Bulletin of the Seismological Society of America, Vol. 83, No. 5, pp. 1420 1441, October 1993

CRUSTAL ANISOTROPY FROM LOCAL OBSERVATIONS OF SHEAR-WAVE SPLITTING IN WEST BOHEMIA,

CZECH REPUBLIC

BY VXCLAV VAVRY~UK

ABSTRACT

The results of a systematic study of shear-wave splitting, observed in the three-component digital seismograms of about 400 local microearthquakes that occurred during the 1985/1986 West-Bohemian earthquake swarm are presented. Two shear phases, polarized nearly perpendicularly in horizontal projection, were observed at all five stations of the local seismic network for most of the events. The polarization of the faster shear wave is aligned in the W N W - ESE direction, regardless of the mechanism and hypocenter location of the individual events, and coincides with the direction of the maximum hori- zontal compressive tectonic stress in the region. These effects are interpreted in terms of effective anisotropy of the upper crust in the region. The maximum delay time between the split shear waves is 0.15 sec and corresponds to 6% anisotropy.

Directional variation of the delay time was observed at the nearest station (epicentral distance = 5 km). This variation was compared with functions predicted by theoretical models of cracked media to resolve which model is the most appropriate for crustal anisotropy. Surprisingly, no agreement could be found for Hudson's model of dry or water-filled parallel cracks that is widely used by many authors. A successful fit was obtained for Schoenberg-- Douma's model of a medium with parallel fractures. The fracture normal pointed N31°E, and the optimum fracture parameters were E N = 0.4 and E T =

0.02. The theoretically calculated fractures are aligned parallel to the tectonic stress direction and do not correspond to any real tectonic lines in the region.

INTRODUCTION

A growing amount of seismic data indicates the existence of anisotropy in the upper crust. Of the various possible mechanisms of crustal anisotropy, the anisotropy associated with crustal tectonic stress and probably due to the presence of fracture systems with preferred orientation appears to be the most frequently observed (Crampin, 1978; 1981; 1984). Wave propagation in effec- tively anisotropic media has been studied both theoretically and experimentally. Theoretical calculations for media containing aligned circular cracks (Garbin and Knopoff, 1973; 1975a, b), ellipsoidal inclusions (Hudson, 1980; 1981; 1986; Nishizawa, 1982) and long, thin, parallel fractures (Schoenberg and Douma, 1988) predict transverse isotropy of the medium and infer its elastic properties from fracture parameters (e.g., crack density, aspect ratio, elastic parameters of material inside the cracks). Papers studying effective crustal anisotropy experi- mentally are based on the analysis of shear-wave splitting (Li et al., 1988; Aster et al., 1990; Kaneshima, 1990; Kaneshima et al., 1990; Savage et al., 1990; Shih and Meyer, 1990; Mjelde, 1991; Graham et al., 1991; Sachpazi and Hirn, 1991). The orientation of the symmetry axis of transverse isotropy is deduced from polarization directions of split shear waves. The degree of anisotropy is esti- mated from the delay time between the split S waves, and ranges prevailingly from 3% to 10%.

1420

ANISOTROPHY OF SHEAR-WAVE SPLITTING 1421

It is desirable to determine the complete elasticity tensor that would allow the anisotropy predicted by different theoretical fracture models to be compared with that of the real structure. This comparison is crucial for a better under- standing of the limits of applicability of simplified fracture models and for determining the fracture parameters of real structures. To determine the com- plete elasticity tensor, it is necessary to measure the delay time variations as a function of ray direction. The conditions that have to be satisfied to construct the directional delay time variation reliably are: (1) well-defined shear-wave splitting has to be observed to enable the interpreter to identify the S2-wave unambiguously and to determine its arrival time correctly; (2) large number of data has to be available, because the delay times should be measured for a wide range of ray directions, and the rays should provide a dense coverage of the region being investigated.

These conditions are severe. This is evident, since no clear reliable directional variation of the delay time has been reported to date, although shear-wave splitting has been experimentally observed for almost ten yr.

Both conditions were satisfied in the case of the local observations of the 1985/1986 West-Bohemian earthquake swarm. These observations represent a data set exceptionally suitable for the above-mentioned purpose. In this paper the polarization directions of the split S waves are studied and the directional variation of the delay time is established. Finally, the fracture parameters are estimated and the complete elasticity tensor for the West Bohemia region is computed.

1985 / 1986 WEST-BOHEMIAN EARTHQUAKE SWARM

From December 1985 to January 1986, an earthquake swarm occurred in West Bohemia (see Fig. 1). Over 7000 weak, shallow earthquakes were recorded in its course; the local magnitudes of the two strongest being 4.6 and 4.1 (Neunhoefer et al., 1989).

The hypocenters of the squarm occurred in the upper crust beneath the northeastern edge of the Cheb Basin, which is situated in the northwestern part of the Bohemian Massif (Fig. 2) and which developed during the Paleozoic and older orogenetic phases. The tectonic structure of the Tertiary Cheb basin represents the intersection of the Eger Graben, oriented WSW-ENE, and the Sudeten fault system running transversely to it (Dudek, 1987). The crystalline basement of the Cheb basin is covered by tertiary sediments with a maximum thickness of 400 m. Three main structural systems control the development of

o ~ the basin (Santrucek, 1986): the Sudeten NW-SE fault system, the Ore-Moun- tain WSW-ENE fault system, and the youngest N-S tectonic lines. The NW-SE fault system is best defined, being manifested by the Mari~nsk~ L~zn~ Fault, the azimuth of which is approximately 150 °. The NW-SE and N-S structural trends, moreover, are also significant tectonic lines from the hydrogeological point of view, because they form the paths of ascent of mineral water and CO 2 from the basement of the basin. The present activity has been monitored by precise surveying that disclosed the lift of the eastern marginal block of the Cheb basin, and indicated that the Mari~nsk~ L/lzn~ Fault is probably still active (VyskoSil and Kopeck:~, 1974).

