ÖTZ OKELMANN

The paper by V. Vavrycuk (1993) studies crustal anisotropy using data of the Western Bohemian earthquake swarm of 1985/1986. He attempts to fit models of effective crustal anisotropy and finds that the Schoenberg-Douma model (1988) of parallel fractures gives a reasonable fit to the splitting delay data. He also concludes that the Hudson model of oriented cracks (Hudson, 1980, 1981) fails to describe the upper-crustal anisotropy in the West Bohemian region. Unfortunately, the validity of this conclusion depends strongly on the chosen fixed orientation of the model. We feel that such a strong conclusion is not required by the data, since the chosen orientation (strike and dip) may not be appropriate. This point is based on the following arguments: 1)The author used a symmetry axis orientation based on fast shear-wave polarizations. However, backazimuths of all events recorded at the station considered (VAC) are in the range of 80$^\circ$ to 120$^\circ$. This coverage alone is not enough to determine the orientation, i.p. the dip of the symmetry axis. A few other stations also show East-West fast polarization, but the coverage does not justify fixing the symmetry axis. 2)The chosen symmetry axis azimuth for VAC does not coincide with best available estimates of the regional stress field. Local stress fields and other possible causes of shear-wave splitting, however, may differ from station to station. This poses the question, whether data from different stations in the region may be interpreted in terms of a single model. 3)The assumed horizontal orientation relates to a model of tensile crack behaviour throughout the crust, which is not required. 4)The author justified the fixed orientation assumption as necessary due to the degree of underdetermination. However, there are data sets which allow inversion for a more comprehensive anisotropic model of the upper crust. One of them is given by P-wave polarizations from the 3-component GERESS array (Bokelmann, 1993), which are sensitive to anisotropy close to the receivers.

In the following we will discuss these arguments and subsequently show that the Hudson model may in fact give good fit to the splitting delay data of Vavrycuk (1993) if the symmetry axis orientation is allowed to deviate somewhat from the one chosen by Vavrycuk.

Recordings of the quake swarm at VAC cover only a narrow range of backazimuths unfortunately. To obtain information for more azimuths, Vavrycuk (1993) implicitly assumed that fast polarizations at several stations are caused by the same effect. This may be the case for example, if the regional stress field is the dominant cause of shear-wave splitting. However, the most reliable values for the regional stress direction are from the KTB borehole (figure 1), since deeper levels may be considered comparatively free from near-surface effects. For different types of measurements values of 149$^\circ$ are found (Brudy et al., 1993), which is consistent with earlier values for $\sigma_H$ (Müller et al., 1992). Vavrycuk (1993) finds fast polarization values which deviate systematically from 149$^\circ$ to lower values suggesting that effects different from the regional stress field are important.

A horizontal symmetry axis orientation is not required from rheological arguments neither. The frequently used concept which includes such an orientation is the model of aligned vertical cracks, where cracks open perpendicular to the direction of the minimum compressive stress which is assumed to be horizontal in this case. In general, we obtain faulting perpendicular to the minimum compressive stress direction only for the purely tensile case. According to the current view (Suppe, 1985) such faulting behaviour requires small deviatoric stresses and relatively large pore fluid pressures. The size of the fluid pressure $P_f$ in the basement is controversial to some degree. While Fournier (1990) gives data allowing tensile fracturing to occur throughout the upper crust, data of Brace (1980) suggest the contrary. Such differences may to some degree reflect regional differences. The one source of data, which perhaps gets closest to ground truth in the region considered, is the KTB drill hole at a distance of less than 50 km from the station of interest in the Western Czech Republic (figure 1). If there were extensive opening of vertical cracks due to the current stress field, this would likely be the case also at this deep drilling site. While in certain depth intervals there are in fact indications of recent sub-vertical cracks (3000-4000m, Brudy et al., 1993), open microcracks often deviate substantially from the direction of maximum horizontal compressive stress (Vollbrecht et al., 1993). The fluid pressure is somewhat enlarged (at 6 km by less than 10 MPa, Huenges, 1993) indicating a pore-fluid pressure slightly larger than the hydrostatic pressure, but probably not sufficient to cause pervasive tensile faulting. Although tensile behaviour throughout the upper crust is not impossible, these observations suggest that it is not likely.

