S-P c o n v e r s i o n at the base o f the crust M . B A T H - E . S T E F A N S S O N R i c e v u t o il 7 M a r z o 1966 SUJIMAEY. — T l i e l o n g - p e r i o d s e i s m i c r e c o r d s a t U m e à ( S w e d e n ) of a n i n t e r m e d i a t e - d e p t h e a r t h q u a k e i n B u r m a 011 27 F e b r u a r y , 1964, e x h i b i t a n e x c e p t i o n a l l y c l e a r c a s e of 8-P c o n v e r s i o n a t t h e M o h o r o v i c i é d i s c o n t - i n u i t y . T h e r e c o r d s a r e e x a m i n e d f r o m v a r i o u s p o i n t s of v i e w ( a r r i v a l t i m e s , a m p l i t u d e r a t i o s , p a r t i c l e m o t i o n s ) a n d c o m p a r i s o n s a r e m a d e f o r e a c h t e s t b e t w e e n o b s e r v a t i o n s a n d t h e o r y . G e n e r a l a s p e c t s of m o d e c o n - v e r s i o n s a t t h e b a s e of t h e c r u s t a r e d i s c u s s e d , b o t h t h e i r i m p o r t a n c e a n d w h y t h e y a r e so s e l d o m o b s e r v e d . RIASSUNTO. — I l t e r r e m o t o d i B u r m a del 27 F e b b r a i o 1964 ( p r o f o n - d i t à i n t e r m e d i a ) , r e g i s t r a t o s u l l u n g o p e r i o d o d e l l a s t a z i o n e d i U m e à ( S v e z i a ) , m o s t r a u n c a s o e c c e z i o n a l m e n t e c h i a r o d i c o n v e r s i o n e d i o n d e S - P a l l a d i s c o n t i n u i t à d i M o l i o r o v i c i c . I s i s m o g r a m m i s o n o s t a t i e s a m i n a t i d a v a r i p u n t i d i v i s t a ( t e m p i d i a r r i v o , r a p p o r t i f r a le a m p i e z z e , m o v i m e n t i di p a r t i c e l l e . . .) e p e r o g n u n o d i essi è s t a t o f a t t o il c o n f r o n t o f r a d a t i di os- s e r v a z i o n e e t e o r i a . V e n g o n o d i s c u s s i , i n o l t r e , gli a s p e t t i g e n e r a l i d e l m o d o di c o n v e r s i o n e a l l a b a s e d e l l a c r o s t a , i n s i e m e a l l a l o r o i m p o r t a n z a e d al p e r c h é p o s s o n o o s s e r v a r s i t a n t o r a r a m e n t e . I N T R O D U C T I O N . F o r seismic waves which do not penetrate deeper than the m a n t l e (that is, lip to about 103° distance), t h e most pronounced internal dis- continuity encountered during the propagation is t h e base of the crust, the Mohorovicic discontinuity. A t this surface, not only reflections and refractions occur, b u t also conversions of 8 to P and of P to 8. Such phenomena m a y occur both near the hypocenter and near the station as well as in between (for reflected waves). Due to t h e relative p r o x i m i t y of the Moho to t h e E a r t h ' s surface, waves deriving f r o m Moho arrive only within a few seconds f r o m the p a r e n t waves. This naturally often makes it difficult to discover such waves. They m a y be 1 2 0 M. B A T H - R. S T E F A N S S O N immersed in already existing motion, as e.g. for P-S converted waves which arrive a few seconds a f t e r P. The S-P converted waves, on the other h a n d , arrive before the t r u e S and m a y therefore be easier to discover. They are also of great significance as t h e y m a y give rise to too early, false readings of S. The relative difficulty to establish reliably the existence of Moho- derived waves is the probable explanation why the seismological li- t e r a t u r e contains only some scattered information on this point. Be- floctions against Moho f r o m below will give rise to too early arrivals (as sometimes observed for PP). Such reflections were studied b y Choudhury (1958) and Treskov (1961) and were used for estimating erustal thickness a t t h e reflection point. Reflections against Moho f r o