esrj-31288	96	16	(	(	PUNCT
esrj-31288	96	17	flat	flat	ADJ
esrj-31288	96	18	)	)	PUNCT
esrj-31288	96	19	.	.	PUNCT
esrj-31288	97	1	finally	finally	ADV
esrj-31288	97	2	the	the	DET
esrj-31288	97	3	matrix	matrix	NOUN
esrj-31288	97	4	of	of	ADP
esrj-31288	97	5	curvature	curvature	NOUN
esrj-31288	97	6	of	of	ADP
esrj-31288	97	7	the	the	DET
esrj-31288	97	8	posterior	posterior	ADJ
esrj-31288	97	9	surface	surface	NOUN
esrj-31288	97	10	in	in	ADP
esrj-31288	97	11	the	the	DET
esrj-31288	97	12	vicinity	vicinity	NOUN
esrj-31288	97	13	of	of	ADP
esrj-31288	97	14	the	the	DET
esrj-31288	97	15	central	central	ADJ
esrj-31288	97	16	ray	ray	NOUN
esrj-31288	98	1	k	k	PROPN
esrj-31288	98	2	n	n	PROPN
esrj-31288	98	3	is	be	AUX
esrj-31288	98	4	obtained	obtain	VERB
esrj-31288	98	5	:	:	PUNCT
esrj-31288	98	6	k	k	X
esrj-31288	98	7	=	=	SYM
esrj-31288	98	8	q{i	q{i	PROPN
esrj-31288	98	9	s	s	PART
esrj-31288	98	10	q}-l_n	q}-l_n	NOUN
esrj-31288	98	11	_	_	PUNCT
esrj-31288	99	1	_	_	PUNCT
esrj-31288	100	1	n	n	CCONJ
esrj-31288	101	1	_	_	NOUN
esrj-31288	101	2	now	now	ADV
esrj-31288	101	3	,	,	PUNCT
esrj-31288	101	4	we	we	PRON
esrj-31288	101	5	can	can	AUX
esrj-31288	101	6	know	know	VERB
esrj-31288	101	7	numerically	numerically	ADV
esrj-31288	101	8	the	the	DET
esrj-31288	101	9	transfer	transfer	NOUN
esrj-31288	101	10	matrix	matrix	NOUN
esrj-31288	101	11	which	which	PRON
esrj-31288	101	12	describes	describe	VERB
esrj-31288	101	13	the	the	DET
esrj-31288	101	14	ray	ray	NOUN
esrj-31288	101	15	propagation	propagation	NOUN
esrj-31288	101	16	through	through	ADP
esrj-31288	101	17	the	the	DET
esrj-31288	101	18	n	n	CCONJ
esrj-31288	101	19	"	"	PUNCT
esrj-31288	101	20	layer	layer	NOUN
esrj-31288	101	21	,	,	PUNCT
esrj-31288	101	22	substituting	substitute	VERB
esrj-31288	101	23	the	the	DET
esrj-31288	101	24	terms	term	NOUN
esrj-31288	101	25	vn	vn	VERB
esrj-31288	101	26	'	'	PUNCT
esrj-31288	101	27	sn	sn	PROPN
esrj-31288	101	28	'	'	PUNCT
esrj-31288	101	29	/).t	/).t	PUNCT
esrj-31288	101	30	n	n	CCONJ
esrj-31288	101	31	'	'	CCONJ
esrj-31288	101	32	f3n	f3n	PROPN
esrj-31288	101	33	'	'	PUNCT
esrj-31288	101	34	k	k	PROPN
esrj-31288	101	35	n	n	PROPN
esrj-31288	101	36	in	in	ADP
esrj-31288	101	37	equation	equation	NOUN
esrj-31288	101	38	(	(	PUNCT
esrj-31288	101	39	5	5	NUM
esrj-31288	101	40	)	)	PUNCT
esrj-31288	101	41	.	.	PUNCT
esrj-31288	102	1	traveltime	traveltime	PROPN
esrj-31288	102	2	function	function	NOUN
esrj-31288	102	3	in	in	ADP
esrj-31288	102	4	depth	depth	NOUN
esrj-31288	102	5	it	it	PRON
esrj-31288	102	6	will	will	AUX
esrj-31288	102	7	be	be	AUX
esrj-31288	102	8	necessary	necessary	ADJ
esrj-31288	102	9	to	to	PART
esrj-31288	102	10	introduce	introduce	VERB
esrj-31288	102	11	different	different	ADJ
esrj-31288	102	12	central	central	ADJ
esrj-31288	102	13	rays	ray	NOUN
esrj-31288	102	14	in	in	ADP
esrj-31288	102	15	the	the	DET
esrj-31288	102	16	model	model	NOUN
esrj-31288	102	17	,	,	PUNCT
esrj-31288	102	18	a	a	DET
esrj-31288	102	19	central	central	ADJ
esrj-31288	102	20	ray	ray	NOUN
esrj-31288	102	21	for	for	ADP
esrj-31288	102	22	each	each	DET
esrj-31288	102	23	"	"	PUNCT
esrj-31288	102	24	piece	piece	NOUN
esrj-31288	102	25	"	"	PUNCT
esrj-31288	102	26	of	of	ADP
esrj-31288	102	27	seismic	seismic	ADJ
esrj-31288	102	28	system	system	NOUN
esrj-31288	102	29	.	.	PUNCT
esrj-31288	103	1	the	the	DET
esrj-31288	103	2	first	first	ADJ
esrj-31288	103	3	niece	niece	NOUN
esrj-31288	103	4	of	of	ADP
esrj-31288	103	5	seismic	seismic	ADJ
esrj-31288	103	6	system	system	NOUN
esrj-31288	103	7	is	be	AUX
esrj-31288	103	8	defined	define	VERB
esrj-31288	103	9	between	between	ADP
esrj-31288	103	10	the	the	DET
esrj-31288	103	11	uppermost	uppermost	ADJ
esrj-31288	103	12	surface	surface	NOUN
esrj-31288	103	13	(	(	PUNCT
esrj-31288	103	14	zero	zero	NUM
esrj-31288	103	15	interface	interface	NOUN
esrj-31288	103	16	)	)	PUNCT
esrj-31288	103	17	and	and	CCONJ
esrj-31288	103	18	the	the	DET
esrj-31288	103	19	first	first	ADJ
esrj-31288	103	20	reflecting	reflect	VERB
esrj-31288	103	21	surface	surface	NOUN
esrj-31288	103	22	,	,	PUNCT
esrj-31288	103	23	the	the	DET
esrj-31288	103	24	second	second	NOUN
esrj-31288	103	25	between	between	ADP
esrj-31288	103	26	the	the	DET
esrj-31288	103	27	first	first	ADJ
esrj-31288	103	28	one	one	NUM
esrj-31288	103	29	and	and	CCONJ
esrj-31288	103	30	the	the	DET
esrj-31288	103	31	second	second	ADJ
esrj-31288	103	32	one	one	NUM
esrj-31288	103	33	,	,	PUNCT
esrj-31288	103	34	and	and	CCONJ
esrj-31288	103	35	so	so	ADV
esrj-31288	103	36	on	on	ADV
esrj-31288	103	37	.	.	PUNCT
esrj-31288	104	1	each	each	DET
esrj-31288	104	2	piece	piece	NOUN
esrj-31288	104	3	is	be	AUX
esrj-31288	104	4	considered	consider	VERB
esrj-31288	104	5	a	a	DET
esrj-31288	104	6	seismic	seismic	ADJ
esrj-31288	104	7	system	system	NOUN
esrj-31288	104	8	with	with	ADP
esrj-31288	104	9	a	a	DET
esrj-31288	104	10	central	central	ADJ
esrj-31288	104	11	ray	ray	NOUN
esrj-31288	104	12	perpendicular	perpendicular	NOUN
esrj-31288	104	13	to	to	ADP
esrj-31288	104	14	the	the	DET
esrj-31288	104	15	corresponding	correspond	VERB
esrj-31288	104	16	reflecting	reflect	VERB
esrj-31288	104	17	surface	surface	NOUN
esrj-31288	104	18	at	at	ADP
esrj-31288	104	19	the	the	DET
esrj-31288	104	20	midpoint	midpoint	NOUN
esrj-31288	104	21	position	position	NOUN
esrj-31288	104	22	(	(	PUNCT
esrj-31288	104	23	see	see	VERB
esrj-31288	104	24	figure	figure	NOUN
esrj-31288	104	25	2	2	NUM
esrj-31288	104	26	)	)	PUNCT
esrj-31288	104	27	.	.	PUNCT
esrj-31288	104	28	.	.	PUNCT
esrj-31288	105	1	the	the	DET
esrj-31288	105	2	determination	determination	NOUN
esrj-31288	105	3	of	of	ADP
esrj-31288	105	4	the	the	DET
esrj-31288	105	5	travel	travel	NOUN
esrj-31288	105	6	time	time	NOUN
esrj-31288	105	7	function	function	NOUN
esrj-31288	105	8	in	in	ADP
esrj-31288	105	9	depth	depth	NOUN
esrj-31288	105	10	is	be	AUX
esrj-31288	105	11	interpreted	interpret	VERB
esrj-31288	105	12	like	like	ADP
esrj-31288	105	13	if	if	SCONJ
esrj-31288	105	14	sources	source	NOUN
esrj-31288	105	15	and	and	CCONJ
esrj-31288	105	16	detectors	detector	NOUN
esrj-31288	105	17	were	be	AUX
esrj-31288	105	18	moved	move	VERB
esrj-31288	105	19	from	from	ADP
esrj-31288	105	20	the	the	DET
esrj-31288	105	21	uppermost	uppermost	ADJ
esrj-31288	105	22	surface	surface	NOUN
esrj-31288	105	23	,	,	PUNCT
esrj-31288	105	24	following	follow	VERB
esrj-31288	105	25	the	the	DET
esrj-31288	105	26	raypaths	raypath	NOUN
esrj-31288	105	27	,	,	PUNCT
esrj-31288	105	28	to	to	ADP
esrj-31288	105	29	the	the	DET
esrj-31288	105	30	anterior	anterior	ADJ
esrj-31288	105	31	surface	surface	NOUN
esrj-31288	105	32	of	of	ADP
esrj-31288	105	33	the	the	DET
esrj-31288	105	34	deepest	deep	ADJ
esrj-31288	105	35	layer	layer	NOUN
esrj-31288	105	36	of	of	ADP
esrj-31288	105	37	the	the	DET
esrj-31288	105	38	seismic	seismic	ADJ
esrj-31288	105	39	system	system	NOUN
esrj-31288	105	40	(	(	PUNCT
esrj-31288	105	41	see	see	VERB
esrj-31288	105	42	figure	figure	NOUN
esrj-31288	105	43	3	3	NUM
esrj-31288	105	44	)	)	PUNCT
esrj-31288	105	45	.	.	PUNCT
esrj-31288	106	1	we	we	PRON
esrj-31288	106	2	will	will	AUX
esrj-31288	106	3	show	show	VERB
esrj-31288	106	4	how	how	SCONJ
esrj-31288	106	5	to	to	PART
esrj-31288	106	6	determine	determine	VERB
esrj-31288	106	7	the	the	DET
esrj-31288	106	8	travel	travel	NOUN
esrj-31288	106	9	time	time	NOUN
esrj-31288	106	10	function	function	NOUN
esrj-31288	106	11	at	at	ADP
esrj-31288	106	12	the	the	DET
esrj-31288	106	13	anterior	anterior	ADJ
esrj-31288	106	14	surface	surface	NOUN
esrj-31288	106	15	of	of	ADP
esrj-31288	106	16	the	the	DET
esrj-31288	106	17	deepest	deep	ADJ
esrj-31288	106	18	layer	layer	NOUN
esrj-31288	106	19	from	from	ADP
esrj-31288	106	20	the	the	DET
esrj-31288	106	21	knowledge	knowledge	NOUN
esrj-31288	106	22	of	of	ADP
esrj-31288	106	23	the	the	DET
esrj-31288	106	24	travel	travel	NOUN
esrj-31288	106	25	time	time	NOUN
esrj-31288	106	26	functions	function	NOUN
esrj-31288	106	27	at	at	ADP
esrj-31288	106	28	the	the	DET
esrj-31288	106	29	upper	upper	ADJ
esrj-31288	106	30	interfaces	interface	NOUN
esrj-31288	106	31	of	of	ADP
esrj-31288	106	32	the	the	DET
esrj-31288	106	33	seismic	seismic	ADJ
esrj-31288	106	34	system	system	NOUN
esrj-31288	106	35	.	.	PUNCT
esrj-31288	107	1	the	the	DET
esrj-31288	107	2	propagator	propagator	NOUN
esrj-31288	107	3	matrix	matrix	NOUN
esrj-31288	107	4	describes	describe	VERB
esrj-31288	107	5	the	the	DET
esrj-31288	107	6	ray	ray	NOUN
esrj-31288	107	7	propagation	propagation	NOUN
esrj-31288	107	8	of	of	ADP
esrj-31288	107	9	the	the	DET
esrj-31288	107	10	paraxial	paraxial	ADJ
esrj-31288	107	11	rays	ray	NOUN
esrj-31288	107	12	through	through	ADP
esrj-31288	107	13	the	the	DET
esrj-31288	107	14	system	system	NOUN
esrj-31288	107	15	,	,	PUNCT
esrj-31288	107	16	and	and	CCONJ
esrj-31288	107	17	can	can	AUX
esrj-31288	107	18	be	be	AUX
esrj-31288	107	19	decomposed	decompose	VERB
esrj-31288	107	20	in	in	ADP
esrj-31288	107	21	a	a	DET
esrj-31288	107	22	product	product	NOUN
esrj-31288	107	23	of	of	ADP
esrj-31288	107	24	manyray	manyray	NOUN
esrj-31288	107	25	segment	segment	NOUN
esrj-31288	107	26	propagator	propagator	NOUN
esrj-31288	107	27	matrices	matrix	NOUN
esrj-31288	107	28	.	.	PUNCT
esrj-31288	108	1	in	in	ADP
esrj-31288	108	2	a	a	DET
esrj-31288	108	3	system	system	NOUN
esrj-31288	108	4	with	with	ADP
esrj-31288	108	5	n	n	DET
esrj-31288	108	6	layers	layer	NOUN
esrj-31288	108	7	the	the	DET
esrj-31288	108	8	propagator	propagator	NOUN
esrj-31288	108	9	matrix	matrix	NOUN
esrj-31288	108	10	is	be	AUX
esrj-31288	108	11	written	write	VERB
esrj-31288	108	12	as	as	ADP
esrj-31288	108	13	the	the	DET
esrj-31288	108	14	product	product	NOUN
esrj-31288	108	15	of	of	ADP
esrj-31288	108	16	the	the	DET
esrj-31288	108	17	n	n	PRON
esrj-31288	108	18	individual	individual	ADJ
esrj-31288	108	19	propagator	propagator	NOUN
esrj-31288	108	20	matrices	matrix	NOUN
esrj-31288	108	21	of	of	ADP
esrj-31288	108	22	each	each	DET
esrj-31288	108	23	"	"	PUNCT
esrj-31288	108	24	piece	piece	NOUN
esrj-31288	108	25	"	"	PUNCT
esrj-31288	108	26	:	:	PUNCT
esrj-31288	108	27	b	b	X
esrj-31288	108	28	]	]	X
esrj-31288	108	29	k	k	X
esrj-31288	108	30	~	~	SYM
esrj-31288	108	31	n	n	CCONJ
esrj-31288	108	32	-	-	PUNCT
esrj-31288	108	33	l[a	l[a	ADJ
esrj-31288	108	34	b]_n	b]_n	PROPN
esrj-31288	108	35	ii	ii	PROPN
esrj-31288	108	36	-	-	PUNCT
esrj-31288	108	37	]	]	X
esrj-31288	108	38	-	-	PUNCT
esrj-31288	108	39	]	]	X
esrj-31288	109	1	d	d	X
esrj-31288	109	2	.	.	PUNCT
esrj-31288	110	1	c	c	X
esrj-31288	110	2	d_n	d_n	X
esrj-31288	111	1	]	]	X
esrj-31288	111	2	~l	~l	PUNCT
esrj-31288	111	3	-	-	PUNCT
esrj-31288	111	4	]	]	X
esrj-31288	111	5	-	-	PUNCT
esrj-31288	111	6	]	]	X
esrj-31288	111	7	(	(	PUNCT
esrj-31288	111	8	25	25	NUM
esrj-31288	111	9	)	)	PUNCT
esrj-31288	111	10	if	if	SCONJ
esrj-31288	111	11	we	we	PRON
esrj-31288	111	12	have	have	AUX
esrj-31288	111	13	solved	solve	VERB
esrj-31288	111	14	the	the	DET
esrj-31288	111	15	system	system	NOUN
esrj-31288	111	16	composed	compose	VERB
esrj-31288	111	17	by	by	ADP
esrj-31288	111	18	the	the	DET
esrj-31288	111	19	upper	upper	ADJ
esrj-31288	111	20	n	n	PRON
esrj-31288	111	21	ilayers	ilayer	NOUN
esrj-31288	111	22	,	,	PUNCT
esrj-31288	111	23	i.e.	i.e.	X
esrj-31288	111	24	,	,	PUNCT
esrj-31288	111	25	the	the	DET
