The lowermost section of the continental superdeep drill hole German Continental Deep Drilling Program (KTB) (south Germany) has been investigated for the first time by vertical seismic profiling (VSP). The new VSP samples the still accessible range of 6–8.5 km depth. Between 7 and 8.5 km depth, the drill hole intersects a major cataclastic fault zone which can be traced back to the Earth's surface where it forms a lineament of regional importance, the Franconian line. To determine the seismic properties of the crust in situ, in particular within and around this deep fault zone, was one of the major goals of the VSP. For the measurements a newly developed high-pressure/high-temperature borehole geophone was used that was capable of withstanding temperatures and pressures up to 260°C and 140 MPa, respectively. The velocity-depth profiles and reflection images resulting from the VSP are of high spatial resolution due to a small geophone spacing of 12.5 m and a broad seismic signal spectrum. Compared to the upper part of the borehole, we found more than 10% decrease of the P wave velocity in the deep, fractured metamorphic rock formations. P wave velocity is ∼5.5 km/s at 8.5 km depth compared to 6.0–6.5 km/s at more shallow levels above 7 km. In addition, seismic anisotropy was observed to increase significantly within the deep fracture zone showing more than 10% shear wave splitting and azimuthal variation of S wave polarization. In order to quantify the effect of fractures on the seismic velocity in situ we compared lithologically identical rock units at shallow and large depths: Combining seismic velocity and structural logs, we could determine the elastic tensors for three gneiss sections. The analysis of these tensors showed that we need fracture porosity in the percent range in order to explain seismic velocity and anisotropy observed within the fault zone. The opening of significant pore space around 8 km depth can only be maintained by differential tectonic stress combined with intense macroscopic fracturing. VSP reflection imaging based on PP and PS converted reflected waves showed that the major fault system at the KTB site is wider and more complex than previously known. The so-called SE1 reflection previously found in two- and three-dimensional surface seismic surveys corresponds to the top of an ∼1 km wide fault system. Its lower portion was not illuminated by surface seismic acquisition geometry. VSP imaging shows that the fault zone comprises two major and a number of smaller SE dipping fault planes and several conjugate fracture planes. The previously recognized upper fault plane is not associated with a strong velocity anomaly but indicates the depth below which the dramatic velocity decrease starts. Regarding the complexly faulted crustal section of the KTB site as a whole, we found that fluctuation spectra of rock composition and seismic velocity show similar patterns. We could verify that a significant amount of P wave energy is continuously converted into shear energy by forward scattering and that multipathing plays an important role in signal formation. The media behaves effectively smoothly only at wavelength larger than 150 m. It was shown by moving source profiling that the media is orthorhombic on a regional scale. The tilt of the symmetry axes of anisotropy varies with depth following the dip of the geological structure.
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 The superdeep KTB drill hole is located in the Variscan mountain belt of southeastern Germany. After intersecting a stack of complexly folded and faulted metamorphic rocks, known as Erbendorf-Vohenstrauss zone (ZEV), it ends at 9.1 km depth in a tectonically crushed felsic rock unit, only 2 km above a prominent midcrustal layer, the so-called Erbendorf body (Figure 1).
 The German Continental Deep Drilling Project (KTB) comprises a pilot hole drilled to 4 km depth and a main borehole drilled to 9.1 km depth (KTB-Oberpfalz VB and HB, respectively). Today the main borehole is accessible to 8.5 km. While vertical seismic profiles had been recorded to 6 km in the KTB borehole in the early 1990s [e.g., Dürbaum et al., 1990, 1992; Lüschen et al., 1996], the deep part of the borehole (6–8.5 km) had never been profiled seismically leaving the most critical part a question mark. This superdeep KTB section was recently investigated for the first time with vertical seismic profiling. The measurements became possible only after a special high-pressure/high-temperature (HP/HT) borehole geophone had been developed capable to withstand fluid pressures and temperatures of up to 140 MPa and 260°C, respectively, which are found in the deepest part of the borehole.
 A large number of fundamental questions regarding the crust can be addressed by the new VSP. Many of these revolve around the effects of fluids but other important aspects such as the nature of reflecting zones in the middle crust are also involved. In the present article we are concentrating on in situ seismic velocities and the reflection structure of the upper crust and its changes near the brittle-ductile transition zone. In particular, we are studying the following questions:
 1. Which P and S wave velocities are found in situ, in particular, in deep cataclastic fault zones such as drilled at the KTB site and near the brittle-ductile transition zone?
 2. What is the influence of fractures, fluids and rock texture on these seismic interval velocities and on anisotropy?
 3. Is the upper crust brine saturated and do the fluids influence the brightness of reflections?
 4. Do anisotropy, rock texture, fractures correlate with tectonic stress, and how do they change with depth?
 5. Can the surface seismic image of the major fault zone drilled at the KTB site be verified and calibrated by high-resolution VSP imaging?
 6. To which extent does scattering obscure seismic results? How do P and S wave fields evolve with depth before they enter and image, for instance, the lower crust?
 Our article is arranged as follows: Section 2 is a brief description of the geological situation at the KTB site and of previous seismic investigations relevant for this study. The concept and some practical aspects of data acquisition are outlined in section 3 including information on the new borehole geophone. Results on the seismic velocity field are shown next with a focus on the heterogeneity of P wave velocity (section 4.1) and on the depth variation of S wave anisotropy, S wave polarization (section 4.2) and of regional P wave anisotropy (section 4.3). The influence of fractures and water on seismic velocity, anisotropy, and reflectivity is quantified in section 5 by comparing lithologically identical rock units from different depth levels (section 5.1). Downhole reflection seismics with P and PS converted waves is applied in order to link seismic velocities found along the borehole to the fault zone structure off the borehole and to evaluate respective surface seismic sections (section 5.2). Results are summarized and discussed in section 6.
2. Geological and Seismic Framework at the KTB Site
 The Erbendorf-Vohenstrauss zone is an example of metamorphic crystalline crust found in many places of the Earth where multiple tectonometamorphic cycles finally created a complex geological structure from initially simple strata. The rock column drilled at the KTB site basically consists of alternating felsic and mafic layers, mainly biotite gneiss and amphibolite. They were steeply folded and squeezed mainly under ductile conditions and finally displaced and stacked along various conjugate and azimuthally varying fault planes. The deformation processes started in the middle Paleozoic when the Variscan terranes of the Saxothuringian, Bohemian, and Moldanubian subsequently collided. In the late Carboniferous, between 335 and 305 Ma, the final and postorogenic collapse initiated the ascent of granite bodies found today north and east of the KTB site (Figure 1). Major compressional faulting phases occurred in the late Variscan (300 Ma) and in the Cretaceous (130–65 Ma), and high-angle normal and strike-slip faults were active in the Neogene (<22 Ma). Today maximum horizontal stresses at the KTB site are directed approximately NW-SE. They are consistent with the average stress field in central Europe, which is still dominated by the push of the Alpine orogeny. Comprehensive descriptions of the geological evolution and faulting history of the Variscan suture area around the KTB site are, for example, given by Hirschmann , Emmermann and Lauterjung , O' Brien et al. , and Wagner et al. .