m above have been observed repeatedly in seismic field investigations (see e.g. B a t h and Tryggvason, 1962). PS converted waves were reviewed b y Cook, Algermissen and Costain (1962) and SP converted waves were studied b y P a c h a d z h a n o v a (1962). Additional references can be found in t h e papers mentioned. Also more complicated wave p a t h s , involving multiple passages between Moho a n d t h e E a r t h ' s surface, have been reported in t h e l i t e r a t u r e (see e.g. J u n - J u , 1965). The present p a p e r explores records of SP converted waves obtained a t Umea (Sweden) f r o m an intermediate-depth e a r t h q u a k e in B u r m a . Of the publications mentioned, it has t h e closest relations to the paper by P a c h a d z h a n o v a (1962). I t will be convenient to h a v e some notation for Moho-derived waves and we are suggesting the following scheme, which is constructed in conformity with existing wave notations: 1) Ps for PS converted waves, and Sp for SP converted waves (conforming to t h e rule t h a t small letters, s and p, are used for waves which p r o p a g a t e only upwards). 2) PmP, Pmp and pmP for reflected waves (in conformity with PcP; this n o t a t i o n was suggested b y Choudhury, 1958). m can be used to denote reflection against Moho f r o m either side. 3) More complicated wave p a t h s can t h e n be easily described in t h e same system. F o r example, SpPmp is an incident S against Molio f r o m below, which is converted into P , t h e n reflected as P against the surface and a f t e r t h a t against Moho, before it finally arrives a t the surface. 4) I n case of more t h a n one layer, indices 1 , 2 , 3 , . . . referring to t h e respective layers, should be added to the symbols. S - P C O N V E R S I O N AT T H E B A S E OF T H E CUUST 1 2 1 O B S E R V A T I O N A L D A T A . U.S. Coast and Geodetic Survey reports t h e following d a t a for t h e investigated e a r t h q u a k e : D a t e a n d origin t i m e : 27 F e b r u a r y , 1964, 15h10m48s8 GMT. Epicenter coordinates: 21°.7 N, 94°.4 E (Burma). Focal d e p t h : 102 k m . Magnitude (Uppsala, Iviruna): 6 . 5 . Recording s t a t i o n U m e a (Sweden): 6 3 ° 4 8 ' . 9 N , 2 0 ° 1 4 ' . 2 E . I n s t r u m e n t s : long-period standardized Press-Ewing seismographs (T0 = 15 sec, Ta = 100 sec). ? r - i rr-S /VM^W^V/V '̂AVVV '̂̂ V^/'̂ VAV \ v ^ Y w W W V M v r w y - ^ V • V 1 " A . . J . . . 1 Wwwvi/V y t / v a A j ^ ^ ^ ^ ^ \lAl\iy m h / Ì F i g . 1 - S - w a v e g r o u p r e c o r d e d b y U m e a l o n g - p e r i o d s e i s m o g r a p h s B u r m a e a r t h q u a k e 27 F e b r u a r y , 1964. T i m e i n c r e a s e s f r o m l e f t t o a n d t h e r e is o n e m i n u t e b e t w e e n e a c h t i m e m a r k . f r o m r i g h t E p i c e n t r a l distance: 63°.8. Epicenter azimuth a t t h e station: 94° (i.e. only 4° south of east). Time reading (see records in Fig. 1) for fif (actually Sp) on E: 15h29m31s. Time difference = 6 . 3 sec. 1 2 2 M. B Â T H - R . S T E F A N S S O N Amplitude readings are summarized in Table I. Resolving t h e motion into $ 7 , SH a n d Sp components we find (u = horizontal component, w — vertical component): uSv = 1 7 . 8 m m WD (i.e. directed west and down), us a = 2 0 . 7 m m NE (i.e. directed n o r t h and east), Usp = 4 . 2 m m ED (i.e. directed east and down). T a b l e I - AMPLITUDE READINGS ( m m t r a c e a m p l i t u d e ) C o m p o n e n t Sp S E 4 . 2 E 1 6 . 3 W N — 2 1 . 9 N Z 2 . 8 D 5 . 6 D D i r e c t i o n of m o t i o n is i n d i c a t e d b y : E = e a s t N = n o r t h W = w e s t D = d o w n . W e t h e n f o r m t h e following ratios: Usv : usp = 4 . 