Source Parameters of Injection-Induced Microearthquakes at 9 km ...

Bulletin of the Seismological Society of America, Vol. 88, No. 3, pp. 815-832, June 1998

Source Parameters of Injection-Induced Microearthquakes at 9 km Depth at the KTB Deep Drilling Site, Germany b y M. L. Jost, T. Btif3elberg, O. Jost, and H.-P. Harjes

Abstract A fluid injection-induced seismicity experiment was undertaken in the KTB (German Continental Deep Drilling Program) main borehole at 9 km depth. Several hundred microearthquakes were recorded by a three-component geophone at 4 km depth in the pilot hole of the KTB about 200 m west of the main hole. More than 100 of these events were also recorded with good signal-to-noise ratio by a 73element temporary network at the surface. Several different clusters of microearthquakes with distinct waveforms were defined. Compound fault-plane solutions for the two most prominent clusters of seismic events were determined: a strike-slip mechanism for cluster 1 at an average depth of about 8.9 km and a strike-slip/reverse mechanism for cluster 4 (with the " m a i n " ML = 1.2 event) at an average depth of 8.6 kin. For both fault-plane solutions, the P axis is subhorizontal and oriented NNW-SSE, similar to the N160°E direction of maximum horizontal stress observed in the well bore. Both clusters were analyzed using an empirical Green's function method to derive the relative source time function (RSTF). Azimuthal variations of the RSTF were used to determine rupture directions and velocities. By combining the information about rupture directions with fault-plane solutions, it was possible to identify the active fault planes (NE striking nodal planes) for both clusters. Although injection-induced events are supposed to exhibit a dilatational component due to the tensile character of the source, the moment tensor inversion for both microearthquake clusters resulted in a double-couple contribution of about 90% and P axes similar to the direction of maximum horizontal stress observed in the borehole. The isotropic components of the moment tensors are insignificant due to the size of the location uncertainties. From records of the sensor at 4 km depth, we found seismic moments of the microearthquakes ranging from 10 7 tO 1011 N-re. The spectra were corrected for Q [Q(f) = 420 fo.5 for P, and Q(f) = 230 f0.5 for S-waves, which were determined assuming an co2 model]. Following Brune (1970, 1971), we found source radii between 12 and 28 m and stress drops between 0.01 and 6 MPa. The average ratio of S- to P-wave energy was determined as 14.2. Our relation between seismic moment and ML is log M0 = 1.01 ML + 9.68, and between energy and seismic moment, log E = 2.0 log M0 - 15.35. These seismic scaling relations suggest that stress drop increases with seismic moment for this data set. However, it cannot be precluded that our data, covering only somewhat more than three orders of magnitude, fall in a larger trend of constant-stress-drop scaling over many orders of magnitude due to the large scatter observed over several orders of magnitude.

Introduction Numerous studies of small to large earthquakes indicate that stress drop is mainly independent of the size of the event expressed as seismic moment (Kanamori and Anderson, 1975; Abercrombie, 1995). Even some mining-induced events appear to obey a constant-stress-drop scaling (Gibowicz and Kijko, 1994). The constant-stress-drop model also

implies a self-similar rupture process that is independent of the size of the earthquake and that seismic moment M0 is proportional to the cube of the source radius, after Brune (1970, 1971). However, there is a significant number of studies that suggest a breakdown in self-similarity between large and small events at a seismic moment of roughly 1013 N-m 815

816

M.L. Jost, T. Btigelberg, 121.Jost, and H.-P. Harjes

(e.g., Fletcher et al. 1986; Gibowicz and Kijko, 1994). Fletcher et al. (1986) observed constant source radii over four orders of magnitude in seismic moment. Especially small, mining-induced seismicity recorded on underground seismic networks have shown the most convincing evidence (e.g., Gibowicz, 1985; Gibowicz et al., 1990). The apparent breakdown in self-similarity is closely linked to causes that limit high-frequencies ~max, Hanks, 1982) of the radiated wave field. Especially, the highly attenuating region just below the Earth' s surface may limit the frequencies observable with surface instruments. In mines, a characteristic length corresponding to the characteristic width of mine longwalls has been proposed as cause. Therefore, the injection-induced microearthquakes at about 9 km depth at the KTB (German Continental Deep Drilling Program; Emmermann and Lauterjung, 1997) render additional data that are free from surface effects (low Q) and any inherent characteristic length scale. The KTB drilling site is located in NE Bavaria, Germany, at the western margin of the Bohemian Massif, at the contact zone of the two southern units of the Variscan belt in Europe (Saxothuringian and Moldanubian; Wagner et al., 1997). At this suture zone, the Saxothuringian plate in the NW collided with the Moldanubian plate in the SE about 320 million years ago. The Franconian Lineament is the surface expression of a major NW-SE striking and east-dipping Cretaceous thrust fault. Gneisses and amphibolites of the Bohemian Massif were thrust westward over Permo-Mesozoic sediments. The Franconian Lineament was cut at about 7 km depth in the borehole ( " S E I " seismic reflector) in addition to other numerous faults at various depths (Harjes et al., 1997). Natural microearthquakes in the area around the KTB site occurred up to 13 km depth. But within a radius of about 50 km, the regional seismicity is sparse (Dahlheim et aI., 1997). In 1994, the KTB borehole in Germany had reached a final depth of 9101 m and temperatures of about 270°C. After completing drilling, hydraulic-fracturing and fluid injection experiments were performed for evaluating the brittleductile transition hypothesis in the crystalline crust at an unprecedented depth level (Zoback and Harjes, 1997; Brudy et aL, 1997). Aside from the rheological background of the injection experiment, the induced seismicity enabled a detailed study of source properties and scaling relations for these unique data.

Event Locations and Fault-Plane Solutions The induced seismicity was recorded by a temporary network of 73 short-period seismic stations (200-Hz sampling rate, 1-Hz sensors) at the surface around the KTB drill site. The network was configured in four concentric rings of about 1 km (A-ring), 5 km (B-ring), 10 km (C-ring), and 15 km (D-ring) radius (Fig. 1). This configuration ensured a good coverage of the focal hemisphere. The stations of the inner two rings were arranged in subarrays with 4 and 9

0" 60"

•

~

10" :

20" ,~,

60"

50~" 0"

50"

10"

20"

kit

.O1

20

.C2

D2

o'~°oB1 o,~ B5 I o

,C8

A1 A~ ~HBBO g~° B2 134 ~ ~ A2

10

A3 •o1~o ~ B3 ,D4

q4

,C7

.C6

0

D3

,C5 i

0

10

1

30 km

20

W m

J 4

-2000--

Pil

Hole

-4000 Main Hol~

-6000 -8000 0

1 5

10

15

20

25

30

35 km

Figure 1. Temporary seismic network of 73 stations installed in the region surrounding the KTB drill site (49.82° N, 12.13° E, see overview map on top). Center: Map of the network that was configured in four concentric rings of about 1, 5, 10, and 15 km from the borehole. Station codes are indicated and HBBO (cross) is the location of the injection interval at the bottom of the main hole. Open circles indicate vertical sensors; filled circles, three-component stations. Bottom: west-east cross section showing the position of the main hole and the pilot hole. The injection interval is an open hole section extending 70 m upward from the bottom of the main hole (depth of 9.1 kin). Depth scale is with respect to sea level.

