On amplitudes of P near the shadow zone (*) I. L E U M A N N Some years ago I iliade a studv (Leh- m a n u 1953) in order to find out whetlier or not t h e r e was a sudden drop in t h e P amplitude a t 105° or another neiglibouring distance m a r k i n g clearly t h e beginning of the shadow zone. I made use p a r t l y of the I.S.S. d a t a and p a r t l y of Copenhagen records. I t is well known t h a t P is often recorded at distances greater tlian 105°, b u t usually it is small and it is considered to be a dif- fracted wave. I found, however, t h a t in the I.S.S. t h e r e were sometimes series of P entries u p to 110° or more t h e residuals of wliich were consistenti enough to show t h a t t h e onset was sharp and therefore not likely t o be due to a diffracted wave. On the otlier h a n d I sometimes found t h a t P of a n e a r t h q u a k e had considerable uncer- t a i n t y al ready a t distances of a b o u t 95° or so and y e t was recorded beyond 105° as if no deerease of amplitude took place at t h a t distance. Using- Copenhagen re- cords I found also t h a t in some earthquakes P was very clearly recorded u p to and con- siderably beyond 105° while in otlier earth- quakes of similar magnitude P became small and insignificant already a t distances smaller t h a n 100°. Thus t h e variation of amplitude with distance is diiferent in dif- ferente earthquakes. The shadow zone seems to begin a t diiferent distances and it is usually not possible to say exactly wliere it begins; there is no sudden deerease of a m p l i t u d e to m a r k its boundaiy. A t t h e Laniont Geologica! Observatory the surface waves of the Samo aearthquake (*) L a m o n t G e o l o g i c a l O b s e r v a t o r y (Co- l u m b i a U n i v e r s i t y ) C o n t r i b u t i o n N ° 319. 14 Aprii 1957 were being studied witli t h e object of fìnding variations of phase velo- city and hence of crustal thickness aerosa t h e United States and Canada. 51 records of short-period vertical m s t r u m e n t s had been collected. They were from epicentral distances ranging from 71° to 114°. I t was suggested to me b y Dr. Ewing t h a t I examine t h e records for t h e greatest dis- tances in order to see how P varied near t h e shadow zone. I t was immediately apparent t h a t there was a considerable drop in amplitude from t h e nearer t o the greatest epicentral dis- tances, b u t it was clear also t h a t no precise determination of the variation of amplitude with distance could be iliade, for t h e in- struments varied and their responso was not a c c m a t e l y known. Also, t h e distances are subject to errors, an epicentre in t h e Sa- moan region not being determinable with great precision. However, t h e two indepen- dent determinations of t h e U.S.C.G.S. and the Central Bureau at Strasbourg differed by less t h a n 1°. The seismological stations are not evenly distributed over t h e continent. There are a great m a n y stations in the western p a r t and t h e y were a t epicentral distances ran- ging from 71° to 84°. There were 10 stations in the eastern p a r t a t distances greater t h a n 100° and t h e r e were not m a n y stations in between. P amplitudes were very large a t t h e western stations, t h e phase being marked by a group, or two groups, of large swings continuing for about a minute. The wave period was two seeonds or a little less. E a p i d City a t an epicentral distance of 87° stili had very large amplitudes thougli 154 I. L E U M A N N somewhat smaller t h a n tlie western sta- tions. Fayetteville a t 90°.4, however, hacl considerably smaller amplitudes though t h e phase was stili quite large. Columbia a t d i s t a n t e 100°.2 was the nearest of t h e 10 stations a t distances greater t h a n 100° and Halifax at 114° 6 t h e most distant. This station and Palisades a t 106°.9 did not record P , b u t ali the others did record it. greater magniftcation t h a n the Spreng- nether i n s t r u m e n t in the period range in question, b u t tliat would be of no avail if t h e core b o u n d a r y were grazed b y tlie ray emerging at 105°. I t is obvious t h a t the p a t h to Shawinigan Falls has t h e sanie general character as tliose to t h e nearer stations and t h a t t h e waves recorded are not difEracted waves. The reason w h y the Cleveland record is shown and not tlie one S a m o a e a r t h q u a k e r e c o r d e d a t C l e v e l a n d , A = 101°, 3 Tlie Cleveland record from epicentral distance 101°.3 is shown in the figure. I t is from a