The swarm activity was monitored by the local analog one-component stations Olov~ (OLV), Klingenthal (KLI), Wernitzgruen (WRG) and Bad Elster (BDE), and local digital three-component stations Vackov (VAC), Tisov~ (TIS), Selb

1422

50°20'N -

50°O0'N -

V. VAVRYCUK

12 ° 10'E I

I 20 km

' , _ -" , , BDE I

I

S E L r - - I I I

1 I

I

I I

HOH' ,. I t

1 2 ° 30% I

K L I / • i

/ "-i TIS s

S

WRCl s

I r - -, ~ •

,, ,VAC • \

OLV

KOS

'IO°E '~ 120°E 5 1 ° N ~

I I

FIG. 1. Map of the West Bohemia region showing locations of digital (solid squares) and analog (solid triangles) seismic stations. The epicentral area is hatched.

(SEL), and Hohenberg (HOH) (Fig. 1). In addition, the permanent digital station Nov~ Kostel (KOS) was installed after the swarm to monitor the subsequent weak seismic activity of the region. The digital stations operated in the trig- gered mode. They were equipped with short-period SM-3 seismometers with a velocity-proportional output in a bandwidth of 0.6 to 30 Hz. The data were sampled at frequencies of 116 to 250 Hz and stored by Lennartz PCM-5800 recording equipment on PCM magnetic tapes. The effective dynamic range was above 100 dB (gain ranging used: 10-bit mant issa and 4-bit exponent). Detailed information about the stations can be found in Hor~lek and JedliSka (1987; VAC and KOS), Klime~ et al. (1987; TIS), and Neunhoefer et al. (1989; remaining stations).

K o l ~ and VavrySuk (1990) located 143 events of the swarm by the FHYPO computer program (Herrmann, 1979). A simple model of a homogeneous, isotropic halfspace with Vp = 5.76 km/sec , constructed experimentally by HorAlek et al. (1987), with different values of Vp/V s was applied. Carefully reinterpreted P- and S-wave arrival times at stations VAC, TIS, and OLV (approximate epicentral distances of 5, 15, and 9 km, respectively) were used in the location procedure. The P (S) onset t imes were measured with an accuracy better than _+0.01 sec (_+0.03 sec) for VAC and TIS and _+0.05 sec (+0 .1 sec)

50 o 20'N

ANISOTROPHY OF SHEAR-WAVE SPLITTING

12°lO'E 12°50'E ,

\ I \ / +

t 20 km I ~ + +

+

\ \ \ \

\

\ \ +

+

+

÷

1423

/

..•,/+ + + \~-

+ + 4 - \ . +

50°O0'N

1

C

FIG. 2. Tectonic sketch of the West Bohemia region (after Dudek, 1987). (1) Tertiary basins; (2) Hercynian granitoid massifs; (3) faults; (A) Cheb Basin; (B) Ore-Mountain fault system; and (C) Mari~nsk~ L~zn~ fault. The epicentral area is hatched.

for OLV. The results show tha t the swarm activity was concentrated in a small elongated area. The earthquake epicenters form a belt, about 4 km long and 1 km wide, oriented nearly in the nor th-south direction (see Fig. 3). In the deep section, the hypocenters form a cluster, 1.5 km high dipping southward. The position of the focal area depends on the velocity model used. For low values of Vp/V s the hypocenters shift to the south and to greater depths, for high values to the north and upward. The position does not change in the eas t -wes t direction. For Vp/V s = 1.62 the hypocenters are located at depths of 8.5 to 10.5 km, for Vp/V s = 1.73 at depths of 6 to 8 km. The nor th-south difference in positions between the two models amounts to about 1.5 km. The same depen- dence applies to changes in P-wave velocities at a constant Vp/V s ratio.

POLARIZATION OF SPLIT S WAVES

Data and Method

The S-wave polarization was studied for selected events of the swarm recorded at stations VAC, TIS, SEL, and HOH and for selected events of the 1986 to 1990

1424 v.V.~VRYCUK

N2!

- 2

- 4

1 6 Z v t

. . . . . . . . . L ~ . . . . . . L . . . . . . . . .

e, , i

1 Q . . . . . . . . . . . . . . . . . . . . . .

' 2 k m

1 2 3 5 . . . . . . . . . 7 . . . . . . . . . 9 E

I o I

I °,.. : . " ° .

'* 2 k m 2 k r n . . . . . . . . . I . . . . . . . . . I . . . . . . . . . 2 . . . . . . . . . I . . . . . . . . . . . . . . . . .

5 7 - 4 - 2 0 E N

FIG. 3. Hypocenter projections of located events. The origin of Car tes ian coordinates is placed at the VAC station. The velocity model with vp = 5.76 k m / s e c and V p / V s = 1.65 was used. The solid line displays the prevail ing direction of the be l t of the hypocenters.

period, recorded at KOS. Events located by Kolfi~ and Vavry~uk (1990) were used for VAC (141 events), TIS (139 events), and HOH (29 events). Stations SEL and KOS triggered poorly, therefore, all the recorded events, for which the signal-to-noise ratio was high enough to study S-wave polarization reliably, were used (23 events for SEL and 39 events for KOS).

