Stress field in the Northern Rhine area, Central Europe, from earthquake fault plane solutions

Tectonophysics 377 (2003) 325 – 356 www.elsevier.com/locate/tecto

Stress field in the Northern Rhine area, Central Europe, from earthquake fault plane solutions Klaus-G. Hinzen * Department of Earthquake Geology, Geological Institute, University of Cologne, Vinzenz-Pallotti-Str. 26, D-51429 Bergisch Gladbach, Germany Received 16 January 2003; accepted 9 October 2003

Abstract Fault plane solutions (FPS) from 110 earthquakes in the northern Rhine area with local magnitudes, ranging from 1.0 to 6.1, and occurring between 1976 and 2002 are determined. FPS are retrieved from P-wave first motions using a grid search approach allowing a detailed exploration of the parameter space. The influence of the 1D velocity model on take-off angles and resulting FPS is examined. All events were relocated with a recently developed minimum 1D model of the velocity structure [J. Geophys. Res. (2003)]. Rose diagrams of the orientation of P, T and B axes show a clear preference of trends of P and T axes at N292jE and N27jE, respectively. The majority of B axes trend in northerly directions. Plunges of P and T axes are mostly around 45j while most B axes are subhorizontal. The main direction of the maximum horizontal stress directly inferred from the fault plane solutions is N118jE. To calculate the orientations of the principal stress axes and the shape of the stress tensor, the inversion method of Gephard and Forsyth [J. Geophys. Res. 89 (1984) 9305] was applied to the whole data set and to several subsets of data. The subsets were formed by grouping events from various geological and tectonic areas and by grouping events into different depth ranges. The subset areas include the Lower Rhine Embayment, the Rhenish Massif, the middle Rhine area, the Neuwied Basin and the area known as the Stavelot – Venn Massif. Inversion of the entire data set shows some ambiguity between a strike-slip and extensional stress regime, with a vertical axis for the medium principal stress and a trend of N305jE and N35jE for the r1 and r3 axis, respectively, as the best fitting tensor. Earthquakes from the Lower Rhine Embayment and, to some degree, from the middle Rhine area indicate an extensional stress regime. In the Lower Rhine Embayment, plunge and trend of the r1 axis are 76j and N162jE and for the r3 axis 7j and N42jE. The best fitting solution for the area of the Stavelot – Venn Massif is a strike-slip regime with subhorizontal r1 and r3 axes with a trend of N316jE and N225jE, respectively. Stress orientations found here agree overall with the results from earlier studies based on smaller data sets. The directions of the maximum and minimum horizontal stresses inverted from focal mechanisms agree well with the stress field predicted by the European Stress Map. This confirms earlier interpretations that the stress field of the Rhine Graben system is controlled by plate driving forces acting on the plate boundaries. However, amplitudes of the stresses change on a local scale and with depth. Estimates of the absolute magnitude of principal stresses favor a normal faulting regime in the shallow crust (above 12-km depth) and a strike-slip regime in the lower crust. D 2003 Elsevier B.V. All rights reserved. Keywords: Earthquake; Fault plane solutions; Stress inversion; Northern Rhine area

* Tel.: +49-2204-985211; fax: +49-2204-985220. E-mail address: [email protected] (K.-G. Hinzen). 0040-1951/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2003.10.004

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1. Introduction Focal mechanisms of earthquakes have long been used to probe the stress field in continental crust (e.g. Wallace, 1951; Bott, 1959; McKenzie, 1969). In the most simple model, the P, B, and T axes representing the orientation of an assumed pure double-couple source are taken as proxies of the rough orientation of the stress field. However, P and T axes are strictly oriented at 45j to the auxiliary and rupture plane. The angle between the largest principal stress r1 and the fault plane is generally not 45j, but rather in the range of 30j depending on the coefficient of internal friction and the normal stress. The same accounts for the smallest principal stress r3 and the auxiliary plane. When earthquakes occur on pre-existing faults and zones of weakness produced by former stress

field orientations, the geometry of the P, T, and B axes can deviate substantially from principal stress directions (McKenzie, 1969). For the central European rift system with its complex tectonic history (Van den Berg, 1994; Ziegler, 1994), the existence of such faults and zones of weakness is certain. In this case, therefore, the slip vectors from ensembles of fault plane solutions (FPS) can be used as input to a stress tensor inversion, which best explains the observations and allows the slip to occur on preexisting faults. Various inversion procedures have been developed in the past (Angelier, 1979; Gephard and Forsyth, 1984; Gephard, 1990a,b; Michael, 1984; Reches, 1987; Rivera and Cisternas, 1990; Abers and Gephard, 2001). In the present study, earthquakes which have been relocated with a new minimum 1D velocity model for the northern Rhine area and occurring

Fig. 1. Simplified geologic map of the area of investigation. The rectangle in the inset in the upper right with an overview of the Rhine Graben system in northwest Europe (after Ziegler, 1982) gives the outline of the large map. Circles show the epicenters of earthquakes used in this study. Symbol labels give the event numbers (s. Table 1). White polygons show four of the analyzed subregions. The dashed white lines indicate the trend of the two profiles shown in Fig. 2.

K.-G. Hinzen / Tectonophysics 377 (2003) 325–356

between 1976 and 2002 (Reamer and Hinzen, submitted) are used to derive FPS from P-wave polarities and resolve the orientation of the stress tensor. The stress field in the northern Rhine area has been investigated previously by several authors. Ahorner et al. (1983) interpreted P, T, and B axes from FPS of 30 earthquakes which occurred between 1975 and 1982 in Central Europe, with about a dozen events in the northern Rhine area. Mu¨ller et al. (1992) investigated the area as part of a study of the regional patterns of tectonic stress in Europe. Delouis et al. (1993) examined the stress tensor in France and neighboring regions including the northern Rhine area. Plenefisch and Bonjer (1997) studied the stress field in the Rhine Graben area and completed a detailed analysis of the stress tensor in the Upper Rhine Graben. Included in their study were 19 published FPS from events between 1997 and 1992 used to calculate a separate stress tensor inversion for

327

the northern Rhine Graben area. All previous stress inversions were based on catalog data or source orientations from several publications based on different velocity models and procedures. In the current study, FPS of 110 earthquakes (Fig. 1) were determined with the same grid search procedure on the basis of the new velocity model (Reamer and Hinzen, submitted), which was optimized for the area under investigation. The distribution of the hypocenter depths of these earthquakes is shown in Fig. 2.

2. Database The earthquake data catalog of the Department of Earthquake Geology of Cologne University (BENS) was used as the database for this study. For the years between 1976 and 2002, the catalog contains data from ca. 2500 local earthquakes in the northern Rhine and

Fig. 2. Depth distribution of the 110 earthquakes used in this study along NW – SE (top) and SW – NE (bottom) trending profiles. The locations are labeled with the event numbers. Dashed lines roughly indicate the observed maximum depth of events. The location of the profiles is shown in Fig. 1.