sensors. Additionally, a three-component borehole geophone (1000-Hz sampling rate, 28-Hz sensor) was installed at 3990 m depth in the KTB pilot hole, about 200 m west of the main hole. About 400 microearthquakes were triggered at a depth range between 8 and 9 km by injecting 200 m 3 of KBr/KC1 brine and were detected by the downhole geophone in the pilot hole. Figure 2 shows the temporal distribution of the flow rate, the pressure at the top of the well, and the induced seismicity over a 60-hr period. The induced seismicity started during the second frac-cycle, about 2 hr after the initiation of injection, and continued for about 30 hr after the end of injection when the seismic recording was stopped. The highest frequency of microearthquakes was associated

Source Parameters of lnjection-Induced Microearthquakes at 9 km Depth at the KTB Deep Drilling Site, Germany

817

J

800

600

~

400

o E

20O

0

10

20

J 4O

30 Time [hi

510

--60

60 5O

lO

40

~3o

3o _

!

~.2o

i 10

2~0

310 Time [h]

4~0

5q0

60

25

~2o

=El0 Z

5 0~ 0

.II

.iI 10

20

30 Time [hi

40

Ii

,

• ..

50

60

Figure 2. Temporal distribution of the flow rate (top), pressure at the wellhead (middle), and induced seismicity (bottom) over a 60-hr period. Twenty-four hours of injection were followed by 12 hr of maintaining pressure, and by 24 hr of additional monitoring after pressurization ended. Approximately 400 microearthquakes were detected by the 28-Hz borehole geophone (sampled at 1 kHz) in the pilot hole during the experiment. The largest earthquake was an ML = 1.2 event that occurred 18 hours after the injection started. with the highest injection pressures that were also the times of highest flow rate. The largest event was detected by earthquake observatories in Germany and the Czech Republic with a magnitude of ML = 1.2. Consequently, seismograms of this "mainshock" were used to calibrate the magnitudes of the other events. As a result, magnitudes of all other events were found to range between - 2 < ML < 0 (Fig. 3). Approximately 100 events were detected by the surface network with a good signal-to-noise ratio to determine hypocenters. The locations of all events detected by the borehole geophone and surface network were calculated from P and S-P arrival times using a master event technique. The bottom of the hole was used as a starting solution. This technique resulted in event depths that were especially well constrained by the S-P times of the borehole geophone at a depth of 3.99 km. The absolute location errors in depth were estimated as _+ 100 m, in the horizontal plane in the order of _+200 m,

o -2.5

-2

-1.5

-1

-0.5 0 Magnitude

0.5

1

1.5

Figure 3. ML distribution of the induced microseismicity.

caused by uncertainties in arrival-time determinations at the surface stations and using the simple 1D velocity model. This half-space model with a P velocity of 6.15 km/sec was derived from a vertical seismic profile down to 6 km depth in the main hole. In addition, the S-wave velocity was derived from a Wadati diagram resulting in a P- to S-wave velocity ratio of 1.73. All ray paths were close to the borehole and remained within crystalline basement rocks from the source to the subset of stations used for location. However, effects of lateral varying velocity and shear-wave anisotropy observable on some records were ignored by the chosen velocity model. Unfortunately, the planned shot near the bottom of the borehole was canceled due to technical difficulties, consequently leaving the velocity model uncalibrated. Figure 4 shows the locations of 94 hypocenters for which homogeneous observations with good SNR were available. For all events, data from the geophone in the pilot hole and eight fixed surface stations were used. We note that all events occurred above the bottom of the hole at a median depth of 8.8 kin, 300 m above the injection interval, where a significant fault was cut by the borehole (Zoback and Harjes, 1997). Also, events 1.5 km above the injection interval did occur (depth of 7.6 km). The N-S cross section shows that the hypocenters appear to be located about 200 m south of the hole. This offset can be related to systematic errors in the location as mentioned earlier. The map (Fig. 4) displays a diffuse zone of epicenters oriented SSE of the injection interval. McGarr (1976) noted that hydraulic fracturing generates fractures that extend along the direction of maximum horizontal principal stress and open parallel to the minimum horizontal principal stress. Talebi and Comet (1987) similarly observed injection-induced events in granite that were located in the direction of the maximum horizontal principal stress. Our data were also analyzed with respect to temporal and spatial patterns that would indicate the generation of a

818

M.L. Jost, T. Btigelberg, 0. Jost, and H.-P. Harjes -1.5

-1.5 E

K

-1

i.+..

(l:,

c~

~ '-0.5

0 0.5

4,'

0 -

-.

-0.5

0

W - 1 .fi

0~5 [km]

E

0.5~ •

Z

r~ -0.~

Empirical G r e e n ' s Function Deconvolution Procedure and Rupture Directivity

-0,5 • .-

-

.q,.,~

-0.5 S

0 [km]

i

,

~

0.5 N

-11

,

-0.5 W

0

1975; Snoke et al., 1984). Since most events were too weak to reliably read the first-motion polarity, we used the similarity of waveforms to produce compound fault-plane solutions (Btitelberg et al., 1995; Zoback and Harjes, 1997). All events belonging to the same cluster apparently have the same or at least a very similar focal mechanism (Fig. 6). We obtained a strike-slip mechanism for cluster 1 at an average depth of about 8.9 km and a strike-slip/reverse mechanism for cluster 4 (with the M L = 1.2 event) at an average depth of 8.6 km. For both fault-plane solutions, the P axis is subhorizontal and oriented NNW-SSE, similar to the N160°E direction of maximum horizontal stress observed in the well bore (Brudy et al., 1997).

.

0.5 [km]

E

Figure 4. Hypocenters of 94 induced microearthquakes. All locations are given with respect to the bottom of the borehole (large circle at a depth of 9.1 km). The solid line indicates the borehole. Top left: perspective view; top right and bottom left; cross sections; bottom right: map view. The most dense concentration of events occurred in the 600 m (+ 100 m) above the bottom of the borehole. The majority of events (median) occurred 300 m above the bottom of the hole, at a depth of 8.8 kin. No events were located below the injection interval.

new fracture system. However, conclusive results were not obtained. Almost all of the microearthquakes could be grouped into 10 clusters of events that were defined by a waveform similarity measure: waveforms of all events were cross-correlated and the correlation coefficients were subjected to a single linkage clustering analysis (nearest-neighbor technique, Everitt, 1993; Schulte-Theis, 1996). Repeated events with highly similar waveforms appear to indicate successive movements of adjacent fault patches (e.g., Ellsworth, 1995). In the following, we will restrict the discussion to clusters 1 and 4 only (Table 1). Figure 5 shows waveforms of the three strongest events of cluster 1 (consisting of 52 events, master event is number 9) and cluster 4 [consisting of 18 events, using the M L = 1.2 event (number 1) as master]. Displayed is the vertical component from the 28-Hz geophone in the pilot hole at 3.99 km depth. The hypocenters of cluster 1 define a zone of seismicity about 150 m in extent about 200 m above the bottom of the borehole (at a depth of 8.9 km; Fig. 6); the hypocenters of cluster 4 occupy a volume of rock about 150 m across and 500 m above the injection interval (at a depth of 8.6 km; Fig. 6). We have determined fanlt-plane solutions for several microearthquakes using first-motion polarities and S H I P amplitude ratios from records of the surface stations (Herrmann,