All records were preprocessed by frequency filtering. The importance of frequency filtering is demonstrated in Figures 4a b. Figure 4a shows a three- component velocity seismogram of the event of 31 December 1985 at 04:39:34 (VAC, M L = 1.7) with P and S waves plotted at an expanded timescale together with the respective polarization diagrams in horizontal projection. It is evident at first sight that the polarization diagrams are complicated and hardly interpretable. Figure 4b shows the numerically integrated record of the same event. The P waveform is dominated by a one-sided pulse, and the S-wave polarization displays a clear case of S-wave splitting. Because particle motion plots are simpler in displacement, the S-wave polarization was studied in ground displacement records.

The S-wave particle motions were plotted in horizontal projection and the prevailing polarization directions of the S1 and $2 waves were est imated by visual inspection. The analyst measured both polarization directions and as- signed them to one of four classes according to their reliability. The first class consists of high-quality readings with an error of + 5 °. For the second class the error is about _ 10 °. In the third class cases the polarization direction could be identified only approximately and the error is about + 20 °. The fourth class consists of events for which no prevailing polarization direction could be identi- fied.

R e s u l t s

The results of the analysis are presented in Figures 5 and 6, evaluated in Tables 1 and 2, and summarized in the following items.

(1) All five stations recorded events with well-defined S-wave splitting. How- ever, not all events displayed S-wave splitting. The S-wave polarization varied considerably for various events and from station to station in the same way as the delay times between two arriving S waves. In many cases the delay time was not long enough to separate the two S phases so that the polarization was the result of their interference. The polarization direction of the two S waves could thus only be est imated very roughly.

A N I S O T R O P H Y OF SHEAR-WAVE S P L I T T I N G 1425

velocity

N

Z P $

E

i | I

1 s e c

P ~gave

Z

E

O.l sec

l

N

E _

~; ~ave

1 I I

0.1 s e e

I

$1

FIG. 4A. Three-component velocity seismogram of the event of 31 December 1985 at 04:39:34 (VAC, M n = 1.7) with detailed P and S waveforms and polarization diagrams in horizontal projection.

1426 v. VAVRYCUK

d i s p l a c e m e n t

N

Z

E

1 s~c

P wave

N

E

I

N

O. i s ec

w a v e

N

Z 4 , - -

E

t I

0. f s e c

I

N

E

SI

$2

FIG. 4B. Three-component displacement seismogram of the event from Figure 4a obtained by numerical integration of the velocity records.

A N I S O T R O P H Y OF SHEAR-WAVE S P L I T T I N G 1427

station: VAC

P S

J

E :

N

, ! , !

S1 $2

S2

St

station: T[$

Z

P S

| i

S1 $2

N

Z i

i

i ! s

N

P.

S1

station: SEL

P S S1 52

z! !

FIG. 5. Examples of dist inct shear-wave spli t t ing for five different events recorded by tlve different stations. A three-component seismogram is shown wi th marked P- and S- wave arr ivals ( l e f t ) , the detail of an S-wave group wi th split S waves ( m i d d l e ) and the particle motions of the split S waves in the horizontal projection ( r i g h t ) . Displacement records are presented for s tat ions VAC, TIS, HOH, and KOS, and velocity record is shown for s ta t ion SEL. For SEL the displayed event has a relatively long-period S wave; the split S waves are, therefore, separated bet ter in the velocity record. The events of 30 December 1985 at 21:49:56 (SEL, M L = 2.5), 20 J a n u a r y 1986 at 23:43:21 (VAC, M L = 1.2), 23 J a n u a r y 1986 at 07:09:16 (HOH, M L = 1.6), 6 February 1986 at 09:17:15 (TIS, M n = 2.6) and 23 December 1989 at 21:23:50 (KOS, M L = 2.0) were used.

1428

station: ll0tt

P S

I

V. V £ V R Y ( ~ U K

$I $2

z l

, | f ~ '

$27 $1

station: K0S

P s

z il

S1 S2

N ~

; , T

E

FIG. 5, Continued.

N

$1

(2) The quality of the reading of polarization directions was station-dependent. The $1- and S2-wave could be best read at VAC and SEL, respectively. The scatter of measurements for both waves was least at VAC. The high reading error of the S2-wave polarization direction in some records is probably due to the above-mentioned interference of split S waves, which results in the contamination of the S2-wave arrival by the Sl-wave.

(3) The prevailing $1- or S2-wave polarization directions tha t could be mea- sured were about the same for different stations and various events, although the mechanisms of some events evidently differed (different P- wave polarities at some stations).

(4) The pie diagrams in Fig. 6 indicate tha t the scatter of polarization direc- tions for a particular station is caused by reading error ra ther than by actual variation of the polarization directions for different events.

(5) The more scattered values of the polarization directions, measured at more distant stations (SEL and HOH), are probably due to complex wave inter- action with the surface: the waves reach these stations probably outside the shear-wave window. The averaged values of the polarization directions

50

50

40

30

20

10

0

A N I S O T R O P H Y O F S H E A R - W A V E S P L I T T I N G 1429

SI wave . . . , . . . , . • . - . . : . . : . ; . . - . . , . . - . . - . . : . . , . . . . . . : . : . , . . . ,

. . . . . . . ! . . . . . . . . i . . . . . . . . . ~

l o . . . . . . . . . . . . . . . . . . . . . . . . i..

i .................... " ; . . . , . . . . . . . . . . . , . . . , . . . .

50 70 90 t t 0 130 150 170

station: VAC

40

30

20

$2 wave • . . , . . . , . . . , . : . : . - . . , , . : . . . . . : . . , . . . . . : . : . . . . .