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Table 1 List of earthquakes used in this study No. Date Time Latitude Longitude Depth Region ML Polarity Ploarity Solutions P-axis T-axis Weight (yyyy – mm – dd) (hh:mm) (jN) (jE) (km) readings errors (%) Trend Plunge Trend Plunge (j) (j) (j) (j) 001 1976 – 06 – 29

05:00

51.157

5.826

17.1

LRE

3.2

6

0

0.08

002 1977 – 05 – 08 003 1977 – 10 – 07

23:09 23:07

50.074 50.719

7.907 6.107

12.1 14.0

MRA HVA

3.0 10 1.9 7

0 0

0.36 3.13

004 005 006 007 008 009 010 011 012 013 014 015 016

1977 – 11 – 02 1977 – 11 – 06 1978 – 06 – 10 1979 – 07 – 23 1979 – 07 – 23 1979 – 09 – 08 1980 – 03 – 01 1980 – 06 – 05 1980 – 07 – 28 1980 – 12 – 31 1981 – 03 – 14 1981 – 12 – 13 1981 – 12 – 15

14:42 01:22 13:58 10:42 20:41 17:56 12:48 12:11 02:58 00:01 19:42 00:17 18:08

50.953 50.950 50.636 50.223 50.236 49.849 50.539 51.205 49.981 50.171 50.334 50.050 50.135

6.791 6.795 6.198 8.280 8.284 8.310 5.389 5.848 8.105 7.707 7.433 7.595 7.898

7.4 9.5 3.9 3.8 12.5 4.0 2.4 4.1 4.7 4.0 7.0 9.1 7.7

LRE LRE HVA MRA MRA RHS HVA LRE RHS MRA NWB MRA MRA

3.3 3.7 3.0 2.3 1.7 2.0 1.9 3.8 2.3 2.9 1.2 2.2 2.0

15 21 14 10 5 9 9 20 9 22 7 17 9

0 1 1 0 0 0 0 0 0 2 0 2 1

0.05 0.14 0.09 2.76 2.98 0.01 0.17 0.00 4.13 0.01 0.50 0.27 0.06

017 1981 – 12 – 20

10:38

50.899

5.90

14.8

HVA

2.7 12

0

0.57

018 1982 – 03 – 02 019 1982 – 03 – 07

01:27 21:26

51.030 50.524

5.873 7.116

11.2 8.6

LRE MRA

3.7 13 1.8 7

0 0

0.01 1.83

020 1982 – 05 – 22

06:00

51.043

5.981

10.4

LRE

3.9 23

2

0.05

021 1982 – 06 – 22 022 1982 – 06 – 26

12:44 13:57

50.662 50.675

8.042 8.010

11.4 14.0

BMB BMB

2.6 14 3.2 15

0 2

0.35 0.27

023 1982 – 06 – 28 024 1983 – 03 – 22

09:57 07:20

50.638 50.385

7.987 7.401

11.6 3.3

BMB NWB

5.0 34 3.0 13

2 1

0.06 0.25

025 026 027 028 029 030

1983 – 03 – 22 1983 – 03 – 22 1983 – 05 – 07 1983 – 06 – 06 1983 – 11 – 08 1983 – 11 – 08

07:24 07:34 12:08 18:50 00:49 02:13

50.370 50.381 50.354 50.394 50.640 50.623

7.408 7.398 7.403 7.590 5.518 5.492

8.4 7.7 7.8 6.8 4.6 3.0

NWB NWB NWB MRA HVA HVA

3.3 2.9 2.3 1.8 5.0 2.9

20 15 17 14 33 14

0 1 1 0 0 1

0.40 1.22 0.25 0.00 0.04 0.32

031 032 033 034 035 036 037

1983 – 11 – 18 1984 – 07 – 09 1984 – 12 – 08 1985 – 01 – 15 1985 – 05 – 12 1985 – 07 – 12 1985 – 07 – 16

22:18 23:19 19:06 04:20 21:47 15:33 05:33

50.579 50.770 50.587 50.400 50.452 50.028 50.861

7.291 5.418 7.300 7.369 6.078 7.406 5.523

11.4 5.6 11.2 7.3 11.0 10.1 8.1

MRA HVA MRA NWB HVA MRA HVA

2.9 3.1 1.4 2.2 2.4 2.3 3.2

19 15 7 15 20 14 20

1 0 0 2 0 0 1

0.01 0.47 0.24 0.95 0.03 0.14 0.05

038 1985 – 07 – 28 039 1985 – 08 – 31

21:49 23:47

50.382 50.357

7.380 7.414

8.8 9.9

NWB NWB

1.2 8 1.8 12

0 0

1.05 1.10

242.5 271.0 314.6 284.0 248.2 164.4 149.9 329.2 306.4 267.1 20.6 328.5 288.1 136.2 331.1 142.9 115.7 81.9 315.4 327.3 330.7 180.3 153.9 3.6 317.3 338.8 320.7 25.0 317.7 310.9 288.7 21.5 286.3 290.1 344.5 197.1 297.6 145.0 200.3 27.9 153.7 314.8 284.2 101.1 296.1 324.4 354.6 97.9 103.9 239.9

6.9 31.2 16.3 45.9 4.0 58.1 57.4 57.1 33.3 2.3 24.2 50.1 55.4 34.7 53.4 41.8 65.3 55.4 39.8 27.2 74.8 43.5 20.8 25.4 63.9 30.4 45.3 70.0 63.1 49.9 42.1 74.7 13.7 6.1 51.1 52.2 17.4 25.0 45.6 16.3 14.9 46.7 17.6 56.5 54.7 25.8 39.8 16.3 20.8 76.2

350.3 178.2 167.5 149.2 156.4 330.4 298.0 199.1 201.7 173.1 149.8 184.2 27.8 45.1 217.9 36.6 232.2 342.2 145.5 217.9 205.7 10.0 58.4 222.8 226.1 238.0 213.0 205.0 154.4 50.8 180.3 211.3 21.6 23.4 252.2 30.3 204.2 325.0 351.6 141.1 316.7 153.9 17.5 214.0 105.7 95.0 164.5 211.1 2.7 20.7

68.5 4.6 70.8 34.3 24.4 31.1 28.5 22.7 21.1 60.4 54.6 34.2 6.6 1.6 16.3 17.5 11.6 6.6 49.8 32.9 8.9 46.1 14.1 58.4 0.6 17.8 16.8 20.0 25.9 8.3 19.2 15.1 21.1 28.1 1.9 37.0 10.6 65.0 40.6 53.4 74.5 41.7 10.3 14.4 34.8 53.3 49.8 53.4 27.1 10.8

1.6 1.6 3.0 1.0 1.0 3.3 3.7 3.0 2.3 1.7 2.0 1.9 3.8 2.3 2.9 1.2 2.2 1.0 1.0 1.4 1.4 3.7 0.9 0.9 2.0 2.0 2.6 1.6 1.6 5.0 1.5 1.5 3.3 2.9 2.3 1.8 5.0 1.5 1.5 2.9 3.1 1.4 2.2 2.4 2.3 1.6 1.6 1.2 0.9 0.9

K.-G. Hinzen / Tectonophysics 377 (2003) 325–356

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Table 1 (continued) No. Date Time Latitude Longitude Depth Region ML Polarity Ploarity Solutions P-axis T-axis Weight (yyyy – mm – dd) (hh:mm) (jN) (jE) (km) readings errors (%) Trend Plunge Trend Plunge (j) (j) (j) (j) 040 1985 – 12 – 07