esrj-31288	111	26	transfer	transfer	NOUN
esrj-31288	111	27	matrix	matrix	NOUN
esrj-31288	111	28	for	for	ADP
esrj-31288	111	29	each	each	DET
esrj-31288	111	30	superimposed	superimpose	VERB
esrj-31288	111	31	layer	layer	NOUN
esrj-31288	111	32	is	be	AUX
esrj-31288	111	33	known	know	VERB
esrj-31288	111	34	,	,	PUNCT
esrj-31288	111	35	then	then	ADV
esrj-31288	111	36	(	(	PUNCT
esrj-31288	111	37	25	25	NUM
esrj-31288	111	38	)	)	PUNCT
esrj-31288	111	39	is	be	AUX
esrj-31288	111	40	rewritten	rewrite	VERB
esrj-31288	111	41	:	:	PUNCT
esrj-31288	111	42	(	(	PUNCT
esrj-31288	111	43	26	26	NUM
esrj-31288	111	44	)	)	PUNCT
esrj-31288	111	45	where	where	SCONJ
esrj-31288	111	46	the	the	DET
esrj-31288	111	47	matrix	matrix	NOUN
esrj-31288	111	48	in	in	ADP
esrj-31288	111	49	the	the	DET
esrj-31288	111	50	middle	middle	NOUN
esrj-31288	111	51	of	of	ADP
esrj-31288	111	52	(	(	PUNCT
esrj-31288	111	53	26	26	NUM
esrj-31288	111	54	)	)	PUNCT
esrj-31288	111	55	propagates	propagate	VERB
esrj-31288	111	56	the	the	DET
esrj-31288	111	57	ray	ray	NOUN
esrj-31288	111	58	in	in	ADP
esrj-31288	111	59	the	the	DET
esrj-31288	111	60	nth	nth	NOUN
esrj-31288	111	61	layer	layer	NOUN
esrj-31288	111	62	(	(	PUNCT
esrj-31288	111	63	assumed	assume	VERB
esrj-31288	111	64	unknown	unknown	ADJ
esrj-31288	111	65	)	)	PUNCT
esrj-31288	111	66	,	,	PUNCT
esrj-31288	111	67	and	and	CCONJ
esrj-31288	111	68	the	the	DET
esrj-31288	111	69	left	left	ADJ
esrj-31288	111	70	most	most	ADJ
esrj-31288	111	71	matrix	matrix	NOUN
esrj-31288	111	72	in	in	ADP
esrj-31288	111	73	(	(	PUNCT
esrj-31288	111	74	26	26	NUM
esrj-31288	111	75	)	)	PUNCT
esrj-31288	111	76	corresponds	correspond	VERB
esrj-31288	111	77	to	to	ADP
esrj-31288	111	78	the	the	DET
esrj-31288	111	79	product	product	NOUN
esrj-31288	111	80	of	of	ADP
esrj-31288	111	81	the	the	DET
esrj-31288	111	82	n	n	NOUN
esrj-31288	111	83	ipropagator	ipropagator	NOUN
esrj-31288	111	84	matrices	matrix	NOUN
esrj-31288	111	85	of	of	ADP
esrj-31288	111	86	the	the	DET
esrj-31288	111	87	upper	upper	ADJ
esrj-31288	111	88	n	n	NOUN
esrj-31288	111	89	i	i	PRON
esrj-31288	111	90	solved	solve	VERB
esrj-31288	111	91	layers	layer	NOUN
esrj-31288	111	92	,	,	PUNCT
esrj-31288	111	93	i.e.	i.e.	X
esrj-31288	111	94	,	,	PUNCT
esrj-31288	111	95	it	it	PRON
esrj-31288	111	96	has	have	AUX
esrj-31288	111	97	been	be	AUX
esrj-31288	111	98	assumed	assume	VERB
esrj-31288	111	99	that	that	SCONJ
esrj-31288	111	100	the	the	DET
esrj-31288	111	101	transfer	transfer	NOUN
esrj-31288	111	102	matrix	matrix	NOUN
esrj-31288	111	103	for	for	ADP
esrj-31288	111	104	each	each	DET
esrj-31288	111	105	superimposed	superimpose	VERB
esrj-31288	111	106	layer	layer	NOUN
esrj-31288	111	107	is	be	AUX
esrj-31288	111	108	numerically	numerically	ADV
esrj-31288	111	109	known	know	VERB
esrj-31288	111	110	.	.	PUNCT
esrj-31288	112	1	the	the	DET
esrj-31288	112	2	transfer	transfer	NOUN
esrj-31288	112	3	matrix	matrix	NOUN
esrj-31288	112	4	posses	posse	NOUN
esrj-31288	112	5	the	the	DET
esrj-31288	112	6	property	property	NOUN
esrj-31288	112	7	of	of	ADP
esrj-31288	112	8	simplecticity	simplecticity	NOUN
esrj-31288	112	9	(	(	PUNCT
esrj-31288	112	10	borfeld	borfeld	NOUN
esrj-31288	112	11	&	&	CCONJ
esrj-31288	112	12	kempert	kempert	PROPN
esrj-31288	112	13	,	,	PUNCT
esrj-31288	112	14	1990	1990	NUM
esrj-31288	112	15	)	)	PUNCT
esrj-31288	112	16	,	,	PUNCT
esrj-31288	112	17	this	this	DET
esrj-31288	112	18	property	property	NOUN
esrj-31288	112	19	means	mean	VERB
esrj-31288	112	20	that	that	SCONJ
esrj-31288	112	21	the	the	DET
esrj-31288	112	22	inverse	inverse	NOUN
esrj-31288	112	23	of	of	ADP
esrj-31288	112	24	the	the	DET
esrj-31288	112	25	propagator	propagator	NOUN
esrj-31288	112	26	matrix	matrix	NOUN
esrj-31288	112	27	of	of	ADP
esrj-31288	112	28	the	the	DET
esrj-31288	112	29	system	system	NOUN
esrj-31288	112	30	composed	compose	VERB
esrj-31288	112	31	of	of	ADP
esrj-31288	112	32	n	n	PROPN
esrj-31288	112	33	iupper	iupper	ADJ
esrj-31288	112	34	layers	layer	NOUN
esrj-31288	112	35	is	be	AUX
esrj-31288	112	36	:	:	PUNCT
esrj-31288	112	37	(	(	PUNCT
esrj-31288	112	38	27	27	NUM
esrj-31288	112	39	)	)	PUNCT
esrj-31288	112	40	the	the	DET
esrj-31288	112	41	super	super	ADJ
esrj-31288	112	42	index	index	NOUN
esrj-31288	112	43	means	mean	VERB
esrj-31288	112	44	the	the	DET
esrj-31288	112	45	matrix	matrix	NOUN
esrj-31288	112	46	transposed	transpose	VERB
esrj-31288	112	47	,	,	PUNCT
esrj-31288	112	48	and	and	CCONJ
esrj-31288	112	49	by	by	ADP
esrj-31288	112	50	the	the	DET
esrj-31288	112	51	same	same	ADJ
esrj-31288	112	52	argument	argument	NOUN
esrj-31288	112	53	the	the	DET
esrj-31288	112	54	inverse	inverse	NOUN
esrj-31288	112	55	of	of	ADP
esrj-31288	112	56	the	the	DET
esrj-31288	112	57	propagator	propagator	NOUN
esrj-31288	112	58	matrix	matrix	NOUN
esrj-31288	112	59	of	of	ADP
esrj-31288	112	60	the	the	DET
esrj-31288	112	61	n	n	CCONJ
esrj-31288	112	62	"	"	PUNCT
esrj-31288	112	63	layer	layer	NOUN
esrj-31288	112	64	is	be	AUX
esrj-31288	112	65	:	:	PUNCT
esrj-31288	113	1	[	[	X
esrj-31288	113	2	~	~	PUNCT
esrj-31288	113	3	!	!	PUNCT
esrj-31288	113	4	l]-i	l]-i	PROPN
esrj-31288	114	1	[	[	X
esrj-31288	114	2	d	d	X
esrj-31288	114	3	'	'	PUNCT
esrj-31288	114	4	b	b	NOUN
esrj-31288	114	5	]	]	X
esrj-31288	115	1	_	_	PUNCT
esrj-31288	115	2	_	_	PUNCT
esrj-31288	116	1	n	n	DET
esrj-31288	116	2	_	_	NOUN
esrj-31288	116	3	n	n	X
esrj-31288	116	4	!	!	NOUN
esrj-31288	116	5	2	2	NUM
esrj-31288	116	6	-~n	-~n	PROPN
esrj-31288	117	1	a~	a~	PROPN
esrj-31288	117	2	(	(	PUNCT
esrj-31288	117	3	28	28	NUM
esrj-31288	117	4	)	)	PUNCT
esrj-31288	117	5	(	(	PUNCT
esrj-31288	117	6	24	24	NUM
esrj-31288	117	7	)	)	PUNCT
esrj-31288	117	8	using	use	VERB
esrj-31288	117	9	(	(	PUNCT
esrj-31288	117	10	27	27	NUM
esrj-31288	117	11	)	)	PUNCT
esrj-31288	117	12	and	and	CCONJ
esrj-31288	117	13	(	(	PUNCT
esrj-31288	117	14	28	28	NUM
esrj-31288	117	15	)	)	PUNCT
esrj-31288	117	16	we	we	PRON
esrj-31288	117	17	transform	transform	VERB
esrj-31288	117	18	(	(	PUNCT
esrj-31288	117	19	26	26	NUM
esrj-31288	117	20	)	)	PUNCT
esrj-31288	117	21	in	in	ADP
esrj-31288	117	22	:	:	PUNCT
esrj-31288	117	23	[	[	PUNCT
esrj-31288	117	24	[	[	X
esrj-31288	117	25	2~	2~	NOUN
esrj-31288	117	26	-c'_n	-c'_n	X
esrj-31288	118	1	[	[	PUNCT
esrj-31288	118	2	d~	d~	PROPN
esrj-31288	118	3	-c'_n	-c'_n	PROPN
esrj-31288	118	4	!	!	PUNCT
esrj-31288	119	1	in	in	ADP
esrj-31288	119	2	.	.	PUNCT
esrj-31288	120	1	]	]	X
esrj-31288	120	2	[	[	PUNCT
esrj-31288	120	3	[	[	X
esrj-31288	120	4	2	2	NUM
esrj-31288	120	5	'	'	PUNCT
esrj-31288	120	6	!	!	PUNCT
esrj-31288	121	1	l	l	NOUN
esrj-31288	121	2	'	'	X
esrj-31288	121	3	]	]	X
esrj-31288	122	1	d	d	X
esrj-31288	122	2	-c	-c	NOUN
esrj-31288	122	3	'	'	PUNCT
esrj-31288	122	4	a'-n	a'-n	PROPN
esrj-31288	122	5	·	·	PUNCT
esrj-31288	122	6	_	_	PUNCT
esrj-31288	123	1	_	_	PUNCT
esrj-31288	123	2	(	(	PUNCT
esrj-31288	123	3	29	29	NUM
esrj-31288	123	4	)	)	PUNCT
esrj-31288	123	5	su	su	NOUN
esrj-31288	124	1	~	~	NOUN
esrj-31288	124	2	dipoksurfa	dipoksurfa	NOUN
esrj-31288	124	3	\~	\~	NUM
esrj-31288	124	4	~0	~0	NUM
esrj-31288	124	5	layers	layer	NOUN
esrj-31288	124	6	:	:	PUNCT
esrj-31288	124	7	traveltime	traveltime	VERB
esrj-31288	124	8	an	an	PRON
esrj-31288	124	9	.	.	PUNCT
esrj-31288	125	1	~functionin	~functionin	ADJ
esrj-31288	125	2	tenor	tenor	NOUN
esrj-31288	125	3	de	de	X
esrj-31288	125	4	th	th	X
esrj-31288	125	5	surfa	surfa	X
esrj-31288	125	6	~	~	SYM
esrj-31288	125	7	cs*\-/g	cs*\-/g	PROPN
esrj-31288	125	8	*	*	PROPN
esrj-31288	125	9	p	p	NOUN
esrj-31288	125	10	unknown	unknown	ADJ
esrj-31288	125	11	layer	layer	NOUN
esrj-31288	125	12	poste~	poste~	VERB
esrj-31288	125	13	v	v	NOUN
esrj-31288	125	14	~	~	PUNCT
esrj-31288	125	15	<	<	X
esrj-31288	125	16	»	»	X
esrj-31288	125	17	:	:	PUNCT
esrj-31288	125	18	surfa~~-	surfa~~-	ADJ
esrj-31288	125	19	'	'	PUNCT
esrj-31288	125	20	~	~	PUNCT
esrj-31288	125	21	figure	figure	NOUN
esrj-31288	125	22	3	3	NUM
esrj-31288	125	23	.	.	PUNCT
esrj-31288	126	1	if	if	SCONJ
esrj-31288	126	2	the	the	DET
esrj-31288	126	3	sources	source	NOUN
esrj-31288	126	4	and	and	CCONJ
esrj-31288	126	5	detectors	detector	NOUN
esrj-31288	126	6	were	be	AUX
esrj-31288	126	7	moved	move	VERB
esrj-31288	126	8	from	from	ADP
esrj-31288	126	9	the	the	DET
esrj-31288	126	10	superior	superior	ADJ
esrj-31288	126	11	surface	surface	NOUN
esrj-31288	126	12	to	to	ADP
esrj-31288	126	13	the	the	DET
esrj-31288	126	14	anterior	anterior	ADJ
esrj-31288	126	15	surface	surface	NOUN
esrj-31288	126	16	following	follow	VERB
esrj-31288	126	17	the	the	DET
esrj-31288	126	18	ray	ray	NOUN
esrj-31288	126	19	paths	path	NOUN
esrj-31288	126	20	,	,	PUNCT
esrj-31288	126	21	then	then	ADV
esrj-31288	126	22	the	the	DET
esrj-31288	126	23	travel	travel	NOUN
esrj-31288	126	24	time	time	NOUN
esrj-31288	126	25	function	function	NOUN
esrj-31288	126	26	is	be	AUX
esrj-31288	126	27	determined	determine	VERB
esrj-31288	126	28	at	at	ADP
esrj-31288	126	29	the	the	DET
esrj-31288	126	30	top	top	NOUN
esrj-31288	126	31	of	of	ADP
esrj-31288	126	32	the	the	DET
esrj-31288	126	33	deeper	deep	ADJ
esrj-31288	126	34	system	system	NOUN
esrj-31288	126	35	.	.	PUNCT
esrj-31288	127	1	geoff	geoff	PROPN
esrj-31288	127	2	sica	sica	PROPN
esrj-31288	127	3	colombiana	colombiana	PROPN
esrj-31288	127	4	,	,	PUNCT
esrj-31288	127	5	5	5	NUM
esrj-31288	127	6	,	,	PUNCT
esrj-31288	127	7	diciembre	diciembre	PROPN
esrj-31288	127	8	de	de	X
esrj-31288	127	9	2001	2001	NUM
esrj-31288	127	10	interval	interval	NOUN
esrj-31288	127	11	velocity	velocity	NOUN
esrj-31288	127	12	determination	determination	NOUN
esrj-31288	127	13	by	by	ADP
esrj-31288	127	14	downward	downward	ADJ
esrj-31288	127	15	continuation	continuation	NOUN
esrj-31288	127	16	of	of	ADP
esrj-31288	127	17	the	the	DET
esrj-31288	127	18	traveltime	traveltime	NOUN
esrj-31288	127	19	function	function	NOUN
esrj-31288	127	20	,	,	PUNCT
esrj-31288	127	21	paraxial	paraxial	ADJ
esrj-31288	127	22	ray	ray	NOUN
esrj-31288	127	23	approximation	approximation	NOUN
esrj-31288	127	24	factorizing	factorize	VERB
esrj-31288	127	25	d	d	NOUN
esrj-31288	127	26	'	'	PUNCT
esrj-31288	127	27	at	at	ADP
esrj-31288	127	28	left	left	NOUN
esrj-31288	127	29	of	of	ADP
esrj-31288	127	30	(	(	PUNCT
esrj-31288	127	31	31	31	NUM
esrj-31288	127	32	)	)	PUNCT
esrj-31288	128	1	d	d	PUNCT
esrj-31288	129	1	~	~	PUNCT
esrj-31288	129	2	cn	cn	PROPN
esrj-31288	129	3	=[	=[	NOUN
esrj-31288	129	4	dnkc	dnkc	PROPN
esrj-31288	129	5	-cnkd'][(ank	-cnkd'][(ank	PROPN
esrj-31288	129	6	-bnkc	-bnkc	PROPN
esrj-31288	129	7	d-1)d'r1	d-1)d'r1	PROPN
esrj-31288	129	8	(	(	PUNCT
esrj-31288	129	9	32	32	NUM
esrj-31288	129	10	)	)	PUNCT
esrj-31288	129	11	the	the	DET
esrj-31288	129	12	product	product	NOUN
esrj-31288	129	13	of	of	ADP
esrj-31288	129	14	symetric	symetric	ADJ
esrj-31288	129	15	matrices	matrix	NOUN
esrj-31288	129	16	is	be	AUX
esrj-31288	129	17	conmutative	conmutative	ADJ
esrj-31288	129	18	,	,	PUNCT
esrj-31288	129	19	then	then	ADV
esrj-31288	129	20	d	d	X
esrj-31288	129	21	~	~	PUNCT
esrj-31288	129	22	cn	cn	PROPN
esrj-31288	130	1	=[	=[	PRON
esrj-31288	130	2	dnkc	dnkc	PROPN
esrj-31288	130	3	-cnkdl]dl[(ank	-cnkdl]dl[(ank	PROPN
esrj-31288	130	4	-bnkc	-bnkc	PROPN
esrj-31288	130	5	d-1)j1r1	d-1)j1r1	NOUN
esrj-31288	130	6	(	(	PUNCT
esrj-31288	130	7	c33	c33	NOUN
esrj-31288	130	8	)	)	PUNCT
esrj-31288	130	9	dt)cn	dt)cn	PROPN
