Shorter Contributions

V E L O C I T Y - D E P T H F U N C T I O N O F P - W A V E S I N T H E R E G I O N

O F T H E C E N T R A L B O H E M I A N M A S S I F

KAREL HOLUB

Geophysical Institute, Czechosl. Acad. Sci., Prague*)

S u m m a r y : By applying the Wiechert-Herglotz method the seismic wave velocity distribution with depth was determined in the upper part o f the Earth's crust along the profile D S S VII in the Bohemian Massif, especially in the Central Bohemian Massi f The velocity-depth function is com- pared with the results of similar measurements in the field [2, 3], as well as with laboratory investiga- tions [4].

1. I N T R O D U C T I O N

During summer 1970 the Institute of Applied Geophysics performed seismic measurements along the Internat ional Profile VII between shotpoints Vimperk (231.3) and Nymburk (74-9) by the cont inuous profiling method [1]. Simultaneously, however, experiments with broad-band seismographs were carried out by the Geophysical Institute CSAS at discrete sites which were spaced at distances of 6-00--9-25 km. Due to the interesting position of the studied segment of the profile, mentioned above, mostly passing through the Central Bohemiant~ Massif which is a variscian instrusive body built by igneous rocks with a predominant complement of grano- diorites, an at tempt was made to estimate the velocity-depth distribution of seismic waves in this

area.

2. E X P E R I M E N T A L D A T A A N D M E T H O D APPLIED

One of the possible methods of investigating the velocity distribution with depth is the Wiecher t - Herglotz method, or its modifications, applicable for this purpose under several assumptions, e.g., tha t travel-time curve is a continuous, increasing function, that the derivative of the travel-time curve, d~/dx, is not an increasing function, and that the velocity is only a function of depth. To satisfy the first assumption, we fitted a smoothed curve to the experimental data of first arrivals of the refracted wave and, since the calculation of the velocity distribution, with a view to the method applied, required equidistant time data along the profile, the first arrivals were taken from the smoothed travel-time curve at intervals of 2 km, al though the field measure- ments were carried out at larger step (see data printed in italics in Tab. 1). After the numerical differentiation of the travel-time curve, the data were arranged in such a way that this functions had the character of a non-increasing function, thus satisfying the second assumption. The data obtained by this method are given in Tab. 1 and they are also plotted in the form of a reduced travel-time curve in Fig. 1. The legibility of the first arrivals is reliable up to distances of 110.85 km from shotpoint Vimperk while the onsets of the refracted wave at larger distances disappear on the background of short-period microseismie noise.

*) Address: Bo~ni II, 141 31 Praha 4 - Spo~ilov.

390 studia geoph, et geod. i8 (1ff741

Kpam~.ue coo6ulenua

Table I,

r (kin)

2'00 4'00 6"00 7"64 8"00

10"00 12"00 14"00 14"25 16"00 18 "00 20"00 20"25 22"00 24.00 26-00 26"80 28"00 30.00 32.00 34.00 34.05 36"00 38.00

t (s)

0"371 0.734 1 '090 1.39 1-441 1.787 2,130 2.471 2.51 2-810 3'147 3"483 3"51 3.818 4-I53 4.487 4"66 4.821 5,145 5,487 5-820 5,80 6'153 6,485

r (km)

40.00 41.85 42.00 44,00 46-00 48-00 50.00 51.10 52.00 54.00 56"00 57"78 58'00 60.00 62-00 64"00 64"45 66"00 68.00 70.00 70.90 72-00 74.00 76.00

t (s)

6-817 7.12 7.149 7.481 7-813 8.145 8.477 8.63 8-809 9-141 9.473 9.72 9-804

10-135 10-446 10.777 10.83 11-108 11.439 11.770 11-90 12.101 12.432 12.763

r (kin)

77.30 78.00 80,00 82.00 84"00 84"05 86.00 88.00 90,00 90.65 92,00

[I 94"00 !!

96.00 97.15 98.00

100.00 102.00 104.00 104.10 i06.00 108-00 t 11-00 110.85

t (s)

13.00 13.094 13,425 13,755 14.085 t4.15 14.415 14.745 15.075 15.17 15-405 15.734 16.063 16.25 16-391 16-718 17.045 17.371 I7.39 17.696 18.020 18.342 18.46

The whole problem of determining the velocity-depth function is principally based on solving the equation

(1) Z~ = rc -1 fo r a r g c o s h ( v * / v * ) d r ,

°20 f

; J , _ . . . . . . . . " \ \

0 0 0 _ _ i 2 .50 r(km} IO0

Fig. 1. Reduced travel-time curve of a refracted P-wave in the area of the Central Bohemian Massif.

