Sympos ium on Seismic Models, Caxtfe a[ Liblice near Pra.gue, 9 - 12 November I965

D is clt.qs/o t',

L a v e r g n e : Your results show that the tow-velocity layer does not act as a wave-gu ide when

the wave- length is large. Have you carried ou t precise m e a s u r e m e n t s to de t e rmine the ratio o f the m i n i m u m thickness to the wave- length to ob ta in the wave-guide p r o p a g a t i o n in the

par t icular case for a wave-guide with a c o n t i n u o u s velocity gradient?

l v a k i n : Only two models o f this type were investigated; this was insufficient for so lv ing this ques t ion .

G i l b e r t : Us ing the classical W K B a p p r o x i m a t i o n , it would appear tha t wave - l eng ths g rea te r than 4 th icknesses of the wave-guide will not " 'see" the wave-guide.

A SIMPLE THREE-DIMENSIONAL MODEL OF THE EARTH'S CRUST

KaREL HOLU8, ViT K,~R'4iK, VL.aDIMfi.: Tonv.;,g

Geophysical ln~'titute, Czechosl. Acad. Sci., Prague*)

This paper contains preliminary results based on our first test model fabricated quite recently. The final interpretation is not yet finished but we have been able to draw some conclusions which might be of immediate interest.

The problems of a sound interpretation of seismic time-distance curves are well known. The application of first arrivals only is still the general method of determining

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Fig. 1. Supposed (dot ted line) and realized (full line) veloci ty-depth d i s t r ibu t ion o f the tes t ing

model .

*) Address: Bodni 11, P raha 4 - Spofi lov, (2SSR.

370 Stadia geoph, et ~eod. 10 rlq6,':;)

5 ) : m p o s i u m on S e i s m i c M o d e l s , Cas t le tU L i b h c e near Pi'ague, 9 - 12 . ,Vovembe" 1965

the v e l o c i t y - d e p t h f u n c t i o n o f the c rus t a l t h o u g h severa l theo) 'e t ica l p a p e r s d e m o n -

s t r a t e the a m b i g u i t y o f such a p r o c e d u r e . T h u s the p o s i t i o n s o f c r i t ica l p o i n t s and

a m p l i t u d e s o f l a t e r a r r iva l s m u s t be e m p l o y e d in i n c r e a s i n g t he r e s o l v i n g p o w e r of

field i n v e s t i g a t i o n s . H o w e v e r , we

h a v e to k n o w w h a t a r r iva l s a re

s u f f i c i e n t l y la rge to be ident i f ied

a b o v e t h e b a c k g r o u n d no ise level

a n d t h e i r r e l a t i o n to v a r i o u s veloc-

i t y - d e p t h f u n c t i o n s .

In C z e c h o s l o v a k i a we are n o w

fac ing s i m i l a r p r o b l e m s in e v a l u a t i n g

t he first t r a v e l - t i m e p lo t s o b t a i n e d o n

a r e f r a c t i o n p rof i l e in 1964 a n d 1965.

W e h o p e t h a t the t e c h n i q u e s o f

t h r e e - d i m e n s i o n a l m o d e l l i n g deve-

l oped in o u r s e i s m o l o g i c a l sec t ion

will be ve ry he lp fu l in c o m p l e t i n g

t he t h e o r e t i c a l as well as field in-

ves t iga t io ns.

Tr~J I T'flg a')j

3ot~ I I

2o ~

.,,,4,. &.

The main purpose of the first three-

dimensional mode! of the crust was to

test the influence of a second-order dis-

continuity and of a layer with constant

positive gradient on the general wave

pattern. We used gelatine with water for the upper layer of the crust and three components, gelatine, water and glycerol mixed in different ratios, for the lower layer [tl. The modelling velocities were 1'52 km/sec., t-537 -- l 8 5 k m / s e c , cor- responding to 5.5 kin/see, and 56- -6 .7 kin/see, respectively. The velocity below the crust is too high, being about 10-4 kin/see. (the velocity in plexiglass is 2-865 kin/see), but no other plate material of plexiglass with lower velocity was avai-

I I

T ? I

, . , . , , , . , ,

Fig. 2. Travel time e l all distinct phases measured

on the three-dimensional model.