esrj-31288	131	1	=[	=[	NOUN
esrj-31288	131	2	dm(c	dm(c	NOUN
esrj-31288	131	3	'	'	PUNCT
esrj-31288	131	4	d-')-cnd[ank	d-')-cnd[ank	PROPN
esrj-31288	131	5	-bw(c	-bw(c	PROPN
esrj-31288	131	6	d	d	X
esrj-31288	131	7	-	-	PUNCT
esrj-31288	131	8	t)r1	t)r1	NOUN
esrj-31288	131	9	(	(	PUNCT
esrj-31288	131	10	34	34	NUM
esrj-31288	131	11	)	)	PUNCT
esrj-31288	131	12	by	by	ADP
esrj-31288	131	13	symmetry	symmetry	NOUN
esrj-31288	131	14	d-1	d-1	NOUN
esrj-31288	131	15	~	~	PUNCT
esrj-31288	131	16	=	=	SYM
esrj-31288	131	17	c	c	X
esrj-31288	131	18	'	'	X
esrj-31288	131	19	d-	d-	X
esrj-31288	131	20	'	'	PUNCT
esrj-31288	131	21	then	then	ADV
esrj-31288	131	22	d~	d~	PROPN
esrj-31288	131	23	'	'	PUNCT
esrj-31288	131	24	~n	~n	NUM
esrj-31288	131	25	=	=	PUNCT
esrj-31288	132	1	[	[	X
esrj-31288	132	2	dnk	dnk	NOUN
esrj-31288	132	3	(	(	PUNCT
esrj-31288	132	4	d	d	X
esrj-31288	132	5	-	-	PUNCT
esrj-31288	132	6	i~	i~	ADJ
esrj-31288	132	7	)	)	PUNCT
esrj-31288	132	8	~nk	~nk	PROPN
esrj-31288	132	9	harlk	harlk	VERB
esrj-31288	132	10	~nk	~nk	PROPN
esrj-31288	132	11	(	(	PUNCT
esrj-31288	132	12	d-1	d-1	NOUN
esrj-31288	132	13	~)]-i	~)]-i	SYM
esrj-31288	132	14	(	(	PUNCT
esrj-31288	132	15	35	35	NUM
esrj-31288	132	16	)	)	PUNCT
esrj-31288	132	17	following	follow	VERB
esrj-31288	132	18	a	a	DET
esrj-31288	132	19	similar	similar	ADJ
esrj-31288	132	20	process	process	NOUN
esrj-31288	132	21	we	we	PRON
esrj-31288	132	22	demonstrate	demonstrate	VERB
esrj-31288	132	23	that	that	SCONJ
esrj-31288	132	24	~~ian	~~ian	NOUN
esrj-31288	132	25	=	=	PUNCT
esrj-31288	132	26	u2nk	u2nk	X
esrj-31288	132	27	[	[	X
esrj-31288	132	28	~-i	~-i	X
esrj-31288	132	29	a	a	X
esrj-31288	132	30	]	]	X
esrj-31288	132	31	~nk	~nk	PROPN
esrj-31288	132	32	hank	hank	NOUN
esrj-31288	132	33	~nk	~nk	PROPN
esrj-31288	132	34	[	[	PUNCT
esrj-31288	132	35	~-i	~-i	X
esrj-31288	132	36	an	an	DET
esrj-31288	132	37	(	(	PUNCT
esrj-31288	132	38	36	36	NUM
esrj-31288	132	39	)	)	PUNCT
esrj-31288	132	40	this	this	DET
esrj-31288	132	41	step	step	NOUN
esrj-31288	132	42	makes	make	VERB
esrj-31288	132	43	possible	possible	ADJ
esrj-31288	132	44	to	to	PART
esrj-31288	132	45	know	know	VERB
esrj-31288	132	46	the	the	DET
esrj-31288	132	47	matrices	matrix	NOUN
esrj-31288	132	48	u	u	NOUN
esrj-31288	132	49	;	;	PUNCT
esrj-31288	132	50	an	an	PRON
esrj-31288	132	51	and	and	CCONJ
esrj-31288	132	52	!	!	PUNCT
esrj-31288	133	1	2~1	2~1	NUM
esrj-31288	133	2	~	~	NOUN
esrj-31288	133	3	n	n	X
esrj-31288	133	4	in	in	ADP
esrj-31288	133	5	depth	depth	NOUN
esrj-31288	133	6	.	.	PUNCT
esrj-31288	134	1	the	the	DET
esrj-31288	134	2	two	two	NUM
esrj-31288	134	3	-	-	PUNCT
esrj-31288	134	4	way	way	NOUN
esrj-31288	134	5	time	time	NOUN
esrj-31288	134	6	ton	ton	NOUN
esrj-31288	134	7	and	and	CCONJ
esrj-31288	134	8	the	the	DET
esrj-31288	134	9	slowness	slowness	NOUN
esrj-31288	134	10	vector	vector	NOUN
esrj-31288	134	11	jj	jj	PROPN
esrj-31288	134	12	on	on	ADP
esrj-31288	134	13	complete	complete	VERB
esrj-31288	134	14	the	the	DET
esrj-31288	134	15	knowledge	knowledge	NOUN
esrj-31288	134	16	of	of	ADP
esrj-31288	134	17	the	the	DET
esrj-31288	134	18	travel	travel	NOUN
esrj-31288	134	19	time	time	NOUN
esrj-31288	134	20	function	function	NOUN
esrj-31288	134	21	in	in	ADP
esrj-31288	134	22	depth	depth	NOUN
esrj-31288	134	23	,	,	PUNCT
esrj-31288	134	24	these	these	DET
esrj-31288	134	25	last	last	ADJ
esrj-31288	134	26	two	two	NUM
esrj-31288	134	27	parameter	parameter	NOUN
esrj-31288	134	28	are	be	AUX
esrj-31288	134	29	calculated	calculate	VERB
esrj-31288	134	30	by	by	ADP
esrj-31288	134	31	ray	ray	NOUN
esrj-31288	134	32	tracing	trace	VERB
esrj-31288	134	33	through	through	ADP
esrj-31288	134	34	the	the	DET
esrj-31288	134	35	model	model	NOUN
esrj-31288	134	36	,	,	PUNCT
esrj-31288	134	37	as	as	SCONJ
esrj-31288	134	38	it	it	PRON
esrj-31288	134	39	is	be	AUX
esrj-31288	134	40	shown	show	VERB
esrj-31288	134	41	in	in	ADP
esrj-31288	134	42	the	the	DET
esrj-31288	134	43	next	next	ADJ
esrj-31288	134	44	procedure	procedure	NOUN
esrj-31288	134	45	.	.	PUNCT
esrj-31288	135	1	ray	ray	NOUN
esrj-31288	135	2	tracing	trace	VERB
esrj-31288	135	3	in	in	ADP
esrj-31288	135	4	this	this	DET
esrj-31288	135	5	step	step	NOUN
esrj-31288	135	6	,	,	PUNCT
esrj-31288	135	7	the	the	DET
esrj-31288	135	8	interfaces	interface	NOUN
esrj-31288	135	9	limiting	limit	VERB
esrj-31288	135	10	the	the	DET
esrj-31288	135	11	n	n	CCONJ
esrj-31288	135	12	upper	upper	ADJ
esrj-31288	135	13	layers	layer	NOUN
esrj-31288	135	14	and	and	CCONJ
esrj-31288	135	15	the	the	DET
esrj-31288	135	16	their	their	PRON
esrj-31288	135	17	interval	interval	NOUN
esrj-31288	135	18	velocities	velocity	NOUN
esrj-31288	135	19	are	be	AUX
esrj-31288	135	20	known	know	VERB
esrj-31288	135	21	.	.	PUNCT
esrj-31288	136	1	the	the	DET
esrj-31288	136	2	paths	path	NOUN
esrj-31288	136	3	of	of	ADP
esrj-31288	136	4	rays	ray	NOUN
esrj-31288	136	5	traveling	travel	VERB
esrj-31288	136	6	across	across	ADP
esrj-31288	136	7	those	those	DET
esrj-31288	136	8	layers	layer	NOUN
esrj-31288	136	9	can	can	AUX
esrj-31288	136	10	be	be	AUX
esrj-31288	136	11	calculated	calculate	VERB
esrj-31288	136	12	(	(	PUNCT
esrj-31288	136	13	see	see	VERB
esrj-31288	136	14	figure	figure	NOUN
esrj-31288	136	15	4	4	NUM
esrj-31288	136	16	)	)	PUNCT
esrj-31288	136	17	.	.	PUNCT
esrj-31288	137	1	in	in	ADP
esrj-31288	137	2	the	the	DET
esrj-31288	137	3	vicinity	vicinity	NOUN
esrj-31288	137	4	of	of	ADP
esrj-31288	137	5	the	the	DET
esrj-31288	137	6	central	central	ADJ
esrj-31288	137	7	ray	ray	NOUN
esrj-31288	137	8	,	,	PUNCT
esrj-31288	137	9	the	the	DET
esrj-31288	137	10	nth	nth	NOUN
esrj-31288	137	11	interface	interface	NOUN
esrj-31288	137	12	is	be	AUX
esrj-31288	137	13	approximated	approximate	VERB
esrj-31288	137	14	by	by	ADP
esrj-31288	137	15	the	the	DET
esrj-31288	137	16	second	second	ADJ
esrj-31288	137	17	order	order	NOUN
esrj-31288	137	18	polynom	polynom	NOUN
esrj-31288	137	19	z	z	NOUN
esrj-31288	137	20	=	=	PUNCT
esrj-31288	138	1	+	+	PUNCT
esrj-31288	138	2	(	(	PUNCT
esrj-31288	138	3	x	x	NOUN
esrj-31288	138	4	,	,	PUNCT
esrj-31288	138	5	y	y	PROPN
esrj-31288	138	6	)	)	PUNCT
esrj-31288	138	7	.	.	PUNCT
esrj-31288	139	1	k	k	PROPN
esrj-31288	140	1	n	n	PROPN
esrj-31288	140	2	(	(	PUNCT
esrj-31288	140	3	x	x	NOUN
esrj-31288	140	4	,	,	PUNCT
esrj-31288	140	5	y	y	PROPN
esrj-31288	140	6	)	)	PUNCT
esrj-31288	140	7	,	,	PUNCT
esrj-31288	140	8	where	where	SCONJ
esrj-31288	140	9	k	k	PROPN
esrj-31288	140	10	n	n	NOUN
esrj-31288	140	11	=	=	SYM
esrj-31288	140	12	(	(	PUNCT
esrj-31288	140	13	k11	k11	PROPN
esrj-31288	140	14	'	'	PUNCT
esrj-31288	140	15	k12	k12	PROPN
esrj-31288	140	16	,	,	PUNCT
esrj-31288	140	17	kn	kn	PROPN
esrj-31288	140	18	)	)	PUNCT
esrj-31288	140	19	is	be	AUX
esrj-31288	140	20	the	the	DET
esrj-31288	140	21	matrix	matrix	NOUN
esrj-31288	140	22	~f	~f	PUNCT
esrj-31288	140	23	curvature	curvature	NOUN
esrj-31288	140	24	.	.	PUNCT
esrj-31288	141	1	central	central	ADJ
esrj-31288	141	2	1'1	1'1	NUM
esrj-31288	141	3	ray	ray	NOUN
esrj-31288	141	4	r3	r3	PROPN
esrj-31288	141	5	paraxial	paraxial	ADJ
esrj-31288	141	6	rays	ray	NOUN
esrj-31288	141	7	v.	v.	ADP
esrj-31288	141	8	figure	figure	NOUN
esrj-31288	141	9	4	4	NUM
esrj-31288	141	10	.	.	NOUN
esrj-31288	141	11	ray	ray	NOUN
esrj-31288	141	12	tracing	tracing	NOUN
esrj-31288	141	13	of	of	ADP
esrj-31288	141	14	the	the	DET
esrj-31288	141	15	c;,nl~~l	c;,nl~~l	PROPN
esrj-31288	141	16	and	and	CCONJ
esrj-31288	141	17	the	the	DET
esrj-31288	141	18	paraxial	paraxial	ADJ
esrj-31288	141	19	rays	ray	NOUN
esrj-31288	141	20	through	through	ADP
esrj-31288	141	21	the	the	DET
esrj-31288	141	22	last	last	ADJ
esrj-31288	141	23	solved	solve	VERB
esrj-31288	141	24	layer	layer	NOUN
esrj-31288	141	25	.	.	PUNCT
esrj-31288	142	1	the	the	DET
esrj-31288	142	2	new	new	ADJ
esrj-31288	142	3	coordinate	coordinate	NOUN
esrj-31288	142	4	system	system	NOUN
esrj-31288	142	5	(	(	PUNCT
esrj-31288	142	6	i.	i.	NOUN
esrj-31288	142	7	,	,	PUNCT
esrj-31288	142	8	.i	.i	PROPN
esrj-31288	142	9	)	)	PUNCT
esrj-31288	142	10	has	have	AUX
esrj-31288	142	11	rotated	rotate	VERB
esrj-31288	142	12	an	an	DET
esrj-31288	142	13	angle	angle	NOUN
esrj-31288	142	14	e	e	PROPN
esrj-31288	142	15	geofislca	geofislca	PROPN
esrj-31288	142	16	colombiana	colombiana	PROPN
esrj-31288	142	17	,	,	PUNCT
esrj-31288	142	18	5	5	NUM
esrj-31288	142	19	,	,	PUNCT
esrj-31288	142	20	diciembre	diciembre	PROPN
esrj-31288	142	21	de	de	X
esrj-31288	142	22	2001	2001	NUM
esrj-31288	142	23	according	accord	VERB
esrj-31288	142	24	figure	figure	NOUN
esrj-31288	142	25	5	5	NUM
esrj-31288	142	26	,	,	PUNCT
esrj-31288	142	27	the	the	DET
esrj-31288	142	28	normal	normal	ADJ
esrj-31288	142	29	ray	ray	NOUN
esrj-31288	142	30	to	to	ADP
esrj-31288	142	31	the	the	DET
esrj-31288	142	32	n	n	NOUN
esrj-31288	142	33	+	+	CCONJ
esrj-31288	143	1	i	i	PRON
esrj-31288	143	2	interface	interface	NOUN
esrj-31288	143	3	is	be	AUX
esrj-31288	143	4	refracted	refract	VERB
esrj-31288	143	5	at	at	ADP
esrj-31288	143	6	the	the	DET
esrj-31288	143	7	n	n	NUM
esrj-31288	143	8	surface	surface	NOUN
esrj-31288	143	9	in	in	ADP
esrj-31288	143	10	the	the	DET
esrj-31288	143	11	point	point	NOUN
esrj-31288	143	12	:	:	PUNCT
esrj-31288	143	13	(	(	PUNCT
esrj-31288	143	14	x	x	X
esrj-31288	143	15	,	,	PUNCT
esrj-31288	143	16	y	y	PROPN
esrj-31288	143	17	,	,	PUNCT
esrj-31288	143	18	z	z	NOUN
esrj-31288	143	19	)	)	PUNCT
esrj-31288	143	20	=	=	PUNCT
esrj-31288	144	1	-rl	-rl	NOUN
esrj-31288	144	2	+	+	CCONJ
esrj-31288	144	3	£	£	NOUN
esrj-31288	144	4	...	...	PUNCT
esrj-31288	145	1	r	r	NOUN
esrj-31288	145	2	+	+	NUM
esrj-31288	145	3	r2	r2	PROPN
esrj-31288	145	4	(	(	PUNCT
esrj-31288	145	5	37	37	NUM
esrj-31288	145	6	)	)	PUNCT
esrj-31288	145	7	where	where	SCONJ
esrj-31288	145	8	si	si	AUX
esrj-31288	145	9	'	'	PUNCT
esrj-31288	145	10	sz	sz	NOUN
esrj-31288	145	11	are	be	AUX
esrj-31288	145	12	the	the	DET
esrj-31288	145	13	respective	respective	ADJ
esrj-31288	145	14	path	path	NOUN
esrj-31288	145	15	lengths	length	NOUN
esrj-31288	145	16	of	of	ADP
esrj-31288	145	17	the	the	DET
esrj-31288	145	18	paraxial	paraxial	ADJ
esrj-31288	145	19	and	and	CCONJ
esrj-31288	145	20	central	central	ADJ
esrj-31288	145	21	ray	ray	NOUN
esrj-31288	145	22	in	in	ADP
esrj-31288	145	23	the	the	DET
esrj-31288	145	24	nth	nth	NOUN
esrj-31288	145	25	layer	layer	NOUN
esrj-31288	145	26	,	,	PUNCT
esrj-31288	145	27	~	~	PUNCT
esrj-31288	145	28	=	=	SYM
esrj-31288	145	29	(	(	PUNCT
esrj-31288	145	30	0,0	0,0	NOUN
esrj-31288	145	31	,	,	PUNCT
esrj-31288	145	32	s	s	PART
esrj-31288	145	33	i	i	NOUN
esrj-31288	145	34	)	)	PUNCT
esrj-31288	145	35	and	and	CCONJ
esrj-31288	145	36	£	£	ADP
esrj-31288	145	37	...	...	PUNCT
esrj-31288	146	1	r	r	NOUN
esrj-31288	146	2	=	=	SYM
esrj-31288	146	3	(	(	PUNCT
esrj-31288	146	4	£	£	NOUN
esrj-31288	146	5	...	...	PUNCT
esrj-31288	146	6	rl	rl	PART
esrj-31288	146	7	'	'	PUNCT
esrj-31288	146	8	/sr	/sr	ADJ
esrj-31288	146	9	,	,	PUNCT
esrj-31288	146	10	,	,	PUNCT
esrj-31288	146	11	£	£	NOUN
esrj-31288	146	12	...	...	PUNCT
esrj-31288	146	13	r3	r3	PROPN
esrj-31288	146	14	)	)	PUNCT
esrj-31288	146	15	are	be	AUX
esrj-31288	146	16	known	know	VERB
esrj-31288	146	17	.	.	PUNCT
esrj-31288	147	1	therefore	therefore	ADV
esrj-31288	147	2	(	(	PUNCT
esrj-31288	147	3	37	37	NUM
esrj-31288	147	4	)	)	PUNCT
esrj-31288	147	5	is	be	AUX