23:09

50.882

5.933

2.8

HVA

2.7 28

3

0.01

041 1985 – 12 – 16 042 1986 – 02 – 07 043 1986 – 10 – 27

04:32 18:48 20:40

50.379 50.383 50.381

7.407 7.364 7.410

8.0 9.9 7.9

NWB NWB NWB

2.2 14 1.0 8 2.0 9

0 0 0

0.64 0.21 0.30

044 045 046 047 048

1988 – 03 – 14 1988 – 10 – 17 1988 – 12 – 11 1988 – 12 – 27 1988 – 12 – 31

15:49 19:39 12:38 11:53 02:14

50.373 50.804 50.686 50.527 50.409

7.354 5.920 7.177 5.678 7.368

7.3 21.8 6.1 18.6 8.6

NWB HVA MRA HVA NWB

2.8 3.4 2.1 3.5 1.9

17 31 16 25 7

1 2 1 1 0

0.01 0.00 0.22 0.03 0.17

049 050 051 052 053 054

1989 – 01 – 08 1989 – 06 – 17 1990 – 02 – 07 1990 – 04 – 19 1990 – 11 – 18 1991 – 01 – 13

22:28 22:13 02:43 05:35 14:20 06:03

50.674 50.375 50.467 50.688 50.160 50.979

7.932 7.390 6.032 5.513 7.869 6.244

8.4 7.8 6.1 16.3 10.7 8.4

BMB NWB HVA HVA MRA LRE

2.4 2.3 2.1 2.9 3.1 1.9

12 11 16 16 21 9

1 1 0 0 2 0

0.06 0.00 0.00 0.24 0.00 0.42

055 1991 – 03 – 27

23:00

50.294

5.954

10.2

HVA

2.3 13

0

0.01

056 1991 – 08 – 10

14:55

50.714

5.668

10.7

HVA

2.8 14

0

0.69

057 058 059 060 061 062 063 064 065 066 067 068 069

1992 – 03 – 09 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13 1992 – 04 – 13

01:33 01:20 01:33 01:46 02:05 02:30 03:03 03:17 04:32 04:37 05:25 06:02 21:50

50.389 51.157 51.150 51.136 51.090 51.143 51.160 51.172 50.842 51.063 51.163 51.145 51.166

7.421 5.933 5.926 6.008 5.964 5.961 5.935 5.890 6.265 6.041 5.908 5.979 5.974

7.5 16.8 11.2 16.7 10.9 11.2 8.4 15.4 14.0 11.5 14.0 12.9 6.3

NWB LRE LRE LRE LRE LRE LRE LRE LRE LRE LRE LRE LRE

2.4 6.1 2.2 1.7 1.8 1.8 2.2 2.1 2.5 2.3 2.3 3.0 2.1

19 53 17 11 15 11 17 19 18 14 12 24 13

1 0 1 1 2 0 1 4 3 0 0 3 1

1.07 0.02 0.00 0.02 0.01 0.00 0.03 0.06 0.11 0.47 0.04 0.04 0.48

070 1992 – 04 – 13 071 1992 – 04 – 14 072 1992 – 04 – 14

22:59 01:06 01:36

51.142 50.946 50.829

5.989 6.189 6.243

8.4 14.0 15.3

LRE LRE LRE

1.9 14 4.0 40 3.0 33

0 1 2

0.00 0.02 0.12

073 1992 – 04 – 14 074 1992 – 04 – 14

02:31 12:41

51.153 51.153

5.970 5.903

11.7 14.0

LRE LRE

2.4 18 2.9 17

1 2

0.06 0.27

075 1992 – 04 – 14 076 1992 – 04 – 15 077 1992 – 04 – 20

12:56 22:05 16:50

51.157 50.823 50.825

5.967 6.253 6.238

11.2 16.3 15.9

LRE LRE LRE

2.8 19 2.1 13 2.3 19

2 1 0

0.03 0.02 1.16

158.3 186.1 118.1 295.5 71.5 186.8 36.6 113.8 334.4 313.4 62.6 303.6 25.9 161.6 285.1 121.3 38.9 91.9 287.7 351.4 212.8 282.1 266.9 86.5 315.4 257.3 70.5 155.0 14.2 20.7 270.5 202.2 148.9 104.7 32.2 234.1 74.6 144.5 287.8 190.7 340.6 135.3 315.2 195.2 108.8 136.9 317.3 119.7 281.8 320.5 326.6

60.9 40.2 20.3 27.7 10.7 55.4 54.6 34.7 38.0 21.1 36.9 24.4 59.7 40.6 1.6 13.7 48.4 31.4 26.1 53.4 58.4 32.9 72.5 35.2 8.4 24.4 56.7 85.0 12.7 68.9 43.1 54.8 57.6 74.5 47.2 30.0 63.9 43.2 52.2 42.5 52.1 54.6 7.1 46.9 42.0 60.4 67.5 43.5 27.6 60.0 14.1

1.6 3.5 357.2 201.4 331.8 27.2 222.0 204.9 82.4 48.7 204.5 211.8 211.8 10.3 16.2 216.6 211.8 219.1 167.3 161.0 353.6 172.7 152.5 220.3 211.3 355.2 220.1 335.0 126.9 120.8 99.9 82.0 276.3 206.0 159.7 57.1 241.7 24.1 32.4 30.2 212.1 45.0 223.4 24.3 280.6 42.9 49.3 290.0 167.4 198.5 231.1

27.1 49.8 54.3 7.6 42.0 32.9 35.3 1.6 21.7 13.7 46.3 4.0 30.2 45.6 34.7 21.1 41.4 44.7 45.9 36.2 25.4 27.2 7.5 44.4 58.6 16.9 29.6 5.0 59.7 3.8 46.5 19.5 21.1 3.1 29.4 59.9 25.5 28.3 11.1 45.9 25.8 0.2 14.0 42.7 47.7 2.3 0.8 46.1 38.4 17.0 20.8

1.4 1.4 2.2 1.0 1.0 1.0 2.8 3.4 2.1 3.5 1.0 1.0 2.4 2.3 2.1 2.9 3.1 1.0 1.0 0.6 0.6 0.6 0.6 1.4 1.4 2.4 6.1 2.2 1.7 1.8 1.8 2.2 2.1 2.5 2.3 2.3 3.0 1.1 1.1 1.9 4.0 1.5 1.5 2.4 1.0 1.0 1.0 2.8 2.1 1.2 1.2

(continued on next page)

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Table 1 (continued) No. Date Time Latitude Longitude Depth Region ML Polarity Ploarity Solutions P-axis T-axis Weight (yyyy – mm – dd) (hh:mm) (jN) (jE) (km) readings errors (%) Trend Plunge Trend Plunge (j) (j) (j) (j) 078 1992 – 04 – 20 079 1992 – 04 – 24 080 1992 – 04 – 26

19:52 10:35 01:45

50.822 51.137 50.835

7.009 5.982 6.214

3.2 6.1 14.0

LRE LRE LRE

2.1 25 2.3 13 1.5 8

0 1 1

0.01 0.02 1.22

081 082 083 084

1993 – 01 – 22 1993 – 02 – 15 1993 – 06 – 03 1993 – 06 – 11

18:47 10:46 12:57 17:04

50.512 51.146 51.163 51.209

6.830 5.982 5.947 5.770

11.7 15.0 12.0 14.3

MRA LRE LRE LRE

2.0 2.8 3.4 2.8

12 16 24 13

0 0 3 1

0.00 0.03 0.01 0.54

085 1993 – 08 – 17 086 1993 – 10 – 14 087 1993 – 12 – 24

08:02 17:13 08:32

50.847 50.825 50.774

6.232 6.335 6.871

18.7 12.0 8.3

LRE LRE LRE

2.0 7 2.2 13 2.7 26

0 0 2

3.36 0.11 0.15

088 1994 – 01 – 05 089 1994 – 03 – 21

02:25 13:53

50.984 50.916

6.275 6.153

5.6 17.4

LRE LRE

1.8 8 1.9 11

0 1

0.34 0.05

090 1994 – 05 – 20

03:34

50.404

7.366

8.6

NWB

2.3 14

0

4.83

091 1994 – 06 – 25 092 1995 – 01 – 16 003 1995 – 03 – 10

19:18 22:20 22:59

50.052 50.905 50.917

7.419 6.131 6.113

10.0 13.4 10.4

LRE LRE

1.3 7 2.5 18 2.2 14

0 0 0

0.53 0.47 0.02

094 095 096 097 098 099 100 101

1995 – 03 – 30 1996 – 03 – 06 1996 – 08 – 23 1996 – 10 – 29 1997 – 11 – 29 1998 – 11 – 07 1999 – 04 – 03 1999 – 11 – 27