 At a depth of ∼9 km, where the brittle-ductile transition zone is supposed to begin, rocks were found crushed and in a mechanically critical state as the onset of hundreds of microearthquakes right after the start of fluid injection experiments has shown [Zoback and Harjes, 1997; Baisch et al., 2002]. The most important finding of the investigations at the KTB site was probably the presence of open fractures, water, and hydraulic connections even at the largest depth levels [Möller et al., 1997]. On the basis of the migration of seismicity during fluid injection, hydraulic permeability and diffusivity on the orders of 10−16 m2 and 1 m2 s−1, respectively, were found at the depth level of 7.5–9 km [Shapiro et al., 1997].
 Geological details of the KTB site can best be recognized from a three-dimensional (3-D) view created by Hirschmann  on the basis of reflection seismic images, drilling results, borehole measurements, and thorough analyses of geologic data (Figure 1). Along the borehole the dip of the folded gneiss and amphibolite layers is steep, between 30° and 90°. Displaced along various, partly conjugate fault planes they form a crisscrossing pattern of rock blocks. The most prominent of these fault zones can be followed up to the Earth's surface where its outcrop is found, the so-called Franconian Line. It was identified prior to drilling in a reflection survey of the German Continental Reflection Seismic Program (DEKORP). Its reflection image the so-called SE1 reflection, has been attributed to a sequence of partly cataclastic, partly water-bearing fracture zones drilled at 7 km depth and below [de Wall et al., 1994]. At these depths, an increasing number of borehole instabilities were observed, probably caused by fluid pressure and tectonic stress acting on weak, steeply dipping and mechanically anisotropic rock [Engeser, 1996; Borm et al., 1997]. These instabilities brought the drilling activity to end at 9.1 km. Below the KTB main hole the dip of layering seems to flatten because the prominent and crustal reflections of the Erbendorf body at 11 km depth are clearly subhorizontal.
 The KTB site was previously investigated comprehensively both with surface and, to a depth of 6 km, with borehole seismic methods. Results were compiled and summarized by Dürbaum et al. [1990, 1992], Lüschen et al. , and Harjes et al. . Buske [1999a, 1999b] provided a 3-D reflection image of the upper and middle crust at the KTB site based on prestack Kirchhoff migration of surface seismic data. One of the most important objectives of these previous measurements was to investigate the causes of seismic reflectivity of the crystalline crust, that is, to accurately image the subsurface structure in 2-D and 3-D and to calibrate the surface seismic response by linking it to the drilled geological section through vertical seismic profiling. The Harjes et al. [1997, p. 18,267] analysis showed that the “… strongest reflected signals originated from fluid-filled and cataclastic fracture zones rather than from lithological boundaries or from texture- and/or foliation-induced anisotropy…”. However, the most important seismic targets were below 6 km and thus beyond the reach of the previous VSP: in particular the SE1 fault zone and the weak rock material which had caused so expensive complications in the final drilling phase.
3. Acquisition of Seismic Borehole Data
3.1. Experimental Setup
 The sequence of seismic borehole measurements treated in the present article was performed in 1999 and 2000. It comprises two vertical seismic profiles (VSPs) with shot points at near offset (∼300 m) and 8 km offset SE, respectively, and six moving source profiles (MSPs; see section 4.3).
 The major objectives of the near-offset VSP were (1) to determine accurate velocity-depth functions of P and split S waves along the borehole, and to compare them with sonic logs and other borehole and laboratory data, (2) to image details of the steeply dipping SE1 fault zone taking advantage of the vertical arrangement of geophone positions, and (3) to study details of wave propagation such as scattering and absorption and their relation to rock structure. Between 5.2 and 8.5 km the near offset VSP, termed VSP101, was gathered with a geophone spacing of only 12.5 m providing high spatial resolution. In the depth range of 3.0–5.2 km, overlapping with previous measurements, geophone spacing was increased to 25 m.
 The complementing far-offset VSP, termed VSP819, was intended to image the midcrustal structure and to investigate shear wave splitting and scattering at oblique incidence angles, corresponding to wave propagation paths common in deep seismic reflection and wide-angle studies. The geophone spacing of this VSP was 25 m over the whole depth range. The borehole geophone described below had to be clamped to the steel casing of the KTB borehole. Therefore its orientation had to be determined from the polarization of the obliquely incident P waves arriving from the offset shot point of VSP819. Test measurements, previously performed with shot points at different azimuths, showed that the accuracy of the geophone orientation is about ±5°, provided the signal-to-noise ratio is on the order of 10 or better.
 In order to generate signals with a broad frequency spectrum, we used explosive charges of 0.5 to 2 kg. They were detonated in 15 to 30 m deep shot holes drilled in solid amphibolite and filled with water so the holes could be reloaded several times. In total, 578 shots were fired from 85 holes consuming 840 kg of dynamite. Probably because of relatively low destruction of the holes, the shots generated pulses of very uniform shape at frequencies between 10 and 300 Hz. The survey thus provides images of geological structure at scale lengths between some 100 m and some 10 m. Signal shape and timing accuracy for static corrections were controlled by four three-component reference geophones, three of them placed at different positions at the Earth's surface, and one at 3.8 km depth in the KTB pilot hole only 200 m apart from the KTB borehole.
 The main goal of moving source profiling was to determine the regional pattern of seismic anisotropy and possible changes of its azimuthal orientation with depth. We used two vertical vibrator trucks as seismic sources radiating 20 s linear sweeps at 10–130 Hz with 2 × 100 kN maximum force at 430 source points. The source points covering an area of ∼12 km diameter around the KTB borehole were arranged in six azimuthally equidistant profiles (see section 4.3). Signals were recorded in three orthogonal components at the Earth's surface, at 3800 m depth in the KTB pilot hole and at 7800 m depth in the KTB superdeep borehole.