esrj-31288	147	6	equivalent	equivalent	ADJ
esrj-31288	147	7	to	to	ADP
esrj-31288	147	8	equation	equation	NOUN
esrj-31288	147	9	(	(	PUNCT
esrj-31288	147	10	38	38	NUM
esrj-31288	147	11	)	)	PUNCT
esrj-31288	147	12	.	.	PUNCT
esrj-31288	148	1	dr\	dr\	PROPN
esrj-31288	148	2	r2	r2	PROPN
esrj-31288	148	3	law	law	NOUN
esrj-31288	148	4	n	n	ADV
esrj-31288	148	5	normal	normal	ADJ
esrj-31288	148	6	~~ector	~~ector	NUM
esrj-31288	148	7	(	(	PUNCT
esrj-31288	148	8	x	x	X
esrj-31288	148	9	,	,	PUNCT
esrj-31288	148	10	y	y	PROPN
esrj-31288	148	11	,	,	PUNCT
esrj-31288	148	12	z	z	PROPN
esrj-31288	148	13	)	)	PUNCT
esrj-31288	148	14	ii	ii	PROPN
esrj-31288	148	15	ii	ii	PROPN
esrj-31288	148	16	figure	figure	NOUN
esrj-31288	148	17	5	5	NUM
esrj-31288	148	18	.	.	PUNCT
esrj-31288	149	1	the	the	DET
esrj-31288	149	2	ray	ray	NOUN
esrj-31288	149	3	'	'	PUNCT
esrj-31288	149	4	2	2	NUM
esrj-31288	149	5	is	be	AUX
esrj-31288	149	6	normal	normal	ADJ
esrj-31288	149	7	to	to	ADP
esrj-31288	149	8	the	the	DET
esrj-31288	149	9	next	next	ADJ
esrj-31288	149	10	interface	interface	NOUN
esrj-31288	149	11	in	in	ADP
esrj-31288	149	12	depth	depth	NOUN
esrj-31288	149	13	,	,	PUNCT
esrj-31288	149	14	been	be	AUX
esrj-31288	149	15	refracted	refract	VERB
esrj-31288	149	16	in	in	ADP
esrj-31288	149	17	(	(	PUNCT
esrj-31288	149	18	x	x	NOUN
esrj-31288	149	19	,	,	PUNCT
esrj-31288	149	20	y	y	PROPN
esrj-31288	149	21	,	,	PUNCT
esrj-31288	149	22	z	z	NOUN
esrj-31288	149	23	)	)	PUNCT
esrj-31288	149	24	.	.	PUNCT
esrj-31288	150	1	a	a	DET
esrj-31288	150	2	,	,	PUNCT
esrj-31288	150	3	f3	f3	ADJ
esrj-31288	150	4	:	:	PUNCT
esrj-31288	150	5	incidence	incidence	NOUN
esrj-31288	150	6	and	and	CCONJ
esrj-31288	150	7	transmission	transmission	NOUN
esrj-31288	150	8	angles	angle	NOUN
esrj-31288	150	9	.	.	PUNCT
esrj-31288	151	1	substituing	substitue	VERB
esrj-31288	151	2	x	x	SYM
esrj-31288	151	3	,	,	PUNCT
esrj-31288	151	4	y	y	PROPN
esrj-31288	151	5	in	in	ADP
esrj-31288	151	6	the	the	DET
esrj-31288	151	7	third	third	ADJ
esrj-31288	151	8	expression	expression	NOUN
esrj-31288	151	9	of	of	ADP
esrj-31288	151	10	(	(	PUNCT
esrj-31288	151	11	38	38	NUM
esrj-31288	151	12	)	)	PUNCT
esrj-31288	151	13	we	we	PRON
esrj-31288	151	14	obtain	obtain	VERB
esrj-31288	151	15	:	:	PUNCT
esrj-31288	151	16	s;[sinz	s;[sinz	NUM
esrj-31288	151	17	f3(~	f3(~	X
esrj-31288	151	18	kll	kll	X
esrj-31288	151	19	cos	cos	PROPN
esrj-31288	151	20	'	'	PART
esrj-31288	151	21	8	8	NUM
esrj-31288	151	22	+	+	NOUN
esrj-31288	151	23	~	~	PUNCT
esrj-31288	151	24	k22	k22	NOUN
esrj-31288	151	25	sin	sin	NOUN
esrj-31288	151	26	'	'	PART
esrj-31288	151	27	8	8	NUM
esrj-31288	151	28	+	+	NUM
esrj-31288	151	29	k'2	k'2	PROPN
esrj-31288	151	30	sin8cos8	sin8cos8	PROPN
esrj-31288	151	31	)	)	PUNCT
esrj-31288	151	32	]	]	PUNCT
esrj-31288	152	1	+	+	CCONJ
esrj-31288	152	2	s2[sinf3{k11	s2[sinf3{k11	VERB
esrj-31288	152	3	cos8fuj	cos8fuj	NOUN
esrj-31288	152	4	+	+	CCONJ
esrj-31288	152	5	k2z	k2z	NOUN
esrj-31288	152	6	sin8&z	sin8&z	VERB
esrj-31288	152	7	+	+	NOUN
esrj-31288	152	8	'	'	PUNCT
esrj-31288	152	9	sz(sin8fuj	sz(sin8fuj	NOUN
esrj-31288	152	10	+	+	PROPN
esrj-31288	152	11	cos8&2	cos8&2	PROPN
esrj-31288	152	12	)	)	PUNCT
esrj-31288	152	13	}	}	PUNCT
esrj-31288	152	14	cosf3	cosf3	X
esrj-31288	152	15	]	]	PUNCT
esrj-31288	153	1	+	+	CCONJ
esrj-31288	153	2	[	[	X
esrj-31288	153	3	s	s	X
esrj-31288	153	4	,	,	PUNCT
esrj-31288	153	5	-11r	-11r	ADJ
esrj-31288	153	6	"	"	PUNCT
esrj-31288	153	7	+	+	CCONJ
esrj-31288	153	8	~(kl	~(kl	NUM
esrj-31288	153	9	,	,	PUNCT
esrj-31288	153	10	fujz	fujz	NOUN
esrj-31288	153	11	+	+	CCONJ
esrj-31288	153	12	k22&z2	k22&z2	NOUN
esrj-31288	153	13	+	+	CCONJ
esrj-31288	153	14	'	'	X
esrj-31288	153	15	s2fuj&2	s2fuj&2	NOUN
esrj-31288	153	16	)	)	PUNCT
esrj-31288	153	17	]	]	PUNCT
esrj-31288	154	1	=	=	PUNCT
esrj-31288	154	2	a	a	PRON
esrj-31288	154	3	(	(	PUNCT
esrj-31288	154	4	39	39	NUM
esrj-31288	154	5	)	)	PUNCT
esrj-31288	154	6	which	which	PRON
esrj-31288	154	7	has	have	VERB
esrj-31288	154	8	the	the	DET
esrj-31288	154	9	form	form	NOUN
esrj-31288	154	10	as	as	ADP
esrj-31288	154	11	;	;	PUNCT
esrj-31288	154	12	+	+	CCONJ
esrj-31288	154	13	bs	bs	NOUN
esrj-31288	154	14	z	z	NOUN
esrj-31288	154	15	+	+	NUM
esrj-31288	154	16	c	c	NOUN
esrj-31288	154	17	=	=	PUNCT
esrj-31288	154	18	o.	o.	NOUN
esrj-31288	154	19	with	with	SCONJ
esrj-31288	154	20	s2	s2	PROPN
esrj-31288	154	21	known	know	VERB
esrj-31288	154	22	,	,	PUNCT
esrj-31288	154	23	we	we	PRON
esrj-31288	154	24	calculated	calculate	VERB
esrj-31288	154	25	:	:	PUNCT
esrj-31288	154	26	the	the	DET
esrj-31288	154	27	position	position	NOUN
esrj-31288	154	28	(	(	PUNCT
esrj-31288	154	29	x	x	X
esrj-31288	154	30	,	,	PUNCT
esrj-31288	154	31	y	y	PROPN
esrj-31288	154	32	,	,	PUNCT
esrj-31288	154	33	z	z	PROPN
esrj-31288	154	34	)	)	PUNCT
esrj-31288	154	35	,	,	PUNCT
esrj-31288	154	36	the	the	DET
esrj-31288	154	37	normal	normal	ADJ
esrj-31288	154	38	vector	vector	NOUN
esrj-31288	154	39	in	in	ADP
esrj-31288	154	40	this	this	DET
esrj-31288	154	41	point	point	NOUN
esrj-31288	154	42	v	v	ADP
esrj-31288	154	43	·	·	PUNCT
esrj-31288	154	44	by	by	ADP
esrj-31288	154	45	n	n	PROPN
esrj-31288	154	46	=	=	SYM
esrj-31288	154	47	1'11:::1	1'11:::1	PROPN
esrj-31288	154	48	and	and	CCONJ
esrj-31288	154	49	the	the	DET
esrj-31288	154	50	incidence	incidence	NOUN
esrj-31288	154	51	angle	angle	NOUN
esrj-31288	154	52	in	in	ADP
esrj-31288	154	53	the	the	DET
esrj-31288	154	54	nth	nth	NOUN
esrj-31288	154	55	interface	interface	NOUN
esrj-31288	154	56	by	by	ADP
esrj-31288	154	57	cos	cos	PROPN
esrj-31288	154	58	an	an	DET
esrj-31288	154	59	=	=	X
esrj-31288	154	60	f,"1	f,"1	PROPN
esrj-31288	154	61	.	.	PUNCT
esrj-31288	155	1	using	use	VERB
esrj-31288	155	2	the	the	DET
esrj-31288	155	3	snell	snell	NOUN
esrj-31288	155	4	's	's	PART
esrj-31288	155	5	law	law	NOUN
esrj-31288	155	6	,	,	PUNCT
esrj-31288	155	7	the	the	DET
esrj-31288	155	8	refracted	refract	VERB
esrj-31288	155	9	angle	angle	NOUN
esrj-31288	155	10	f3n+i	f3n+i	NOUN
esrj-31288	155	11	of	of	ADP
esrj-31288	155	12	the	the	DET
esrj-31288	155	13	paraxial	paraxial	ADJ
esrj-31288	155	14	ray	ray	NOUN
esrj-31288	155	15	is	be	AUX
esrj-31288	155	16	determined	determine	VERB
esrj-31288	155	17	.	.	PUNCT
esrj-31288	156	1	now	now	ADV
esrj-31288	156	2	is	be	AUX
esrj-31288	156	3	possible	possible	ADJ
esrj-31288	156	4	to	to	PART
esrj-31288	156	5	estimate	estimate	VERB
esrj-31288	156	6	the	the	DET
esrj-31288	156	7	time	time	NOUN
esrj-31288	156	8	used	use	VERB
esrj-31288	156	9	by	by	ADP
esrj-31288	156	10	the	the	DET
esrj-31288	156	11	paraxial	paraxial	ADJ
esrj-31288	156	12	ray	ray	NOUN
esrj-31288	156	13	to	to	PART
esrj-31288	156	14	travel	travel	VERB
esrj-31288	156	15	through	through	ADP
esrj-31288	156	16	the	the	DET
esrj-31288	156	17	upper	upper	ADJ
esrj-31288	156	18	known	know	VERB
esrj-31288	156	19	layers	layer	NOUN
esrj-31288	156	20	and	and	CCONJ
esrj-31288	156	21	the	the	DET
esrj-31288	156	22	remaining	remain	VERB
esrj-31288	156	23	time	time	NOUN
esrj-31288	156	24	to	to	PART
esrj-31288	156	25	reach	reach	VERB
esrj-31288	156	26	the	the	DET
esrj-31288	156	27	posterior	posterior	ADJ
esrj-31288	156	28	interface	interface	NOUN
esrj-31288	156	29	of	of	ADP
esrj-31288	156	30	the	the	DET
esrj-31288	156	31	next	next	ADJ
esrj-31288	156	32	unknown	unknown	ADJ
esrj-31288	156	33	layer	layer	NOUN
esrj-31288	156	34	,	,	PUNCT
esrj-31288	156	35	i.e	i.e	PRON
esrj-31288	156	36	,	,	PUNCT
esrj-31288	156	37	we	we	PRON
esrj-31288	156	38	estimate	estimate	VERB
esrj-31288	156	39	the	the	DET
esrj-31288	156	40	travel	travel	NOUN
esrj-31288	156	41	time	time	NOUN
esrj-31288	156	42	function	function	NOUN
esrj-31288	156	43	at	at	ADP
esrj-31288	156	44	the	the	DET
esrj-31288	156	45	anterior	anterior	ADJ
esrj-31288	156	46	surface	surface	NOUN
esrj-31288	156	47	of	of	ADP
esrj-31288	156	48	the	the	DET
esrj-31288	156	49	unknown	unknown	ADJ
esrj-31288	156	50	layer	layer	NOUN
esrj-31288	156	51	,	,	PUNCT
esrj-31288	156	52	to	to	PART
esrj-31288	156	53	be	be	AUX
esrj-31288	156	54	solved	solve	VERB
esrj-31288	156	55	.	.	PUNCT
esrj-31288	157	1	application	application	NOUN
esrj-31288	157	2	to	to	ADP
esrj-31288	157	3	synthetic	synthetic	ADJ
esrj-31288	157	4	data	datum	NOUN
esrj-31288	157	5	synthetic	synthetic	ADJ
esrj-31288	157	6	data	datum	NOUN
esrj-31288	157	7	were	be	AUX
esrj-31288	157	8	generated	generate	VERB
esrj-31288	157	9	in	in	ADP
esrj-31288	157	10	several	several	ADJ
esrj-31288	157	11	models	model	NOUN
esrj-31288	157	12	using	use	VERB
esrj-31288	157	13	the	the	DET
esrj-31288	157	14	ray	ray	NOUN
esrj-31288	157	15	tracing	trace	VERB
esrj-31288	157	16	program	program	NOUN
esrj-31288	157	17	anis	anis	PROPN
esrj-31288	157	18	ray_3d	ray_3d	PROPN
esrj-31288	157	19	,	,	PUNCT
esrj-31288	157	20	developed	develop	VERB
esrj-31288	157	21	by	by	ADP
esrj-31288	157	22	costa	costa	PROPN
esrj-31288	157	23	et	et	PROPN
esrj-31288	157	24	al	al	PROPN
esrj-31288	157	25	,	,	PUNCT
esrj-31288	157	26	at	at	ADP
esrj-31288	157	27	the	the	DET
esrj-31288	157	28	ufpa	ufpa	NOUN
esrj-31288	157	29	in	in	ADP
esrj-31288	157	30	brazil	brazil	PROPN
esrj-31288	157	31	(	(	PUNCT
esrj-31288	157	32	1993	1993	NUM
esrj-31288	157	33	)	)	PUNCT
esrj-31288	157	34	,	,	PUNCT
esrj-31288	157	35	but	but	CCONJ
esrj-31288	157	36	only	only	ADV
esrj-31288	157	37	two	two	NUM
esrj-31288	157	38	of	of	ADP
esrj-31288	157	39	them	they	PRON
esrj-31288	157	40	are	be	AUX
esrj-31288	157	41	shown	show	VERB
esrj-31288	157	42	here	here	ADV
esrj-31288	157	43	.	.	PUNCT
esrj-31288	158	1	two	two	NUM
esrj-31288	158	2	programs	program	NOUN
esrj-31288	158	3	were	be	AUX
esrj-31288	158	4	developed	develop	VERB
esrj-31288	158	5	,	,	PUNCT
esrj-31288	158	6	the	the	DET
esrj-31288	158	7	first	first	ADJ
esrj-31288	158	8	one	one	NUM
esrj-31288	158	9	to	to	PART
esrj-31288	158	10	estimate	estimate	VERB
esrj-31288	158	11	the	the	DET
esrj-31288	158	12	travel	travel	NOUN
esrj-31288	158	13	time	time	NOUN
esrj-31288	158	14	function	function	NOUN
esrj-31288	158	15	at	at	ADP
esrj-31288	158	16	the	the	DET
esrj-31288	158	17	uppermost	uppermost	ADJ
esrj-31288	158	18	interface	interface	NOUN
esrj-31288	158	19	of	of	ADP
esrj-31288	158	20	the	the	DET
esrj-31288	158	21	seismic	seismic	ADJ
esrj-31288	158	22	system	system	NOUN
esrj-31288	158	23	,	,	PUNCT
esrj-31288	158	24	and	and	CCONJ
esrj-31288	158	25	the	the	DET
esrj-31288	158	26	second	second	ADJ
esrj-31288	158	27	one	one	NOUN
esrj-31288	158	28	to	to	PART
esrj-31288	158	29	determine	determine	VERB
esrj-31288	158	30	the	the	DET
esrj-31288	158	31	interval	interval	NOUN
esrj-31288	158	32	velocities	velocity	NOUN
esrj-31288	158	33	by	by	ADP
esrj-31288	158	34	the	the	DET
esrj-31288	158	35	estimation	estimation	NOUN
esrj-31288	158	36	of	of	ADP
esrj-31288	158	37	the	the	DET
esrj-31288	158	38	travel	travel	NOUN
esrj-31288	158	39	time	time	NOUN
esrj-31288	158	40	in	in	ADP
esrj-31288	158	41	depth	depth	NOUN
esrj-31288	158	42	as	as	SCONJ
esrj-31288	158	43	was	be	AUX
esrj-31288	158	44	explained	explain	VERB
esrj-31288	158	45	in	in	ADP
esrj-31288	158	46	before	before	ADV
esrj-31288	158	47	.	.	PUNCT
esrj-31288	159	1	luis	luis	PROPN
esrj-31288	159	2	montes	montes	PROPN
esrj-31288	159	3	vioes	vioe	NOUN
esrj-31288	159	4	o	o	NOUN
esrj-31288	159	5	-05	-05	PUNCT
esrj-31288	159	6	-i	-i	PUNCT
esrj-31288	160	1	~-15	~-15	PUNCT