2 and wSv : wSP — 2 . 0 . [1] Trace amplitudes can be used as the periods of Sp and S are prac- tically t h e same (8-10 sec) and we use only ratios of amplitudes in the following. The Sp-S doublet is most pronounced on t h e -B-coinponent, as expected, and t h e r e is no trace of Sp on the jV-component, The 2-component shows a more complicated motion prior to S, and on Z we h a v e measured t h e amplitudes which coincide with E. I t should be added t h a t t h e phase here interpreted as Sp is a signi- ficant onset and it cannot be explained as due to microseisms. A R R I V A L T I M E S . a) - Absolute arrival times. The Jeffreys-Bullen (1940) tables give a t o t a l travel time for S of 18 min 4 8 . 7 sec for t h e given focal d a t a . This means a computed arrival time of S a t 15h29m37s5. This is in good agreement with the S-reading, whereas t h e $p-phase arrives about 6 sec T a b l e I I - C R U S T A L M O D E L S U S E 1 ) . M o d e l C h a r a c t e r i s t i c s C r u s t a l v e l o c i t i e s k m / s e c P 8 M a n t l e v e l o c i t i e s k m / s e c P S C r u s t a l t h i c k n e s s k m R e f e r e n c e A S i n g l e - l a y e r e d c r u s t 6 . 3 4 3 . 6 6 8 . 2 0 4 . 7 3 35 R i c h t e r (1958) B » » » 6 . 5 7 3 . 7 7 8 . 1 8 4 . 6 2 35 Sellevoll (1964) 0 T w o - l a y e r e d c r u s t ( 6 . 1 0 j 6 . 6 5 i 3 . 5 0 I 3 . 7 5 8 . 2 0 4 . 6 0 2 0 + 1 3 S a a s t a m o i n e n (1963) D S a m e a s A b u t Molio s l o p i n g 3° w e s t w a r d s , E a r t h ' s s u r f a c e h o r i z o n t a l 6 . 3 4 3 . 6 6 8 . 2 0 4 . 7 3 35 I1) E S a m e a s A, b u t a n g l e of inci- d e n c e is 33° i n s t e a d of 30° 6 . 3 4 3 . 6 6 8 . 2 0 4 . 7 3 35 (!) V e r t i c a l l y b e n e a t h t h e s t a t i o n . o o 2! H O H a H o w Ci to co 1 2 4 M. BATII - K. S T E F Á N S S O N earlier t h a n this time. There is almost exact agreement between the observed and calculated arrival times of P . b) - Time difference S-Sp. W i t h the notation of Fig. 2, we get t h e following formula for the time difference S-Sp: a, „ / c o s t ' s cos i'p\ ro, A t = H \ r , - r , ) 1 2 1 SV Earth's s u r f a c e y — w u Moho F i g . 2 - S c h c m a t i c a l p i c t u r e s h o w i n g t h e w a v e p r o p a g a t i o n ( i n c i d e n t S a t M o h o f r o m u n d e r n e a t h , SV a n d Sp i n t h e c r u s t ) . T h e h e a v y , o p e n a r r o w s i n d i c a t e t h e d i r e c t i o n of first m o t i o n a n d r e l a t i v e a m p l i t u d e s . Obviously, we h a v e to make some assumptions about the crustal struc- t u r e under t h e station in order t o apply equation [2]. The models which were used are given in Table I I . Model B represents an average of available measurements in Fenno- scandia for t h e lower crust a n d the upper m a n t l e . Model G is based on explosion studies in Finland in 1959-1961. I n Model D a moderate westward slope of t h e Moho has been introduced, such as could be expected f r o m t h e general topography of t h e area around Umea. The angles of incidence, calculated b y Ritsema's (1958) tables, are subject t o some uncertainties and therefore also a Model E was calculated, the same structure as A b u t with an angle of incidence of S from below to Moho of 33° instead of 30°. S - P C O N V E R S I O N AT T H E B A S E OF T H E C U U S T 1 2 5 The calculated time differences S-Sp are given in Table I I I , which also gives t h e crostili thicknesses necessary to give t h e observed time difference of 6 . 