3.2. The BG-250 HP/HT Borehole Geophone
 The basic condition for performing deep VSPs was, of course, the availability of a three-component HP/HT borehole geophone capable to withstand the temperature and pressure conditions at the deepest accessible part of the KTB well. Commissioned by the GeoForschungsZentrum Potsdam the so-called BG-250 borehole sonde was newly developed (Figure 2). It consists of a triaxial assembly of 15-Hz sensors (OYO Geospace HS1) withstanding maximum temperature and pressure of 260°C and of 140 MPa, respectively. For safe operation the maximum borehole deviation from vertical is 30° for the two horizontal geophones and 60° for the vertical one. This is sufficient for all occurring borehole deviations in the KTB HB well where a maximum deviation of 20° is found (Figure 2, insert). The tool is 93 mm in diameter and equipped with a spiral spring driven anchoring arm. The arm can be opened and closed with an AC motor. Exchangeable arms with different length enable to clamp the sonde in boreholes of 120–320 mm diameter. The electronics, including 40–100 dB preamplifiers, is housed in a Dewar flask. The heating of the electronics, the critical temperature of which is 175°C, limits the operation time of the BG-250. Tests showed that the tool could work for 6.5 hours at 8.5 km depth. At this depth the formation temperature is ∼250°C. The time required for getting the geophone to this maximum depth or back to the surface is 5 hours for one way. Electronics has to be switched off while the tool is running in to avoid internal heating. After each run, intensive maintenance is required during which special HP/HT sealing rings, HP/HT electrical feed throughs, and other HP/HT spare parts have to be changed to guarantee safe operation.
 The geophone response was tested in situ at different depths between 6 and 8.5 km. Seismic signals were generated by dynamite charges of 1–2 kg placed in shallow drill holes at 3–5 m depth at three different azimuths. The spectra of the test records showed that the responses of the vertical and horizontal components are similar between 10 and 150 Hz. At frequencies higher than 150 Hz the spectra of the horizontal components are slightly different. Since the main seismic signal energy was below 150 Hz during the VSP experiments, the differences in the response at higher frequencies are acceptable.
4. Seismic Velocity Field in Situ
 General features of the seismic structure of the KTB site can be established directly from the near-offset VSP after travel time reduction. A low-pass-filtered version combining previous and new VSP sections is shown in Figure 3. It covers the depth range from 450 to 8500 m. The three-component records of the VSPs show compressional, shear and PS converted waves, both in transmission and reflection. Major PP and PS reflections originating from the SE1 fault zone, are labeled Rpp and Rps on the NE horizontal and vertical components, respectively. The nearly 60° dip of the shear zone causes the PP reflection to appear on the horizontal geophone component and, vice versa, the PS reflection on the vertical component (labeled RPS in Figure 3). Another characteristic is a broad band of downward traveling PS converted waves caused by a more or less continuous forward scattering process (labeled Tps in Figure 3).
4.1. Velocity-Depth Function of P Waves and Scattering
 In situ seismic velocities were determined from the travel time curves of the direct waves of the near-offset VSP. The corresponding velocity-depth profile (Figure 4a) shows that low P wave velocities of 5400–6300 m/s are associated with the gneisses found in the top and bottom parts of the borehole whereas the central part of the section consisting of amphibolites shows velocities of 6300–6800 m/s (gneiss and amphibolite sections can be recognized in Figure 4c by their high mica and high amphibole contents, respectively). Therefore the gneiss formation below 7.8 km represents a low-velocity zone of 20% reduction compared to the velocity of the hanging wall.
 A closer inspection of the velocity-depth profile (Figure 4a) reveals that the P wave velocity in the depth range below 7800 m is ∼9% lower than the velocity of the petrologically identical gneiss formation at 2 km depth. Surprisingly, the depth interval between 6.8 and 7.2 km, where the SE1 fault zone is located (e.g., Hirschmann, 1996), does not show any pronounced low-velocity anomaly. Instead, the velocity at this depth does not exceed the velocities found anywhere else along the profile.
 The variation of the P wave velocity-depth function shows quasiperiodic oscillations with depth the amplitude of which is on the order of 10–15% of the background velocity. In order to describe this periodicity more quantitatively we computed spatial spectra of the velocity fluctuation function. The fluctuation is defined as the velocity-depth function after removal of a background velocity model. To determine this background velocity, we subtracted best fit polynomials of increasing order from the velocity-depth function and computed the variance of the residuals. The results are displayed as a graph of residual variance versus order of fitting polynomial (Figure 5a). It shows that ∼60% of the initial variance is reduced by a second-order polynomial representing a parabolic trend with depth. This second-order trend is caused by the velocity reduction below 7 km depth. Another increase in the order of the fitting polynomial does not further reduce the residual variance significantly (on average less than 1% per step in order).
 Therefore the polynomial of second order was chosen for removing the trend from the velocity-depth function. The resulting fluctuation can be characterized by the spatial Fourier spectrum of the residual velocity-depth function (Figure 5b). It shows a “low-pass” characteristic where maximum amplitudes of velocity variation occur at wave numbers smaller than 1/250 m−1 corresponding to wavelengths larger than 250 m. Since previous investigations of well log statistics were mainly based on sonic log analysis [see Müller and Shapiro, 2001, and references therein], we compare the seismic fluctuation spectrum with the corresponding fluctuation spectrum of the sonic log (Figure 5c). Both spectra agree in their basic features. However, because of its higher spatial resolution, the sonic log shows slightly larger amplitudes at higher wave numbers (Figure 5c). The velocity variation should be correlated with both spatial changes in rock composition and orientation of rock foliation. To verify this relation, we show the spatial fluctuation spectra of the amphibole content (Figure 5d) and of the dip of rock foliation along the borehole (Figure 5e). This comparison confirms that both seismic velocity and geological parameters have their largest amplitudes in the same spectral range at wavelengths larger than 250 m. The highest similarity is observed between seismic velocity and amphibole content (compare Figure 5b to Figure 5d).
 Geological heterogeneity scaled in this way has an important influence on the structure of seismic wave fields. The important role of seismic scattering at the KTB was recently addressed, for example, by Holliger , Goff and Holliger , and Müller and Shapiro . Regarding the VSP data under consideration, it finds its most obvious expression in a continuous conversion of compressional into shear wave energy and in a scattered appearance of the direct shear wave arrivals. As an example, we show an enlarged VSP section, containing the whole original signal spectrum of 10 to >200 Hz (Figure 6), where the broad band of scattered S arrivals is in contrast with a rather sharp signal of the downward traveling P wave. The amplitudes of forward scattered PS waves are between 5 and 10% of the incident P wave [Beilecke, 2003].