esrj-31288	160	2	r	r	NOUN
esrj-31288	160	3	:	:	PUNCT
esrj-31288	160	4	r	r	NOUN
esrj-31288	160	5	·	·	SYM
esrj-31288	160	6	2	2	NUM
esrj-31288	160	7	-25	-25	PUNCT
esrj-31288	160	8	-3	-3	INTJ
esrj-31288	160	9	-5	-5	INTJ
esrj-31288	160	10	xikml	xikml	PROPN
esrj-31288	160	11	vjm	vjm	PROPN
esrj-31288	160	12	/	/	SYM
esrj-31288	160	13	s	s	PART
esrj-31288	160	14	]	]	X
esrj-31288	160	15	vlm	vlm	PROPN
esrj-31288	160	16	/	/	SYM
esrj-31288	160	17	s	s	X
esrj-31288	160	18	]	]	PUNCT
esrj-31288	160	19	erro[m	erro[m	PROPN
esrj-31288	160	20	/	/	SYM
esrj-31288	160	21	s	s	PROPN
esrj-31288	160	22	]	]	X
esrj-31288	160	23	erro[m	erro[m	PROPN
esrj-31288	160	24	/	/	SYM
esrj-31288	160	25	s	s	PROPN
esrj-31288	160	26	]	]	X
esrj-31288	160	27	0	0	NUM
esrj-31288	160	28	0	0	NUM
esrj-31288	160	29	0	0	NUM
esrj-31288	160	30	0	0	NUM
esrj-31288	160	31	200	200	NUM
esrj-31288	160	32	200	200	NUM
esrj-31288	160	33	200	200	NUM
esrj-31288	160	34	200	200	NUM
esrj-31288	160	35	400	400	NUM
esrj-31288	160	36	400	400	NUM
esrj-31288	160	37	400	400	NUM
esrj-31288	160	38	400	400	NUM
esrj-31288	160	39	goo	goo	NOUN
esrj-31288	160	40	goo	goo	NOUN
esrj-31288	160	41	goo	goo	NOUN
esrj-31288	160	42	goo	goo	NOUN
esrj-31288	160	43	800	800	NUM
esrj-31288	160	44	800	800	NUM
esrj-31288	160	45	l800	l800	PROPN
esrj-31288	160	46	lj	lj	PROPN
esrj-31288	160	47	800	800	NUM
esrj-31288	160	48	k	k	NOUN
esrj-31288	160	49	1000	1000	NUM
esrj-31288	160	50	000	000	NUM
esrj-31288	160	51	e	e	NOUN
esrj-31288	160	52	000	000	NUM
esrj-31288	160	53	k	k	X
esrj-31288	160	54	000o£	000o£	NOUN
esrj-31288	160	55	o£	o£	SYM
esrj-31288	160	56	n	n	CCONJ
esrj-31288	160	57	n	n	CCONJ
esrj-31288	160	58	n	n	CCONJ
esrj-31288	160	59	n	n	CCONJ
esrj-31288	160	60	'	'	NUM
esrj-31288	160	61	1200	1200	NUM
esrj-31288	160	62	200	200	NUM
esrj-31288	160	63	200	200	NUM
esrj-31288	160	64	200	200	NUM
esrj-31288	160	65	1400	1400	NUM
esrj-31288	160	66	400	400	NUM
esrj-31288	160	67	)	)	PUNCT
esrj-31288	160	68	400	400	NUM
esrj-31288	160	69	400	400	NUM
esrj-31288	160	70	11	11	NUM
esrj-31288	160	71	goo	goo	NOUN
esrj-31288	160	72	goo	goo	NOUN
esrj-31288	160	73	600	600	NUM
esrj-31288	160	74	600	600	NUM
esrj-31288	160	75	1800	1800	NUM
esrj-31288	160	76	800	800	NUM
esrj-31288	160	77	800	800	NUM
esrj-31288	160	78	800	800	NUM
esrj-31288	160	79	2000	2000	NUM
esrj-31288	160	80	000	000	NUM
esrj-31288	160	81	000	000	NUM
esrj-31288	160	82	000	000	NUM
esrj-31288	160	83	0	0	NUM
esrj-31288	160	84	5000	5000	NUM
esrj-31288	160	85	0	0	NUM
esrj-31288	160	86	5000	5000	NUM
esrj-31288	160	87	0	0	NUM
esrj-31288	160	88	50	50	NUM
esrj-31288	160	89	0	0	NUM
esrj-31288	160	90	50	50	NUM
esrj-31288	160	91	figure	figure	NOUN
esrj-31288	160	92	6	6	NUM
esrj-31288	160	93	.	.	PUNCT
esrj-31288	161	1	on	on	ADP
esrj-31288	161	2	top	top	ADJ
esrj-31288	161	3	the	the	DET
esrj-31288	161	4	model	model	NOUN
esrj-31288	161	5	used	use	VERB
esrj-31288	161	6	to	to	PART
esrj-31288	161	7	test	test	VERB
esrj-31288	161	8	the	the	DET
esrj-31288	161	9	algorithm	algorithm	NOUN
esrj-31288	161	10	.	.	PUNCT
esrj-31288	162	1	on	on	ADP
esrj-31288	162	2	bottom	bottom	ADJ
esrj-31288	162	3	interval	interval	NOUN
esrj-31288	162	4	velocities	velocity	NOUN
esrj-31288	162	5	and	and	CCONJ
esrj-31288	162	6	erros	erro	NOUN
esrj-31288	162	7	obtained	obtain	VERB
esrj-31288	162	8	in	in	ADP
esrj-31288	162	9	two	two	NUM
esrj-31288	162	10	points	point	NOUN
esrj-31288	162	11	at	at	ADP
esrj-31288	162	12	the	the	DET
esrj-31288	162	13	superior	superior	ADJ
esrj-31288	162	14	surface	surface	NOUN
esrj-31288	162	15	.	.	PUNCT
esrj-31288	163	1	besides	besides	SCONJ
esrj-31288	163	2	,	,	PUNCT
esrj-31288	163	3	the	the	DET
esrj-31288	163	4	second	second	ADJ
esrj-31288	163	5	program	program	NOUN
esrj-31288	163	6	also	also	ADV
esrj-31288	163	7	calculates	calculate	VERB
esrj-31288	163	8	the	the	DET
esrj-31288	163	9	matrices	matrix	NOUN
esrj-31288	163	10	of	of	ADP
esrj-31288	163	11	curvature	curvature	NOUN
esrj-31288	163	12	of	of	ADP
esrj-31288	163	13	the	the	DET
esrj-31288	163	14	interfaces	interface	NOUN
esrj-31288	163	15	an	an	DET
esrj-31288	163	16	the	the	DET
esrj-31288	163	17	points	point	NOUN
esrj-31288	163	18	where	where	SCONJ
esrj-31288	163	19	the	the	DET
esrj-31288	163	20	rays	ray	NOUN
esrj-31288	163	21	intercept	intercept	VERB
esrj-31288	163	22	them	they	PRON
esrj-31288	163	23	.	.	PUNCT
esrj-31288	164	1	figure	figure	VERB
esrj-31288	164	2	6	6	NUM
esrj-31288	164	3	shows	show	NOUN
esrj-31288	164	4	on	on	ADP
esrj-31288	164	5	top	top	NOUN
esrj-31288	164	6	the	the	DET
esrj-31288	164	7	first	first	ADJ
esrj-31288	164	8	model	model	NOUN
esrj-31288	164	9	used	use	VERB
esrj-31288	164	10	to	to	PART
esrj-31288	164	11	generate	generate	VERB
esrj-31288	164	12	the	the	DET
esrj-31288	164	13	travel	travel	NOUN
esrj-31288	164	14	time	time	NOUN
esrj-31288	164	15	and	and	CCONJ
esrj-31288	164	16	in	in	ADP
esrj-31288	164	17	bottom	bottom	NOUN
esrj-31288	164	18	the	the	DET
esrj-31288	164	19	interval	interval	NOUN
esrj-31288	164	20	velocity	velocity	NOUN
esrj-31288	164	21	model	model	NOUN
esrj-31288	164	22	obtained	obtain	VERB
esrj-31288	164	23	by	by	ADP
esrj-31288	164	24	the	the	DET
esrj-31288	164	25	program	program	NOUN
esrj-31288	164	26	,	,	PUNCT
esrj-31288	164	27	in	in	ADP
esrj-31288	164	28	two	two	NUM
esrj-31288	164	29	different	different	ADJ
esrj-31288	164	30	positions	position	NOUN
esrj-31288	164	31	fo	fo	ADP
esrj-31288	164	32	the	the	DET
esrj-31288	164	33	model	model	NOUN
esrj-31288	164	34	.	.	PUNCT
esrj-31288	165	1	the	the	DET
esrj-31288	165	2	two	two	NUM
esrj-31288	165	3	leftmost	leftmost	ADJ
esrj-31288	165	4	graphics	graphic	NOUN
esrj-31288	165	5	in	in	ADP
esrj-31288	165	6	figure	figure	NOUN
esrj-31288	165	7	6	6	NUM
esrj-31288	165	8	shows	show	VERB
esrj-31288	165	9	the	the	DET
esrj-31288	165	10	errors	error	NOUN
esrj-31288	165	11	in	in	ADP
esrj-31288	165	12	estimating	estimate	VERB
esrj-31288	165	13	the	the	DET
esrj-31288	165	14	interval	interval	NOUN
esrj-31288	165	15	velocities	velocity	NOUN
esrj-31288	165	16	,	,	PUNCT
esrj-31288	165	17	being	be	AUX
esrj-31288	165	18	fewer	few	ADJ
esrj-31288	165	19	than	than	ADP
esrj-31288	165	20	50	50	NUM
esrj-31288	165	21	mls	mls	NOUN
esrj-31288	165	22	.	.	PUNCT
esrj-31288	166	1	a	a	DET
esrj-31288	166	2	second	second	ADJ
esrj-31288	166	3	model	model	NOUN
esrj-31288	166	4	was	be	AUX
esrj-31288	166	5	used	use	VERB
esrj-31288	166	6	to	to	PART
esrj-31288	166	7	show	show	VERB
esrj-31288	166	8	the	the	DET
esrj-31288	166	9	program	program	NOUN
esrj-31288	166	10	estimating	estimate	VERB
esrj-31288	166	11	the	the	DET
esrj-31288	166	12	points	point	NOUN
esrj-31288	166	13	where	where	SCONJ
esrj-31288	166	14	the	the	DET
esrj-31288	166	15	rays	ray	NOUN
esrj-31288	166	16	reach	reach	VERB
esrj-31288	166	17	the	the	DET
esrj-31288	166	18	interfaces	interface	NOUN
esrj-31288	166	19	;	;	PUNCT
esrj-31288	166	20	the	the	DET
esrj-31288	166	21	model	model	NOUN
esrj-31288	166	22	is	be	AUX
esrj-31288	166	23	shown	show	VERB
esrj-31288	166	24	in	in	ADP
esrj-31288	166	25	top	top	ADJ
esrj-31288	166	26	,	,	PUNCT
esrj-31288	166	27	figure	figure	NOUN
esrj-31288	166	28	7	7	NUM
esrj-31288	166	29	,	,	PUNCT
esrj-31288	166	30	and	and	CCONJ
esrj-31288	166	31	in	in	ADP
esrj-31288	166	32	bottom	bottom	NOUN
esrj-31288	166	33	the	the	DET
esrj-31288	166	34	final	final	ADJ
esrj-31288	166	35	position	position	NOUN
esrj-31288	166	36	reached	reach	VERB
esrj-31288	166	37	by	by	ADP
esrj-31288	166	38	the	the	DET
esrj-31288	166	39	rays	ray	NOUN
esrj-31288	166	40	calculated	calculate	VERB
esrj-31288	166	41	by	by	ADP
esrj-31288	166	42	the	the	DET
esrj-31288	166	43	program	program	NOUN
esrj-31288	166	44	.	.	PUNCT
esrj-31288	167	1	in	in	ADP
esrj-31288	167	2	the	the	DET
esrj-31288	167	3	third	third	ADJ
esrj-31288	167	4	interface	interface	NOUN
esrj-31288	167	5	the	the	DET
esrj-31288	167	6	program	program	NOUN
esrj-31288	167	7	srnoothes	srnoothe	VERB
esrj-31288	167	8	it	it	PRON
esrj-31288	167	9	,	,	PUNCT
esrj-31288	167	10	satisfying	satisfy	VERB
esrj-31288	167	11	the	the	DET
esrj-31288	167	12	restriction	restriction	NOUN
esrj-31288	167	13	impossed	imposse	VERB
esrj-31288	167	14	on	on	ADP
esrj-31288	167	15	the	the	DET
esrj-31288	167	16	surfaces	surface	NOUN
esrj-31288	167	17	of	of	ADP
esrj-31288	167	18	the	the	DET
esrj-31288	167	19	models	model	NOUN
esrj-31288	167	20	.	.	PUNCT
esrj-31288	168	1	the	the	DET
esrj-31288	168	2	others	other	NOUN
esrj-31288	168	3	points	point	NOUN
esrj-31288	168	4	show	show	VERB
esrj-31288	168	5	a	a	DET
esrj-31288	168	6	well	well	ADV
esrj-31288	168	7	fitted	fit	VERB
esrj-31288	168	8	with	with	ADP
esrj-31288	168	9	the	the	DET
esrj-31288	168	10	interfaces	interface	NOUN
esrj-31288	168	11	.	.	PUNCT
esrj-31288	169	1	conclusions	conclusion	NOUN
esrj-31288	169	2	the	the	DET
esrj-31288	169	3	second	second	ADJ
esrj-31288	169	4	order	order	NOUN
esrj-31288	169	5	approximation	approximation	NOUN
esrj-31288	169	6	of	of	ADP
esrj-31288	169	7	the	the	DET
esrj-31288	169	8	travel	travel	NOUN
esrj-31288	169	9	time	time	NOUN
esrj-31288	169	10	and	and	CCONJ
esrj-31288	169	11	the	the	DET
esrj-31288	169	12	paraxial	paraxial	ADJ
esrj-31288	169	13	ray	ray	NOUN
esrj-31288	169	14	theory	theory	NOUN
esrj-31288	169	15	make	make	VERB
esrj-31288	169	16	possible	possible	ADJ
esrj-31288	169	17	to	to	PART
esrj-31288	169	18	develop	develop	VERB
esrj-31288	169	19	an	an	DET
esrj-31288	169	20	inversion	inversion	NOUN
esrj-31288	169	21	method	method	NOUN
esrj-31288	169	22	to	to	PART
esrj-31288	169	23	estimate	estimate	VERB
esrj-31288	169	24	the	the	DET
esrj-31288	169	25	interval	interval	NOUN
esrj-31288	169	26	velocities	velocity	NOUN
esrj-31288	169	27	in	in	ADP
esrj-31288	169	28	models	model	NOUN
esrj-31288	169	29	with	with	ADP
esrj-31288	169	30	no	no	DET
esrj-31288	169	31	structural	structural	ADJ
esrj-31288	169	32	complexity	complexity	NOUN
esrj-31288	169	33	or	or	CCONJ
esrj-31288	169	34	strong	strong	ADJ
esrj-31288	169	35	dipping	dipping	NOUN
esrj-31288	169	36	interfaces	interface	NOUN
esrj-31288	169	37	.	.	PUNCT
esrj-31288	170	1	the	the	DET
esrj-31288	170	2	method	method	NOUN
esrj-31288	170	3	is	be	AUX
esrj-31288	170	4	a	a	DET
esrj-31288	170	5	tool	tool	NOUN
esrj-31288	170	6	to	to	PART
esrj-31288	170	7	estimate	estimate	VERB
esrj-31288	170	8	interval	interval	NOUN
esrj-31288	170	9	velocity	velocity	NOUN
esrj-31288	170	10	and	and	CCONJ
esrj-31288	170	11	reflector	reflector	NOUN
esrj-31288	170	12	depths	depth	NOUN
esrj-31288	170	13	,	,	PUNCT
esrj-31288	170	14	based	base	VERB
esrj-31288	170	15	on	on	ADP
esrj-31288	170	16	post	post	NOUN
esrj-31288	170	17	stacked	stack	VERB
esrj-31288	170	18	seismic	seismic	ADJ
esrj-31288	170	19	data	datum	NOUN
esrj-31288	170	20	.	.	PUNCT
esrj-31288	171	1	due	due	ADP
esrj-31288	171	2	to	to	ADP
esrj-31288	171	3	the	the	DET
esrj-31288	171	4	paraxial	paraxial	ADJ
esrj-31288	171	5	ray	ray	NOUN
esrj-31288	171	6	theory	theory	NOUN
esrj-31288	171	7	difficulties	difficulty	NOUN
esrj-31288	171	8	could	could	AUX
esrj-31288	171	9	occur	occur	VERB
esrj-31288	171	10	when	when	SCONJ
esrj-31288	171	11	the	the	DET
esrj-31288	171	12	positions	position	NOUN
esrj-31288	171	13	of	of	ADP
esrj-31288	171	14	sources	source	NOUN
esrj-31288	171	15	and	and	CCONJ
esrj-31288	171	16	detectors	detector	NOUN