3 sec. Despite t h e differences between observed and calculated values, there is no doubt t h a t t h e agreement is satisfactory, taking error limits into account. The measured time difference of 6.3 sec has an error of a t least ± 0-4 sec, a n d t h e requested crustal thickness is only slightly above 40 k m . This thickness is verified b y phase ve- locities of surface waves (Tryggvason, 1961, and Crampin, 1964). Taking also t h e u n c e r t a i n t y in the assumed velocities into account, we can safely say t h a t our observation falls within reasonable limits. A M P L I T U D E R A T I O S . Classical theory was applied to calculate t h e transmission across the Mohorovicic discontinuity (Costain, Cook and Algermissen, 1963), assuming a density ratio of 0.8 a t t h e b o u n d a r y and a Poisson ratio of 0.25. The amplitudes incident a t the E a r t h ' s surface calculated in this way, were converted into ground displacements b y means of Gu- tenberg's (1944) graphs. The calculated amplitude ratios (Table I I I ) are then directly comparable with the observed ratios [1]. T a b l e I I I - T I M E D I F F E R E N C E S A N D A M P L I T U D E R A T I O S F O R G I V E N M O D E L S . M o d e l T i m e d i f f e r e n c e S-Sp sec C r u s t a l t h i c k n e s s ( k m ) f o r t i m e d i f f e r e n c e S-Sp = 6 . 3 sec A m p l i t u d e r a t i o s usv'MSP WSV-WSP A 4 . 8 46 5 . 3 2 . 8 B 4 . 7 47 5 . 9 3 . 4 G 4 . 7 D 4 . 8 46 4 . 5 2 . 3 E 4 . 9 4 5 4 . 3 2 . 8 We find t h a t Models D and E give t h e best agreement. Taking into account t h a t t h e error limits of the observed ratios [1] can be estim- ated as a b o u t ± 0.4, the agreement with Models D and E is satisfactory. This m a y even be t a k e n as a suggestion t h a t Moho is in f a c t gently sloping westwards in t h e Umea area- 1 2 6 M. B Â T I I - II. S T E F Â N S S O N [4] P A R T I C L E M O T I O N . a) - Direction of first motion. With common notations (see B â t h , 1961) we h a v e : iw D

a; Sz i s 3a; with ip = B exp [ilc (x + ßz — coi)] + B, exp [¿7c (x — ßz — wt)] > y = B' exp [ilc (x + ß'z — cot)] 0 = exp [¿7c (x — az — coi)] 0, iv < 0, and for t h e t r a n s m i t t e d SV t h a t u > (I, w < 0, and for t h e t r a n s m i t t e d P ( S p ) t h a t u < 0, to < 0, because t h e ratios B'\B and A!/B are real and positive (B'\B = + 0.90 and A!\B = + 0.29 according to B a t h , 1961, table 3, for e = 60°). These theoretical displacements are shown in Fig. 2 and t h e y agree with the observations (Fig. 1). The f a c t t h a t t h e first motion of Sp is opposite to t h a t of SV on t h e horizontal (7?) component, certainly facilitates its discovery, as distinct from t h e vertical component where Sp and SV have t h e same sign. b) - Total particle motion. W e have so f a r been considering only the first onsets of t h e respective waves. E x a m i n i n g the entire particle motion we find t h a t it is nearly linear both for Sp and for S, and t h a t S - P C O N V E R S I O N AT T H E B A S E OF T H E C U U S T 1 2 7 t h e motions of b o t h waves agree closely with theoretically expected motions (assuming Model A). The minor deviations can be explained p a r t l y b y readiDg difficulties, especially of Sp on the vertical component, p a r t l y b y inaccuracies in t h e angles of incidence. Anyway, t h e r e is no doubt t h a t Sp is a longitudinal wave related to SV as expected from theory. D I S C U S S I O N . Considering b o t h t h e error limits in t h e observations and inevitable uncertainties in t h e theoretical models, we conclude t h a t t h e interpre- tation of t h e $p-phase is convincing. This is t h e simplest interpreta- tion, and as it has proven successful there is no need for investigation of more complicated wave