 Previous investigations of scattering at the KTB concentrated mainly on analyzing sonic logs and on discussing implications for wave propagation assuming random types of media. In case of the actual VSP it can be shown that the basic features of the observed wave field can be explained at least qualitatively by a large-scale, rather “deterministic” type of geological model. In order to get some insight into the buildup of wave fronts under realistic conditions we performed finite difference computations based on the geological model of the KTB site derived by Hirschmann  (compare Figure 1). The dimension of the faulted blocks and layers of this model are in the range of 200 to 2000 m (white contours in Figure 7), roughly corresponding to the wavelengths where the Vp fluctuation spectra show maximum amplitudes (Figure 6). For the computations, we attributed constant isotropic Vp and Vs velocity values to each lithological unit based on the VSP measurements. The difference in P and S wave propagation can be verified from wave field snapshots (Figure 7). Although multipathing causes the energy of the downward traveling P wave to split into a number of interfering branches, it remains concentrated behind the first break within a zone no wider than a few wavelengths. In contrast, the S wave suffers heavily from multipathing, possibly because of the shorter wavelength. In addition, the edges and tips of the block structure act as scattering centers fanning out the front of the S wave train by creating PS converted waves filling the “time gap” between the direct P and S arrivals. The distance along the ray over which the S wave energy finally spreads is ∼3 times the distance covered by the P wave energy.
4.2. Velocity and Polarization of Split S Waves
 One practical consequence of the scattering is that representative S wave velocities, in terms of effective media theory, can only be determined for the low-frequency part of the wave field. Below 25 Hz, corresponding to wavelengths larger than ∼150 m, the shear wave trains are coherent from top to bottom, whereas at higher frequencies interference of differently dipping arrivals and shingling effects complicate the picking of travel time curves. Split shear waves could be separated by horizontally rotating the geophone components into the ray coordinate system (note travel time delay and hodograms of split S waves in Figure 8), where the horizontal coordinates coincide with the polarization of the S1 and S2 waves, respectively. Here “S1” and “S2” denote the split S waves arriving first and second at the borehole geophone, respectively. Shear wave splitting is ∼200 ms at 8500 m depth corresponding to 9% of the S wave travel time. This is in good agreement with previous findings from the upper part of the borehole [e.g., Rabbel, 1994].
 The variation of the shear wave velocities is quite similar to that of the compressional waves: high and low S wave velocities are found in the amphibolite and gneiss sections, respectively (Figure 4b). In the amphibolite the S1 and S2 wave velocities are 3.6–4.0 km/s and 3.5–3.9 km/s, respectively. In the gneiss the S1 and S2 velocities vary between 3.1 and 4.0 km/s and 3.3 and 3.6 km/s. Velocities of the split shear waves differ as much as 12% in the gneiss section of the lower portion of the borehole. Within the amphibolites a maximum shear wave splitting of 9% is observed between 6800 m and 7200 m.
 At the bottom part of the drill hole, below 7 km, the S1 wave velocity decreases as dramatically as the P wave velocity whereas the decrease of the S2 wave velocity is much smaller. This is the only interval of the drill hole where the velocity of the leading S1 wave drops significantly below the S2 velocity.
 These crossover points of the S1 and S2 wave velocity curves are typical for many cracked solid rocks if they are probed seismically at incidence angles oblique to the foliation plane. This fact was often neglected in laboratory investigations when measurements were performed only parallel and perpendicular to the foliation plane. A large part of the velocity fluctuation is obviously caused by anisotropy, or more precisely, by the variation of rock foliation or fracture orientation with respect to the ray path.
 This is also supported by S wave polarization (Figure 9b). Down to 7200 m depth the leading shear wave is the “faster” one having a higher propagation velocity than the S2 wave (Figure 9a). S1 is polarized nearly parallel to the strike directions of both rock foliation and fractures, which coincide more or less (Figures 9c and 9d). Below 7200 m, the foliation plane flips back and forth by 90° twice, whereas the average fracture plane performs independent turns ending up 90° from the foliation plane at 8600 m depth. The corresponding polarization of the leading S1 wave toggles around north. It is worth looking at this in detail: From 7200 to 7600 m (left grey bar in Figure 9) and from 7900 to 8100 m (right grey bar in Figure 9), both strike directions agree again but are turned 90° compared to the hanging wall. Therefore with respect to foliation and fracture orientation, S1 and S2 change their roles, the first one now being perpendicular and the second one parallel to the common strike direction. Consequently, the S2 velocity is faster than the S1 velocity here (grey bars in Figure 9a). Between these zones, from 7600 to 7800 m, S1 is again faster; its polarization coincides with fracture strike rather than with foliation strike which are different at these depths. Below 8100 m, the fracture strike turns away from the foliation up to 90° difference. The S1 wave follows the foliation plane in polarization but takes the role of the slower S wave, whereas the S2 wave ends up as the faster one polarized parallel to fracture plane. Apparently, the fracture influence dominates fabric at this depth with regard to anisotropy.
4.3. Regional Anisotropic P Wave Velocity Field
 Moving source profiling was performed in order to determine average seismic velocities and anisotropy on a more regional scale. Examples of MSP seismogram sections from the two KTB boreholes and schematic ray paths are shown in Figure 10. The interpretation is based on the first break travel times of P waves recorded at 3800 und 8000 m depth. To remove the influence of near surface geology, static corrections based on the ISO89 survey [cf. Lengeling, 1989; Dürbaum et al., 1992] were applied to the data. The average P wave velocity determined from first break arrival times of the MSP is shown in Figure 11 as a function of source coordinate for both geophone depths. The lateral variation of the average velocity is well resolved for the deep geophone position (Figure 11b) where six MSPs were recorded. The velocity pattern reflects the contours of the geological units mapped at the surface (Figure 11c). The velocity maximum SE of the KTB site can be regarded as evidence for obliquely oriented P wave anisotropy within the metamorphic zone of Erbendorf-Vohenstrauss (ZEV). It is quantified below.
 The KTB boreholes form the axis of two cones of 120° and 90° opening angle (Figure 10c), limiting the incidence angles under which the upper and lower rock sections can be probed assuming straight rays. To determine an average anisotropic function of P wave velocity, we applied the following travel time inversion approach and constraints based on previous investigations:
 1. With regard to the geological map and to the geological depth profile the inversion scheme was set up as a “three body problem” considering the upper 0–4000 m and lower 4000–8000 m portions of the ZEV as well as the granite as separate units. This subdivision in depth is motivated and justified, to a certain extent, by a lithological change occurring at ∼4000 m (Figures 1 and 12). Ray paths through the Mesozoic sediments west of the crystalline rocks of the Bohemian Massif were not considered.
 3. ZEV units and granite were assumed to be elliptically anisotropic and isotropic, respectively [cf. Rabbel, 1994; Jahns, 1996].
 4. A two-step least squares inversion was applied to first break arrival times of the MSP experiment. In the first step, average isotropic velocities of the three “bodies” were determined forming constraints for the second step. The second step was a linearized anisotropic inversion of the travel time residuals resulting from the first step (see Appendix A formulae).