The empirical Green's function (EGF) deconvolution method has been applied with great success for extracting relative source time functions (RSTF) from microearthquakes in California (Frankel et al., 1986; Mori and Frankel, 1990; Mori, 1993, 1996), Hawaii (Li and Thurber, 1988), New York (Xie et al., 1991), and Canada (Mueller, 1985; Li et al., 1995) using waveforms recorded from local seismic networks. Analysis of the RSTFs also revealed rupture complexity and rupture directivity of microearthquakes (e.g., Frankel et al., 1986; Li and Thurber, 1988; Mori and Frankel, 1990). It has been demonstrated that the rupture directivity along with the focal mechanism of an earthquake can be used to determine the fault plane from the two nodal planes (Frankel et al., 1986; Li and Thurber, 1988; Mori and Hartzell, 1990; Mori, 1993). A seismogram u(t) can be expressed as a convolution of the source time function s(t), the impulse response of the path p(t), the effect of the recording site r(t), and the instrument response i(t): u(t) = s(t) * p(t) * r(t) * i(t).

(1)

A smaller, reference event g(t), whose source time function is assumed to be a Dirac delta function, can be treated as an EGF: g(t) = 5 ( 0 * p(t) * r(t) * fit).

(2)

It is assumed that the large and the small events have almost the same location (2/4 criterion), the focal mechanisms of the events are similar (correlation coefficient c >= 0.9), and the rupture duration of the small event is short enough so that its source-time function can be considered as a delta function. Then, the waveform of the smaller event can be deconvolved from the waveform of the larger event to obtain the RSTF. The deconvolution method removes the effects of the wave path, recording site, and instrument from the seismogram of the larger event. This deconvolution can be expressed in the frequency domain as

Source Parameters of lnjection-lnduced Microearthquakes at 9 km Depth at the KTB Deep Drilling Site, Germany

Table

819

1

I n j e c t i o n - i n d u c e d m i c r o e a r t h q u a k e s at t h e KTB. E v e n t n u m b e r s are i n d i c a t e d for 9 4 e v e n t s t h a t c o u l d b e l o c a t e d w i t h t h e s u r f a c e n e t w o r k a n d the s e n s o r in the p i l o t h o l e . F o r 157 e v e n t s , s o u r c e p a r a m e t e r s w e r e d e t e r m i n e d f r o m r e c o r d s o f the s e n s o r i n the pilot hole. Event doyhhmmss 352002540 352003250 352013710 352034805 352035020 352035125 352040605 352040815 352041545 352042110 352043335 352043635 352043955 352045005 352045350 352050740 352051620 352051710 352051925 352052120 352052800 352053140 352053520 352053645 352054745 352055105 352055900 352060340 352061350 352064020 352064240 352065445 352071945 352072915 352111705 352125705 352131530 352132130 352133715 352143210 352143805 352150155 352150630 352152715 352153115 352153340 352154825 352155050 352160715 352165255 352172940 353064850 352055535 352115340 352140710 352162540 352163420 352182200

No.

118 24

25 23

92 89 40 16 19

12 9 29 79 74 83 67 93

43 49 39

48 47

77

4 6 20 36 69 53 11

Cluster

ML

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2

- 2.0 - 1.9 - 1.4 -0.9 - 1.4 -0.8 - 1.9 - 1.7 - 1.5 -0.8 - 1.2 - 0.8 - 1.2 - 1.6 - 1.3 - 1.6 - 1.2 -0.9 -0.7 -0.7 - 1.4 - 1.2 - 1.5 - 0.9 -0.5 -0.5 -0.8 - 1.6 - 1.2 - 1.2 - 1.2 - 1.1 - 1.5 - 1.3 - 1.7 - 1.6 -0.9 - 1.0 - 1.4 -0.9 - 1.5 - 1.4 - 1.3 - 1.0 - 1.0 - 1.6 - 1.7 - 1.2 - 1.4 - 1.5 - 1.7 - 0,3 -0,3 -0,7 -0.9 - 1.1 - 1.0 - 0.5

fp (Hz)

f~ (Hz)

M0 (109 N-m)

Seismic Energy (103 J)

Stress Drop (10-1 MPa)

96.60 89.28 94.20

81.97 72.71 66.37

0.091 0.117 0.281

0.004 0.004 0.056

0.074 0.065 0.170

98.21 100.18 91.03 81.21 86.07 100.22 92.29 92.41 95.52 93.51

67.61 79.96 72.70 55.33 59.45 81.06 72.18 69.51 66.80 75.03

0.280 0.782 0.152 0.190 0.250 0.931 0.540 1.520 0.562 0.131

0.050 0.672 0.012 0.010 0.024 0.826 0.175 1.308 0.116 0.017

0.133 0.688 0.095 0.060 0.087 0.943 0.373 0.968 0.331 0.093

93.73 89.81 95.89 94.49 100.46 82.26 96.07 91.15 91.59 85.17 89.68 75.82 88.41 97.70 96.06 88.54 97.44 90.90 97.83 78.25 93.20 102.03 92.90 90.66 95.92 80.29 91.28 83.76 88.28 92.97 87.46 89.51 100.82 90.36 80.23 95.70

62.78 66.36 70.04 72.23 72.66 68.29 75.46 74.64 74.09 72.10 78.63 62.63 60.42 78.16 83.16 92.41 74.86 80.03 82.37 72.16 83.97 76.06 73.35 82.83 75.22 66.88 72.06 70.87 72.71 70.92 84.38 68.02 81.58 79.30 70.19 77.77

0.186 0.447 1.201 1.324 1.218 0.453 0.040 0.196 0.878 2.672 2.688 1.510 0.222 0.519 0.432 0.525 0.577 0,255 0.442 0.282 0.237 0.603 0.723 0.318 0.768 0.263 0.276 0.377 0,758 0,746 0,138 0,200 0.590 0.332 0.230 0.184

0.018 0.100 0.862 1.741 1.424 0.082 0.167 0.031 0.857 2.746 5.068 1.326 0.025 0.129 0.147 0.083 0.321 0.033 0.108 0.022 0.053 0.471 0.130 0.049 0.663 0.381 0.039 0.088 0.149 0.154 0.024 0.045 0.130 0.066 0.040 0.034

0.090 0.226 0.850 0.986 0.946 0.239 0.036 0.137 0.683 1.484 2.159 0.579 0.096 0.419 0.329 0.378 0.469 0.196 0.394 0.112 0.177 0.602 0.523 0.253 0.682 0.118 0.179 0.227 0.550 0.538 0.098 0.096 0.473 0.260 0.143 0.135

86.24

85.06

4.103

15.050

2.954

85.33

84.37

0.767

0.567

0.611

(continued)

820

M.L.