20:29 20:03 19:35 12:00 20:06 16:16 18:09 23:06

50.847 50.753 50.398 50.408 50.271 50.195 50.370 50.396

5.875 6.287 7.371 6.936 8.249 7.862 7.385 7.372

21.7 11.2 7.7 3.1 5.0 6.1 5.7 5.1

HVA LRE NWB MRA MRA MRA NWB NWB

2.4 2.9 3.3 3.0 4.2 3.0 3.1 1.9

15 14 10 15 10 12 8 6

0 2 0 1 0 0 0 0

0.02 0.15 0.55 0.07 0.01 0.03 0.78 1.91

102 103 104 105 106 107 108 109 110

2000 – 01 – 20 2000 – 04 – 29 2000 – 06 – 30 2000 – 07 – 26 2000 – 11 – 20 2002 – 07 – 22 2002 – 07 – 22 2002 – 07 – 22 2002 – 07 – 22

03:03 09:27 22:33 12:19 19:05 05:45 05:50 09:09 12:39

50.622 50.771 50.885 50.288 50.699 50.885 50.886 50.886 50.886

7.088 6.718 6.214 7.862 7.158 6.189 6.179 6.188 6.201

11.4 13.9 19.9 10.7 6.5 14.4 16.3 15.1 15.3

MRA LRE LRE MRA MRA LRE LRE LRE LRE

3.9 2.1 2.2 3.5 1.8 5.0 2.3 2.6 2.6

20 7 5 9 6 41 13 20 21

2 0 0 0 0 0 0 0 0

0.12 1.60 2.93 0.13 0.09 0.02 0.04 0.07 0.01

surrounding area. The beginning time period was constrained by the development during the mid-1970s of a network of local stations in Germany, Belgium and the Netherlands sufficiently dense to allow source studies of microearthquakes. At first all tectonic earthquakes with epicenters between 49.5 –52.0j northern latitude and 5.0 – 9.0j eastern longitude including at least five clear polarity readings of the first P-wave first motion

119.4 272.6 28.5 148.8 311.1 77.9 27.7 122.3 164.3 230.1 288.2 89.1 144.1 332.8 282.3 45.2 85.0 90.4 265.1 346.6 167.4 164.2 152.4 301.1 101.0 283.9 308.2 24.7 22.6 110.4 70.1 297.1 162.1 165.0 277.7 95.0 52.2 87.3 139.7 105.7 104.7

47.7 11.2 53.4 28.7 72.4 52.2 63.1 27.2 77.9 44.4 37.9 64.1 47.5 46.5 24.4 73.8 0.0 13.1 24.3 14.1 52.7 40.1 69.3 20.8 51.8 22.7 86.5 37.0 49.5 40.0 24.3 41.1 44.2 62.9 47.9 46.1 58.4 75.6 79.4 71.8 74.5

291.2 160.0 242.1 274.1 212.6 244.7 224.4 12.9 55.6 60.0 167.9 237.5 49.5 231.5 126.1 179.3 180.0 340.7 47.9 251.1 17.7 346.0 39.1 42.3 214.8 37.9 216.5 138.8 206.9 289.5 212.9 123.6 276.1 52.4 161.0 265.3 271.4 204.1 44.5 220.9 206.0

42.0 62.9 31.7 46.5 2.7 37.0 25.9 32.9 3.9 45.2 32.9 22.5 4.2 10.6 63.7 11.4 90.0 55.5 60.4 20.8 33.4 49.9 8.5 27.1 17.6 44.2 0.1 28.6 40.4 50.0 60.4 48.7 22.7 11.2 22.1 43.5 25.4 6.6 1.0 8.0 3.1

2.1 2.3 0.8 0.8 2.0 2.8 3.4 0.9 0.9 0.9 2.0 2.2 1.4 1.4 1.8 1.0 1.0 1.2 1.2 1.3 2.5 1.1 1.1 2.4 2.9 3.3 3.0 4.2 3.0 3.1 1.0 1.0 3.9 2.1 2.2 3.5 1.8 5.0 2.3 2.6 2.6

were selected from the phase data catalog. For 110 events (Fig. 1, Table 1), FPS could be derived. The events occurred at depths between 2.4 and 21.8 km in the magnitude range from 1.0 V ML V 6.1. Fig. 3 shows the number of P-polarity readings per event in relation to the earthquake magnitudes. As expected, the number of P-polarities increases with increasing magnitude, as polarity readings are observed at increasingly distant

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source for a given distance and source depth. The takeoff angle subsequently determines the position of the piercing-points of the seismic rays through the focal sphere. Fig. 4 shows the take-off angles with respect to the distance of observation and the depth of the source. At the velocity discontinuities (2-, 4- and 10-km depth), the take-off angle changes abruptly even though the changes in velocity are only 3.8%, 2.3% and 2.9%, respectively. Seismic rays corresponding to depth/distance combinations above the black line in Fig. 4 leave the source area through the upper hemisphere and those below that line leave through the lower hemisphere.

3. Fault plane solutions

Fig. 3. Number of first P-wave polarity readings is plotted versus the local magnitude for 110 tectonic earthquakes in the northern Rhine area. Total number of polarity readings is 1708 with a median of 14 readings per event.

stations. However, the number of P-polarities for events with magnitudes around 3 differs from less than 10 to more than 30. This relatively large range of polarity readings results from: (1) variance in the sharpness of the first movement due to the individual source time functions, (2) effect of changing signal-tonoise levels during day and night times, and (3) the increased number of stations in the northern Rhine area over the study period. The average, median and maximum numbers of polarities per event are 15.5, 14 and 53, respectively. In a recent study, a minimum 1D velocity model for the northern Rhine area was determined in a joint inversion for the hypocenters and P-wave velocity depth distribution from 498 earthquakes (Reamer and Hinzen, submitted). The events in this study (Table 1) were taken from the earthquake database used for the model inversion. A seven-layer model without low velocity zones and a constant vP/vS ratio of 1.74 was used (Fig. 4). Take-off angles for all FPS were determined with a ray tracer based on work by Lienert (1994) using the minimum 1D velocity model. This velocity model influences location and depth of the earthquakes. In addition, a one-dimensional model also fixes the take-off angles of seismic rays at the