Sprengnether short-period ver- tical i n s t r u m e n t . Tlie P amplitudes are here quite small as compared with tliose a t the western stations. Where and how quickly t h e amplitudes fall off cannot be said because of a lack of stations a t intermediate distances. The wave period is about 2 sec. as a t t h e smaller distances. The Kirkland Lake record from a dis- tance of 103°.4 is almost exactly like t h e Cleveland record. The p a t t e r n is the sanie and t h e amplitudes are equal. I t is also from a Sprengnether instrument. Chapel Hill at 102°.2 has similar amplitudes b u t t h e p a t t e r n is dilferent; there is not the same division of t h e phase. I t is somewhat surprising to And t h a t Shawinigan Falls a t an epicentral distance of 108°.2 has a record similar to t h e Cle- veland record and only slightly smaller. Tlie p a t t e r n is t h e sanie and t h e waves have period of about 2 sec. The seismograph is a Willmore instrument and it m a y have from Shawinigan Falls is t h a t t h e trace of t h e lattei- is a little fainter. Of t h e other stations beyond 100° Co- lumbia a t 100°.2 has a much smaller P phase t h a n tlie stations mentioned, but t h e p a t t e r n is the same. This is also trae for Ottawa a t 106°.0. Montreal at 107°.5 has quite a small b u t distinct P. State College a t 103°.9 has also a clear but small P. W e have seen t h a t t h e P amplitudes are small in t h e 8° range of distance 100° to 108°. No precise determination of the variation of amplitude with distance can be iliade, not even for t h e distances of tlie m a n y western stations, but t h e decrease of amplitude between 84° and 100° is very great, undoubtedly f a r greater t h a n the decrease between 71° and 84°. The strong decrease of amplitude will be due to a m a r k e d decrease of velocity gradient at deptli. The lack of observations a t inter- mediate distances makes it impossible to say whether t h e decrease is graduai or ab- r u p t or to determine even roughly the deptli ON A M P L I T U D E S OF P N E A R T H E S H A D O W ZONE 155 at which it occurs. B u t our fìnding is in suppoi't of t h e assumption t h a t K . E . Bul- len's region D divides itself into two re- gions of wliich the inner one, D", is cliarac- terised by a velocity gradient t h a t is very small and distinctly smaller t h a n t h a t of D' (see e. g. Bullen 1956). The f a c t t h a t t h e time-curve straightens before t h e shadow zone is reached has led to this result. The Jeffreys-Bullen P curve straightens a t about 90° and has very little curvature from t h e r e onwards. The Samoa P curve runs practically parallel to it a t these distances. I t does not, however, r u n parallel to the J.-B. curve ali t h e way f r o m 70° to 108°. Taking t h e t i m e of occurrence of t h e earth- quake to be 19:17:57 as determined by t h e U.S.C.G.S. we fincl t h e following mean residuals: 70° - 75° 10 observations 0S.96±0S.17 75° - 80° 8 » l s . 6 9 ± 0 s . l l 100° - 108°.2 8 » 2S.39±0S.17 There is some scatter of t h e residuals near 85°. Between 90° and 100° there are only 1 observations; t h e mean of their residuals is 2S.23 ± 0S.22. The azimuths of ali the observing stations is between 30° and 58° so it is evident t h a t the Samoa earthquake P curve is steeper t h a n t h e J.-B. curve from 70° up to about 90°. The distances taken were geographie distances, b u t el- lipticity corrections were applied to t h e transmission times. Silice the amplitude of t h e direct P wave usually is quite small a t t h e greatest distances where it occurs it will not be easy to decide whether a P phase as recorded is due to a direct or to a diffracted wave and to iind where the shadow zone begins. There is as a rule no short period waves in distant P's, and this has been t a k e n to indicate diffraction. W h e t h e r it is a sure criterion is not known and it is not appli- catale unless t h e recording instruments have a good response to short period waves. I t does not seem to have been a t t e m p t e d to fix the beginning of the shadow zone of an individuai earthquake by a method similar to the one applied here, by direct compar- ison of records. To obtain definite results it would be necessary to clioose earthquakes well recorded a t the distances in question by a dense net-work of stations as e. g. t h a t of western Xortli America. Stations equipped witli short period instruiiients would be required and it would be higlily desh'able t h a t the relative response of the instruments as mounted