J o s t , T. B i i l 3 e l b e r g , O . J o s t , a n d H . - P . H a r j e s

Table 1 Continued. Event doyhhmmss 352192800 352205825 352210720 353012930 353072550 353080705 353090925 353121830 353170310 352041415 352131930 352152625 352153220 352153255 352154645 352163240 352165420 352165615 352171750 352174945 352184000 352193710 352203400 353020010 353043310 353073500 353080030 352073455 352080500 352080545 352090400 352091345 352091715 352102035 352105730 352110915 352111515 352120920 352125445 352132225 352140905 352142100 352144515 352144720 352151045 352152515 352155550 352161545 352162230 352163645 352165520 352170200 352172505 352180705 352190725

fp (Hz)

f~ (Hz)

Mo (109 N-m)

Seismic Energy (103 J)

Stress Drop (10-I MPa)

87.90 87.79 81.47

70.38 69.77 65.42

0.488 0.699 4.286

0.159 0.350 8.192

0.273 0.432 1.806

95.28 99.93 80.94 97.82 116.03

77.76 86.50 59.79 83.50 101.32

1.209 1.721 143.139 0.280 0.471

1.798 2,124 6856.21 0.120 0.477

1.113 1.779 59.353 0.251 0.769

108.28

84.47

1.033

0.807

0.963

102.51 116.73 119.14

87.74 90.26 93.37

0.454 0.606 0.623

0.178 0.594 0.569

0.406 0.823 0.844

116.14 93.09 105.74 109.86 95.49 83.83 94.58 119.36 92.34 101.14 85.63 79.47 85.06 88.24 93.60 88.88 96.38 69.91 100.60 92.86 89.68 91.09 87.75 101.74 92.46 91.79 95.76 84.94 103.13 90.79 87.38

84.18 77.75 91.30 76.35 83.01 80.78 86.20 98.73 83.00 79.01 90.04 76.36 72.49 66.83 77.20 69.47 83.25 55.26 78.34 83.18 72.55 78.37 75.00 73.95 91.75 81.82 93.44 69.41 88.98 75.88 83.97

0.278 0.344 0.193 0.106 0.280 0.144 0.153 0.064 0.070 0.110 0.102 0.296 0,276 0,137 0,150 0,348 0.159 2,073 0.246 0.130 0.154 0.263 0.246 0.109 0.107 0.126 0.179 0.109 0.078 0.261 0.152

0.404 0.216 0.038 0.008 0.056 0.006 0.008 0.004 0.003 0.009 0.005 0.021 0.055 0.926 0.009 0.074 0.009 1.636 0.020 0.004 0.009 0.015 0,025 0.010 0.008 0.011 0.016 0.005 0.004 0.017 0.008

0.309 0.333 0.214 0.082 0.222 0.076 0.108 0.058 0.052 0.082 0.070 0.135 0.155 0.071 0.097 0.188 0.111 0.571 0.175 0.080 0.090 0.145 0.127 0.083 0.082 0.087 0.152 0.056 0.071 0.143 0.094

1.1 1.7 1.5 1.6 1.7

92.34 84.52 84.19 92.03

78.44 83.81 83.31 82.71

0.107 0.127 0.136 0.075

0.004 0.004 0.004 0.006

0.065 0.071 0.068 0.048

- 1.3 - 1.6

99.92

79.03

0.118

0.005

0.082

No.

Cluster

ML

114 115 59 45 54 41 2 101 109 37 10 1

2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

-0.0 -0.5 - 1.1 - 1.0 1.0 -0.9 -0.1 - 1.1 -0.4 -0.9 - 0.5 1.2 - 1.4 - 1.0 - 1.2 -0.6 -0.3 -0.2 -0.4 -0.3 - 1.0 - 0.9 -0.8 -0.3 - 1.2 - 1.4 - 1.5 - 1.5 - 0.9 - 1.6 - 1.5 - 1.7 - 1.7 - 1.4 - 1.6 - 1.3 - 1.1 - 1.4 - 1.5 -0.9 - 1.4 -0.4 - 1.1 - 1.6 - 1.2 - 1.3 -0.8 - 1.4 - 1.5 - 1.4 - 1.4 - 1.5 - 1.6 - 1.2 -1.5

5 5 5 5 5

-

5 5

50 105 14 106 107 110 111 58 38 3l 117 88

35

61

44 7 62 90 33

84

352191705 352193015 352204205 352213405 352232010

112

352232630 353000310

91

(conanued)

821

Source Parameters of Injection-Induced Microearthquakes at 9 km Depth at the KTB Deep Drilling Site, Germany

Table

1

Continued. Event doyhhmmss 353013155 353023925 353054645 352004940 352024755 352031650 352034215 352045045 352202220 352223715 352170220 352185240 353021855 352192610 352193145 352212855 352230805 352235810 353004025 353030330 353061345 353131620 352000220 352000605 352011605 352012055 352014230 352014550 352024905 352025225 352030100 352034030 352035335 352052900 352054600 352064940 352133825 352134230 352141840 352141950 352142640 352143555 352145455 352145725 352150910 352151445 352152345 352154915 352160550 352164400 352165830 352170850 352173905 352183440 352054245 352164025 352190430 352195035 352212450 353022845 353084620 353091830

No.

68 46 65 85 71 30 5 108 22 21 113 8 3 42 78 18 56 94 104

26

17

32 27

86 96

75 98

97

28

15

ML

fp

f~

114o

Cluster

(Hz)

(Hz)

(109 N-m)

Seismic Energy (103 J)

Stress Drop (10 ~MPa)

5 5 5 6 6 6 6 6 7 7 8 8 8 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

- 1.7 - 1.7 - 1.8 - 1.1 - 1.0 - 1.1 - 1.2 - 1.1 -0.8 -0.3 - 0.7 -0.7 - 0.7 -0.7 -0.5 -0.2 -0.9 - 1.2 -0.7 - 1.0 - 1.3 -0.9 - 1.1 - 1.5 - 1.4 -0.8 - 1.4 - 1.3 - 1.4 -0.7 - 1.5 - 1,7 -0,8 - 0.8 - 1.5 - 1.4 - 1.2 - 1.6 - 1.3 - 1.5 - 1.3 - 1.6 - 1.6 - 1.3 - 1.5 - 1.2 - 1.3 - 1.3 - 1.3 - 1.5 - 1.4 - 1.5 - 1.3 - 1.4 - 1.l - 1.1 - 1.0 -0.8 - 1.0 - 1.0 - 1.0 - 0.6

92.84 95.33 101.73 77.25 121.45 84.31 110.20 115.31 107.43 92.25

96.34 92.67 102.61 75.53 77.43 67.81 75.09 71.77 86.58 85.68

0.066 0.087 0.069 0.200 0.290 0.298 0.137 0.117 0.361 9.557

0.006 0.004 0.002 0.029 0.115 0.040 0.011 0.011 0.045 15.150

0.051 0.068 0.066 0.113 0.292 0.143 0.096 0.085 0.265 7.328

92.80 86.47

87.35 76.25

0.661 1.052

0.282 0.426

1.089 1.158

110.75 107.57 114.27

73.98 82.50 81.36

0.776 1.188 3.332

0.639 1.840 10.371

0.688 1.275 3.976

115.33 118.88 124.00

74.03 108.31 79.78

0.400 0.167 0.128

0.120 0.051 0.026

0.351 0.282 0.138

81.34 86.37 88.97 88.24 93.46 86.39 93.49 86.14 92.31 107.76 81.27 80.14 102.60 91.98 90.08 102.04 91.92 97.50 80.57 110.74 85.59 92.73 114.08 85.83 82.14 90.03 92.47 78.64 114.02 84.22 90.84 99.53 77.45 87.91 82.52 76.25 94.40 85.87 71.11 93.00