A grid search algorithm was used to find FPS compatible with the observations (Hinzen, 1986). The strike and dip of the fault plane and the rake, following the convention of Aki and Richards (1980), represent the orientation of the assumed double-couple source mechanism. The parameter space of these three angles of source orientation is sampled in increments of 5j. Considering the limitations due to the use of a one-dimensional velocity model, this sampling results in a reasonable resolution of the parameter space. Fig. 5 shows the digitized parameter space in the form of a vector plot (Pearce, 1977; Hinzen, 1986). As an example, the double-couple orientation of the magnitude 5.0 Alsdorf earthquake (2002/07/22) in the Lower Rhine Embayment is shown. The 5j increment fixes the total number of possible orientations of the double-couple source to 93,312. In the grid-search program, the minimum number of bad polarities is first determined. If all observed polarities are in agreement with at least one certain orientation, this number is 0. In a second step, all orientations that explain the data with a minimum number of bad polarities are determined. Rays leaving the source at orientations with a P-wave radiation less than 1% of the maximum radiation were regarded as nodal Porientations. Polarities connected to nodal P-orientations were not taken into account for this source orientation (Fig. 6). Fig. 7 shows a histogram of the number of polarity readings, which are incompatible with a double-couple model in a parameter space digitized at 5j and located using the 1D velocity

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Fig. 4. The upper right diagram shows the minimum 1D velocity model for the northern Rhine area from Reamer and Hinzen (2003). The main diagram shows the take-off angle of P-waves on the focal sphere as a function of source depth and distance of observation. The gray-scale (bottom right) indicates the angle measured from vertical-down direction (0j) to vertical-up direction (180j). The thick black line separates rays leaving the source through the lower and upper focal half-sphere, respectively.

model. The maximum of relative polarity errors in the data set is 21% for an event with 4 errors and 19 polarity readings. For 57% of the earthquakes, a double-couple orientation can explain all observations without polarity errors and 82% of the events have one or no incompatible first motion polarities. The relative number of compatible solutions RNCS is shown in Fig. 8 with respect to the number of observed first P-wave motion directions. For 87% of the earthquakes, the observations reduce the number of solutions to less than 1% of the model space. The total number of double-couple orientations for the whole data set is 48,188. The distribution of P, T and B axes orientations of these solutions is shown in compass rose diagrams with 5j bins (Fig. 9). Both, P and T axes show clear preferred trends in WNW – ESE and NE – SW directions, respectively. Most P trends are found in the bin N290jE –N295jE and preferred T axes trend toward N25jE – N30jE. A relative maxi-

mum of P and T axes trends is observed in the bins ranging from N150jE – N155jE to N160jE – N165jE, respectively. The trend of the B axes is more diffuse, but the number of B axes trending EW is significantly lower than in the more NS orientation. The plunges of P and T axes display maxima around 45j. More than 70% of the P axes plunges are less than or equal to 45j. The bin with the most plunges for the B axis is between 0j and 5j. Fig. 10 shows the orientation of the P, T and B axes for all 110 events. For 82 events, the parameter space of source orientation angles was narrowed down enough to represent the source orientation by one preferred FPS. For 25 events, two different FPS were regarded as representative, two events are represented by three source orientations, and for one event, four different FPS were chosen from the compatible solutions. Table 1 lists all source orientations by the trend and plunge of the P and T axes,

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Fig. 5. Vector plot of the parameter space of orientations of a double-couple earthquake source. The insets give the corresponding focal sphere projections (‘beach balls’) for a north – south striking fault plane. The arrows show as an example the 16 double-couple orientations which agree with the 41 polarity readings of the 22. July 2002 ML = 5.0 event (#107 in Table 1).

which were selected for the 110 earthquakes, used in the stress tensor inversion. A general scheme suggested by Zoback (1992a) was used to distinguish between normal faulting, strike-slip, and thrust faulting stress regimes. Sixtyone percent of the 48,188 double-couple orientations can be classified with Zoback’s (1992a) scheme. For the rest, the stress regime was regarded as unknown. Among the classified orientations, ca. 31% fall into the strike-slip category, 39% are of thrust or oblique thrust/strike-slip type and 30% show normal fault or oblique normal/strike-slip mechanism. The distribution of the orientation of the principal horizontal stress SHmax (Fig. 11) shows a clear preferred direction at N117.5jE. Approximately 45% show orientations in the intervals N100jE – N140jE and N280jE – N320jE, respectively.

4. Inversion of stress field The inversion method of Gephard and Forsyth (1984) (Gephard, 1990a,b) was used to estimate the stress tensor from the FPS given in Table 1. The

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method regards earthquakes as passive markers of stress and attempts to estimate the best uniform stress field from multiple events within limited space and time windows (Abers and Gephard, 2001). It must be assumed that the stress in the region under investigation is uniform in space and time. A basic constraint is that the direction of slip reflects the orientation of shear stress on each fault plane. Faulting may occur on preexisting zones of weakness. Therefore, the data set should contain focal mechanisms of diverse dislocation types. In this method, the dimensionless deviatoric stress tensor is characterized by four independent parameters. Three parameters define the orientation of the principle stress axes with r1 z r2 z r3 (Gephard and Forsyth, 1984). The fourth parameter, the shape factor or R-value, fixes the magnitude of r2 relative to the maximum and minimum principal stresses r1 and r3, respectively, R¼

r2  r1 : r3  r1

A grid search procedure is used to perform the inversion of the stress tensor (Gephard, 1990b). For different R-values, the parameter space of stress orientations is searched for those principal stress axes with the smallest misfit. The misfit of the stress models is defined as the sum of the absolute values of rotation angles of all faults that are needed to match observed and predicted slip directions. Rotation angles are calculated using the exact method as given by Gephard (1990b), which finds the minimum rotation about any axis of general orientation. For all inversions, the same general strategy was applied as follows. (1) For the first iteration, the R-value was increased in steps of 0.1 from 0.1 to 1.0. (2) r1 was chosen as the primary stress direction for the search and r3 as the secondary direction. (3) With 10j grid spacing, r1 was varied with a variance of 90j around a selected primary stress axis. This procedure resulted in 145 r1 directions and ca. 2900 tensors coarsely sampling the whole parameter space. A typical distribution of the r1 directions is shown in Fig. 12. In step (4), the stress direction with the smallest misfit was selected as the new primary stress axis and a second grid search with 5j grid spacing and 30j variance about the primary stress axis was performed. This calculation resulted in an additional 85 r1 directions and ca. 1000 tensors (Fig. 12).

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Fig. 6. Stereographic projection of the lower focal spheres for 110 earthquakes from the northern Rhine area. Dots and circles show compressions and dilatations of P-waves, respectively. Great circles indicate nodal planes of double-couple source orientations as listed in Table 1.

For step (5), the calculations were repeated, exchanging r1 and r3 as the primary and secondary directions of search, respectively. From these calculations, the results with the smallest misfit were chosen as new primary search directions and in a second iteration, the entire procedure was repeated with R-values ranging over 0.2 units centered on the R-value with the smallest misfit from the first calculations and steps of R-values were lowered to 0.02. The results from the first and

second iteration were combined and the distribution of the misfit was determined for the three principal stress directions. With this inversion scheme, not only is the ‘best’ fitting orientation found, but the relative minima in the misfit also become obvious (Plenefisch and Bonjer, 1997). In order to indicate the relative significance of the representative double-couple orientations, weights were assigned to all FPS. After several tests, the

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Fig. 7. Histogram of the number of polarity readings (errors) that are not compatible with a double-couple mechanism in a parameter space digitized at 5j increment for 110 earthquakes.

numerical values of the local magnitudes of the events were chosen as weights. In cases where two or more FPS were used to characterize one event, corresponding fractions of the magnitude value were assigned to the separate FPS. In this weighting scheme, an event with magnitude six imposes four times the effect of a magnitude 1.5 microearthquake. The choice of weighting was arbitrary, but tests showed that equal weighting did not alter the results significantly; additionally, it was assumed that the stronger events are more representative of the stress tensor than small events.