should be known. This lattei' requirement is not easily ful- fìlled, b u t it m a y be indispensable if we are to succeed in deriving more detailed knowledge about t h e E a r t h ' s interior from seismological d a t a . Unless the error in t h e epicentre is unu- sually large, Shawinigan Falls is a t an epicentral distance greater t h a n 105°, and t h e shadow zone of our Samoan shock does not begin a t this distance. Taking t h e direct P ray to reach out to different epicentral distances in diiferent shocks, and t h e relative amplitudes to dif- fer, we shall have to look for a possible explanation, and we find t h a t slight region- al variations in t h e coniposition of the region D" would account for it. The ve- locity gradient in D" is quite small and a small regional variation would alter slightly t h e curvature in D" of t h e rays having their deepest points in t h e region. The rays are long and therefore a small bending or straightening of t h e m in their deepest portion would give rise to an appreciable change in t h e epicentral distance a t wliich t h e y emerged. I t would alter also t h e spreading of the rays and therefore affect amplitudes. Actually it is not known a t present whether t h e difference in a m p h t u d e variation is regionally conditioned, but it would be of great interest to have it in- vestigated. My t h a n k s are due to Dr. Maurice Ewing by whose kind invitation I worked a t t h e Lamont Geologica! Observatory and who allowed me to use the records of t h e Samoa earthquake collected there. Silice t h e precedili»' was written the study by A. Vogel: Uber Unregelmàssig- keiten der àusseren Begrenzung des Erd- kerns (doctor's tliesis, not printed) has become known to me. Observed regional variations in the transmission times of t h e ] 56 I. L E U M A N N waves reflected a t the core boundary are p u t down to irregularities in this boundary. Undulations in t h e core boundary would account also for t h e sliadow zone for P beginning a t diflerent epicentral distances in different earthquakes, b u t not for t h e observed differences in amplitude variation They seem to require for their explanation t h e (additional) assumption of regional variation of velocity in D " . ABSTRACT 51 short-period vertical North American and Canadian records of the Samoa earth- quake 14 Aprii 1957 were examined. Am- plitudes of P ivere very largo at the western stations (A < 84°) and small at the stations to the cast, 8 of which recorded P at distances greater than 100°. There ivas a lack of stations at intermediate distances. At the greatest distance, 108°.2, the P waves were not diffracted ioaves, for the pliase had the same general character as at sliorter distances-, the period, ivas 2 sec. From 70° to about 90° the Samoa P timedistance curve is steeper than the J.-B. curve. It had been found previously that from about 900 epicentral distance onivards the variation of the P amplitude with distance ivas not always the same and also that the sliadow zone seemed to begin at different distances. It is suggested that this be due to small regional differences of velocity in the deepest layer D" of the mantle. RIASSUNTO Sono state prese in esame 51 registrazioni della componente verticale a corto periodo, relative al Nord America e al Canadà, del terremoto di Samoa del 14 Aprile 1957. Le ampiezze della P sono molto grandi presso le stazioni occidentali (A < 84°) e piccole presso quelle orientali, 8 delle quali registrarono la P ad una distanza maggiore di 100 C'è stato un ritardo nelle stazioni a di- stanza intermedia. Alla distanza massima, 108°.2, le onde P non furono onde diffratte, poiché la fase ha avuto lo stesso carattere generale di quella registrata a distanza mi- nore-, il periodo fu di 2 sec. Da 70° a circa 90° la curva tempo-distanza delle P del terremoto di Samoa, è più ripida di quella J.-B. È stato precedentemente trovato che da una distanza epicentrale di circa 90° ed oltre, la variazione dell'ampiezza della P con la distanza, non era sempre la stessa e inoltre che la zona d'ombra sembrava cominciare a distanze diverse. Si fa l'ipotesi che ciò sia dovuto a piccole differenze regionali nello strato più pro- fondo D" del mantello. R E F E R E N C E S BULLEN, K . E . , Seismology and the broad structure of the Earth's interior. « P h y s i c s and C h e m i s t r y of t l i e E a r t h », 1, 68-93. P e r - g a m o n Press, 1956. LEUMANN, I., On the shadow of the Earth's core. « B u l l . Seismol. Soc. A i n e r . », 4 3 , 291- 306. 1953.