92.38 73.90 73.10 90.05 89.13 82.34 81.64 76.07 95,83 113.66 79.56 83.19 96.50 88.41 94.94 98.52 83.34 86.38 83.53 109.24 95.00 90.81 88.94 78.45 89.62 76.73 99.46 77.06 85.84 79.81 79.99 93.16 82.86 85.75 73.00 101.90 76.78 96.00 78.03 85.04

0.228 0.135 0.159 0.575 0.072 0.152 0.122 0.665 0.118 0.048 0.538 0.559 0.140 0.152 0.115 0.086 0.135 0.075 0.143 0.065 0.096 0.094 0.062 0.184 0.137 0.150 0.126 0.128 0.080 0.104 0.165 0.086 0.230 0.234 0.438 1.352 0.553 0.293 0.289 0.754

0.017 0.007 0.011 0.116 0.01l 0.015 0.008 0.135 0.009 0.002 0.107 0.084 0.012 0.014 0.009 0.004 0.008 0.008 0.012 0.004 0.004 0.008 0.003 0.010 0.012 0.009 0.012 0.003 0.007 0.004 0.012 0.005 0.046 0.032 0.075 0.567 0.137 0.070 0.072 0.428

0.142 0.081 0.102 0.392 0.086 0.116 0.085 0.352 0.106 0.062 0.308 0.295 0.137 0.126 0.105 0.088 0.093 0.075 0.098 0.085 0.074 0.085 0.063 0.100 0.108 0.094 0.123 0.055 0.087 0.061 0.110 0.084 0.162 0.169 0.231 0.580 0.255 0.257 0.169 0.546

822

M.L. Jost, T. BtilSelberg, (). Jost, and H.-P. Harjes u(co)

s(co) p(co) r(co) i(co)

g(co)

c~(o9)p(co) r(co) i(co)

: S(co).

(3)

The division by small values ( " h o l e s " ) in the spectrum of the smaller event can cause large unstable values in the result. There are two possibilities to stabilize the deconvolution (Moil and Frankel, 1990): first, a water-level criterion to fill up the " h o l e s " in the spectrum or second, the use of the spectrum below the corner frequency. In our data, the S waveforms of four small events and the strongest event of each cluster were windowed to a length of 0.25 sec, filtered between 1 and 40 Hz, padded with zeros to 128 points, and then Fourier transformed into the frequency domain. The amplitude spectrum of the larger event was divided by that of each smaller event, and each phase spectrum of the EGF events was subtracted from that of the larger event. The resulting amplitude and phase spectra were inverse transformed to obtain the RSTF. To stabilize the deconvolution procedure, a Gaussian filter was used to slightly smooth the amplitude spectra before spectral divi-

sion, effectively removing spectral holes (Li et al., 1995) similar to the "water-level" correction. We also remained below the corner frequency. In addition, stacking the RSTFs for each cluster enabled a further stabilization of the results (Table 2). Figure 7 illustrates the EGF deconvolution method that we used to extract RSTFs for larger events. This method was successfully applied to events of cluster 1 and cluster 4 to

~

-0.6~ ' -0.4

o

O~ 4,

-o,

0.5

o

~

-0

5

"

o

W



80

I

70

O_

o°

• •

o~ •

oo

E o o

0o

°e

100 90

•

O0o aJ

I w° ~

•

•

•

•

60 50

(o

•

,/_

J •

..

Oo

t

60 70 80 90 100 110 120 S-Wave Corner Frequency [Hz]

Figure 11. P-wave comer frequency fe versus Swave comer frequency fs. The two straight lines indicate the ratiofJfs for 1.25 and 1.00.

similar rupture process independent of size, and seismic moment Mo proportional to the cube of the source radius after Brune (1970, 1971). In contrast, a marked decrease of stress drop with decreasing seismic moment (breakdown in selfsimilarity) seems to be valid for small earthquakes with seismic moments below 1013 N-m (Chouet et al., 1978; Fletcher et al., 1986; Dysart et al., 1988; Gibowicz and Kijko, 1994). Fletcher et al. (1986) observed constant source radii over four orders of magnitude in seismic moment, indicating a strong dependence of stress drop on seismic moment. Especially small, mining-induced seismicity recorded on underground seismic networks at small hypocentral distances have shown the most convincing evidence (e.g., Gibowicz, 1985; Gibowicz et aI., 1990). The apparent breakdown in self-similarity is closely linked with causes that limit high frequencies ( j ] ~ of Hanks, 1982) of the radiated wave field such as the highly attenuating region just below the Earth's surface or the characteristic width of mine long walls. The evidence from our data is shown in Figure 12, where seismic moment versus source radius, bounded by the lines of con-

829

Source Parameters of lnjection-lnduced Microearthquakes at 9 km Depth at the KTB Deep Drilling Site, Germany

1012

10 8 _ _ 107

1011

106 :-~ >.1 05

E 101o

z

E

0.1

lo 4 I.U

E o 10 9

103 I-102

10 8

101 10 7 101

100 102

07

108

Radius [m]

1010

1011

1012

Moment [Nm]

Figure 12. Seismic moment versus source radius after Brune (1970, 1971). Straight lines indicate constant stress drop. Note that the source radii are essentiaUy constant indicating increasing stress drop with increasing seismic moment.

Figure 13. Total seismic energy versus seismic moment (Table 1). The two parallel lines indicate constant stress drop of 0.1 and 0.01 MPa. There is a general trend of the stress drop to increase with seismic moment as has been suggested earlier by Mayeda and Walter (1996; line M). Our data follow the relation log E = 2.0 log M0 - 15.35.

stant stress drop, is presented. This relation clearly suggests that the stress drop is moment dependent. Note that our hypocentral distances are all smaller than 5 kin; the Q between sources at about 8.8 km depth and receiver at 4 km depth is clearly large and was corrected for. Errors in stress drop are in the order of a factor of 10 (Abercrombie, 1995). Seismic energy has been determined by various authors (e.g., Boatwright and Fletcher, 1984; Gibowicz et al., 1990; Abercrombie, 1995; Mayeda and Walter, 1996) because energy divided by moment is proportional to apparent stress (Wyss, 1970). This stress parameter has been considered more reliable than the static stress drop with its dependency on corner frequency cubed. The radiated seismic energy of either P or S waves can be estimated directly from the integral J (expressing the energy flux of either P or S waves): E c = 4 zcpc (Fc}

109

2 j,

(13)

where (Fc}2 is the mean-square radiation pattern coefficient for P and S waves, that is, (Fp) 2 = 4/15 and (Fs) 2 = 2/5 (Aki and Richards, 1980). The values of total seismic energy are listed in Table 1 and are displayed versus seismic moment in Figure 13. There is a general trend of stress drop to increase with increasing seismic moment as has been stated earlier by Mayeda and Walter (1996) based on data ranging b e t w e e n 10 7 and 1017 Nm. Also, Abercrombie (1995) noted that apparent stress increases with seismic moment. Our energy-moment relation is log E ----2.0 log M0 - 15.35, which is clearly steeper than Mayeda and Walter's relation. P-wave energy Ep versus S-wave energy E s is shown in

106 •

1

104

,

10

e

¸

100

uJ 102

nI i0 o

10-2 / 10°

p

102

104 106 S-Wave Energy [J]

108

Figure 14. P-wave energy Ep versus S-wave energy E s. Constant Es/Ep ratios of 1, 10, and 100 are indicated by straight lines.