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Embayment (LRE). Events with epicenters west of these, the majority of which are in the Stavelot – Venn Massif north of the Ardenne anticline (Walter, 1992), were grouped as the Hohe Venn area (HVA). The subregion in the central part of the Rhenish Massif including Hunsru¨ck anticline, Taunus anticline, Mosel syncline, Osteifel main saddle and Ahrtal saddle was named Middle Rhine Area (MRA). Events in the Westerwald including the Bad Marienberg sequence (Ahorner, 1983) were not included in the MRA group. Earthquakes in the tectonic depression of the Neuwied Basin were grouped as Neuwied Basin (NWB) and not included in the MRA group. Under the name Rhenish Massif (RHS), the groups MRA and NWB were combined with the three events in the Westerwald, east of the MRA area. Some of these subregions have the same nomenclature as regions used in the third level regionalization of Germany (Leydecker and Aichele, 1998) but are not congruent. Inversion results for the subregions are summarized in Table 2. As the inversion of the stress tensor is a nonlinear problem, it is important to study the distribution of the misfit over the whole model space in addition to the direction associated with the absolute

5. Results of inversions As a first test, the inversion scheme described above was applied to the whole data set of 110 earthquakes represented by 142 FPS from the northern Rhine area (NRA). Numerous tests were made to separate events into different geologic/tectonic regions. The polygons in Fig. 1 show the final selection of subregions. A first rough separation was made between events with epicenters inside and outside the Rhenish Massif. Events north of the Rhenish Massif and east of the Feldbiss fault were grouped in the subregion Lower Rhine

Fig. 8. Digitization of the parameter space of the double-couple source at 5j leads to a total number of possible solutions of 93312. The relative number of compatible solutions (RNCS) is plotted versus the number of first motion readings. A RNCS of 1% corresponds to 923 compatible orientations.

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Fig. 9. Orientation of the P, T and B axes of 48,188 orientations of double-couple sources compatible with the observed P-wave first motion of 110 earthquakes in the northern Rhine Area. Radius axes in the six rose diagrams show the number of trends and plunges falling into bins of 5j width. The upper and lower rows of rose diagrams show the trend and plunge of the P, T and B axes, respectively.

minimum of the misfit. The distribution of the angle of rotation or misfit in the model space is shown in Fig. 13. For each subregion, the number of FPS and the sum of weighting factors are given. The distribution of misfits may display a single sharp absolute minimum, clearly indicating one direction of the principle stress; however, local minima of the misfit might just as well exist. To resolve this question, the misfit angle U5 which includes the best fitting stress models corresponding to 5% of the number of total tested models was determined for each inversion result. The values of U5 and the corresponding isolines are shown in Fig. 13.

fitting model (0.48) indicates almost equal differences between the maximum and medium stresses and the medium and minimum stresses. The smallest misfit is 9.82j. However, the U5 region in Fig. 13 shows that a relative minimum of rotation angles exists close to the vertical for the direction of r1 with the smallest misfit of 11.3j, and which is smaller than the value for U5 of 11.66j. As opposed to r1, the result for the smallest principal stress r3 shows a clear horizontal direction. Thus, for the complete data set of the northern Rhine area, there remains some ambiguity between a strikeslip and normal faulting regime.

6. Northern rhine area

7. Subregions

The principal stress axes of the best fitting model for the whole data set are oriented horizontal in the case of r1 and r3 (plunges of 0j and 2j, respectively) and close to vertical for r2 (plunge of 88j). This result clearly indicates a strike-slip regime. The maximum horizontal compression is in a NW – SE direction with a trend of N235jE. The shape factor for the best

7.1. Lower rhine embayment The 61 double-couple orientations for the LRE region also show a horizontal to subhorizontal r3 axis with a plunge of 7j for the best fitting model. The trend of the r3 axes is 42j, representing a 7j clockwise rotation with respect to the complete data set. Never-

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Fig. 10. Fault plane solutions of 110 earthquakes of the northern Rhine area. Orientation of the P, T and B axes on the lower focal hemisphere is given by dots, open circles and filled triangles, respectively. Numbers on the upper right of each focal sphere are event numbers as listed in Table 1.

theless, the U5 region includes a broader range of trend values than in the result for the whole data set. The subvertical r1 and subhorizontal r2 axes with 76j and 12j plunges, respectively, favor an extensional normal faulting regime for the LRE subregion. A small secondary minimum for the angle of misfit for r1 with a plunge of 12j and trend of N107jE and a corresponding subvertical

r2 axis (78j plunge) is observed. This result shows that the slip directions from some of the events selected as part of the LRE subregion are explained better by a strike-slip regime. The shape factor of 0.54 is only slightly larger than for the whole data set. As the LRE subset of data contains 28 FPS from the aftershock series of the 1992 Roermond earthquake (Camelbeeck et al., 1994), the inversion

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Fig. 11. Rose diagram of the direction of the greatest horizontal stress SHmax deduced from the azimuths of 29,491 P, T, or B axes following the scheme by Zoback (1992a). Bin size of the angle is 5j.

was repeated with a reduced data set of 33 FPS and with a sum of weights of 61. As shown by the small insets in Fig. 13, the outcome of the calculations with the reduced LRE data set is quasiidentical with the results obtained for all LRE data; however, the secondary minimum is more pronounced in the r1 misfit distribution. This result indicates that the events with slip directions more compatible with a strike-slip regime are still in the reduced LRE data set. 7.2. Middle rhine area The MRA subregion uniquely resulted in an oblique r3 axis, with a plunge of 41j for a best fitting model with a minimum angle of rotation of 5.58j. The largest principle stress also shows an oblique direction with a plunge of 48j. However, a local minimum of the misfit exists for the vertical direction. Combined with an almost horizontal r2 axis (plunge of 8j), this result indicates a stress regime of normal faulting character. The shape factor (0.54) is slightly higher than the R-value inverted for the whole data set.

7.3. Neuwied basin Though it covers only a small fraction of the study area, the events from the tectonic depression of the Neuwied Basin were treated as a separate data set. This decision was based on the unique tectonic regime. Also, with 25 FPS of normal and strike-slip, the number of data is comparable to MRA or HVA. The largest and smallest principal stresses of the best fitting tensor show subhorizontal to horizontal directions (plunges of 20j and 3j, respectively). The distribution of the misfit for r3 shows relatively small errors also for more vertical directions, although these are not included in the U5 range. A noticeable feature is the large shape factor of 0.72, the largest observed for all subregions indicating a significantly larger difference between Ar2 and r1A than Ar3 and r2A. The stress regime for NWB shows a strong tendency towards a strike-slip regime. 7.4. Rhenish massif The RHS subset of 53 source orientations is basically a combination of the MRA and NWB data.

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Fig. 12. Example of orientations of r1 axes (open circles) and r3 axes (closed circles) as used in the inversion calculations. For the top and bottom rows of equal area projections, r1 and r3 are the primary stress directions (black symbols), respectively. In the left column, 145 primary r1 and r3 stress directions, respectively, with 10j grid spacing and a variance of 90j of the central primary stress axes are shown. Gray symbols show the directions of the secondary stress axes (r3 and r1 in the upper and lower row, respectively). For the following search with 5j grid spacing (middle column), the solution with the smallest misfit (best r) is chosen as new central primary stress axes. Here 85 primary stress directions within a cone of 30j width are tested. The right column shows the combination of all tested stress tensors for this example.