, , , iiii i .iiii il

O ] i . . , , . . , i , , , , . . • , . • . i . . .

-40 -20 0 20 40 60 80

50

40

30

20

t0

0

S1 wave , . . . , . . . , • . . ~ . : . . . . . - . , , , ; . . : . 1 . . , . . . - . . : . : . . , . . .

~ ~ o ~ ..... i~ . . . . . . . . . . . . . . . .

........ i ....... ....... :. i:i i 50 70 90 tiO t30 t50 t70

station: TIS

$2 wave

0 1 . . - ' " " " ' " " " ' " - " ' , . . : . . . . . ' , - . . . . , : . - . ' . . . . : . : . . . . .

o - i . . . . . . . . . . . . . . i . . . . . . . . . :=-

5 i 3 27 i . . . . . . . . . . . . .

o . - . . . . . . . . : . . . . . . . . . : . . . . . . . . . ! . "~ . . . . . . . . . i -

-40 - 2 0 0 20 40 80 80

S1 wave

2

l.fi

.2

.8

.4

0

ii i ii i iiiiiiii! '̧ i 50 70 90 ttO t30 t50 i70

station: SEL

S2 wave

......... e, ii iiiiiiiiiiiiiiiiiiiiii! -40 - 2 0 0 20 40 rio 80

FiG. 6. H i s t o g r a m s of t h e p o l a r i z a t i o n a z i m u t h s of t h e s p l i t w a v e s a n d p i e d i a g r a m s d i s p l a y i n g t h e m e a s u r e m e n t q u a l i t y of a n a l y s e d e v e n t s a t a p a r t i c u l a r s t a t i o n . T h e a z i m u t h w a s m e a s u r e d w i t h a n e r r o r o f + 5 ° (1), + 10 ° (2), a n d + 20 ° (3), o r no S - w a v e s p l i t t i n g w a s d e t e c t e d (4).

(Tables 1 and 2), however, coincide well with the values for the other stations. Therefore, these data were not removed from the analysis.

Anisotropy Hypothesis The constant S1- and S2-wave polarization directions in horizontal projection,

regardless of the station positions and event locations, indicate tha t the polar-

1 4 3 0 v . VAVRYCUK

S1 w a v e

1 o

8

6

4

2

o

50 70 90

s t a t i o n : HOIt

itO 130 150 t70

2

t .6

.2

.8

.4

0

S2 w a v e

o ..... i i i :: t

, - • • , - . • , . . . t . , . i , . . , . . . ,

-40 -20 0 2 0 40 60 80

~8

t5

9

6

3

0

S1 w a v e

' " " " ' " " " ' " " " ' . . . : . . . . . . I . . . . . . : . . ' . . . . . : . : . . ' . . -

il iiii: iiiiiiiiiiiiiiiiii::ii

!i iil i iiiiiiiiiill ~0 70 90 ~ 0 ~30 ~50 ~70

s t a t i o n : KOS

S2 w a v e

11 . . . . ; . . . . . . . . i . . . . . . . . . i . . . . . . . . . i

• . • . , . i . . . , . . . , . . , . , ,

-40 -20 0 20 40 60 80

[ ] 1 ~ 2 [ ] 3 [2] 4 FIG. 6. Continued.

TABLE 1

SI-WAVE POLARIZATION DIRECTIONS

Station N 1 N 2 (a) (~ (°)

VAC 141 132 114.1 114 3.9 TIS 139 134 135.3 136 6.6 SEL 23 9 121.0 117 17.9 H O H 29 28 119.3 120 9.1 KOS 39 38 116.7 118 6.9

a o = 121°; a = averaged value of the shear -wave polarizat ion az imuth for a

par t icu la r station; N~ = n u m b e r of analyzed events; N 2 = n u m b e r of events for which the az imuth could be measured; m = median of the shear -wave polarizat ion az imuth; $ = s t anda rd deviation; a 0 = averaged value of the shear -wave polarizat ion az imu ths for all s tat ions.

A N I S O T R O P H Y OF S H E A R - W A V E S P L I T T I N G

TABLE 2

S2-WAVE POLARIZATION DIRECTIONS

a rn Station N 1 N 2 (°) (°) (°).

VAC 141 114 25.4 25 6.5 TIS 139 112 40.6 42 9.0 SEL 23 17 19.6 21 9.4 H O H 29 13 38.8 32 18.7 KOS 39 16 28.9 33 14.6

a o = 31 ° For symbols see Table 1.

1431

ization directions are not controlled by the focal mechanism. This observation can be consistently explained by the presence of a t ransversely isotropic medium with the axis of rotation symmetry in the horizontal plane (see Crampin, 1985). The S wave passing through this medium is split into two waves that propagate at different velocities and exhibit orthogonal polarizations. The direction of the horizontal symmetry axis can be inferred from the polarization of the split S waves and should coincide with the horizontal projection of the $1- or S2-wave polarization direction.

Upper crustal t ransverse isotropy with a horizontal axis of rotation symmetry is most frequently at t r ibuted to the presence of vertical parallel fracture sys- tems in an isotropic medium. The fractures should be aligned parallel to the direction of the maximum horizontal compressive tectonic stress in the particu- lar region, or close to it (Crampin et al., 1984). Figure 7 shows a comparison of the stress direction in the West Bohemia region, determined by the hydraulic fracturing method (Rummel et al., 1983), by the fault plane solution of the main swarm shock (Antonini, 1988) and by geodetic measurements of recent horizon- tal deformations (VyskoSil, 1987) with the Sl-wave polarization direction. The polarization direction of the faster shear wave apparent ly correlates with the regional direction of stress. This result supports the hypothesis of stress- induced anisotropy in the region and indicates tha t the azimuth of the symme- try axis is probably a = 31 °.