Figure 14. The ratio of S- to P-wave energy ranges from 1 to 100. Part of this scatter may result from directivity effects due to the observation at a single station (Boatwright and Fletcher, 1984). Boatwright and Fletcher (1984) determined an average Es/Ep ratio of about 15 for reservoir-induced seismicity at Monticello, South Carolina. Recently, Abercrombie (1995) also found a ratio of 14.3 for Californian earthquakes ( - 1 < M L < 5.5) recorded at 2.5 km depth (Cajon Pass scientific drill hole). Observations of mining-

830

M.L. Jost, T. Btil3elberg, O. Jost, and H.-P. Harjes

induced events by Gibowicz et al. (1990) resulted in Es/E P ratio of somewhat less than 10, indicated a depletion of S waves that the authors ascribed to the influence of non-double-couple sources. In our data, no S-wave energy depletion on average or non-double-couple mechanisms are present. From our average fe/fs ratio of 1.18 +_ 0.16, we obtained for the Es/Ep ratio 14.2 following the method of Boatwright and Fletcher (1984). We conclude that the KTB data show similar energy ratios as other studies (e.g., Boatwright and Fletcher, 1984; Abercrombie, 1995). Various relations have been determined for seismic moment versus M L (e.g., Bungum et al., 1982; Pearson, 1982; Hanks and Boore, 1984; Sereno et al., 1988; Gibowicz et al., 1990). From Table 1, we obtained log Mo = 1.01 M L + 9.68, which compares well with similar relations. However, moment magnitudes (M = 2/3 log Mo - 10.73; Hanks and Kanamori, 1979) are about one magnitude larger than M L on average for our data (Table 1). The moment magnitude was introduced for large events to extrapolate the surface-wave magnitude scale beyond its saturation point at about M S = 8.0. Correspondingly, a one to one relation between M and M L in the range of microearthquakes cannot be expected. In addition, our M L values were determined from S phases recorded in the borehole at 3.99 km depth at frequencies significantly above 1 Hz, at which M L is commonly determined (Lg phase). Rheological Implications of the Results Some of the seismological results previously described have served as basis for an extended rheological interpretation of the injection experiment (e.g., Emmermann and Lauterjung, 1997; Zoback and Harjes, 1997). The locations of the induced microearthquakes far from the injection interval were interpreted as evidence for their generation by only small pore-pressure perturbations (in the order of 1%; Zoback and Harjes, 1997) on preexisting fractures in the rock. These authors also suggested the existence of critically stressed, permeable fault zones at this level of the crust and concluded that Byerlee's law is still satisfied at 9 km depth; that is, the crust is still in a state of frictional equilibrium at that depth. This conclusion is also supported by our observation of source mechanisms that are, within error bounds, pure double couples. Finally, also our impulsive RSTFs indicated brittle failure. Our seismic data suggest that the crust behaved brittlely. Indications of a gradual onset of the brittle-ductile transition could not be resolved. On the other hand, petrological data (St0ckhert, 1994), temperature (270°C), and the fact that all microearthquakes located above the injection interval indicate that the hole reached the onset of the brittle-ductile transitional range (Emmermann and Lauterjung, 1997). Discussion and Conclusions The injection experiment at the KTB, where 200 m 3 of KBr/KC1 brine was injected into the crystalline crust, re-

sulted in the generation of some 400 microearthquakes in a depth range between 8 and 9 kin. Location of 94 events showed a somewhat diffuse volume oriented SSE of the injection interval (close to the direction of the maximum horizontal stress) and a median depth of 300 m above the bottom of the hole. Talebi and Cornet (1987) similarly observed injection-induced events in granite that were located in the direction of the maximum horizontal principal stress. The seismic moment tensors show double-couple source mechanisms for clusters 1 and 4. Their isotropic (volumetric) components are insignificant. Events close to the injection interval show nearly perfect strike-slip character, whereas the shallower cluster, which contains many of the stronger events, shows a predominantly thrust mechanism. The P axes are horizontal with an azimuth of ~N154°E for cluster 1 and an azimuth of ~N330°E for cluster 4. The P axes of both groups are consistent with the direction of the maximum horizontal stress Sn (N160°E) that was found down to 6 and 7.7 km by hydraulic fracturing measurements and from borehole breakouts as well as from drilling-induced tensile wall fractures (Brudy et al., 1997), respectively. The analysis of rupture directivity indicated that the active fault planes are the NE-striking nodal planes for both clusters. Seismic records obtained from the geophone at 3.99 km depth in the pilot hole were used to calculate broadband spectra covering a frequency range from 30 to 300 Hz. The spectra were corrected for Q, where Q = 420 f0.5 for P waves and Q = 2 3 0 f °5 for S waves, assuming an o92 model. Spectral parameters were related to the physical size of the rupture process, to stress drop, and seismic moment. Values of stress release are typical for induced events and somewhat lower than for tectonic events (e.g., Gibowicz et al., 1990; Fehler and Phillips, 1991; Abercrombie and Leary, 1993). Our corner frequencies ranged from 50 to 110 Hz, the mean ratio o f f e / f s is 1.2, and source radii ranged from 12 to 28 m. These source radii are model dependent (Brune, 1970, 1971), and the model of Madariaga (1976) would result in radii about half that size. Our relation between seismic moment and M L is log 3//o = 1.01 ML + 9.68, and the energymoment relation is log E -- 2.0 log Mo - 15.35. The stress drops range between 0.1 and 6 MPa. The resulting seismic scaling relations indicate that stress drop increases with seismic moment for this data set, contradicting results by Abercrombie (1995). This discrepancy may be related to path effects: our hypocentral distances are all smaller than 5 km and highly similar, where hypocentral distances of Abercrombie's events vary and range between 5 and 120 km. In addition, the frequency dependence of Q values was not resolved by Abercrombie (1995). On the other hand, our seismic moments are partially smaller than Abercrombie's data and do not cover her significantly larger range. Therefore, it cannot be precluded that our data, covering only somewhat more than three orders of magnitude, still fall in the larger trend (8 magnitude units) compiled by Abercrombie (1995) due to the large scatter observed over several orders of magnitude.