l ane at the time of the experiment (Fig. l). Thus the seal-,: factors were S T --~ T ~ t / l =

= 10-~ -- f .... 10-5, Sv p = v .u /v __ 1.52,5.5 -= 0.276. i.e. 1 psec corresponds to 0.1 sec aad 2-76 mm to 1 km. The same instruments employed in all experiments aheady was used [2, 3]. The transmitter was placed in two positions, on the upper edge of the model and on its surface respectively. The receiver moved along a profile at distances corresponding to 20 km up to) 190 km in steps or" about 2 and 4 kin, respectively {5 mm and 10 ram on the surface of the model). The seismograms were photographed from the screen and all distinct phases were measured on a film reader. The accuracy of reading the arrival was • psec. The arrival times corrected for the delay time of the apparatus were plotted and the travel time curves were constructed. Amplitude curves of the most prominent phases were also drawn separately. The resulting curves

' I ' ~ tud !a ge,~ph, e l _g~.od. IO E ia~j61 0 7 _

Symposium on Sei.~mic :~4ode/s, C'ast/e o f Lib~ice near Prague, 9.- 12 November 1965

are shown in Fig. 2 and 3. The example of s e i s m o g r a m s is in Fig. 4. We may c o n c l u d e that PI

c o r r e s p o n d s to the direct wave p ropaga t ing in the upper layer and P3 is the h e a d wave in the lowest plate. The s t ronges t wave groups arr iving as later phases were in te rp re ted as waves

reflected f rom the b o u n d a r y 2 - 3 ( 5 1 ) : they emerge up to 1 2 0 k m where a new phase , the wave

refracted wi thin the second layer with gradient , arrives at a lmos t the same travel t ime . This wave

is focused near 125 km and can be followed up to the last point of the profile. On t he records we

can trace also the wave reflected f rom the b o t t o m of the third layer (see no ta t ion Pt23 .o123 in

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Fig. 3. Ampl i t ude -d i s t ance curves o f the phases Pt and P t z P t 2 - P2 err. for two pos i t ions of the

t ransmi t te r .

Fig. 21. The travel t imes of these waves

have been found to be i ndependen t f rom the posi t ion o f the t ransmi t te r .

Several phases r u n n i n g paral le l to the main phases are observed wi th the delay

rang ing f rom 5 to 25 ,user. The delays

depend on the posi t ion o f the t r ansmi t t e r

and belong p robab ly to paras i t i c effects. The average periods of the ,a, ave P t are

2 laser. Those of the reflected a n d ref rac ted waves are 3 - 4 psec respect ively. T h u s the

wavelength of the pulse is l onge r or c o m - parable with the th ickness of a single

h o m o g e n e o u s Ia}er c o m p o s i n g the gra-

dient med ium. The a m p l i t u d e s o f the wave P~ decrease rapidly but c o n t i n u o u s l y with the distance. The a m p l i t u d e curve

co r r e spond ing to reflected (P t eP t 2 ) and refracted waves (P 2 refr.) has two dis t inct max ima: the first can be re la ted to the

usual ly observed increase o f a m p l i t u d e s behind the critical point , the second cor-

r esponds to the caust ics on the cusp o f the t ravel- t ime curve. The ra t io o f bo th

m a x i m a is influenced by the or ien ta t ion

o f the t ransmi t t e r (see Fig. 311. Our test demons t r a t e s the difficulties

in detect ing layers with a posi t ive velocity

gradient . Apply ing the usua l s imple inter-

p re ta t ion procedure to our t ravel - t ime plot, i.e. suppos ing a direct wave P~,

a head wave P3 and the reversed segmen t o f s t r ong reflections, we ob ta in a one- layer c rus t with the M o h o d iscont inui ty at a depth o f 25 kin. i.e. 5 km sha l lower t han the real one.

The only p h e n o m e n a which indicate the existence o f the in te rmedia te gradient layer are the rapid

change in the cu rva tu re of the b ranch P t 2 P t 2 - P2 refr. and then the second m a x i m u m on the c o r r e s p o n d i n g ampl i t ude curve respectively. However , only the second p h e n o m e n o n can be

obse rved du r ing the o rd inary refract ion field m e a s u r e m e n t s , the slight change in the cu rva tu r e o f the b ranch PP would escape the a t ten t ion and would p robab ly be masked even by a smal l

sca t te r of observa t ions .