DELAY TIME OF SPLIT S WAVES

Data and Method

The major problem in determining the delay time is to identify the S2-wave arrival reliably. The $2 wave is frequently superimposed on S1 or mixed with a number of secondary waves. The result is complex polarization in which the S2-wave onset is difficult to identify and the time delay difficult to measure. Currently, various methods are used for delay time determination (for an overview see MacBeth and Crampin, 1991): visual inspection, automated algo- r i thms using the cross-correlation function of horizontal rotated components (Shih et al., 1991), or variance tensor analysis (Aster et al., 1990). The simplest method was used in this study. Using polarization diagrams the S2-wave arrival was picked up by an analyst at the time at which an abrupt change in the prevailing Sl -wave polarization direction appeared. The author believes that it is not the method, but a large number of high-quality data tha t is decisive in successful determination of the delay time.

1432 v. VAVRYCUK

N

50.3 °.

5 0 . 0 ° •

TIS ,,

K O S "

VAC " - ,~7,,-. S E L ' -

2 "

H O H ~ -, ,.

1 4 9 . 7 "

1 2 . 0 ° 1 2 ' . 3 ° 12 ' . 6 °

E FIG. 7. Comparison of the maximum horizontal tectonic compressive stress direction in the

epicentral region (solid line; 1: Rummel et al., 1983; 2: Antonini, 1988; 3: Vysko~il, 1987) with the horizontal projection of the averaged Sl-wave polarization directions (dashed line).

The records from VAC (epicentral distance about 5 km) are exceptionally suitable for shear-wave splitting analysis: the waveforms are very simple and display distinct shear-wave splitting. The seismometers were installed on a rock massif without sedimentary cover (HorAlek and JedliSka, 1987), so tha t the seismograms are free of multiple reflections generated in subsurface layers. 249 swarm events were analyzed: in the first step the 141 events located by KolA~ and VavrySuk (1990), and in the second step another 108 events were added to provide dense coverage of the delay times for various ray directions. Incidence angles were determined for all the events from the apparent angles measured in the P-wave particle motions. The incidence angles are less than 25 °, and thus all the events lie within the shear-wave window.

Ray Geometry

As mentioned above, the hypocenters of the swarm form a narrow belt, 4 × 1 km in area, directed nor th-south. The belt dips to the south. For simplicity, we will approximate the belt by a line tha t runs through its center. The line position and orientation depend on the parameters of the velocity model used in the location procedure. Because the model is not precisely defined, we consid- ered four positions of the hypocenter line, obtained for four isotropic, homoge- neous models with vp = 5.76 km/sec and vp / v 8 = 1.62 (model 1), 1.65 (model 2), 1.69 (model 3), and 1.73 (model 4). The difference in the positions of the hypocenter line for models (1) and (4) amounts to 2.5 km in depth and 1.5 km (0.3 km) in the N-S (E-W) direction. Using the four alternative positions, we estimated the errors introduced into the ray direction calculations by inaccurate hypocenter locations.

The rays connecting the points distributed along the hypothetical line of hypocenters with the station form a set of straight lines (see Fig. 8) for which the directional variation of the delay time was studied. In a transversely isotropic medium it is sufficient to observe only its dependence on the ray

N 6

2

~-~ 0

--2

ANISOTROPHY OF SHEAR-WAVE SPLITTING

sym rn e{ry axis

-2" '6' ';,' " / , ' "8 [kin] E

a=31 °

/

V.. x, , - .....

'~ , o a

1433

/

/ FIG. 8. Horizontal projection of rays connecting station VAC with epicenters (left; located for

velocity model 2) and a spatial scheme of rays connecting VAC with the hypothetical line of hypocenters (right).

deviation from the symmetry axis (hereafter angle a). Figure 9 depicts a as a function of hypocenter position, which is uniquely determined by the difference in the arrival t imes of the P and $1 waves (hereafter t ime ts_ P) at the station. The rays arriving at VAC cover approximately only one third of the entire angle interval 0 ° to 90 °.

Results

The delay times between the split S waves range from 0.02 sec to 0.15 sec. Under the assumption tha t the s t ructure is uniformly anisotropic along the entire ray length, for the est imated hypocentral distance r = 8.8 km and averaged S-wave velocity v S = 3.5 k m / s e c the S-wave anisotropy amounts to 6%. However, this value is only the lower limit, because the measurement of the delay time does not include all the propagation directions, and thus it cannot be guaranteed tha t the delay time of ts2_sl = 0.15 sec is really the maximum.

We sought varit ions of the delay t ime as a function of time t s p. Figure 10 shows tha t this function was successfully established and is nonlinear. The least-squares method was applied to 249 events to construct an averaged function. An exponential function in the form ts2_sl = exp(a + b • ts_ P) was used to reproduce the observed nonlinear decay in data, and values a = 3.89 and b = - 5 . 9 0 have been found. The decrease in the delay t ime for growing ts_ p (and thus also for growing hypocentral distance) is caused by the promi- nent dependence of the delay t ime on ray direction. To the author 's knowledge it is the first reliably measured dependence of the delay time on hypocenter position.