propagations. Moreover, comparisons of observations and theoretical models suggest a crustal thickness of about 40-45 k m in t h e U m e a area, with t h e Moliorovicic discontinuity pos- sibly sloping gently westwards. I t is a justified question w h y this phenomenon is observed so seldom. A correct s t a t e m e n t would probably be to say t h a t it exists much more frequently t h a n generally realized, b u t it is only seldom t h a t very clear cases are observed. There are a n u m b e r of factors which contribute to this effect: 1) I t is advantageous for discovery t h a t t h e direction t o t h e epicenter coincides with one of t h e cardinal directions, as otherwise a n y earlier wave wTill show up on b o t h E and N components and will easily escape detection. 2) I t should show u p on the Z-component independent of azimuth, b u t Z is usually b a d for the /S'-wave group, and S is generally read from t h e horizontal components. 3) Certain angles of incidence a t Moho f r o m below are more favourable for S-P conversion t h a n others. This means t h a t certain distances in combination with certain slopes of the Moho discontinuity are more favourable t h a n others (see B a t h , 1961). 4) The ratios of ground displacements (i.e. corresponding t o re- corded displacements) to incident amplitudes v a r y considerably with t h e angles of incidence a t t h e surface (Gutenberg, 1944, Pig. 3). I n our case we are close to optimum conditions, b u t only smaller changes 1 2 8 M . b A ' I ' I I - I t . S T E F A N S S O N in the angles of incidence will entail considerable changes in the recorded amplitudes. 5) A substantial S F-component radiated in t h e direction of the recording station is needed (this means a certain restriction on t h e focal mechanism). 6) The microseismic noise level should not be too high, as other- wist; a small Sp m a y be lost or difficult to discover reliably. 7) Two sharp onsets (Sp a n d S) are required in clear cases, b u t in most cases S-phases are more blunt t h a n P-pliases and even if a mul- tiplicity exists in S this can often not be established with full certainty. A combination of the factors mentioned is probably enough to explain why clear cases are observed so seldom. Press-Ewing seismographs are also operated a t Uppsala, b u t in the case studied here t h e y do not exhibit the Sp-phase. This could p a r t l y be due to smaller magnification a t Uppsala t h a n a t Umea, p a r t l y to unfavourable conditions a t Molio. Also, t h e phenomenon does n o t show up on the U m e a short-period records, as t h e periods (8-10 sec) are too long for these i n s t r u m e n t s . Other cases of Sp have been observed a t our stations, though less clear t h a n t h e present one. Several of t h e aftershocks of t h e Alaska e a r t h q u a k e on 28 March, 1964, gave »Sip-phases on t h e ^ - c o m p o n e n t s a t Uppsala, K i r u n a a n d Umea. This was especially the case for the after- shocks on 3 April (22 33 42.2), a n d 4 April (17"46ra08a.6 and 22"16m54*.5), 1964. Reliable readings of S are of basic importance for our knowledge about t h e E a r t h ' s interior, in calculations of transverse wave velocities, focal mechanism studies a n d for the interpretation of surface wave observations. N e x t to P and pP it is no doubt t h e most i m p o r t a n t phase in a seismic record. I n a more detailed analysis it is t h e n necessary to t a k e the possible existence of Sp into account. Sp is more t r o u - blesome for accurate ¿'-readings than Ps is for P-readings, as Ps arrives a f t e r P , b u t m a y disturb pP. It. is f r e q u e n t l y found in routine