 The result, fitting the observed travel times with ∼1% standard deviation, is shown in stereographic projection in Figure 12. Because of the ray geometry the velocity patterns are well constrained only in the central cones up to 45° to 60° from the vertical (Figure 10c).
 Within these cones we observe 5% to 8% velocity anisotropy depending on the depth interval considered. It has to be emphasized that this anisotropy does not only reflect mineral and fracture alignment but also the spatial arrangements of 100 m to kilometer-scale lithological units. As it comprises portions of both elastic anisotropy and heterogeneity, this sort of travel time anisotropy has to be regarded as an estimate of the upper limit of “true” seismic anisotropy. Estimates of crustal anisotropy based on deep seismic refraction or reflection surveys would be biased in the same way.
 The average P wave velocity field of the ZEV metamorphic complex is nearly hexagonal with its fast velocity plane striking 150° NE and tilting ∼20° NNE (Figure 12, right ball). This pattern can be decomposed into contributions from the upper 0–4000 m and lower 4000–8000 m segments, both of which are orthorhombic, but again close to hexagonal (Figure 12, top and bottom balls, respectively). The upper and lower velocity functions differ in mean velocity and in the tilt of the high-velocity planes. Their strike directions, however, are almost the same coinciding with the strike of many major lithological units and faults and with the main horizontal tectonic stress component [e.g., Brudy et al., 1997]. The increase of average velocity with depth, from 5900 to 6500 m/s, corresponds to the change from gneissic to amphibolitic rock composition verified along the drill hole (Figure 12, left). In the upper 4000 m of the ZEV (Figure 12, top ball) the high-velocity plane is tilted ∼50° toward NE compatible with the foliation dip of the drilled gneiss units. From 4000 to 8000 m the high-velocity plane is vertical indicating mainly azimuthal anisotropy. A comparison with the geological profile [Hirschmann, 1996] shows that the orientation of both upper and deeper high-velocity planes seem to follow lithological stratification rather than the orientation of the major fault planes which are between 45° and orthogonal to lithological dips (Figure 12, left). If the faults were embedded in isotropic rock units, the plane of high P wave velocity would be parallel to the fault plane. In contrast, our finding suggests that the anisotropy pattern is primarily defined by rock fabric and lithological stratification, and that the influence of major discordant fracture planes is of minor importance. This view is also supported by laboratory investigations of KTB rocks where microcracks were found to be best developed parallel to rock foliation, thus increasing the intrinsic fabric-related portion of anisotropy caused by fabric rather than overprinting it. [e.g., Rasolofosaon et al., 2000].
5. Seismic Expression of Deep Fluid Pathways
 In section 4.3 we have shown that the seismic anisotropy of the crystalline rocks of the KTB site mirrors the tectonically deformed metamorphic strata on both regional and local scales. Below 7200 m a significant velocity decrease in both P and S has been observed suggesting an increased density of fractures in an anisotropic background matrix (see section 5.1). Also, from a fracture test at 9100 m depth carried out in 1994 it was concluded that fractures form distinct hydraulic conduction zones [Huenges et al., 1997]. Even at maximum depth they are connected allowing fluid pressure to propagate over more than 5 km distance. To quantify the seismic aspects of this hydraulic structure, we proceed in the two following steps: (1) determine values of fracture porosity from the VSP velocity data supposed to apply to a Fresnel volume around the borehole and (2) investigate by VSP reflection imaging how the velocity structure found at the borehole relates to the major fault systems, the segments of which are assumed to form the network of fluid pathways.
5.1. Fracture Porosity at 8 km Depth
 To determine the influence of fractures on the velocity decrease, we compare petrologically identical gneiss units at three different depth levels, so velocity variation may be caused by changes in the orientation of the symmetry plane of the anisotropic material or by variation of fracture characteristics, but cannot be caused by changes in mineralogical composition. Theories describing the seismic effect of fractures are formulated in terms of elastic moduli rather than seismic velocity. Therefore as a first step of interpretation, we have to convert the observed P and S wave velocities into elements of the elastic tensor.
 Since the dip direction of rock foliation is known along the borehole and wave propagation is almost vertical for VSP 101, we can simply plot P and S wave velocity versus dip of foliation to determine the anisotropic velocity function (Figure 13). From previous studies it is known that the gneiss structure is effectively hexagonal, and that the majority of microfractures is preferably oriented within the foliation plane [Siegesmund et al., 1993; Jahns et al., 1996; Rasolofosaon et al., 2000]. Therefore we applied the analytical functions describing the phase velocity of hexagonal media [White et al., 1983] to fit the velocity data observed for gneiss and to determine the respective elastic constants (for formulae, see Appendix B).
 We investigated the following three depth intervals, the resulting elastic constants of which are listed in Table 1:
Table 1. Density and Elastic Tensor Elements (Lines 2 and 3a–3e) of Lithologically Identical Gneiss Units at Three Different Depth Intervals of the KTB Well (Line 1)a
Elastic Tensors of Gneiss and Estimates of Fracture Porosity
Type of Rock Property
Properties at 2.2–3.0 km Depth
Properties at 7.6–7.9 km Depth
Properties at 7.9–8.2 km Depth
Elastic tensor elements were derived from anisotropic velocity functions of P, S1, and S2 waves (Figure 13) by applying the formulae of Appendix B. Excess fracture density and porosity with respect to the rock unit at 2.2–3.0 km depth (lines 4a–4c and 5a–5c, respectively) were computed from the elastic tensor elements following the approach of Rasolofosaon et al. . It considers three orthogonal planes of aligned fractures (12, 13, and 23 planes, respectively) where the 12 plane is parallel to rock foliation. Fracture porosity was computed assuming plane penny shaped fractures. For comparison, porosity values based on Gassmann's theory [Gassmann, 1951] and the time average equation [e.g., Wyllie et al., 1956] were computed (lines 6a and b, respectively). To determine the “equivalent” isotropic elastic moduli required for these approaches, we applied equation (B4a) (Appendix B).
mean density, kg m−3
elastic tensor (Cij), GPa
excess fracture density N〈a3〉
excess fracture porosity, %
excess porosity, %
 1. The shallowest level (2.2–3.0 km, Figure 13a) serves as a reference against which the deeper ones are to be compared. The anisotropy of P, S1, and S2 waves is 4.2, 9.0, and 3.5%, respectively. Average isotropic P and S wave velocities are 6120 and 3510 m/s, respectively.