Figures 9 and 10 enable us to determine the directional delay t ime variation, i.e., the delay t ime variat ion as a function of a (see Fig. 11). A new notation for the split shear w a v e s - - S P and SR waves--corresponding to the polarization directions, is introduced in Figure 11. The SP wave is the shear wave polarized in the plane defined by the ray and the symmetry axis, and the SR wave is polarized perpendicularly to tha t plane. Figure 11 indicates tha t the results are

1434

,.....~ 1 O0 •

o

8O:

60

V. VAVRYCUK

s ta t ion : VAC

4 - 0 | ! , , i ! , , , i ! , , , i , , , ! i , , , ,

0.9 1.0 1.1 1.2 1.3 1.4

t S - p [ s ]

FIG. 9. Ray deviation from the symmetry axis as a function of ts_ P, The function is calculated for the hypocenters forming the hypothetical line for four alternative velocity models.

not very sensitive to the position of the hypocenter line. The alternative velocity models produce similar directional delay time functions that differ only slightly in slope and are only displaced a little in a. The errors introduced into the analysis by inaccurate hypocenter locations were suppressed by this lucky coincidence.

INVERSION FOR OPTIMUM FRACTURE MODEL

Inversion for t ransverse isotropy implies evaluating five independent elastic parameters in the coordinate system connected with the symmetry axis. Unfor- tunately, the inversion cannot be solved in general. The reason is the lack of observational data and nonlinearity of the problem. Therefore, we will simplify the problem and search for the optimum model only in transverse isotropies originating in fracture models. The advantage of these models consists of using est imated parameter values of the isotropic background as additional informa- tion for anisotropy inversion. In the following, we will search for the optimum model by comparing the observed directional delay time function with the theoretical functions generated by the most frequently used fracture models: Hudson's crack model (Hudson, 1980; 1981) and Schoenberg--Douma's fracture model (Schoenberg and Douma, 1988).

Hudson's Crack Model

Hudson's model of parallel cracks is described by the elastic parameters of an isotropic background, A, tL, by crack density e, aspect ratio e, and by the elastic parameters of the material contained in the cracks, A', t~'- We consider two types of cracks: dry cracks (A' = 0, tL' = 0) and water-filled cracks (A' = 2.25. 109 N / m 2, tL' = 0) both nearly flat in shape (e = 0.001). The cracks are vertical and oriented parallel to the maximum horizontal tectonic stress, i.e., the azimuth of the crack normal is a = 3i °. Value e = 0.1 is used for the crack

A N I S O T R O P H Y OF SHEAR-WAVE S P L I T T I N G 1435

0. i5 Gq

0.~2 I

.~ 0.09

0.06

0.03

/

. : : : . - . ' . - . - . : : . , . - o - . - . : : : . - . ' . - . , . : : ; - • , . - . : : : . ,

. ~ . : • . •. . . . . . . . . . . . . . . . : . . . . . .'. . . . . . : . . . . . . •

: - . : " . . . . ~ - : : : : : " .~{,:.. . • .

.... ~ . :.._~:. : ........... . ...... . • ''~" .=.ol ~=m m .oo • . -~'~

• i\ ".'-- ........... ........... = InB mo

. . . . . ram. i •

. . . . . . . . . . . . .iiilN , ' - : - . . - . . . . : : -. 2: 1.05 i . i \ i . : ~ 5 1.2 i.P-5 1.3

!

N

Sl on:et $2 on~ot /

E-

1

N

52 ~ onset E

i

N

.~sl E

$I o n~= ~ t ~ n se

FIG. 10. t s 2 _ s 1 as a function of t s _ P for the VAC stat ion with examples of shear-wave spli t t ing for three events. The delay t ime was normalized to 1 sec of t s_ p. Part icle motions in the horizontal projection show events ( le f t ) : of 31 December 1985 at 1:23:44 ( M L = 2.5, t s _ P = 1.02 sec, At = 7 ms), 1 J a n u a r y 1986 at 4:45:29 ( M L = 1.2, t s_ P = 1.10 sec, A t = 7 ms), 24 December 24, 1985 at 8:54:15 ( M L = 1•0, t s _ P = 1.26 sec, At = 8 ms). The distance between two points in particle motion represents the sampling interval At.

densi ty , however , in the di rect ional va r i a t ion of the de lay t ime this p a r a m e t e r only plays the role of a scaling factor and does not change its form. Values A -- 31.3- 109 N / m 2 and /~ = 3 1 . 3 . 1 0 9 N / m 2 were appl ied for the isotropic background. These va lues were der ived f rom the e s t ima ted velocity model in the West Bohemia region ( V p = 5.76 k m / s e c , v s = V p / ~ / 3 , p = 2.85- 103 kg /m3) .

F igure 12 shows t h a t the theore t ica l de lay t ime va r i a t ion c lear ly d isagrees wi th the observa t iona l data . In the angle in te rva l of 50 ° to 90 ° the model predic ts an increase in the de lay t ime, bu t ins tead a drop is observed. For

= 90 ° the theore t ica l de lay t ime displays a m a x i m u m for bo th types of cracks. This p rope r ty is p r e se rved for all va lues of the crack p a r a m e t e r s (see e.g., Douma, 1988; Peacock and Hudson , 1990), and thus the d i sc repancy be tween the observed and theore t ica l de lay t ime funct ion cannot be e l imina ted wi th in the scope of Hudson ' s model of para l le l cracks•

S c h o e n b e r g - D o u r n a ' s F r a c t u r e M o d e l

The model of a m e d i u m wi th para l le l f r ac tu res is based on the idea of an isotropic m e d i u m conta in ing a sys tem of para l le l i n t e rna l f r ac tu re in te r faces on

1436 v. V£VRYCUK

I I

b'3 I

r.D

a = 3 1 ° 0 . 0 2

0.01

0.00 4 5 ' ' 6'0 ' 7 '5 ' 9'0

FIG. 11. N o r m a l i z e d de lay t ime of the spl i t S w a v e s tzR_sp as a function of the ray deviat ion from the s y m m e t r y axis.