The pre l iminary resul ts are in good ag reemen t with the seismic ray theory of Bulten [4] and

with the theoret ical c o m p u t a t i o n s of Green and S te inhar t [5].

These results reveal the possible ambiguities in the interpretation of seismic refrac-

3 7 2 Studia g,..tJph, et ~eod. lo ' !966~

Symposium ,m Seismic .,Wodels. Castle o f Lib~ice ~tear Prague. 9 - ]2 .'~ovember 1965

t ion measurements . It is evident that the tra, ,el-t ime curves alone are not sufficient

for the de te rmina t ion of the structure of the crust. We must use other evidence, e.g.

cusps on t ravel- t ime curves and ampl i tude-d i s tance relat ions in de te rmining the

velocity d is t r ibut ion with depth.

Our immediate task is now to enlarge the range of the model l ing gelatine-like materials and to study a series of simple models o f different velocity distributions before we start s imulating crustal models fitting our refraction profiles. All experi- ments will be guided by theoretical computa t ions .

Received 12. 11. 1965 Reviewer: V. (.erven.f"

References

[l] L. W a n i e k : The System Water -Giycerob-Gela t inc as a Medium for Three-Dimensional

Seismic Models. Stadia geoph, et geod., I0 (1966), 273.

[2] K. K l i m a , Z. P r o s , A. K n o b l o c h o v S . : Electroacoustic Transducers for Seismic Modelling.

Studia geoph, et geod., 10 (1966), 323.

[3] Z. P r o s : Armaparypa j.as TOtfHbl.X H3MepeH}fi.i ynpyrax napa~rerpou ropnstx nopo-L Travaux

Inst. Geophys . Acad. Tchdcosl. Sci. No. 153, Geofysikf.lni sbornik 1961, Nr,)SAV, Praha 1962.

[4] K. E. B u l l e n : Seismic Ray Theory. Geophys. J., 4 (196t), 93.

I51 R. G r e e n , J. S. S t e i n h a r t : On Crustal Structure Deduced from Seismic Time-Distance

Curves. New Zealand Journ. of Geol. and Geophys. , 5 (1962), 579.

Pe3~oMe

F I P O C T A f l TPEXMEPHAS:I MOJ_3,EYlb 3EMHOIJI KOPBI

KAREL HOLUB, ViT KARNiK, VLADIMiR TOBY..~ ~,

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Tpy.2"~O onpeaeJ~aTb np~ rloJleBblX It3Mept~HII:qX a3-3a pa36poca bra6,11o.xe~i~, 6onee aa,~exHbtM

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FIocr)~m~o 12. 1 l. 1965

$It~OL~ geoph, r.t geod. 10 (~966) 373

,5~ymposiurn on Sei,rmic ModeLs', Ca.vHe o f Lib/ice near Prague, 9 - 12 November 1965

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D/.rcu.s'sion

R i z n i c h e n k o : I r e c o m m e n d c o m p a r i n g the results of the mode l expe r imen t with theoret ical

ca lcu la t ions made for the same mode l but for a) solid-solid and b) l iquid-l iquid c o m b i n a t i o n s , respectively. The repor ted case c o r r e s p o n d s more to a l iquid-sol id c o m b i n a t i o n . 1 fu r ther

r e c o m m e n d us ing seismic models for the clarification of the cha rac te r of P* waves in relat ion to reflections beyond the critical point, diffract ion and interference of waves.

Sympos ium on Seismic Models, Castle, o f Libtice near Pra'r 9 - 1 2 November 1965

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at distances up to d.,vt = 337"0 mm the relative magnification V ::~ 1, at ~ , t >= 347.0 mm, V -- �89

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

K ~.rnl k: The uncertainty in the exact character of gel as a modelling material does not influence

our main conclusions about the waves P1, ])2refr and about the existence and positions of

maxima of anapHtude curves, only the form of the amplitude curve for the reflected wave Pt zP12 could be relatively distorted. Our communica t ion refers only to the first trial experiment and

tbe work will continue.

Studia geoph, e', geod. IO (1%6) 375