measurements t h a t the arrival of S differs a few seconds between t h e two horizontal components. I t is then customary to consider the earlier arrival as t h e t r u e S and to report only this onset in bulletins. However, it is obvious f r o m this paper t h a t such a procedure m a y often be incorrect (the earlier arrival m a y be Sp). I n order to decide the question in a n y individual case, it is necessary to apply criteria such as those used here. S - P C O N V E R S I O N AT T H E B A S E OF T H E C U U S T 1 2 9 The time differences Ps-P and Sp-S have sometimes been used for calculation of crustal thicknesses, b u t for higher accuracy this ne- cessarily supposes t h a t crustal velocities are well known. A C K N O W L E D G E M E N T . One of us (R.S.) would like to express his gratitude to the Icelandic Science F o u n d a t i o n for a scholarship enabling him to do this research a t t h e Seismological I n s t i t u t e , Uppsala, Sweden. Seismological I n s t i t u t e , Uppsala, Sweden. March, 1966. R E F E R E N C E S BÂTII M., Polarization of transverse seismic waves. « G e o p l i y s . J o u r . R o y . A s t r . Soo. », 4 , 106-123, (1961). BATH M. a n d TRYGGVASON E . , Deep seismic reflection experiments at Kiruna. « G e o f i s . p u r a e a p p l . », 5 1 , 79-90, (1962). CHOUDHURY M . A . , Étude des ondes séismiques dans quelques tremblements de terre profonds de VHindou-Kouch. « A n n . G é o p h y s . », 14, 31-75, (1958). C O O K K . L . , A L G E R M I S S E N S . T . a n d C O S T A I N J . K . , The status of PS converted waves in crustal studies. « J o u r . G e o p l i y s . R e s . », 6 7 , 4 7 6 9 - 4 7 7 8 , (1962). C O S T A I N J . K . , C O O K K . L . a n d A L G E R M I S S E N S . T . , Amplitude, energy, and phase angles of plane SV ivaves and their application to earth crustal studies. « B u l l . S e i s m . Soe. A m e r . » , 5 3 , 1039-1074, (1963). CRAMPIN S., Higher modes of seismic surface waves: Phase velocities across Scandinavia. « J o u r . G e o p h y s . R e s . » , 6 9 , 4 8 0 1 - 4 8 1 1 , (1964). GUTENBERG B . , Energy ratio of reflected and refracted seismic waves. « B u l l . S e i s m . Soo. A m e r . » , 3 4 , 85-102, (1944). JEFFREYS H . a n d BULLEN K . E . , Seismological Tables. « B r i t . A s s o c . A d v . Sci. », 4 8 p p . , (1940). PACHADZHANOVA G . N . , Study of transformed waves SP type during deep Afghan earthquakes (in R u s s i a n ) . A k a d . n a u k . T a d z k i k S S R , D u s h a n b e , T r u d y , 10, 10S-124, (1962). RICIITER C. F . , Elementary Seismology. W . H . F r e e m a n a n d C o . , S a n F r a n c i s c o , 768 p p . , (1958). RITSEMA A . R . , (i, A)-curves for bodily seismic waves of any focal depth. « L e m b a g a M e t e o r , d a n Geofis.», D j a k a r t a , V e r l i a n d e l , 5 4 , 10 p p . , (1958). 1 3 0 M . B A T H - R . S T E F A N S S O N SAASTAMOINEN P . , Travel times for a erustal model in Finland. P u b l . I n s t . S e i s m . H e l s i n k i , 5 8 . (1963). SELLEVOLL M. A . , A -publications summary on erustal and upper mantle structure in Fennoscandia, Iceland and the Norwegian Sea. Y E S I AC R e p . 4 4 1 0 - 7 5 - X , 111-125, (1964). TRESKOV A. A . , On teleseismic determinations of the Earth's crust thickness. P u b l . B u r . C e n t r . S e i s m . I n t . , A 2 2 , 33-39, (1961). TRYGGVASON E . , Crustal thickness in Fennoscandia from phase velocities of Bayleigh waves. « A n n a l i d i G-eofisica », 14, 2 6 7 - 2 9 3 , (1961). YUN-YU D . , SP' phases and the crustal thickness of China (in C h i n e s e ) . « A c t a G e o p h y s . S i n i c a » , 14, 168-172, (1965).