 2. From 7.6 to 7.9 km (Figure 13b) the same material shows a 3.9% lower average P wave velocity (5880 m/s) and a 0.8% lower average S wave velocity (3480 m/s), whereas anisotropy is increased for all three wave types (6.1%, 11.7% and 6.2% for P, S1, and S2 waves, respectively).
 3. Between 7.9 and 8.2 km, velocities decrease again (Figure 13c). The dip of foliation varies, however, only between 40° and 50°, not enough to construct the anisotropic velocity function from the data alone. However, we can estimate it because the background material is almost identical with the gneiss at 2.1–3 km depth and assuming a velocity reduction which is primarily caused by aligned fractures. Following the solid line in Figure 13c, we obtain 13.2%, 18.3%, and 3.8% as maximum estimates of the anisotropy of P, S1, and S2 waves, respectively. Average isotropic velocities are almost identical with the observed velocities at 45°, that is, 5670 m/s and 3370 m/s, corresponding to reductions of 7.7% and 4%, respectively.
 To determine fracture properties, we applied three different approaches, each of them based on the fact that the elastic constants of the material between 7.6 and 8.2 km depth can be computed from the constants at 2.3–3.0 km by “adding” adequate fracture porosity.
 Results are listed in Table 1. Following the approach of Rasolofosaon et al.  the weakening of the rock matrix caused by fractures can be described by excess compliances (lines 4a–4c and 5a–5d in Table 1). It can be computed from the elements of an elastic tensor if the elastic tensor of an (unfractured) reference rock is known. In this way the influence of differently oriented families of aligned fractures can be identified. A link between excess compliances and fracture properties, such as fracture porosity and density, is provided by formulae of Schoenberg and Douma . Since the elastic tensors of the KTB gneiss section are hexagonal, we can distinguish between the influence of fractures oriented parallel and perpendicular to the foliation plane. Table 1 shows that the velocity variation of the KTB gneiss at 7.6–7.9 km depth can be explained by ∼0.15% fracture porosity (line 5d in Table 1) where the fracture density in the plane parallel to foliation (12 plane in Table 1) is approximately twice the fracture density in both orthogonal planes (13 and 23 planes in Table 1). The anisotropy estimate for the deep interval (7.9–8.2 km depth) implies a total of ∼5% fracture porosity most of which should be aligned parallel to foliation. To cross-check these results, we applied Gassmann's theory [Gassmann, 1951] and the time-average equation [Wyllie et al., 1956] to the average isotropic P wave velocities derived from equation (A3). In the case of Gassmann's theory we applied the Walsh-Zimmermann approach [Mavko et al., 1998, p. 173] to estimate dry rock compressibility. Gassmann theory and time-average equation suggest fracture porosities of 0.8–1.4% and 1.3–2.6%, respectively (Table 1, lines 6a and 6b, respectively).
 To summarize, we find that the decrease of velocity along the deepest segment of the KTB well is connected with an increase of anisotropy. The velocity reduction corresponds to ∼30% reduction of the elastic moduli which could be interpreted as an expression of a weakening of the rock matrix. A comparative application of three different petrophysical models showed that the observed velocity decrease can be explained by an increase of fracture porosity compared to the same material at shallower depth. Depending on the petrophysical model the estimates of excess fracture porosity vary between 0.14–1.3% and 1.4–5.4% for the depth intervals of 7.6–7.9 km and 7.9–8.2 km, respectively.
5.2. VSP Reflection Imaging of Steeply Dipping Fault Systems
 To link in situ velocity and fracture porosity estimates to seismic structure off the borehole, we analyzed reflections recorded along the near-offset VSP101. Migrated PS and PP reflection images are shown in Figures 14 and 15, respectively, in comparison to a migrated surface seismic section.
 Despite velocity perturbation and scattering the SE1 reflection zone can be clearly identified on both vertical and horizontal component sections (Figures 3 and 6). Since the fault zone is ∼60° inclined, PP reflections are recorded mainly on the horizontal geophone component directed toward NE. The strong reflections on the vertical component are PS converted waves which are particularly attractive for imaging because of their high spatial resolution. In order to suppress the direct waves and to enhance reflections from steeply inclined structures, careful dip filtering was applied to the VSP data. An unusual feature to be considered in this case is downward traveling PP reflections to be conserved during dip filtering. PP and PS reflections were depth-migrated using a Kirchhoff migration algorithm and average P and S wave velocities derived from the VSP. Amplitude-normalized versions of the PS and PP migrated sections are shown in Figures 14a and 15a, respectively. Reflection strength is represented by corresponding envelope sections (Figures 14b and 15b, respectively). Details of the processing sequence are described by Frank .
 The images (Figures 14 and 15) show cross sections extending from the borehole 2.5 km toward SW and from 4 to 8 km in depth. The azimuthal orientation of the cross sections could not be derived from the VSP alone but was verified by comparing VSP with surface seismic sections from a 3-D data set (Figures 14c and 15c). For comparison, Figures 14c and 15c show the prominent structures common to all sections copied into the amplitude images. Note that the spatial resolution of the PS migrated image is ∼5 times better than the surface seismic image (compare Figure 14a to Figure 14c). A combined detailed line drawing of reflections from faults and fractures is shown in Figure 16 (left).
 Because of the acquisition geometry the reflection images of the near-offset VSP show mainly steeply dipping structures. The most prominent feature is the SE1 reflection extending from 4 km depth at 2 km distance SW of the KTB site down to 7 km depth where it intersects the borehole. This reflection was previously recognized in surface seismic data (Figure 14c) and is verified in the VSP in both PP and PS reflectivity. The VSP images show, however, that this planar structure is accompanied by a number of subparallel splay faults and parallel fault branches. The most prominent parallel branch appears on the PS envelope section (Figure 14b) where it extends from the center of the figure to the bottom right reaching the borehole at ∼8 km depth. This fault branch coincides with the termination points of some subhorizontal reflections of the 3-D seismic section (compare Figure 14c) but it could not be imaged directly from the Earth's surface, probably because of unfavorable illumination angles of the incident rays. Prestack migrated images based on 3-D surface seismic data [Buske, 1999a, 1999b; Rothert et al., 2003] show a similar structure as the poststack-migrated image (Figure 14c) [cf. Körbe et al., 1997], however, with significantly less coherency and resolution. This indicates that prestack migration cannot solve this illumination problem either. A comparison of the PS image with the PP envelope section (Figure 15b) shows that the PP reflectivity of this fault branch seems to be generally less than the PS reflection strength.