esrj-31288	171	17	exceed	exceed	VERB
esrj-31288	171	18	the	the	DET
esrj-31288	171	19	validity	validity	NOUN
esrj-31288	171	20	of	of	ADP
esrj-31288	171	21	the	the	DET
esrj-31288	171	22	approximation	approximation	NOUN
esrj-31288	171	23	,	,	PUNCT
esrj-31288	171	24	being	be	AUX
esrj-31288	171	25	valid	valid	ADJ
esrj-31288	171	26	only	only	ADV
esrj-31288	171	27	for	for	ADP
esrj-31288	171	28	small	small	ADJ
esrj-31288	171	29	values	value	NOUN
esrj-31288	171	30	of	of	ADP
esrj-31288	171	31	distance	distance	NOUN
esrj-31288	171	32	to	to	ADP
esrj-31288	171	33	the	the	DET
esrj-31288	171	34	zero	zero	NUM
esrj-31288	171	35	-	-	PUNCT
esrj-31288	171	36	offset	offset	VERB
esrj-31288	171	37	ray	ray	NOUN
esrj-31288	171	38	position	position	NOUN
esrj-31288	171	39	.	.	PUNCT
esrj-31288	172	1	its	its	PRON
esrj-31288	172	2	range	range	NOUN
esrj-31288	172	3	of	of	ADP
esrj-31288	172	4	applicability	applicability	NOUN
esrj-31288	172	5	correspond	correspond	NOUN
esrj-31288	172	6	to	to	ADP
esrj-31288	172	7	the	the	DET
esrj-31288	172	8	hyperbolic	hyperbolic	ADJ
esrj-31288	172	9	dynamic	dynamic	ADJ
esrj-31288	172	10	correction	correction	NOUN
esrj-31288	172	11	.	.	PUNCT
esrj-31288	173	1	because	because	SCONJ
esrj-31288	173	2	10	10	NUM
esrj-31288	173	3	:	:	PUNCT
esrj-31288	173	4	~-------------0	~-------------0	PROPN
esrj-31288	173	5	-	-	PUNCT
esrj-31288	173	6	---5	---5	PROPN
esrj-31288	173	7	5	5	NUM
esrj-31288	173	8	·	·	SYM
esrj-31288	173	9	5	5	NUM
esrj-31288	173	10	figure	figure	NOUN
esrj-31288	173	11	7	7	NUM
esrj-31288	173	12	.	.	PUNCT
esrj-31288	174	1	on	on	ADP
esrj-31288	174	2	top	top	VERB
esrj-31288	174	3	the	the	DET
esrj-31288	174	4	second	second	ADJ
esrj-31288	174	5	model	model	NOUN
esrj-31288	174	6	and	and	CCONJ
esrj-31288	174	7	on	on	ADP
esrj-31288	174	8	bottom	bottom	ADJ
esrj-31288	174	9	the	the	DET
esrj-31288	174	10	interfaces	interface	NOUN
esrj-31288	174	11	and	and	CCONJ
esrj-31288	174	12	the	the	DET
esrj-31288	174	13	points	point	NOUN
esrj-31288	174	14	where	where	SCONJ
esrj-31288	174	15	the	the	DET
esrj-31288	174	16	algorithm	algorithm	NOUN
esrj-31288	174	17	estimates	estimate	VERB
esrj-31288	174	18	final	final	ADJ
esrj-31288	174	19	positions	position	NOUN
esrj-31288	174	20	for	for	ADP
esrj-31288	174	21	normal	normal	ADJ
esrj-31288	174	22	rays	ray	NOUN
esrj-31288	174	23	.	.	PUNCT
esrj-31288	175	1	the	the	DET
esrj-31288	175	2	input	input	NOUN
esrj-31288	175	3	data	datum	NOUN
esrj-31288	175	4	are	be	AUX
esrj-31288	175	5	travel	travel	NOUN
esrj-31288	175	6	time	time	NOUN
esrj-31288	175	7	measurements	measurement	NOUN
esrj-31288	175	8	on	on	ADP
esrj-31288	175	9	seismic	seismic	ADJ
esrj-31288	175	10	traces	trace	NOUN
esrj-31288	175	11	,	,	PUNCT
esrj-31288	175	12	a	a	DET
esrj-31288	175	13	good	good	ADJ
esrj-31288	175	14	quality	quality	NOUN
esrj-31288	175	15	on	on	ADP
esrj-31288	175	16	seismic	seismic	ADJ
esrj-31288	175	17	data	datum	NOUN
esrj-31288	175	18	is	be	AUX
esrj-31288	175	19	impossed	imposse	VERB
esrj-31288	175	20	.	.	PUNCT
esrj-31288	176	1	nevertheless	nevertheless	ADV
esrj-31288	176	2	the	the	DET
esrj-31288	176	3	method	method	NOUN
esrj-31288	176	4	provides	provide	VERB
esrj-31288	176	5	the	the	DET
esrj-31288	176	6	inverse	inverse	NOUN
esrj-31288	176	7	solution	solution	NOUN
esrj-31288	176	8	without	without	ADP
esrj-31288	176	9	a	a	DET
esrj-31288	176	10	priori	priori	ADJ
esrj-31288	176	11	knowledge	knowledge	NOUN
esrj-31288	176	12	of	of	ADP
esrj-31288	176	13	the	the	DET
esrj-31288	176	14	model	model	NOUN
esrj-31288	176	15	,	,	PUNCT
esrj-31288	176	16	just	just	ADV
esrj-31288	176	17	using	use	VERB
esrj-31288	176	18	travel	travel	NOUN
esrj-31288	176	19	time	time	NOUN
esrj-31288	176	20	measurements	measurement	NOUN
esrj-31288	176	21	on	on	ADP
esrj-31288	176	22	the	the	DET
esrj-31288	176	23	uppermost	uppermost	ADJ
esrj-31288	176	24	surface	surface	NOUN
esrj-31288	176	25	.	.	PUNCT
esrj-31288	177	1	bibliography	bibliography	NOUN
esrj-31288	177	2	bortfeld	bortfeld	NOUN
esrj-31288	177	3	,	,	PUNCT
esrj-31288	177	4	r.	r.	PROPN
esrj-31288	177	5	1989	1989	NUM
esrj-31288	177	6	:	:	PUNCT
esrj-31288	177	7	geometrical	geometrical	ADJ
esrj-31288	177	8	ray	ray	NOUN
esrj-31288	177	9	theory	theory	NOUN
esrj-31288	177	10	:	:	PUNCT
esrj-31288	177	11	rays	ray	NOUN
esrj-31288	177	12	and	and	CCONJ
esrj-31288	177	13	travel	travel	NOUN
esrj-31288	177	14	times	time	NOUN
esrj-31288	177	15	in	in	ADP
esrj-31288	177	16	seismic	seismic	ADJ
esrj-31288	177	17	systems	system	NOUN
esrj-31288	177	18	.	.	PUNCT
esrj-31288	178	1	geophysics	geophysic	NOUN
esrj-31288	178	2	,	,	PUNCT
esrj-31288	178	3	54	54	NUM
esrj-31288	178	4	,	,	PUNCT
esrj-31288	178	5	342	342	NUM
esrj-31288	178	6	-	-	SYM
esrj-31288	178	7	349	349	NUM
esrj-31288	178	8	.	.	PUNCT
esrj-31288	179	1	bortfelo	bortfelo	PROPN
esrj-31288	179	2	,	,	PUNCT
esrj-31288	179	3	r.	r.	PROPN
esrj-31288	179	4	,	,	PUNCT
esrj-31288	179	5	and	and	CCONJ
esrj-31288	179	6	kemper	kemper	PROPN
esrj-31288	179	7	,	,	PUNCT
esrj-31288	179	8	m.	m.	NOUN
esrj-31288	179	9	1991	1991	NUM
esrj-31288	179	10	:	:	PUNCT
esrj-31288	179	11	geometrical	geometrical	ADJ
esrj-31288	179	12	ray	ray	NOUN
esrj-31288	179	13	theory	theory	NOUN
esrj-31288	179	14	:	:	PUNCT
esrj-31288	179	15	line	line	NOUN
esrj-31288	179	16	foci	focus	NOUN
esrj-31288	179	17	and	and	CCONJ
esrj-31288	179	18	point	point	VERB
esrj-31288	179	19	foci	focus	NOUN
esrj-31288	179	20	in	in	ADP
esrj-31288	179	21	the	the	DET
esrj-31288	179	22	anterior	anterior	ADJ
esrj-31288	179	23	surface	surface	NOUN
esrj-31288	179	24	of	of	ADP
esrj-31288	179	25	seismic	seismic	ADJ
esrj-31288	179	26	systems	system	NOUN
esrj-31288	179	27	(	(	PUNCT
esrj-31288	179	28	second	second	ADJ
esrj-31288	179	29	order	order	NOUN
esrj-31288	179	30	approximation	approximation	NOUN
esrj-31288	179	31	of	of	ADP
esrj-31288	179	32	the	the	DET
esrj-31288	179	33	travel	travel	NOUN
esrj-31288	179	34	times	time	NOUN
esrj-31288	179	35	)	)	PUNCT
esrj-31288	179	36	.	.	PUNCT
esrj-31288	180	1	geophysics	geophysic	NOUN
esrj-31288	180	2	,	,	PUNCT
esrj-31288	180	3	56	56	NUM
esrj-31288	180	4	,	,	PUNCT
esrj-31288	180	5	806	806	NUM
esrj-31288	180	6	-	-	SYM
esrj-31288	180	7	811	811	NUM
esrj-31288	180	8	.	.	PUNCT
esrj-31288	181	1	costa	costa	PROPN
esrj-31288	181	2	,	,	PUNCT
esrj-31288	181	3	1	1	X
esrj-31288	181	4	.	.	NUM
esrj-31288	181	5	,	,	PUNCT
esrj-31288	181	6	schoenber	schoenber	PROPN
esrj-31288	181	7	,	,	PUNCT
esrj-31288	181	8	m.	m.	NOUN
esrj-31288	181	9	and	and	CCONJ
esrj-31288	181	10	urban	urban	ADJ
esrj-31288	181	11	,	,	PUNCT
esrj-31288	181	12	1	1	NUM
esrj-31288	181	13	.	.	NOUN
esrj-31288	181	14	1993	1993	NUM
esrj-31288	181	15	:	:	PUNCT
esrj-31288	181	16	3d	3d	NUM
esrj-31288	181	17	ray	ray	NOUN
esrj-31288	181	18	tracing	trace	VERB
esrj-31288	181	19	through	through	ADP
esrj-31288	181	20	no	no	PRON
esrj-31288	181	21	-	-	PUNCT
esrj-31288	181	22	flat	flat	ADJ
esrj-31288	181	23	homogeneous	homogeneous	ADJ
esrj-31288	181	24	anisotropic	anisotropic	NOUN
esrj-31288	181	25	layers	layer	NOUN
esrj-31288	181	26	.	.	PUNCT
esrj-31288	182	1	3rd	3rd	ADJ
esrj-31288	182	2	international	international	ADJ
esrj-31288	182	3	congress	congress	PROPN
esrj-31288	182	4	of	of	ADP
esrj-31288	182	5	the	the	DET
esrj-31288	182	6	brazilian	brazilian	ADJ
esrj-31288	182	7	geophysical	geophysical	ADJ
esrj-31288	182	8	society	society	NOUN
esrj-31288	182	9	.	.	PUNCT
esrj-31288	183	1	expanded	expand	VERB
esrj-31288	183	2	abstracts	abstract	NOUN
esrj-31288	183	3	,	,	PUNCT
esrj-31288	183	4	vi	vi	PROPN
esrj-31288	183	5	,	,	PUNCT
esrj-31288	183	6	47	47	NUM
esrj-31288	183	7	-	-	SYM
esrj-31288	183	8	52	52	NUM
esrj-31288	183	9	.	.	PUNCT
esrj-31288	184	1	hubral	hubral	ADJ
esrj-31288	184	2	,	,	PUNCT
esrj-31288	184	3	p	p	X
esrj-31288	184	4	,	,	PUNCT
esrj-31288	184	5	schleicher	schleicher	ADJ
esrj-31288	184	6	,	,	PUNCT
esrj-31288	184	7	j.	j.	PROPN
esrj-31288	184	8	and	and	CCONJ
esrj-31288	184	9	tygel	tygel	NOUN
esrj-31288	184	10	,	,	PUNCT
esrj-31288	184	11	m.	m.	NOUN
esrj-31288	184	12	three	three	NUM
esrj-31288	184	13	-	-	PUNCT
esrj-31288	184	14	dimensional	dimensional	ADJ
esrj-31288	184	15	paraxial	paraxial	ADJ
esrj-31288	184	16	ray	ray	NOUN
esrj-31288	184	17	properties	property	NOUN
esrj-31288	184	18	i	i	PRON
esrj-31288	184	19	basic	basic	ADJ
esrj-31288	184	20	relations	relation	NOUN
esrj-31288	184	21	:	:	PUNCT
esrj-31288	184	22	1	1	X
esrj-31288	184	23	.	.	X
esrj-31288	184	24	seis	seis	PROPN
esrj-31288	184	25	.	.	PUNCT
esrj-31288	185	1	expl	expl	PROPN
esrj-31288	185	2	.	.	PUNCT
esrj-31288	185	3	,	,	PUNCT
esrj-31288	185	4	i	i	PRON
esrj-31288	185	5	,	,	PUNCT
esrj-31288	185	6	265	265	NUM
esrj-31288	185	7	-	-	SYM
esrj-31288	185	8	279	279	NUM
esrj-31288	185	9	.	.	PUNCT
esrj-31288	186	1	kahn	kahn	PROPN
esrj-31288	186	2	,	,	PUNCT
esrj-31288	186	3	s.	s.	PROPN
esrj-31288	186	4	u.	u.	PROPN
esrj-31288	186	5	1987	1987	NUM
esrj-31288	186	6	:	:	PUNCT
esrj-31288	186	7	die	die	VERB
esrj-31288	186	8	aufdeckung	aufdeckung	ADJ
esrj-31288	186	9	der	der	NOUN
esrj-31288	186	10	mehrdeutigkeiten	mehrdeutigkeiten	VERB
esrj-31288	186	11	in	in	ADP
esrj-31288	186	12	der	der	ADJ
esrj-31288	186	13	reflexionsseimik	reflexionsseimik	ADJ
esrj-31288	186	14	:	:	PUNCT
esrj-31288	186	15	ph.d	ph.d	PROPN
esrj-31288	186	16	.	.	PUNCT
esrj-31288	186	17	tesis	tesis	PROPN
esrj-31288	186	18	,	,	PUNCT
esrj-31288	186	19	tech	tech	NOUN
esrj-31288	186	20	.	.	PUNCT
esrj-31288	187	1	univ	univ	PROPN
esrj-31288	187	2	.	.	PUNCT
esrj-31288	188	1	clausthal	clausthal	PROPN
esrj-31288	188	2	.	.	PUNCT
esrj-31288	189	1	krey	krey	PROPN
esrj-31288	189	2	,	,	PUNCT
esrj-31288	189	3	t.	t.	PROPN
esrj-31288	189	4	1989	1989	NUM
esrj-31288	189	5	:	:	PUNCT
esrj-31288	189	6	the	the	DET
esrj-31288	189	7	non	non	ADJ
esrj-31288	189	8	uniqueness	uniqueness	NOUN
esrj-31288	189	9	of	of	ADP
esrj-31288	189	10	the	the	DET
esrj-31288	189	11	determination	determination	NOUN
esrj-31288	189	12	of	of	ADP
esrj-31288	189	13	interval	interval	NOUN
esrj-31288	189	14	velocities	velocity	NOUN
esrj-31288	189	15	from	from	ADP
esrj-31288	189	16	moveout	moveout	PROPN
esrj-31288	189	17	velocities	velocity	NOUN
esrj-31288	189	18	.	.	PUNCT
esrj-31288	190	1	geophysics	geophysic	NOUN
esrj-31288	190	2	,	,	PUNCT
esrj-31288	190	3	54	54	NUM
esrj-31288	190	4	,	,	PUNCT
esrj-31288	190	5	1209	1209	NUM
esrj-31288	190	6	-	-	SYM
esrj-31288	190	7	1211	1211	NUM
esrj-31288	190	8	.	.	PUNCT
esrj-31288	191	1	ursrn	ursrn	PROPN
esrj-31288	191	2	,	,	PUNCT
esrj-31288	191	3	b.	b.	PROPN
esrj-31288	191	4	1982	1982	NUM
esrj-31288	191	5	:	:	PUNCT
esrj-31288	191	6	quadratic	quadratic	ADJ
esrj-31288	191	7	wavefront	wavefront	ADJ
esrj-31288	191	8	and	and	CCONJ
esrj-31288	191	9	travel	travel	NOUN
esrj-31288	191	10	time	time	NOUN
esrj-31288	191	11	approximations	approximation	NOUN
esrj-31288	191	12	in	in	ADP
esrj-31288	191	13	inhomogeneous	inhomogeneous	ADJ
esrj-31288	191	14	layered	layered	ADJ
esrj-31288	191	15	media	medium	NOUN
esrj-31288	191	16	with	with	ADP
esrj-31288	191	17	curved	curved	ADJ
esrj-31288	191	18	interfaces	interface	NOUN
esrj-31288	191	19	.	.	PUNCT
esrj-31288	192	1	geophysics	geophysic	NOUN
esrj-31288	192	2	,	,	PUNCT
esrj-31288	192	3	47	47	NUM
esrj-31288	192	4	,	,	PUNCT
esrj-31288	192	5	1012	1012	NUM
esrj-31288	192	6	-	-	SYM