However, the shape factor of 0.32 is significantly lower than the R-values from MRA (0.54) and NWB (0.72). The subhorizontal orientation of r1 and r2 with a plunge of 86j for r2 indicates a clear strike-slip regime for the RHS subregion (Fig. 13). 7.5. Hohe Venn area Among the earthquakes from the HVA subset are those with the largest source depths. Two events have depths larger than 20 km, which is not observed in the other regions. The distribution of misfits for both r1 and r3 are a little more diffuse than for the other subregions, but r1 and r3 show the U5 ranges with subhorizontal plunges. The best

fitting model shows trends for the r1 and r3 directions of 316j and 225j, respectively. Both misfit distributions show a second possible trend within the U5 region around N275jE and N10jE for r1 and r3, respectively (Fig. 13). The shape factor (0.58) is slightly larger than for the neighboring LRE region (0.54).

8. Depth ranges The total number of earthquakes and good coverage of the depth range between 2.4 and 21.8 km (Fig. 14) motivated a test for inversion of the stress tensor for discrete depth horizons. This approach

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Table 2 Orientation of principal stresses inverted from fault plane solutions for the northern Rhine area (NRA), subregions and depth ranges Data set

NRA LRE MRA NWB RHS HVA 0 – 6 km 6 – 9 km 9 – 12 km 12 – 15 km 15 – 22 km

Number of FPS

Sweight

142 61 23 25 53 26 17 23 33 25 22

235 107 43 36 90 38 37 31 54 38 41

r1 (j)

r2 (j)

r3 (j)

R-value

Plunge

Trend

Plunge

Trend

Plunge

Trend

0 76 48 20 4 17 54 75 85 11 7

305 162 28 292 307 316 90 285 128 128 318

88 12 8 69 86 73 27 15 5 75 39

215 310 127 121 99 133 315 121 312 264 53

2 7 41 3 2 1 21 4 0 10 50

35 42 224 23 217 225 213 30 222 36 219

differs from the previous section where a uniform stress pattern in the whole depth range of the subregions was assumed. However, there are significant differences among the depth ranges sampled by the different subregions. Events with source depth greater then 15 km were only observed in LRE and HVA, and events deeper than 21 km were only observed in HVA. On the other hand, in the NWB subregion, the stress field is primarily sampled in the depth range between 6 and 9 km by the available events. Numerous tests were made to select depth intervals for inversion calculations. One criterion for the selection of intervals was preferably an equal number of events within the intervals. A first iteration with the entire data set produced relatively large misfits compared to the results from the regionalization described above. This result was especially true for a 6- to-9 km depth range. Results for these depths are strongly influenced by 14 NWB events. After excluding the NWB events from the data set (Fig. 1), misfit values decreased significantly. A further argument for a separate treatment of the NWB events is the much higher shape factor than for the other regions. The following inversion results were inferred from all events except those from the NWB subregion. The distribution of the misfits for depth intervals 3 – 6, 6 – 9, 9– 12, 12– 15 and 15– 22 km is shown in Fig. 15. The numbers of FPS per range are between 17 and 33. For most depth intervals, clear directions of the principal stresses were found. Only in the range 9 – 12 km, the trend of r3 is not well determined, and the

0.48 0.54 0.54 0.72 0.32 0.58 0.38 0.16 0.36 0.40 0.54

Misfit (j)

9.82 8.84 5.58 6.16 9.35 6.13 8.19 8.24 6.52 5.35 6.21

U5 (j) r1

r3

11.66 11.05 9.53 9.33 11.43 9.34 10.66 11.36 10.16 8.76 9.10

11.80 11.14 9.66 8.55 11.50 8.66 10.49 11.65 9.66 8.99 8.93

15 –22-km range shows a relative large U5 region in the model space of r1 orientation. A clear difference in the orientation of the principal stresses at shallow depths (3– 12 km) and the deep range (15 – 22 km) is observed, with a transition at depths between 12 and 15 km. For the three shallow depth ranges, r1 plunges more vertically than horizontally with subvertical values of 75j and 85j for 6 – 9 and 9 – 12 km, respectively. For the shallow part of the crust (up to 12-km depth), r2 and r3 are oriented subhorizontal. This result indicates a normal faulting regime for the upper crust. The shape factor for the 6 –9-km depth interval (0.16) was significantly lower than for the other ranges. Fig. 16 summarizes the inclination of the principal stress axes for the best fitting stress tensors in individual depth ranges. In the 12– 15-km interval, r3 produced stable results in a subhorizontal direction as in the lower part of the crust. However, the orientations for r1 and r2 are switched. At depths shallower than 12 km, r1 is subvertical and for depths between 12 and 15 km, r1 is subhorizontal. The reverse is true for r2. The stress tensor with the absolute minimal misfit in the 15 – 22-km depth range shows r1 remaining subhorizontal, and r2 and r3 have plunges of 39j and 50j. The distribution of misfits for r3 in this depth range (Fig. 15, bottom right) shows a pronounced secondary minimum of the angle of rotation within the U5 region with a N45jE trend and 13j plunge. In the floating bar chart of Fig. 16, the stress tensor orientation associated with this secondary minimum is shown by

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Fig. 13.

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Fig. 13 (continued).

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Fig. 14. Histograms of the distribution of hypocentral depth of the earthquakes used in this study. The upper left diagram gives the relative number of source depths for all 110 events from the northern Rhine area. The following histograms show the data for the Lower Rhine Embayment (LRE), middle Rhine area (MRA), Neuwied Basin (NWB), the Rhenish Massif (RHS) and the Hohe Venn Area (HVA).

the bars with gray background. In this secondary solution r1, changes minimally with respect to the orientation associated with the absolute smallest misfit, but r2 becomes subvertical and r3 subhorizontal. This orientation again agrees with that found for the 12 –15-km depth range. The depth profiling clearly shows two groups of stress orientations. At depths shallower than 12 km, an extensional normal faulting regime is observed and at depths below 12 km, the stresses change to a strike-slip regime.

9. Estimate of absolute stress amplitudes The shape factor R gives only relative magnitudes of the principal stresses. Zoback (1992b) introduced an approach, also used by Plenefisch and Bonjer (1997), to determine absolute stress magnitudes. This calculation can be justified if the following assumptions are valid: (1) the lithostatic pressure represents the magnitude of one principal stress, which is oriented vertically, (2) the shape factor is a second constraint for the absolute stress magnitudes, and (3)

Fig. 13. Distribution of the misfit from the stress inversion calculations for r1 and r3 in the left and right column, respectively. The top row shows the results for the inversion of all events (NRA) followed by events from the Lower Rhine Embayment (LRE), middle Rhine area (MRA), Neuwied Basin (NWB), Rhenish Massif (RHS) and the Hohe Venn Area (HVA). Numbers in the boxes indicate the number of source orientations, and the sum of weights (top row left and right, respectively). Values in the bottom row give the rotation angle U5 or misfit. This angle includes the best fitting stress models corresponding to 5% of the total number of tested models for r1 and r3 in the left and right column, respectively. The isoline corresponding to U5 is shown by the heavy black lines. The bar indicates the shape factor of the best fitting solution. The small insets left and right of the LRE plots show results in case of a reduced LRE data set, excluding events from the Roermond 1992 aftershock sequence.