 Because of their SW dip, fractures conjugate to the SE1 plane cannot be imaged directly by the VSP, but they can be identified by displacements and disturbances of the oscillating signal pattern attributed to lithology. This is evident in the PP image (Figure 15a) where the subhorizontal reflections of the surface seismic section (Figure 15c) can be identified with horizontal displacements in the layered structure (see Figure 15c). These horizontal displacements can also be verified in the PS section (Figure 14a). Because of their high spatial resolution both PP and PS reflection images consistently show a large number of faults and fractures which have been compiled in Figure 16 (left). Note that only a small part of these features could be detected from the Earth's surface, partly because of unfavorable illumination angles, partly because of low resolution or weak reflection strength.
 In summary, the SE1 reflection is the image of a fault zone of nearly 1 km actual width. In previous prestack migrated sections [e.g., Buske, 1999a] it appeared as a zone of diffuse reflectivity around the borehole. Comprising both PP and PS reflections in high resolution, the migrated VSP sections allow the identification of fracture planes to distinguish them to a certain extent from lithological contrasts and to link the seismic structure to the borehole. The SE1 zone turns out to be bounded by two major fault planes the upper of which had been found previously by surface seismic imaging [e.g., Harjes et al., 1997]. The second deeper branch, and the fractures in between both branches, is important to understand the velocity-depth function found in both VSP and sonic log (Figure 16, right). The upper SEL branch is not associated with a significant velocity anomaly but indicates the depth below which the dramatic velocity decrease starts. The sonic log shows that this velocity decrease is probably not as smooth as suggested by the velocity function derived from the VSP. This is evident also from reflectivity coefficients for which maximum values of 0.35 ± 0.15 were observed for arrivals at 6 km depth [Frank, 2002]. Zillmer et al.  derived reflection coefficients of the same order of magnitude for the SE1 structure by analyzing surface seismic data. These coefficients can only be explained by extreme velocity contrasts plus thin layer tuning effects such as those suggested by the velocity function derived from the sonic log [Trela, 2003; C. Trela et al., Frequency dependence of PS reflections: Fine structure of the SE1–thrust fault system at the KTB superdeep drill hole, submitted to Journal of Geophysical Research, 2004].
6. Discussion and Conclusions
 The VSP measurements in the deep segment of the KTB drill hole provided new insight in the seismic structure of deep fault zones and the associated relation between tectonic stress, fabric and features of wave propagation such as anisotropy and scattering. These aspects are discussed in sections 6.1 and 6.2.
6.1. Seismic Structure of a Deep Fault Zone System
 Seismic reflection imaging based on PP and PS converted reflected waves showed that the major fault system at the KTB site is more complex than hitherto assumed. The so-called SE1 reflection found in P wave surface seismic surveys is only one branch of an ∼1 km wide fault system consisting of two major and a number of smaller SE dipping fault planes and many conjugate fractures (Figures 14–16). The comparison with a migrated section based on 3-D surface seismics showed that the reflections located in this depth range are fault zone images, but they represent only a small part of the whole fault system. The newly discovered deeper branches of the SE1 fault system are linked to a low-velocity zone found below 7.5 km in the lower part of the KTB drill hole. Here the fault system is associated with a 10% decrease in P and S wave velocities and with an increase in seismic anisotropy compared to petrologically identical units at shallow levels (Figures 4, 13, and 16). The low-velocity structure can be explained by 1.5–5% fracture porosity depending on the petrophysical model assumed.
 Since the anisotropic velocity functions derived from the VSP (Figure 13) represent an average over several hundred meter depth, the resulting porosity values have to be regarded as spatial averages. The sonic log (Figure 16) shows that there are narrow zones of even lower seismic velocity than recorded in the VSP (even below 5000 m/s [cf. Harjes et al., 1997]). These low values may be caused by borehole breakouts or they could suggest that there is even higher porosity on a very local scale.
 On the basis of integrated borehole logging, Pechnig et al.  located an accumulation of narrow fractures between 7.0 and 8.6 km depth with fracture porosities of several tens of percent. Although it is not clear how far these fracture porosities can be transferred to the formation off the borehole walls, we see this as a confirmation of our porosity finding which can be regarded as an integral value applying to a Fresnel volume around the borehole.
 Laboratory measurements [Kern et al., 1991; Berckhemer et al., 1997] have shown that rock samples from the KTB drill only rarely exceed 0.5% porosity even under low pressure conditions. Therefore the velocity decrease observed at depth cannot be explained by effective pressure decrease caused by pore fluid pressure. This conclusion is supported by Trela , who measured the velocity dependence on pore pressure under simulated in situ conditions in the laboratory. Instead, the velocity decrease has to be attributed to macroscopic fracturing. This weakening of the rock matrix corresponds to up to 30% decrease of elastic tensor components. Following Mavko et al. [1998, pp. 221–225], the “critical porosity” of crystalline rock defined as the porosity where “the rock simply falls apart” is on the order of 5%. Transferring this to our results, we have to conclude that the rock within the SE1 zone is crushed in large volumes, and that faults are not healed despite their large depth close to the supposed brittle-ductile transition zone. These fault zones seem to provide significant volumes of fluid pathways the hydraulic permeability of which should be anisotropic and heterogeneous because of the alignment of fractures. A recent fluid injection experiment at the KTB site showed that major fluid flow exists even at 9 km depth at very low injection pressure and that fluid pressure signals may move with a velocity of 300 m/day [Baisch and Harjes, 2003]. Analyzing the related microseismicity, Rothert et al.  found a correlation of seismic reflectivity with zones of increased hydraulic diffusivity. It has been concluded that the observed fluid migration took place along a highly permeable network of open fractures [Baisch and Harjes, 2003]. This model is supported by the seismic findings of the deep VSP experiment.
6.2. Seismic Expression of Tectonic Stress, Fractures, Fabric, and Structural Complexity
 Laboratory measurements of rock samples have shown that microcracks are almost closed under confining pressure such as found in the deeper KTB section even if a reduction of effective pressure by near hydrostatic pore pressure is assumed [Kern et al., 1991]. Therefore the opening of fractures at these depths indicated by the VSP is not compatible with “hydrostatic” pressure conditions. Instead, it has to be maintained by differential tectonic stress leading to aligned cracks and “extensive dilatancy anisotropy” [e.g., Crampin, 1987, 1989]. Indeed, stress analysis at the KTB site showed that the maximum differential stress (σ1–σ3) is oriented horizontally and exceeds 100 MPa at depths ≥6 km [Zoback et al., 1993; Brudy et al., 1994, 1997]. The NW direction of maximum horizontal stress σ1 and the horizontal orientation of (σ1–σ3) support the opening of subvertical fractures within the foliation plane of the steeply dipping rock units as it is suggested by the VSP results. Unfortunately, corresponding laboratory measurements establishing an empirical relation between differential stress and seismic velocity and anisotropy are still rare. Simulating the temperature and stress conditions at the KTB well from 0 to 6 km depth in a triaxial pressure unit Kern et al.  found an increase of seismic anisotropy on the order of 1–3% related to differential stress. These values apply to macroscopically intact KTB rock samples of centimeter-scale the microcrack porosity of which increased by up to 0.5% with increasing differential stress. Qualitatively they agree with our in situ findings for the gneiss unit at 7.6–7.9 km depth (Figure 13b). However, the dramatic decrease of seismic velocity at larger depths, probably associated with a further increase in anisotropy (Figures 4 and 13c) cannot be explained by this mechanism alone but requires intense macroscopic rock destruction.