Studia ge,oph, et geod, 3.8 [197~1 391

Shorter Contributions

which was substituted for numerical solution in [2] by the approximate expression

R

(2) ZR = ~-l 2 a r g c o s h ( v* / v* )Ar , i=1

where Zg is the depth of the .point where the ray turns and appears at the epicentral distance R on the surface, vi~ is the velocity at the point of inversion and the values v~ = Ari/zXt ~ were determined from the smoothed travel-time curve at steps of Ar i = 2 km and approximated, taking into account the requirement tha t the derivative of the travel-time curve was to be an non-increasing function. The calculation of the approximate expression (2) was computed by computer and the velocity-depth distribution is tabtilated in Tab. 2 and plotted in Fig. 2, together w~th the results of other investigations of a similar kind [2--4].

Table 2.

Z (kin) v* (km/s) Z (km) v* (km/s) Z (km) v* (km/s) ~

0.000 0-235 0.606 0.960 t .264 1.540 1-761 1.942 2.089 2.171

5"33 5"56 5"74 5"85 5"91 5'96 5"98 6'09 6"0t

, 6"01 T

2.270 6.01 2.405 6.02 2.544 6"02 2"671 6,03 2-808 6.03 2.954 6.03 3.108 6-04 3.26,'3 6,05 3-436 6.05 3.610 6'05

3'790 3"977 4"327 4'968 5"841 6'616 7-7t2 8'953

t0"185

6'05 6"06 6"06 6"08 6-t0 6'13 6-17 6'21 6-26

0 4.5 5.0 5.5. 6.0 ~(k,'nlS) 6,.5

. . . . . . . . ' - - .± .2 /2 ' : -

i L

,° I

Fig. 2. Velocity-depth function: 1 -- Central Bohemian Massif, 2 -- the neighbourhood of the seismic stat ion Coltm (GDR) after [2], 3 -- the vicinity of quarry B6hmischbruck (GFR) in the area of the Bohemian Massif after [3], 4 -- laboratory measurements on granite samples after [4].

3 9 2 Studia geo,ph, et geo,d. IS [1974)

KparnKue coo6utemt:~

3. DISCUSSION OF RESULTS

The experimental data and the application of the Wiechert - Herglotz method made it possible to investigate the velocity-depth f u n c t ~ n up to a depth of 10 km (Fig. 2, curve 1). It is evident that the continuous run of this function could be substituted approximately by two straight lines, representing two different velocity gradients; we can observe the higher gradient in the upper part of the vertical cross-section of the Ear th ' s crust, approximately to the depth of 2 km, and below this limi~t the velocity gradient id is substantially lower.

The assumption that in the region where the velocity gradient is considerably higher, the increase of the.seismic wave velocities is influenced, first of all, by the presure and temperature, was verified by laboratory experiments [4] and in the at tached graph this is shown by the very similar trends of both the dependences. At depths of more than 3 km curves 1 and 4 rather differ due to different velocity gradients. Whereas under the simulated conditions of the Earth 's crust one cannot achieve .an adequate velocity gradient in the granite samples by increasing the pressure further, under real conditions the higher gradient can be explained as a consequence of the dif- ferentiation of the petrogenetic minerals and, therefore, the occurrence of other types of rocks, forming the Ear th 's crust, which may also be represented by higher seismic wave velocities, may be expected.

Analogously, in comparing experimental curves 1 and 3, we concluded that within the range of the determined velocity-depth distribution values both curves have very similar characters, because the field measurements [3] were performed in the crystalline rocks of the Bohemian Massif, a part of which is the Central Bohemian Massif, too.

Finally, curve 2, whose velocity-depth function in the neighbourhood of the seismic station Collm (GDR) can be observed approximately down to a depth of 3.8 km [2], generally displays lower values of seismic wave velocities which are due to a rather different rock composit ion of the studied area, neverthless, this curve displays a considerable velocity gradient in the upper part of the Ear th ' s crust. It is worth-while mentioning that a characteristic feature experimental curves 1, 2 and 3, as well as of curve 4, observed under laboratory conditions, is the considerable velocity gradient in the first few kilometers of the crust which is observed owing to the influence of increasfng pressure and heat gradient at the corresponding depth.

The author thanks W. Pe t r , A. F o u s and F. J e n ~ for help during field experiments.

Received 9. 11. 1933 Reviewer: I. Yanskf:

References

[I] B. Ber~inek , M. Z o u n k o w i , K. H o l u b : Results of Deep Seismic Sounding in Czecho- slovakia. U M P Programme in Czechoslovakia 1962--1970, Geophysics, Final Report, Academia, Praha 1971, 94.

[2] J. Jansk1~, Ch. J u n g e : Die Geschwindigkeit mit der Tiefe in einem Tell der varistischen Faltenzone. Studia geoph, et geod., I0 (1966), 229.

[3] P. G i e s e : Die Geschwindigkeitsverteilung im obersten Bereich des Kristallins, abgeleitet aus Refrakt ionsbeobachtungen auf dem Profil B6hmischbruck -- Eschenlohe. Z. f. Geophys., 29 (1963), 197.

[4] F. B i r c h : Interpretat ion of the Seismic Structure of the Crust in the Light of Experimental Studies of Wave Velocities in Rocks. Contr ibut ions in Geophysics, Vol. 1. Pergamon, New York 1958, 158.

Studia geoph, et gaod. 18 [:[974) 393