esrj-31288	192	7	1021	1021	NUM
esrj-31288	192	8	.	.	PUNCT
esrj-31288	193	1	acknowledgements	acknowledgement	NOUN
esrj-31288	193	2	this	this	DET
esrj-31288	193	3	paper	paper	NOUN
esrj-31288	193	4	is	be	AUX
esrj-31288	193	5	the	the	DET
esrj-31288	193	6	result	result	NOUN
esrj-31288	193	7	obtained	obtain	VERB
esrj-31288	193	8	in	in	ADP
esrj-31288	193	9	the	the	DET
esrj-31288	193	10	montes	montes	PROPN
esrj-31288	193	11	's	's	PART
esrj-31288	193	12	ph	ph	PROPN
esrj-31288	193	13	.	.	PROPN
esrj-31288	193	14	d.	d.	PROPN
esrj-31288	193	15	thesis	thesis	NOUN
esrj-31288	193	16	at	at	ADP
esrj-31288	193	17	the	the	DET
esrj-31288	193	18	federal	federal	ADJ
esrj-31288	193	19	university	university	PROPN
esrj-31288	193	20	of	of	ADP
esrj-31288	193	21	para	para	PROPN
esrj-31288	193	22	,	,	PUNCT
esrj-31288	193	23	brazil	brazil	PROPN
esrj-31288	193	24	.	.	PUNCT
esrj-31288	194	1	the	the	DET
esrj-31288	194	2	project	project	NOUN
esrj-31288	194	3	was	be	AUX
esrj-31288	194	4	supported	support	VERB
esrj-31288	194	5	by	by	ADP
esrj-31288	194	6	a	a	DET
esrj-31288	194	7	fellowship	fellowship	NOUN
esrj-31288	194	8	from	from	ADP
esrj-31288	194	9	coordenacao	coordenacao	PROPN
esrj-31288	194	10	de	de	PROPN
esrj-31288	194	11	aperfeicoamento	aperfeicoamento	PROPN
esrj-31288	194	12	de	de	PROPN
esrj-31288	194	13	pessoal	pessoal	PROPN
esrj-31288	194	14	de	de	PROPN
esrj-31288	194	15	nivel	nivel	PROPN
esrj-31288	194	16	superior	superior	ADJ
esrj-31288	194	17	(	(	PUNCT
esrj-31288	194	18	capes	cape	NOUN
esrj-31288	194	19	)	)	PUNCT
esrj-31288	194	20	.	.	PUNCT
esrj-31288	195	1	appendix	appendix	NOUN
esrj-31288	195	2	determining	determine	VERB
esrj-31288	195	3	the	the	DET
esrj-31288	195	4	interval	interval	NOUN
esrj-31288	195	5	velocity	velocity	NOUN
esrj-31288	195	6	to	to	PART
esrj-31288	195	7	determine	determine	VERB
esrj-31288	195	8	the	the	DET
esrj-31288	195	9	interval	interval	NOUN
esrj-31288	195	10	velocity	velocity	NOUN
esrj-31288	195	11	in	in	ADP
esrj-31288	195	12	the	the	DET
esrj-31288	195	13	n	n	CCONJ
esrj-31288	195	14	"	"	PUNCT
esrj-31288	195	15	layer	layer	NOUN
esrj-31288	195	16	is	be	AUX
esrj-31288	195	17	necessary	necessary	ADJ
esrj-31288	195	18	to	to	PART
esrj-31288	195	19	solve	solve	VERB
esrj-31288	195	20	the	the	DET
esrj-31288	195	21	set	set	NOUN
esrj-31288	195	22	of	of	ADP
esrj-31288	195	23	simultaneous	simultaneous	ADJ
esrj-31288	195	24	equations	equation	NOUN
esrj-31288	195	25	,	,	PUNCT
esrj-31288	195	26	represented	represent	VERB
esrj-31288	195	27	by	by	ADP
esrj-31288	195	28	the	the	DET
esrj-31288	195	29	matrix	matrix	NOUN
esrj-31288	195	30	equation	equation	NOUN
esrj-31288	195	31	b-1	b-1	NOUN
esrj-31288	195	32	a	a	DET
esrj-31288	195	33	:	:	PUNCT
esrj-31288	195	34	geoflslca	geoflslca	PROPN
esrj-31288	195	35	colombiana	colombiana	PROPN
esrj-31288	195	36	,	,	PUNCT
esrj-31288	195	37	5	5	NUM
esrj-31288	195	38	,	,	PUNCT
esrj-31288	195	39	qiciembre	qiciembre	PROPN
esrj-31288	195	40	de	de	PROPN
esrj-31288	195	41	2001	2001	NUM
esrj-31288	195	42	interval	interval	NOUN
esrj-31288	195	43	velocity	velocity	NOUN
esrj-31288	195	44	determination	determination	NOUN
esrj-31288	195	45	by	by	ADP
esrj-31288	195	46	downward	downward	ADJ
esrj-31288	195	47	continuation	continuation	NOUN
esrj-31288	195	48	of	of	ADP
esrj-31288	195	49	the	the	DET
esrj-31288	195	50	traveltime	traveltime	NOUN
esrj-31288	195	51	function	function	NOUN
esrj-31288	195	52	,	,	PUNCT
esrj-31288	195	53	paraxial	paraxial	ADJ
esrj-31288	195	54	ray	ray	NOUN
esrj-31288	195	55	approximation	approximation	NOUN
esrj-31288	195	56	(	(	PUNCT
esrj-31288	195	57	a	a	DET
esrj-31288	195	58	i	i	NOUN
esrj-31288	195	59	)	)	PUNCT
esrj-31288	195	60	(	(	PUNCT
esrj-31288	195	61	a2	a2	PROPN
esrj-31288	195	62	)	)	PUNCT
esrj-31288	195	63	1	1	NUM
esrj-31288	195	64	ui2	ui2	X
esrj-31288	196	1	=	=	PUNCT
esrj-31288	196	2	---cos	---cos	X
esrj-31288	196	3	(	(	PUNCT
esrj-31288	196	4	[	[	X
esrj-31288	196	5	3n)kn	3n)kn	NUM
esrj-31288	196	6	-	-	PUNCT
esrj-31288	196	7	i12	i12	PROPN
esrj-31288	196	8	vnsn	vnsn	NOUN
esrj-31288	196	9	'	'	PUNCT
esrj-31288	196	10	the	the	DET
esrj-31288	196	11	snell	snell	NOUN
esrj-31288	196	12	's	's	PART
esrj-31288	196	13	law	law	NOUN
esrj-31288	196	14	at	at	ADP
esrj-31288	196	15	the	the	DET
esrj-31288	196	16	anterior	anterior	ADJ
esrj-31288	196	17	surface	surface	NOUN
esrj-31288	196	18	of	of	ADP
esrj-31288	196	19	the	the	DET
esrj-31288	196	20	nth	nth	NOUN
esrj-31288	196	21	layer	layer	NOUN
esrj-31288	196	22	(	(	PUNCT
esrj-31288	196	23	a3	a3	NOUN
esrj-31288	196	24	)	)	PUNCT
esrj-31288	196	25	cos2([3n)=i	cos2([3n)=i	NOUN
esrj-31288	196	26	-	-	PUNCT
esrj-31288	196	27	sin2(an_1	sin2(an_1	NOUN
esrj-31288	196	28	)	)	PUNCT
esrj-31288	196	29	{	{	PUNCT
esrj-31288	196	30	vn	vn	X
esrj-31288	196	31	}	}	PUNCT
esrj-31288	196	32	2	2	NUM
esrj-31288	196	33	vn_1	vn_1	NOUN
esrj-31288	196	34	with	with	ADP
esrj-31288	196	35	angles	angle	NOUN
esrj-31288	196	36	an	an	DET
esrj-31288	196	37	-	-	PUNCT
esrj-31288	196	38	l	l	NOUN
esrj-31288	196	39	of	of	ADP
esrj-31288	196	40	incidence	incidence	NOUN
esrj-31288	196	41	and	and	CCONJ
esrj-31288	196	42	f3	f3	ADJ
esrj-31288	196	43	n	n	PRON
esrj-31288	196	44	oftransmission	oftransmission	NOUN
esrj-31288	196	45	,	,	PUNCT
esrj-31288	196	46	and	and	CCONJ
esrj-31288	196	47	the	the	DET
esrj-31288	196	48	interval	interval	NOUN
esrj-31288	196	49	velocity	velocity	NOUN
esrj-31288	196	50	(	(	PUNCT
esrj-31288	196	51	m	m	NOUN
esrj-31288	196	52	)	)	PUNCT
esrj-31288	196	53	2sn	2sn	ADJ
esrj-31288	196	54	vn	vn	PROPN
esrj-31288	196	55	=	=	SYM
esrj-31288	196	56	&	&	CCONJ
esrj-31288	196	57	(	(	PUNCT
esrj-31288	196	58	as	as	ADP
esrj-31288	196	59	)	)	PUNCT
esrj-31288	196	60	n	n	CCONJ
esrj-31288	196	61	in	in	ADP
esrj-31288	196	62	order	order	NOUN
esrj-31288	196	63	to	to	PART
esrj-31288	196	64	solve	solve	VERB
esrj-31288	196	65	(	(	PUNCT
esrj-31288	196	66	ai	ai	NOUN
esrj-31288	196	67	)	)	PUNCT
esrj-31288	196	68	,	,	PUNCT
esrj-31288	196	69	(	(	PUNCT
esrj-31288	196	70	a2	a2	PROPN
esrj-31288	196	71	)	)	PUNCT
esrj-31288	196	72	,	,	PUNCT
esrj-31288	196	73	(	(	PUNCT
esrj-31288	196	74	a3	a3	NOUN
esrj-31288	196	75	)	)	PUNCT
esrj-31288	196	76	,	,	PUNCT
esrj-31288	196	77	(	(	PUNCT
esrj-31288	196	78	a4	a4	NOUN
esrj-31288	196	79	)	)	PUNCT
esrj-31288	196	80	and	and	CCONJ
esrj-31288	196	81	(	(	PUNCT
esrj-31288	196	82	as	as	ADP
esrj-31288	196	83	)	)	PUNCT
esrj-31288	196	84	we	we	PRON
esrj-31288	196	85	will	will	AUX
esrj-31288	196	86	consider	consider	VERB
esrj-31288	196	87	five	five	NUM
esrj-31288	196	88	different	different	ADJ
esrj-31288	196	89	cases	case	NOUN
esrj-31288	196	90	:	:	PUNCT
esrj-31288	196	91	first	first	ADV
esrj-31288	196	92	:	:	PUNCT
esrj-31288	196	93	when	when	SCONJ
esrj-31288	196	94	k	k	PROPN
esrj-31288	196	95	n	n	CCONJ
esrj-31288	196	96	-	-	PUNCT
esrj-31288	196	97	i	i	NOUN
esrj-31288	196	98	,	,	PUNCT
esrj-31288	196	99	ll	ll	NOUN
esrj-31288	196	100	=	=	SYM
esrj-31288	196	101	k	k	PROPN
esrj-31288	196	102	n	n	CCONJ
esrj-31288	196	103	-	-	PUNCT
esrj-31288	196	104	i,12	i,12	VERB
esrj-31288	196	105	=	=	PUNCT
esrj-31288	196	106	k	k	X
esrj-31288	196	107	n-1,22	n-1,22	NOUN
esrj-31288	196	108	=	=	SYM
esrj-31288	196	109	0	0	NUM
esrj-31288	196	110	,	,	PUNCT
esrj-31288	196	111	i.e	i.e	PROPN
esrj-31288	196	112	,	,	PUNCT
esrj-31288	196	113	the	the	DET
esrj-31288	196	114	anterior	anterior	ADJ
esrj-31288	196	115	surface	surface	NOUN
esrj-31288	196	116	is	be	AUX
esrj-31288	196	117	a	a	DET
esrj-31288	196	118	flat	flat	ADJ
esrj-31288	196	119	one	one	NOUN
esrj-31288	196	120	,	,	PUNCT
esrj-31288	196	121	or	or	CCONJ
esrj-31288	196	122	when	when	SCONJ
esrj-31288	196	123	kn-1,12	kn-1,12	PROPN
esrj-31288	196	124	=	=	PUNCT
esrj-31288	196	125	kn_1,22	kn_1,22	PROPN
esrj-31288	196	126	=	=	SYM
esrj-31288	196	127	0	0	PROPN
esrj-31288	196	128	and	and	CCONJ
esrj-31288	196	129	kn_1,11	kn_1,11	PROPN
esrj-31288	196	130	'	'	PUNCT
esrj-31288	196	131	"	"	PUNCT
esrj-31288	196	132	0	0	NUM
esrj-31288	196	133	,	,	PUNCT
esrj-31288	196	134	substituting	substitute	VERB
esrj-31288	196	135	(	(	PUNCT
esrj-31288	196	136	as	as	ADP
esrj-31288	196	137	)	)	PUNCT
esrj-31288	196	138	in	in	ADP
esrj-31288	196	139	the	the	DET
esrj-31288	196	140	reduced	reduce	VERB
esrj-31288	196	141	equation	equation	NOUN
esrj-31288	196	142	(	(	PUNCT
esrj-31288	196	143	a3	a3	NOUN
esrj-31288	196	144	)	)	PUNCT
esrj-31288	196	145	(	(	PUNCT
esrj-31288	196	146	m	m	NOUN
esrj-31288	196	147	)	)	PUNCT
esrj-31288	196	148	second	second	ADJ
esrj-31288	196	149	:	:	PUNCT
esrj-31288	196	150	when	when	SCONJ
esrj-31288	196	151	k	k	PROPN
esrj-31288	196	152	n-1.i2	n-1.i2	PROPN
esrj-31288	196	153	*	*	NOUN
esrj-31288	196	154	0	0	NUM
esrj-31288	196	155	we	we	PRON
esrj-31288	196	156	use	use	VERB
esrj-31288	196	157	equations	equation	NOUN
esrj-31288	196	158	(	(	PUNCT
esrj-31288	196	159	a2	a2	PROPN
esrj-31288	196	160	)	)	PUNCT
esrj-31288	196	161	and	and	CCONJ
esrj-31288	196	162	(	(	PUNCT
esrj-31288	196	163	a4	a4	NOUN
esrj-31288	196	164	)	)	PUNCT
esrj-31288	196	165	to	to	PART
esrj-31288	196	166	get	get	VERB
esrj-31288	196	167	[	[	PUNCT
esrj-31288	196	168	k	k	X
esrj-31288	196	169	]	]	X
esrj-31288	196	170	2	2	NUM
esrj-31288	196	171	[	[	PUNCT
esrj-31288	196	172	22	22	NUM
esrj-31288	196	173	_	_	NOUN
esrj-31288	196	174	n-1,l2	n-1,l2	NOUN
esrj-31288	196	175	,	,	PUNCT
esrj-31288	196	176	2	2	NUM
esrj-31288	196	177	vn	vn	NOUN
esrj-31288	196	178	vn	vn	NOUN
esrj-31288	196	179	u	u	PROPN
esrj-31288	197	1	i	i	PRON
esrj-31288	197	2	sin	sin	VERB
esrj-31288	197	3	(	(	PUNCT
esrj-31288	197	4	0	0	NUM
esrj-31288	197	5	.	.	X
esrj-31288	198	1	n	n	PROPN
esrj-31288	198	2	i	i	NOUN
esrj-31288	198	3	)	)	PUNCT
esrj-31288	198	4	v	v	ADP
esrj-31288	198	5	2	2	NUM
esrj-31288	198	6	12	12	NUM
esrj-31288	198	7	~i	~i	PUNCT
esrj-31288	198	8	and	and	CCONJ
esrj-31288	198	9	finally	finally	ADV
esrj-31288	198	10	(	(	PUNCT
esrj-31288	198	11	a	a	DET
esrj-31288	198	12	7	7	NUM
esrj-31288	198	13	)	)	PUNCT
esrj-31288	198	14	vn=[kui2	vn=[kui2	NOUN
esrj-31288	198	15	]	]	PUNCT
esrj-31288	198	16	2+(sin~(~n	2+(sin~(~n	NUM
esrj-31288	198	17	-	-	PUNCT
esrj-31288	198	18	i)j	i)j	ADJ
esrj-31288	198	19	(	(	PUNCT
esrj-31288	198	20	a8	a8	PROPN
esrj-31288	198	21	)	)	PUNCT
esrj-31288	198	22	n-1.12	n-1.12	NOUN
esrj-31288	198	23	n	n	CCONJ
esrj-31288	198	24	-	-	PUNCT
esrj-31288	198	25	i	i	PRON
esrj-31288	198	26	third	third	NOUN
esrj-31288	198	27	:	:	PUNCT
esrj-31288	198	28	when	when	SCONJ
esrj-31288	198	29	k	k	PROPN
esrj-31288	198	30	n	n	CCONJ
esrj-31288	198	31	-	-	PUNCT
esrj-31288	198	32	l,12	l,12	PROPN
esrj-31288	198	33	=	=	SYM
esrj-31288	198	34	k	k	NOUN
esrj-31288	198	35	n	n	CCONJ
esrj-31288	198	36	-	-	PUNCT
esrj-31288	198	37	i	i	NOUN
esrj-31288	198	38	,	,	PUNCT
esrj-31288	198	39	ll	ll	NOUN
esrj-31288	198	40	=	=	SYM
esrj-31288	198	41	0	0	PROPN
esrj-31288	198	42	and	and	CCONJ
esrj-31288	198	43	k	k	PROPN
esrj-31288	198	44	n	n	CCONJ
esrj-31288	198	45	-	-	PUNCT
esrj-31288	198	46	i,22	i,22	X
esrj-31288	198	47	'	'	PUNCT
esrj-31288	198	48	"	"	PUNCT
esrj-31288	198	49	0	0	NUM
esrj-31288	199	1	we	we	PRON
esrj-31288	199	2	substitute	substitute	VERB
esrj-31288	199	3	(	(	PUNCT
esrj-31288	199	4	as	as	ADP
esrj-31288	199	5	)	)	PUNCT
esrj-31288	199	6	in	in	ADP
esrj-31288	199	7	(	(	PUNCT
esrj-31288	199	8	ai	ai	NOUN
esrj-31288	199	9	)	)	PUNCT