 On the one hand, our measurements confirm the theory of fracture opening under tectonic stress, thus influencing seismic anisotropy. On the other hand, both moving source profiling and VSP have shown that the basic pattern of anisotropy is coined by rock fabric on both microscale and regional scale: Shear wave splitting and corresponding polarization follow closely the azimuth of foliation and changes of average foliation dip with depth could be verified by anisotropic velocity functions.
 As a by-product of our investigation, we could show that the depth profile of horizontal stress orientation at the KTB site [Brudy et al., 1997], which had been derived mainly from borehole breakouts, is strongly correlated with the azimuth of the foliation plane (Figure 17). The only exception is the complex lower part of the borehole, which has been extensively discussed in the context of S wave polarization anomalies (section 4.2). Here fractures seem to overprint the foliation pattern in terms of elasticity and rock strength.
 The tectonic history of the ZEV created a medium of high structural complexity where fluctuation spectra of rock composition and seismic velocity show similar patterns (Figure 5). We could verify that a significant amount of P wave energy is continuously converted to shear energy by forward scattering and that multipathing plays an important role in signal formation. The media behaves effectively smoothly only at wavelengths larger than 150 m. Under these conditions we could show that the integral effect of shear wave splitting is ∼8% along the KTB rock column. For three depth sections, consisting of gneiss and presumed to be hexagonal, we could determine the elements of the elastic tensor and the corresponding average P and S wave velocities as a function of the direction of ray propagation. It was shown by moving source profiling that the media is, strictly speaking, orthorhombic but can be regarded as nearly hexagonal within the cone of observed ray directions. The tilt of the symmetry axes varies with depth apparently following the dip of geological structure.
Appendix A:: Elliptical Seismic Anisotropy
 Elliptical anisotropy is a well known mathematically simple means to describe the basic features of P wave travel time fields in rock units. It is adequate where velocity minima and maxima are parallel to the axes of a Carthesian coordinate system spanned, for example, by vectors normal and parallel to the planes of foliation or layering, respectively. Although representing a special case of orthorhombic anisotropy this sort of anisotropy system has been observed for the P wave velocity in many samples of crystalline rock, in particular, for many gneiss and amphibolite samples found at the KTB site. An elliptical P wave velocity function VP where the principal axes are oriented parallel to the axes of a Carthesian coordinate system is given by
where vi (i = 1, 2, 3) are the velocities along the principal axes and ei (i = 1, 2, 3) are the components of a unit vector pointing in the direction of wave propagation. If the velocity ellipsoid is tilted or rotated equation (A1) transforms to
where vij = vji are velocity coefficients that can be arranged in a symmetrical 3 × 3 matrix. In equation (A2) and in the following the Einstein sum convention has been applied. For seismic travel time inversion a first-order Taylor expansion of the slowness coefficient p = 1/VP is more suitable than equation (A2). It reads
where V0 is an isotropic average velocity defined by
and Δij are normalized coefficients defined by
The approximation of VP based on equation (A3) is better than 1.5% if ∣1 − VP/V0∣ ≤ 10% corresponding to ≤20% anisotropy regarding maximum and minimum velocities. So it is adequate for the conditions found at the KTB site. For seismic travel time inversion seven formal variables plus one constraint are assigned to each underground segment. Following equations (A3) and (A5) these variables are 1/V0 and Δij/V0 (ij = 11, 22, 33, 12, 13, 23). Inserting the terms of (A5) into equation (A4) transforms (A4) to
to be used as a constraint in solving the travel time equations. The advantage of using seven variables plus a constraint instead of six variables, as it would be suggested by equation (A2), is that it splits the inversion problem into “zero”-order isotropic and first-order anisotropic portions. These may be solved simultaneously or separately in successive steps depending on the problem under consideration. In the latter case, V0 or 1/V0, respectively, resulting from isotropic inversion may be used as an additional constraint to be conserved in the anisotropic inversion. Once the Δij or corresponding vij are determined the spatial orientation of the velocity ellipsoid is obtained from principal component analysis.
Appendix B:: Determination of Elastic Moduli and Tensor Elements of KTB Gneiss Units
where C66 = (C11 − C12)/2. For hexagonal media the phase velocities of P and split S waves can be described in exact analytical form. However, we prefer the following approximation of White et al.  applying to weakly anisotropic media because it is more suitable for fitting the observed velocity data by linear inversion:
where ρ, VP, VS1, VS2 are density and propagation velocities of P and split S waves, respectively, observed along the borehole. Here, S1 and S2 apply to S waves polarized parallel and perpendicular to the plane of rock foliation, respectively. The angle β is the angle between the direction of wave propagation and the symmetry axis of the hexagonal medium, that is, the normal of the foliation plane. In our case wave propagation is nearly vertical so β corresponds to the dip of rock foliation known from borehole measurements with a formation microscanner [Hirschmann and Lapp, 1994; Hirschmann and Bram, 1998]. The unknown coefficients wi (i = 1,…, 5) can be determined by linear least squares inversion. They are related to the elements of the elastic tensor as follows:
From equations (B3a)–(B3e) the elastic tensor elements describing the hexagonal case can be determined by simple arithmetic. For rock physical models based on isotropic rock matrix and isotropic crack distributions, such as Gassmann's theory, average shear and compressional moduli (μ and κ, respectively) corresponding to an equivalent isotropic rock are required. They can be computed by applying the following two equations adopted from Gebrande  for the hexagonal case:
 We gratefully acknowledge funding by the German Science Foundation DFG (grants Ra496/8 and Bo764/5), by the International Scientific Continental Drilling Program (ICDP grants 07-98/1 and 03/99), and by the National Science Foundation (grant EAR-9727654). Financial support was also provided by the GeoForschungsZentrum Potsdam. The Operational Support Group of ICDP, harbored at the GFZ Potsdam, essentially supported the downhole measurements at the KTB superdeep drill hole. We are grateful to E. Huenges and one anonymous reviewer for their prompt and constructive reviews. CERI contribution 485.