! i

13.,

I

a = 3 1 °

0 . 0 3

0.00

- 0 . 0 3

/

f f

/ J

i i

, i t i , ! , i , , , i , , a , i

0 3 0 6 0 9 0

Fro. 12. Compar i son of observed direct ional de lay t ime variat ion (solid l ine) wi th theoret ica l funct ions (dashed l ine) ca lculated for Hudson's model of a m e d i u m wi th dry (a) and water-f i l led (b) paral le l cracks. The de lay t ime is normal i zed to 1 k m of the ray length. E l e m e n t s of Hooke's matr ix

6 2 (in 10 m / see ) : dry cracks: e l l = 31.4, c13 = 6.5, ca3 = 19.4, %4 = 8.8, %6 = 11.0; and water-f i l led cracks: c l i = 32.9, cla = 10.8, ca3 = 32.4, c44 = 8 . 8 , C 6 6 = 11.0.

ANISOTROPHY OF SHEAR-WAVE SPLITTING 1437

which reversible displacements take place (Shoenberg and Douma, 1988). In this model, the computation of elastic coefficients of effective anisotropy in- volves the elastic coefficients of an isotropic background, •, tL, and two fracture parameters, E N , E T. The fracture parameters are dimensionless constants char- acterizing the response of fractures to the normal and shear stress, respectively. The stability conditions on the fracture interfaces (see Douma, 1988) restrict E N

and E T to nonnegative values only. For E g = 0 and E T = 0 the model degener- ates to the isotropic medium without fractures.

Analogously to Hudson's model, we take A = 31.3 • 109 N / m 2 and ~ = 31.3 • 109N/m 2 as the isotropic background values, and the fractures are vertical with azimuth of the normal a = 31 °. Figure 13a shows a comparison between the observational data and theoretical functions calculated for four fracture models: E y = 0.4, E T = 0 (model a), E N = 0.2, E T = 0 (model b), E g = O,

E T = 0.2 (model c), and E N = 0.2, E T = 0.2 (model d). Figure 13b gives a detailed comparison of the models with a good agreement with observations: E N = 0.3, E T = 0 (model 1), E N = 0.4, E T = 0 (model 2), and E N = 0.4, E T

0.02 (model 3). A model within the range of models 1, 2, and 3, whose parame- ters are close to values E N = 0.4, E T ~ 0.02, can be considered the model tha t fits the experimental data best.

Hooke's matrix of this effectively anisotropic medium normalized by the medium density has the following form

23.5 7.8 7.8 0 0 0 31.9 9.9 0 0 0

Ci j = 31.9 0 0 0 . 106 m2/sec 2. 11.0 0 0

10.8 0 10.8

Matrix Ci j is specified in a coordinate system in which axis x coincides with the axis of rotation symmetry.

The following facts lend support to this optimum model. The behavior of the fracture interfaces as well as the resul tant transverse isotropy are stable. The orientation of the symmetry axis corresponds to the idea of the presence of cracks or fractures parallel to the direction of the maximum horizontal tectonic stress in the West Bohemia region. The directional delay time function pre- dicted by this model is in satisfactory agreement with the observed delay time function. The directional dependence of P- and S-wave velocities seems to be realistic (see Fig. 14)

G e o l o g i c a l I m p l i c a t i o n s

We are now faced with the questions: How does the theoretical optimum fracture model correspond to the real structure? What can be deduced from this analysis about the existence and nature of real cracks or fractures in the geological structure of the West Bohemia region?

The theoretical model predicts parallel fractures oriented in the maximum tectonic stress direction. However, the theoretically calculated fractures deviate from the direction of the major fault system (see Fig. 2) by 30 ° , and thus the fractures cannot be simply identified with the faults in the region. Therefore, if the detected anisotropy is really induced by the cracks or fractures, the frac- tures should be of a much smaller size than the faults.

1438 v. V£VRYCUK

0.04 ! I

I 0.02 [/3

0.00

- 0 . 0 2

- 0 . 0 4

"~' 0.025 I I

I I:g 0.015

0.005

a.=31 °

/ f

d "

0

a=31 °

'3'0

(a)

, !

6O 9O [o]

1

- 0 . 0 0 5 i i ! i

40 50 60 70 80 90

(b)

FIG. 13. C o m p a r i s o n of obse rved d i rec t iona l de l ay t i m e v a r i a t i o n (solid l ine) w i t h t heo re t i c a l func t ions ca l cu l a t ed for t he S c h o e n b e r g - - D o u m a ' s f r ac tu re models . The de lay t i m e is n o r m a l i z e d to i k m of t he r a y l eng th . E l e m e n t s of Heoke ' s m a t r i x ( in 106 m 2 / s e c 2 ) : model a: c l l = 23.5, c13 = 7.8, c33 = 31.9, c44 = 11.0, c66 = 11.0; model b: Cll = 27.5, c13 = 9.2, c3~ = 32.3, c44 = 11.0, c66 = 11.0; model c: c l l = 32.9, c13 = 11.0, c3~ = 32.9, c44 = 11.0, c66 = 9.2; a r ia mode l d: c l l = 27.5, c13 = 9.2, c38 = 32.3, c44 = 11.0, c66 = 9.2. Cb) D e t a i l e d compar i son of obse rved d i r ec t i ona | de l ay t i m e var ia - t ion (solid l ine) w i t h t heo re t i c a l func t ions (dashed l ine) p roduced by models , for wh ich a q u a l i t a t i v e fi t w a s found. E l e m e n t s of Hooke ' s m a t r i x ( in 10 6 m2 / sec2 ) : mode l 1: c l l = 25.3, c13 = 8.4, c33 = 32.1, c44 = 11.0, c66 = 11.0; mode l 2: c l t = 23.5, c13 = 7.8, c3~ = 31.9, c44 = 11.0, c66 = 11.0; and model 3: Cll = 23.5, c13 = 7.8, c33 = 31.9, c44 = 11.0, c66 = 10.8.