esrj-31288	199	10	_	_	NOUN
esrj-31288	199	11	1	1	NUM
esrj-31288	199	12	[	[	PUNCT
esrj-31288	199	13	1	1	NUM
esrj-31288	199	14	'	'	NUM
esrj-31288	199	15	2	2	NUM
esrj-31288	199	16	)	)	PUNCT
esrj-31288	199	17	v	v	NOUN
esrj-31288	199	18	;	;	PUNCT
esrj-31288	199	19	]	]	PUNCT
esrj-31288	199	20	ull	ull	PROPN
esrj-31288	199	21	-1sin	-1sin	PROPN
esrj-31288	199	22	(	(	PUNCT
esrj-31288	199	23	an-1	an-1	X
esrj-31288	199	24	-0vnsn	-0vnsn	VERB
esrj-31288	199	25	vn'_i	vn'_i	NOUN
esrj-31288	199	26	to	to	PART
esrj-31288	199	27	get	get	VERB
esrj-31288	199	28	(	(	PUNCT
esrj-31288	199	29	a9	a9	NOUN
esrj-31288	199	30	)	)	PUNCT
esrj-31288	199	31	v	v	NOUN
esrj-31288	200	1	i1tnu11	i1tnu11	NOUN
esrj-31288	200	2	+	+	NUM
esrj-31288	200	3	sin	sin	NOUN
esrj-31288	200	4	2	2	NUM
esrj-31288	200	5	(	(	PUNCT
esrj-31288	200	6	an_1	an_1	PROPN
esrj-31288	200	7	)	)	PUNCT
esrj-31288	200	8	n0	n0	NOUN
esrj-31288	200	9	(	(	PUNCT
esrj-31288	200	10	aid	aid	NOUN
esrj-31288	200	11	)	)	PUNCT
esrj-31288	200	12	2	2	NUM
esrj-31288	200	13	vn'_i	vn'_i	NOUN
esrj-31288	200	14	fourth	fourth	ADJ
esrj-31288	200	15	:	:	PUNCT
esrj-31288	200	16	when	when	SCONJ
esrj-31288	200	17	kn-1,22	kn-1,22	X
esrj-31288	200	18	*	*	PUNCT
esrj-31288	200	19	kn_1,1i	kn_1,1i	PROPN
esrj-31288	200	20	*	*	PUNCT
esrj-31288	200	21	0	0	NUM
esrj-31288	200	22	and	and	CCONJ
esrj-31288	200	23	kn-1,12	kn-1,12	PROPN
esrj-31288	200	24	=	=	SYM
esrj-31288	200	25	0	0	NUM
esrj-31288	200	26	we	we	PRON
esrj-31288	200	27	rewrite	rewrite	VERB
esrj-31288	200	28	equation	equation	NOUN
esrj-31288	200	29	(	(	PUNCT
esrj-31288	200	30	ai	ai	NOUN
esrj-31288	200	31	)	)	PUNCT
esrj-31288	200	32	cos	cos	ADP
esrj-31288	200	33	2	2	NUM
esrj-31288	200	34	(	(	PUNCT
esrj-31288	200	35	[	[	NOUN
esrj-31288	200	36	3n	3n	NUM
esrj-31288	200	37	)	)	PUNCT
esrj-31288	200	38	vnsnkn_1,11	vnsnkn_1,11	NOUN
esrj-31288	200	39	(	(	PUNCT
esrj-31288	200	40	a	a	DET
esrj-31288	200	41	it	it	NOUN
esrj-31288	200	42	)	)	PUNCT
esrj-31288	200	43	kn_i	kn_i	PROPN
esrj-31288	200	44	,	,	PUNCT
esrj-31288	200	45	ii	ii	NOUN
esrj-31288	200	46	and	and	CCONJ
esrj-31288	200	47	equation	equation	NOUN
esrj-31288	200	48	(	(	PUNCT
esrj-31288	200	49	a3	a3	PROPN
esrj-31288	200	50	)	)	PUNCT
esrj-31288	200	51	geofislca	geofislca	PROPN
esrj-31288	200	52	colombiana	colombiana	PROPN
esrj-31288	200	53	,	,	PUNCT
esrj-31288	200	54	5	5	NUM
esrj-31288	200	55	,	,	PUNCT
esrj-31288	200	56	diciembae	diciembae	NOUN
esrj-31288	200	57	de	de	X
esrj-31288	200	58	2001	2001	NUM
esrj-31288	200	59	~	~	SYM
esrj-31288	200	60	1	1	NUM
esrj-31288	200	61	cos(f3n	cos(f3n	PROPN
esrj-31288	200	62	)	)	PUNCT
esrj-31288	200	63	kn-1,22	kn-1,22	PROPN
esrj-31288	200	64	vnsnkn-1,22	vnsnkn-1,22	PROPN
esrj-31288	200	65	vn	vn	PROPN
esrj-31288	200	66	(	(	PUNCT
esrj-31288	200	67	ai2	ai2	NOUN
esrj-31288	200	68	)	)	PUNCT
esrj-31288	200	69	subtracting	subtract	VERB
esrj-31288	200	70	(	(	PUNCT
esrj-31288	200	71	a	a	DET
esrj-31288	200	72	12	12	NUM
esrj-31288	200	73	)	)	PUNCT
esrj-31288	200	74	from	from	ADP
esrj-31288	200	75	(	(	PUNCT
esrj-31288	200	76	a	a	DET
esrj-31288	200	77	1i	1i	NOUN
esrj-31288	200	78	)	)	PUNCT
esrj-31288	200	79	and	and	CCONJ
esrj-31288	200	80	factorizing	factorize	VERB
esrj-31288	200	81	the	the	DET
esrj-31288	200	82	factor	factor	NOUN
esrj-31288	200	83	vn	vn	PROPN
esrj-31288	200	84	sn	sn	PROPN
esrj-31288	201	1	we	we	PRON
esrj-31288	201	2	obtain	obtain	VERB
esrj-31288	201	3	v	v	ADP
esrj-31288	201	4	s	s	X
esrj-31288	201	5	(	(	PUNCT
esrj-31288	201	6	kn_1,ll	kn_1,ll	PROPN
esrj-31288	201	7	j+	j+	NUM
esrj-31288	201	8	~n	~n	NUM
esrj-31288	201	9	-	-	SYM
esrj-31288	201	10	l,11	l,11	NOUN
esrj-31288	201	11	=	=	SYM
esrj-31288	201	12	n	n	CCONJ
esrj-31288	201	13	null	null	ADJ
esrj-31288	201	14	ul2	ul2	VERB
esrj-31288	201	15	kn-1,12	kn-1,12	PROPN
esrj-31288	201	16	kn-1,12	kn-1,12	VERB
esrj-31288	201	17	1	1	NUM
esrj-31288	201	18	'	'	NUM
esrj-31288	201	19	2	2	NUM
esrj-31288	201	20	(	(	PUNCT
esrj-31288	201	21	)	)	PUNCT
esrj-31288	201	22	vn	vn	NOUN
esrj-31288	201	23	-	-	PUNCT
esrj-31288	201	24	sin	sin	NOUN
esrj-31288	201	25	an-1	an-1	X
esrj-31288	201	26	-vn_1	-vn_1	PROPN
esrj-31288	201	27	(	(	PUNCT
esrj-31288	201	28	ai3	ai3	NOUN
esrj-31288	201	29	)	)	PUNCT
esrj-31288	201	30	including	include	VERB
esrj-31288	201	31	(	(	PUNCT
esrj-31288	201	32	as	as	ADP
esrj-31288	201	33	)	)	PUNCT
esrj-31288	201	34	in	in	ADP
esrj-31288	201	35	(	(	PUNCT
esrj-31288	201	36	al3	al3	PROPN
esrj-31288	201	37	)	)	PUNCT
esrj-31288	201	38	and	and	CCONJ
esrj-31288	201	39	reorganizing	reorganize	VERB
esrj-31288	201	40	tenns	tenn	NOUN
esrj-31288	201	41	,	,	PUNCT
esrj-31288	201	42	the	the	DET
esrj-31288	201	43	interval	interval	NOUN
esrj-31288	201	44	velocity	velocity	NOUN
esrj-31288	201	45	is	be	AUX
esrj-31288	201	46	v	v	PRON
esrj-31288	201	47	-n(a	-n(a	PROPN
esrj-31288	201	48	14	14	NUM
esrj-31288	201	49	)	)	PUNCT
esrj-31288	202	1	r	r	NOUN
esrj-31288	202	2	:	:	PUNCT
esrj-31288	202	3	k	k	NOUN
esrj-31288	202	4	-	-	PUNCT
esrj-31288	202	5	i	i	PRON
esrj-31288	202	6	n	n	NOUN
esrj-31288	202	7	-	-	PUNCT
esrj-31288	202	8	i	i	PRON
esrj-31288	202	9	n	n	NOUN
esrj-31288	202	10	-	-	PUNCT
esrj-31288	202	11	i	i	PROPN
esrj-31288	202	12	,	,	PUNCT
esrj-31288	202	13	n	n	PRON
esrj-31288	202	14	fifth	fifth	ADJ
esrj-31288	202	15	:	:	PUNCT
esrj-31288	202	16	when	when	SCONJ
esrj-31288	202	17	kn-1,22	kn-1,22	PROPN
esrj-31288	202	18	=	=	SYM
esrj-31288	202	19	kn_1,11	kn_1,11	PROPN
esrj-31288	202	20	*	*	PUNCT
esrj-31288	202	21	0	0	NUM
esrj-31288	202	22	and	and	CCONJ
esrj-31288	202	23	kn-1,12	kn-1,12	PROPN
esrj-31288	202	24	=	=	PUNCT
esrj-31288	202	25	o	o	NOUN
esrj-31288	202	26	,	,	PUNCT
esrj-31288	202	27	i	i	PRON
esrj-31288	202	28	,	,	PUNCT
esrj-31288	202	29	e"theanterior	e"theanterior	ADJ
esrj-31288	202	30	surface	surface	NOUN
esrj-31288	202	31	is	be	AUX
esrj-31288	202	32	a	a	DET
esrj-31288	202	33	spherical	spherical	ADJ
esrj-31288	202	34	one	one	NOUN
esrj-31288	202	35	,	,	PUNCT
esrj-31288	202	36	from	from	ADP
esrj-31288	202	37	(	(	PUNCT
esrj-31288	202	38	a3	a3	NOUN
esrj-31288	202	39	)	)	PUNCT
esrj-31288	202	40	vnu22	vnu22	VERB
esrj-31288	202	41	kn-1,22	kn-1,22	PROPN
esrj-31288	202	42	(	(	PUNCT
esrj-31288	202	43	ais	ais	PROPN
esrj-31288	202	44	)	)	PUNCT
esrj-31288	202	45	and	and	CCONJ
esrj-31288	202	46	using	use	VERB
esrj-31288	202	47	(	(	PUNCT
esrj-31288	202	48	a4	a4	NOUN
esrj-31288	202	49	)	)	PUNCT
esrj-31288	202	50	in	in	ADP
esrj-31288	202	51	(	(	PUNCT
esrj-31288	202	52	a	a	PRON
esrj-31288	202	53	is	be	AUX
esrj-31288	202	54	)	)	PUNCT
esrj-31288	202	55	and	and	CCONJ
esrj-31288	202	56	squaring	square	VERB
esrj-31288	202	57	the	the	DET
esrj-31288	202	58	resulting	result	VERB
esrj-31288	202	59	expression	expression	NOUN
esrj-31288	202	60	we	we	PRON
esrj-31288	202	61	have	have	VERB
esrj-31288	202	62	1	1	NUM
esrj-31288	202	63	'	'	NUM
esrj-31288	202	64	2	2	NUM
esrj-31288	202	65	(	(	PUNCT
esrj-31288	202	66	)	)	PUNCT
esrj-31288	203	1	[	[	X
esrj-31288	203	2	vnj2-	vnj2-	X
esrj-31288	203	3	(	(	PUNCT
esrj-31288	203	4	1	1	NUM
esrj-31288	203	5	vnunj2	vnunj2	NOUN
esrj-31288	203	6	-	-	PUNCT
esrj-31288	203	7	sin	sin	VERB
esrj-31288	203	8	a	a	DET
esrj-31288	203	9	----n	----n	NOUN
esrj-31288	203	10	-	-	ADJ
esrj-31288	203	11	l	l	ADJ
esrj-31288	203	12	vn_1	vn_1	NOUN
esrj-31288	203	13	kn-1,22s	kn-1,22s	NOUN
esrj-31288	203	14	n	n	PRON
esrj-31288	203	15	kn-1,22	kn-1,22	NOUN
esrj-31288	203	16	and	and	CCONJ
esrj-31288	203	17	substituting	substituting	NOUN
esrj-31288	203	18	(	(	PUNCT
esrj-31288	203	19	as	as	ADP
esrj-31288	203	20	)	)	PUNCT
esrj-31288	203	21	in	in	ADP
esrj-31288	203	22	(	(	PUNCT
esrj-31288	203	23	a	a	DET
esrj-31288	203	24	16	16	NUM
esrj-31288	203	25	)	)	PUNCT
esrj-31288	203	26	(	(	PUNCT
esrj-31288	203	27	a	a	DET
esrj-31288	203	28	16	16	NUM
esrj-31288	203	29	)	)	PUNCT
esrj-31288	203	30	(	(	PUNCT
esrj-31288	203	31	a	a	DET
esrj-31288	203	32	17	17	NUM
esrj-31288	203	33	)	)	PUNCT
esrj-31288	203	34	the	the	DET
esrj-31288	203	35	expression	expression	NOUN
esrj-31288	203	36	(	(	PUNCT
esrj-31288	203	37	a	a	DET
esrj-31288	203	38	17	17	NUM
esrj-31288	203	39	)	)	PUNCT
esrj-31288	203	40	is	be	AUX
esrj-31288	203	41	reorganized	reorganize	VERB
esrj-31288	203	42	in	in	ADP
esrj-31288	203	43	terms	term	NOUN
esrj-31288	203	44	of	of	ADP
esrj-31288	203	45	vn	vn	PROPN
esrj-31288	203	46	(	(	PUNCT
esrj-31288	203	47	a	a	DET
esrj-31288	203	48	l8	l8	PROPN
esrj-31288	203	49	)	)	PUNCT
esrj-31288	203	50	the	the	DET
esrj-31288	203	51	expression	expression	NOUN
esrj-31288	203	52	(	(	PUNCT
esrj-31288	203	53	ai8	ai8	PROPN
esrj-31288	203	54	)	)	PUNCT
esrj-31288	203	55	has	have	VERB
esrj-31288	203	56	the	the	DET
esrj-31288	203	57	form	form	NOUN
esrj-31288	203	58	a(v[~	a(v[~	VERB
esrj-31288	203	59	)	)	PUNCT
esrj-31288	204	1	+	+	ADJ
esrj-31288	204	2	b(v	b(v	NOUN
esrj-31288	204	3	;	;	PUNCT
esrj-31288	204	4	)	)	PUNCT
esrj-31288	205	1	+	+	NOUN
esrj-31288	205	2	c	c	NOUN
esrj-31288	205	3	=	=	SYM
esrj-31288	205	4	0	0	NUM
esrj-31288	205	5	and	and	CCONJ
esrj-31288	205	6	its	its	PRON
esrj-31288	205	7	solution	solution	NOUN
esrj-31288	205	8	is	be	AUX
esrj-31288	205	9	given	give	VERB
esrj-31288	205	10	by	by	ADP
esrj-31288	205	11	v~	v~	PROPN
esrj-31288	205	12	=	=	SYM
esrj-31288	205	13	(	(	PUNCT
esrj-31288	205	14	2a)-1	2a)-1	NOUN
esrj-31288	205	15	(	(	PUNCT
esrj-31288	205	16	-b	-b	PUNCT
esrj-31288	205	17	±.j	±.j	PROPN
esrj-31288	205	18	b2	b2	NOUN
esrj-31288	205	19	4ac	4ac	NOUN
esrj-31288	205	20	)	)	PUNCT
esrj-31288	205	21	,	,	PUNCT
esrj-31288	205	22	in	in	ADP
esrj-31288	205	23	consequence	consequence	NOUN
esrj-31288	205	24	the	the	DET
esrj-31288	205	25	square	square	NOUN
esrj-31288	205	26	of	of	ADP
esrj-31288	205	27	the	the	DET
esrj-31288	205	28	interval	interval	NOUN
esrj-31288	205	29	velocity	velocity	NOUN
esrj-31288	205	30	can	can	AUX
esrj-31288	205	31	be	be	AUX
esrj-31288	205	32	known	know	VERB
esrj-31288	205	33	but	but	CCONJ
esrj-31288	205	34	there	there	PRON
esrj-31288	205	35	is	be	VERB
esrj-31288	205	36	an	an	DET
esrj-31288	205	37	ambiguity	ambiguity	NOUN
esrj-31288	205	38	to	to	PART
esrj-31288	205	39	determine	determine	VERB
esrj-31288	205	40	the	the	DET
esrj-31288	205	41	interval	interval	NOUN
esrj-31288	205	42	,	,	PUNCT
esrj-31288	205	43	i.e.	i.e.	X
esrj-31288	205	44	,	,	PUNCT
esrj-31288	205	45	the	the	DET
esrj-31288	205	46	unique	unique	ADJ
esrj-31288	205	47	solution	solution	NOUN
esrj-31288	205	48	does	do	AUX
esrj-31288	205	49	not	not	PART
esrj-31288	205	50	exist	exist	VERB
esrj-31288	205	51	for	for	ADP
esrj-31288	205	52	this	this	DET
esrj-31288	205	53	particular	particular	ADJ
esrj-31288	205	54	situation	situation	NOUN
esrj-31288	205	55	.	.	PUNCT
esrj-31288	206	1	the	the	DET
esrj-31288	206	2	result	result	NOUN
esrj-31288	206	3	shown	show	VERB
esrj-31288	206	4	here	here	ADV
esrj-31288	206	5	was	be	AUX
esrj-31288	206	6	first	first	ADV
esrj-31288	206	7	reported	report	VERB
esrj-31288	206	8	by	by	ADP
esrj-31288	206	9	kahn	kahn	PROPN
esrj-31288	206	10	(	(	PUNCT
esrj-31288	206	11	1987	1987	NUM
esrj-31288	206	12	)	)	PUNCT
esrj-31288	206	13	and	and	CCONJ
esrj-31288	206	14	later	later	ADV
esrj-31288	206	15	by	by	ADP
esrj-31288	206	16	krey	krey	PROPN
esrj-31288	206	17	(	(	PUNCT
esrj-31288	206	18	1989	1989	NUM
esrj-31288	206	19	)	)	PUNCT
esrj-31288	206	20	.	.	PUNCT
esrj-31288	207	1	11	11	NUM