The above arguments show that a horizontal symmetry axis orientation is not required; if this assumption is made nevertheless, one cannot discount models on this basis!

The author claimed that the Hudson crack model cannot fit the splitting delay data for his station at Vackow shown by the solid square in figure 1. Based on the arguments above we suggest that the symmetry axis may very well deviate from the azimuth value used, and also from the horizontal plane. In fact, figure 2 shows the two quasi-shear velocities for a Hudson-type model, which does fit the data. This model has a symmetry plane with strike 114$^\circ$ and dip 50$^\circ$. The model is furthermore specified by a crack density $\epsilon=0.05$ and the Lamé-parameters $\lambda^\prime =\mu^\prime$=0 within the cracks. The aspect ratio is 0.0001 and the background velocity is close to the ones used by Vavrycuk (1993), namely $v_P$=5.8 km/s and a velocity ratio of $\sqrt{3}$.

In such a hexagonal model, one shear-wave (qSP) is polarized within the plane of the ray and the symmetry axis (Crampin, 1981). qSR denotes the shear-wave polarized perpendicularly to that plane. The white traces in figure 2 show the approximate lower hemisphere location of the data of Vavrycuk (1993). Here we do not account for steepening due to sediments under the receivers to better simulate the ray coverage in the upper crust. The two quasi-shear waves have quite different angular dependence and the difference in velocity ranges between -0.1 and 0.2 km/s. The data of Vavrycuk (1993) have spatial coverage essentially of a North-South strip in the Eastern direction of the lower hemisphere. On the Northern part of the strip (closer) they show a larger time difference of about 0.125 seconds between the two quasi-shear waves and in the Southern part (more distant) a smaller time difference of about 0.023 seconds (figure 10 of Vavrycuk 1993). To the first order these time differences (time split) are linearly related to velocity split

$$\Delta t\approx {D\over v^2}\Delta v$$

For $v$=3.3 km/s and $D$$\approx$10 km we find an approximate 1:1 relation of our $\Delta v$ in km/sec and the delay time scale of Vavrycuk (1993) in seconds. Figure 3 shows the velocity split $v_{qSR}-v_{qSP}$ on the left. On the right, the effect for 30$^\circ$ incidence (white circle) is compared with the data of Vavrycuk (1993) using the equivalence. Clearly, the fit is quite good, particularly with regard to the slope. The insignificant offset may be due to a minor shift in the background velocity. This alternative model, which fits the data, suggests that indeed the shear-wave splitting delay data do not constrain the orientation of the symmetry axis very well. Although the author used a large number of events, the angular coverage was clearly rather restricted. For the study of upper-crustal anisotropy using shear-wave splitting delay this represents a typical problem, since only nearby events may be used. Shear-wave splitting delay gives an integral constraint on anisotropy; hence it averages along the whole ray path. Therefore data from more distant events might also contain effects from more distant anisotropy.

Interestingly, this is not a fundamental problem of seismology. Local methods, such as P-wave polarization studies, allow utilization of events from all epicentral distances for the purpose of upper-crustal anisotropy studies. This local property was used in a recent study (Bokelmann, 1993), where 3-component array data were used to fit polarization angles. Deviations of observed polarization angles from array slowness vector directions, averaged over the array, are sensitive to near-receiver anisotropy only, which may be described by a general $c_{ijkl}$-matrix. In the case of the model of Hudson (1980, 1981) we may fit 43% of these data using 5 parameters as variables: Crack density $\epsilon$, Lamé parameters within cracks $\lambda^\prime$, $\mu^\prime$ and strike and dip of the symmetry axis. In fact, the model used above is the result of such an inversion for data from the GERESS array (figure 1), which is located about 200 km to the Southeast. The single exception is a reduced crack density $\epsilon$ (0.05 instead of 0.09). For crack density $\epsilon$=0.09 the fit is slightly worse, but still acceptable. Here this model serves only to demonstrate that Hudson-type models with orientations deviating somewhat from the fixed orientation chosen by Vavrycuk (1993) can also fit the splitting delay data in Western Bohemia. For the GERESS region this model was one of a set of models, which could be related to surface geology. The orientation closely agreed with the observed gneiss foliation direction. For these models a horizontal symmetry axis was ruled out on statistical grounds. Dipping symmetry axis orientations were also found for the KTB deep drilling site (figure 1) by Lüschen et al. (1991). Also in that study the orientation showed the tendency to follow the rock foliation.