ANISOTROPHY OF SHEAR-WAVE SPLITTING 1439

5.5

5.0

0 0 > 4.5

4.0

P w a v e 6.0 3.4

3.3

3.2

3.1

3.0 0 30 60 90 0

,~[°]

SR wave

30 60 90 ~ [ ° ]

3.4

.3.3

3.2

3.1

3,0

SP wave

xx 4 " • \ // x \ / /

7", ,, / /

30 60 90 ~[° ]

FIG. 14. Phase velocity of P, SP, and SR waves as a function of the direction of propagation for model 1 (dashed line), model 2 (dotted line), and model 3 (solid line) from Figure 13b.

Other information about the nature of the fractures, provided by the theoreti- cal fracture model, concerns the type of contact between the fracture surfaces. The optimum fracture parameter values E N = 0.4 and E T = 0.02 indicate tha t the fractures are sensitive to normal stress, but display almost no response to shear stress. One of the possible explanations for this could be the irregularly roughened fracture interfaces, the sides of which are clenched each into the other.

CONCLUSION

The only satisfactory explanation of the S-wave splitting, observed in records of local events which occurred during the 1985/1986 West-Bohemian earth- quake swarm, is effective transverse isotropy of the upper crust in the region. Transverse isotropy has a horizontal axis of rotation symmetry and causes approximately 6% anisotropy of S waves. The polarization direction of the fast shear wave, and thus also the direction of the symmetry axis, are apparently related to the direction of the maximum horizontal tectonic compressive stress in tha t region. Stress-induced anisotropy is accounted for by the presence of vertical parallel cracks or fractures, oriented in the direction of the acting tectonic stress. The reliably measured directional delay time variation enabled the author to perform the first ever test of applicability of theoretical fracture models to real structures.

It is proved tha t the commonly used Hudson model of dry or water-filled parallel cracks cannot be applied to the West Bohemia region, because it is unable to give a satisfactory explanation of the directional delay time variation. The failure of Hudson's crack model need not imply the absence of cracks in the geological structure, but more likely tha t the real crack behavior is not ade- quately described by this model. It could indicate tha t Hudson's model of parallel cracks inadmissibly simplifies the real crack geometry.

An optimum theoretical model fitting all the existing data was found with the aid of Schoenberg-Douma's fracture model. The model assumes an isotropic medium with velocities v p = 5.76 km/sec and v s = V p / { 3 , tha t contains paral- lel vertical fractures with azimuth of the normal a = 31 °. The values of the fracture parameters should be close to E W = 0.4 and E T = 0.02. This model has to be viewed as an approximate solution, which is only one of a variety of other possible solutions. The model, however, has the unique property tha t it is not

1440 v. V£VRYCUK

f o r m a l , i t i s in a c c o r d a n c e w i t h e x i s t i n g k n o w l e d g e of t h e t e c t o n i c s t r e s s in t h e r e g i o n , a n d i t i m p l i c a t e s r e a l i s t i c v a l u e s of P - a n d S - w a v e v e l o c i t i e s .

T h e g e o l o g i c a l i n t e r p r e t a t i o n o f t h e p r o p o s e d o p t i m u m m o d e l i s n o t s t r a i g h t - f o r w a r d . T h e t h e o r e t i c a l l y c a l c u l a t e d f r a c t u r e s c a n n o t be s i m p l y i d e n t i f i e d w i t h s u r f a c e t e c t o n i c l i n e s i n t h e W e s t B o h e m i a r e g i o n . I t c a n b e o n l y h y p o t h e s i z e d t h a t t h e f r a c t u r e s , i f t h e y e x i s t i n t h e r e a l g e o l o g i c a l s t r u c t u r e a n d c a u s e a n i s o t r o p y , s h o u l d b e o f a s m a l l e r s i ze t h a n t h e f a u l t s a n d s h o u l d b e p r e v a i l - i n g l y o r i e n t e d i n t h e m a x i m u m h o r i z o n t a l t e c t o n i c s t r e s s . T h e f r a c t u r e p a r a m e - t e r v a l u e s i n d i c a t e , f u r t h e r m o r e , t h a t t h e f r a c t u r e s a r e n o t s e n s i t i v e to s h e a r s t r e s s b u t o n l y to n o r m a l s t r e s s . T h i s f a c t c o u l d b e e x p l a i n e d b y f r a c t u r e s w i t h i r r e g u l a r l y r o u g h e n e d s u r f a c e s .

ACKNOWLEDGMENTS

The author thanks Vladislav Babu~ka, Axel Ple§inger, and Ivan P~enSik for their review and helpful comments, and M. Antonini and E. Schmedes for making available the data from the SEL and HOH stations.

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GEOPHYSICAL INSTITUTE CZECH ACADEMY OF SCIENCE BO~Nf II / 1401 14131 PRAGUE, CZECH REPUBLIC

Manuscript received 27 March 1992