Source Parameters o f b~jection-Induced Microearthquakes at 9 km Depth at the KTB Deep Drilling Site, Germany

Another caveat for our observation of the breakdown in self-similarity arises from studies by Madariaga (1979) and Fehler and Phillips (1991). Madariaga (1979) found that stress drop may be significantly underestimated in case of varying stress drop over the fault plane. Fehler and Phillips (1991) noted that injection-induced events show a strongly varying stress drop on the fault plane caused by structural heterogeneity. They found that events with the largest stress drops occurred near the edges of the seismically active zone where newly activated faults may be in less heterogeneous rock than in the interior of the seismic zone, which has already been severely fractured. Stress heterogeneities may be present also in our data as indicated by the two different focal mechanisms on similarly oriented fault planes. On the other hand, the data of Fehler and Phillips (1991) were fit as well or even better by a nonconstant stress drop model, and an unambiguous proof of the validity of self-similarity was also not possible.

Acknowledgments The authors want to thank the KTB working group at Ruhr-University Bochum for their help during field work and various stages of data evaluation. Jia contributed her results on Q from an unpublished manuscript. Dahm made his software for moment-tensor inversion available for this study, which is greatfully acknowledged. Maps were produced in parts using GMT by Wessel and Smith (1995). We want to express our thanks to A. McGarr for discussing certain details of the study. The manuscript benefited significantly from the thoughtful comments by the reviewers D. Gendzwill and J. Rutledge, and the associate editor D. Doser.

References Abercrombie, R. E. (1995). Earthquake source scaling relationships from - 1 to 5 ML using seismograms recorded at 2.5 km depth, J. Geophys. Res. 100, 24015-24036. Abercrombie, R. E. and P. Leary (11993). Source parameters of small earthquakes recorded at 2.5 km depth, Cajon Pass, southern California: implications for earthquakes scaling, Geophys. Res. Lett. 20, 15111514. Aki, K. and P. G. Richards (1980). Quantitative Seismology: Theory and Methods, Freeman, New York. Ben-Menahem, A. (1962). Radiation of seismic body waves from a finite moving source in the earth, J. Geophys. Res. 67, 345-350. Ben-Menahem, A. and S. J. Singh (1981). Seismic Waves and Sources, Springer, New York. Boatwright, J. (1980). A spectral theory for circular seismic sources: simple estimates of source dimension, dynamic stress drop, and radiated energy, Bull. Seism. Soc. Am, 70, 1-28. Boatwright, J. and J. B. Fletcher (1984). The partition of radiated energy between P and S-waves, Bull Seism. Soc. Am. 74, 361-376. Brudy, M., M. D. Zoback, K. Fuchs, F. Rummel, and J. Baumg~irtner (1997). Estimation of the complete stress tensor to 8 km depth in the KTB scientific drillholes--implications for crustal strength, J. Geophys. Res. 102, 18453-18475. Brune, J. N. (1970). Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res. 75, 4997-5009. Brnne, J. N. (197l). Correction, J. Geophys. Res. 76, 5002. Bungum, H., S. Vaage, and E. S. Husebye (1982). The Meloy earthquake sequence Northern Norway: source parameters and their scaling relations, Bull. Seism. Soc. Am. 72, 197-206. Bfil3elberg, T., H.-P. Harjes, and M. Knapmeyer (1995). Source parameter

831

of seismic events induced by fluid injection at 9 km depth in the KTBborehole, EOS 76, no. 46/supplement, F559. Chouet, B., K. Aki, and M. Tsnjiura (1978). Regional variations of the scaling law of earthquake source spectra, Bull. Seism. Soc. Am. 68, 49-79. Dahlheim, H.-A., H. Gebrande, E. Schmedes, and H. Soffel (1997). Seismicity and stress field in the vicinity of the KTB location, J. Geophys. Res. 102, 18493-18506. Dahm, T. (1993). Relative moment tensor inversion to determine the radiation pattern of seismic sources, Ph.D. Thesis, Geophysikalisches Institut, University Karlsruhe, Germany (in German). Dahm, T. (1996). Relative moment tensor inversion based on ray-theory: theory and synthetic tests, Geophys. J. Int. 124, 245-257. Dahm, T. and B. Brandsdottir (1997). Moment tensors of microearthquakes from the Eyjafjallajrkull volcano in South Island, Geophys. J. Int. 130, 183-192. Dysart, P. S., J. A. Snoke, and I. S. Sacks (1988). Source parameters and scaling relations for small earthquakes in the Matsushiro region, southwest Honshn, Japan, Bull. Seism. Soc. Am. 78, 571-589. Dziewonski, A. M. and J. H. Woodhouse (1983). Studies of the seismic source using normal-mode theory, in Earthquakes: Obsen,ation, Theory and Interpretation, H. Kanamori and E. Boschi (Editors), NorthHolland, New York. Ellsworth, W. L. (1995). Characteristic earthquakes and long-term earthquake forecasts: implications of central California seismicity, in Urban Disaster Mitigation: The Role of Science and Technology, F. Y. Cheng and M. S. Sheu (Editors), Elsevier, New York, 1-14. Emmermann, R. and J. Lauterjung (1997). The German Continental Deep Drilling Program KTB: overview and major results, J. Geophys. Res. 102, 18179-18201. Everitt, B. S. (1993). Cluster Analysis, Edward Arnold, London. Fehler, M. and W. S. Phillips (1991). Simultaneous inversion for Q and source parameters of microearthquakes accompanying hydraulic fracturing in granitic rock, Bull Seism. Soc. Am. 81, 553-575. Fletcher, J. B., L. C. Haar, F. L. Vernon, J. N. Brune, T. C. Hanks, and J. Berger (1986). The effects of attenuation on the scaling of source parameters for earthquakes at Anza, California, in Earthquake Source Mechanics, S. Das, J. Boatwright, and C. H. Scholz (Editors), Am. Geophys. Union Monograph 6, 331-338. Frankel, A., J. Fletcher, F. Vernon, L. Haar, J. Berger, T. Ranks, and J. Brune (1986). Rupture characteristics and tomographie source imaging of ML ~ 3 earthquakes near Anza, Southern California, J. Geophys. Res. 91, 12633-12650. Gibowicz, S. J. (1985). Seismic moment and seismic energy of mining tremors in the Lubin copper basin in Poland, Acta Geophys. Polon. 33, 243-257. Gibowicz, S. J. and A. Kijko (1994). An Intlvduction to Mining Seismology, Academic Press, San Diego. Gibowicz, S. J., H.-P. Harjes, and M. Sehiifer (1990). Source parameters of seismic events at Heinrieh Robert mine, Ruhr basin, Federal Republic of Germany: evidence for non-double-couple events, Bull. Seism. Soc. Ant. 80, 88-109. Ranks, T. C. (1981). The corner frequency shift, earthquake source models and Q, Bull Seism. Soc. Am. 71, 597-612. Ranks, T. C. (1982).fm,× , Bull. Seism. Soc. Ant. 72, 1867-1880. Hanks, T. C. and D. M. Boore (1984). Moment-magnitude relations in theory and practice, J. Geophys. Res. 89, 6229-6235. Hanks, T. C. and H. Kanamori (1979). A moment magnitude scale, J. Geophys. Res. 84, 2348-2351. Harjes, H.-P., K. Brain, H.-J. Dt~rbanm, H. Gebrande, G. Hirschmann, M. Janik, M. K1/3ckner, E. Ltischen, W. Rabbel, M, Simon, R. Thomas, J. Tormann, and F. Wenzel (1997). Origin and nature of crustal reflections: results from integrated seismic measurements at the KTB superdeep drilling site, J. Geophys. Res. 102, 18267-18288. Hemnann, R. B. (1975). A student's guide to the use of P and S-wave data for focal mechanism determination, Earthquake Notes 46, 29-39.