The model of Vavrycuk (1993) suggested macroscopic fractures where the tangential excess compliance $E_t$ is much smaller than the normal $E_n$, indicating high shear strength, but weak normal strength, which is a rather exotic model. Concerning its orientation, one would expect some relation of these features with the dominant fault systems in the area, a relation, which is not apparent though (Vavrycuk 1993).

The essence of this comment though is that Hudson's model can't be precluded by the argument of Vavrycuk (1993), which is based on splitting delay data.

CKNOWLEDGEMENTS

I acknowledge Hans-Peter Harjes, Bernd Stöckhert and Fritz Rummel for valuable discussions and Paul Wessel and Walter Smith for permission to use the GMT plotting package.

EFERENCES

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Bokelmann, G. (1993). P-wave array polarization analysis and effective anisotropy of the brittle crust, Geophysical Journal International, in press.

Brace, W.F. (1980). Permeability of crystalline and argillaceous rocks, Abstr. Int. J. Rock. Mech. Min. Sci. Geomech. 17, 241-251.

Brudy, M., K. Fuchs, M.D. Zoback (1993). Stress orientation profile to 6 km depth in the KTB main borehole, KTB Report 93-2.

Crampin, S. (1981). A review of wave motion in anisotropic and cracked elastic-media, Wave Motion 3, 343-391.

Fournier, R.O. (1990). Scientific drilling to investigate the physical and chemical nature of fluids in the Earth's crust at 400-500$^\circ$C, in: Super-Deep Continental Drilling and Deep Geophysical Sounding, ed. by K. Fuchs et al., Springer-Verlag.

Hudson, J.A. (1980). Overall properties of a cracked solid, Mathematical Proceedings of the Cambridge Philosophical Society, 88, 371-384.

Hudson, J.A. (1981). Wave speeds and attenuation of elastic waves in material containing cracks, Geophysical Journal of the Royal Astronomical Society 64, 133-150.

Huenges, E. (1993). Profiles of permeability and formation-pressure down to 7,2 km, KTB Report 93-2.

Lüschen, E., W. Söllner, A. Hohrath, W. Rabbel (1991). Integrated P- and S-wave borehole experiments at the KTB deep drilling site in the Oberpfalz area, in: Continental Lithosphere: Deep Seismic Reflections, AGU Geodynamics Series, Vol. 22.

Müller, B., M.L Zoback, K. Fuchs, L. Mastin, S. Gregersen, N. Pavoni, O. Stephansson, C. Ljunggren (1992). Regional patterns of tectonic stress in Europe, Journal of Geophysical Research 97, 11783-11803.

Schoenberg, M., J. Douma (1988). Elastic wave propagation in media with parallel fractures and aligned cracks, Geophysical Prospecting 36, 571-590.

Suppe, J. (1985). Principles of structural geology, Prentice-Hall Inc., Englewood Cliffs, NJ.

Vavrycuk, V. (1993). Crustal anisotropy from local observations of shear-wave splitting in West Bohemia, Czech Republic, Bulletin of the Seismological Society of America 83, 5, 1420-1441.

Vollbrecht, A., H. Dürrast, K. Weber (1993). Open microcracks: indicators for in situ stress directions, KTB Report 93-2.

INSTITUTE OF GEOPHYSICS RUHR-UNIVERSITY BOCHUM, FEDERAL REPUBLIC OF GERMANY

FIGURES

FIG. 1. Region of study in the border area of the Czech Republic and Germany (elevation in meters). The station at Vackow is shown by a solid square. The cross indicates the location of the 1985/86 earthquake swarm. Also locations of the KTB deep drilling hole and the GERESS array are shown.

FIG. 2. Velocities (in %) of the two quasi-shear waves of a Hudson-type model approximately fitting the shear-wave splitting data of Vavrycuk (1993). The white trace gives the approximate location of his data, not accounting for steepening due to sediments under the receivers.

FIG. 3. Velocity splitting for the alternative model (left, in %). The azimuthal effect along the white circle is shown on the right, together with velocity data for Vavrycuk (1993). The data are well-matched, in particular the azimuthal slope, which is controlled by anisotropy.