832

Jost, M. L. and R. B. Herrmann (1989). A student's guide to and review of moment tensors, Seism. Res. Lett. 60, no. 2, 37-57. Kanamori, H. and D. L. Anderson (1975). Theoretical basis of some empirical relations in seismology, Bull. Seism. Soc. Am. 65, 1073-1095. Kanamori, H. and J. W. Given (1981). Use of long-period surface waves for rapid determination of earthquake-source parameters, Phys. Earth Planet. Interiors 27, 8-31. Kennett, B. L. N. (1983). Seismic Wave Propagation in Stratified Media, Cambridge U Press, Cambridge. Knopoff, L. and M. J. Randall (1970). The compensated linear-vector dipole: a possible mechanism for deep earthquakes, J. Geophys. Res. 75, 4957-4963. Li, Y. and C. H. Thurber (1988). Source properties of two microearthquakes at Kilanea volcano, Hawaii, Bull. Seism. Soc. Am. 78, 1123-1132. Li, Y., C. Doll, and M. N. Toksrz (1995). Source characterization and fault plane determinations for MbLg = 1.2 to 4.4 earthquakes in the Charlevoix seismic zone, Quebec, Canada, Bull. Seism. Soc. Am. 85, 16041621. Madariaga, R. (1976). Dynamics of an expanding chcular fault, Bull. Seism. Soc. Am. 66, 639-666. Madariaga, R. (1979). On the relation between seismic moment and stress drop in the presence of stress and strength heterogeneity, J. Geophys. Res. 84, 2243-2250. Mayeda, K. and W. R. Walter (1996). Source parameters of western U. S. earthquakes: moment, energy, stress drop and source spectra from regional coda envelopes, J. Geophys. Res. 101, 11195-11208. McGarr, A. (1976). Seismic moments and volume changes, J. Geophys. Res. 81, 1487-1494. McGarr, A. (1991). Observations constraining near-source ground motion estimated from locally recorded seismograms, J. Geophys. Res. 96, 16495-16508. McGarr, A. (1992). Moment tensors of ten Witwatersrand mine tremors, Pageoph 139, 781-800. Mori, J. (1993). Fault plane determinations for three small earthquakes along the San Jacinto fault California: search for cross faults, J. Geophys. Res. 98, 17711-17722. Mori, J. (1996). Rupture directivity and slip distribution of the M 4.3 foreshock to the 1992 Joshua Tree earthquake, Southern California, Bull. Seism. Soc. Am. 86, 805-810. Mori, J. and A. Frankel (1990). Source parameters for small events associated with the 1986 North Palm Springs, California, earthquake determined using empirical Green's functions, Bull. Seism. Soc. Am. 80, 278-295. Mori, J. and S. Hartzell (1990). Source inversion of the 1988 Upland, California, earthquake: determination of a fault plane for a small event, Bull. Seism. Soc. Am. 80, 507-518. Mueller, C. (1985). Source pulse enhancement by deconvolution of an empirical Green's function, Geophys. Res. Lett. 12, 33-36. Mtiller, B., M. L. Zoback, K. Fuchs, L. Mastin, S. Gregersen, N. Pavoni, O. Stephansson, and C, Ljunggren (1992). Regional patterns of tectonic stress in Europe, J. Geophys. Res. 97, 11783-11803. Pearson, C. (1982). Parameters and a magnitude moment relationship from small earthquakes observed during hydraulic fracturing experiment in crystalline rocks, Geophys. Res. Lett. 9, 404-407.

M . L . Jost, T. Bfil3elberg, (). Jost, and H.-P. Harjes

Reid, H. F. (1910). Elastic rebound theory, Univ. Calif. PUN., Bull. Dept. Geol. Sci. 6, 413-433. Savage, J. C. (1965). The effect of rupture velocity upon seismic first motion, Bull. Seism. Soc. Am. 55, 263~75. Scbulte-Theis, H. (1996). Cluster analysis of European Seismicity, Cahiers du Centre Europeen de Geodynamique et de Seismologie 12, 201223. Sereno, T. J., S. R. Bratt, and T. C. Bache (1988). Simultaneous inversion of regional wave spectra for attenuation and seismic moment in Scandinavia, J. Geophys. Res. 93, 2019-2035. Snoke, J. A, (1987). Stable determination of (Brune) stress drops, Bull. Seism. Soc. Am. 77, 530-538. Snoke, J. A., J. W. Munsey, A. G. Teague, and G. A. Bollinger (1984). A program for focal mechanism determination by combined use of polarity and SV-P amplitude ratio data, Earthquake Notes 55, no. 3, 15. Strckhert, B. (1994). The "Brittle-Ductile Transition" in the KTB Borehole--a tentative prognosis, KTB-Report 94-2, A25. Talebi, S. and F.-H. Cornet (1987). Analysis of the microseismicity induced by a fluid injection in a granitic rock mass, Geophys. Res. Lett. 14, 227-230. Vasco, D. W. and L. R. Johnson (1988). Inversion of waveforms for extreme source models with an application to the isotropic moment component, in Regional Studies with Broadband Data, T. V. Me Evilly and L. R. Johnson (Editors), Report No. 1, Air Force Geophysics Laboratory AFGL-TR-88-0131, Vidale, J. E, (1989). Influence of focal mechanism on peak ground acceleration of strong motions of the Whittier Narrows, California earthquake and an aftershock, J. Geophys. Res. 94, 9607-9613. Wagner, G. A., D. A. Coyle, J. Duyster, F. Henjes-Kunst, A, Peterek, B. Schrrder, B. St~ckhert, K. Wemmer, G. Zulauf, H. Ahrendt, R. Bischoff, E. Hejl, J. Jacobs, D. Menzel, N. Lal, P. Van Den Hante, C. Vercoutere, and B. Welzet (1997). Post-Variscan thermal and tectonic evolution of the KTB site and its surroundings, J. Geophys. Res. 102, 18221-18232. Wessel, P. and W. H. F. Smith (1995). New version of the Generic Mapping Tools released, EOS 76, 329. Wyss, M. (1970). Stress estimates for South American shallow and deep earthquakes, J. Geophys. Res. 75, 1529-1544. Xie, J., Z. Liu, R. B. Herrmann, and E. Cranswick (1991). Source processes of three aftershocks of the 1983 Goodnow, New York, earthquake: high-resolution images of small, symmetric ruptures, Bull. Seism. Soc. Am. 81, 818-843. Zoback, M. D. mad H.-P. Harjes (1997). Injection-induced earthquakes and crustal stress at 9 km depth at the KTB deep drilling site, Germany, J. Geophys. Res. 102, 18477-18491.

Institute of Geophysics Ruhr-University Bochum D-44780 Bochum, Germany

Manuscript received 2 October 1997.