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Fig. 15. Distribution of the misfit from the stress inversion calculations for r1 and r3 in the left and right column, respectively. Between the plots the depth range of the events used for the inversion calculations is indicated. Numbers in the boxes and isolines are the same as in Fig. 13.

the maximum stress differences in the crust are limited by the frictional strength of the crust. The latter assumption is based on Byerlee’s (1978) law using the frictional coefficients: pffiffiffiffiffiffiffiffiffiffiffiffiffi r1  P ¼ ð 1 þ l2 þ lÞ2 r3  P

where P is the pore pressure, and l the frictional coefficient of the most well-oriented faults (e.g. Sibson, 1974; Zoback and Healy, 1984). As r1 for the northern Rhine area was predominantly subvertical for the shallow part of the crust (at least for depths between 6 an 12 km), and r2 is subvertical for the deeper part of the seismogenic layer (if the secondary

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Fig. 16. Orientation of the principal stresses inverted for five separate ranges of earthquake depth. The left diagram shows the plunge of the principal stresses (bottom axes) of the best fitting stress tensor orientations as they were inverted from double-couple source orientations. In addition the R-values (upper axes) are shown. The symbols with the gray background indicate plunges of a secondary minimum of the misfit angle observed in the 15 – 22-km depth range. The right diagram gives the numbers of events and the total weight used in the inversion calculations for each depth interval.

minimum of the misfit in the depth range from 15 to 22 km is regarded), a rough estimation of absolute stress magnitudes can be made. The pore pressure is assumed to be hydrostatic for the whole depth range and the coefficient of friction is assumed to be 0.85 for depths less than 9 km and 0.6 for larger depths (Byerlee, 1978). The lithostatic pressure was based on the velocity model (Reamer and Hinzen, submitted) and the density was tied to seismic velocities through a relation suggested by Gebrande (1982). Under these conditions, the maximum horizontal stress SH is close in magnitude to the vertical stress Sv in the shallow crust (Fig. 17). At a depth somewhere below 12 km SH increases in magnitude, exceeds the vertical stress and stays larger for greater depths. As a secondary minimum of the misfit can still be observed, which is close to the vertical direction in

the 12 – 15 km range, the transition might occur deeper than 12 km but above 15 km (Fig. 15).

10. Discussion and conclusions The Rhine Rift system is the most active presentday tectonic regime in Western Europe north of the Alps (Mu¨ller et al., 1992). This system is characterized by moderate intra-plate seismicity (e.g. Ahorner, 1983, Bonjer, 1997, Reamer and Hinzen, submitted) and recent vertical movements (Meyer et al., 1983; Meyer and Stets, 2002). The rift zone consists of two major segments: the NNE striking Upper Rhine Graben and the NW striking Lower Rhine Embayment (Fig. 1). The opening of the Upper Rhine Graben in late Eocene to early Oligocene was controlled by a

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Fig. 17. Magnitudes of vertical, maximum horizontal and minimum horizontal stresses, Sv, SH and Sh, respectively, as function of depth.

paleostress field with a NNE –SSW orientation of the maximum horizontal stress (Ahorner, 1975). After a period of relative quiescence, a second short phase of extension began in early Miocene time (Ahorner, 1975). The present stress field after Mu¨ller et al. (1992) based on FPS and borehole measurements is characterized by a NW to NNW direction for the maximum horizontal stress. Fig. 18 summarizes the directions of principal stresses from this study and previous results from several other authors. Plenefisch and Bonjer (1997) report a stable horizontal r3 striking (N55jE to N69jE) in the seismogenic crust for the Northern Alpine foreland, the Upper Rhine Graben and the Northern Rhine Graben. Inverting principal stresses with the method of Gephard and Forsyth (1984), they found an ambiguity between strike-slip and extensional regimes for all three subregions when looking at the entire depth range of available FPS. By dividing the data from the upper Rhine Graben into events

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with depths below and above 15 km, they found evidence for a change from a strike-slip regime in the upper crust to an extensional regime in the lower crust. Azimuths of the principal stress axes were similar in both depth ranges. However, the dip of r1 changed with depth from horizontal to vertical and vice versa for r2. This result was interpreted to be caused by: (1) an increase in the vertical component of the stress tensor with depth due to the increase of the overburden, and (2) the geodynamic effects of the continent – continent collision in the Alps and adjacent areas. Plenefisch and Bonjer (1997) argued that the upper crust of the European plate and the African Plate is under collision, whereas the lower European crust is subducted beneath the Alps and the Adriatic plate. A stress tensor inversion for the Northern Rhine Graben is obtained by Plenefisch and Bonjer (1997) based on the published FPS of 19 earthquakes, which occurred between 1977 and 1992 with source depths ranging from 5 to 15 km. They find obliquely oriented principal stress axes r1 and r2 trending NW – SE and a horizontally oriented r3 axes with a SW –NE trend (Fig. 18). The shape factor of the best-fitting tensor from their data set is 0.4. Due to the distribution of the misfit, a definite distinction between a strike-slip and extensional regime is not possible. Nevertheless, the r3 trend found by Plenefisch and Bonjer (1997) is in good agreement with their results from the Northern Alpine foreland and the southern Rhine Graben. They observe a 30j counterclockwise rotation of the plane made up of r3 and the vertical direction from south to north. Delouis et al. (1993) derive an orientation of the stress tensor based on 14 FPS for the Rhenish Massif and the Lower Rhine Embayment. They find a uniaxial extensional stress regime with r1 = r2 oriented in a quasi-vertical plane with N105jE azimuth and a quasi-horizontal r3 with N15jE trend. The depth range of the data set is 2 – 9 km. The SH directions derived directly from the orientation of the FPS in this study and the trend of r1 and r2 are in good agreement with the general trend of the regional stress field in Western Europe (e.g. Zoback, 1992b; Mu¨ller et al., 1992; Gru¨nthal and Stromeyer, 1992). The broader database of FPS used in this study results in a counterclockwise rotation of the SH direction of 13.5j compared to the earlier

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Fig. 18. Directions of principal stresses for the best fitting models from this study, Plenefisch and Bonjer (1997) and Delouis et al. (1993) for the northern Rhine area. Delouis et al. (1993) give for r1 and r2 a general orientation in a N105jE striking quasi-vertical plane, indicated by the gray pie pieces. Results from this study are shown for the complete data set (NRA) for five subregions and six depth ranges (see legend). Orientations marked with a * show directions of secondary minima from the distribution of the angle of misfit. The rose diagram of SH directions in the plot of r1 orientations is from Fig. 10 with the main direction indicated by the dark gray filled arrow. The open arrow is the SH direction from Mu¨ller et al. (1992), which partly based on the directions indicated by the thin arrows from FPS (Ahorner et al., 1983) and borehole measurements (Baumann and Illies, 1983).

estimation by Mu¨ller et al. (1992), but is still within the range of one standard deviation from the previous result. This result also agrees with finite element model calculations which predict a S H of ca. N120jE for the study area (Gru¨nthal and Stromeyer, 1993). As found in the previous studies (e.g. Delouis et al., 1993; Plenefisch and Bonjer, 1997), smallest principal stress r3 is the most stable axis in the Rhine rift system. The inversion of the complete data set for the northern Rhine area as well as the inversion of separate subregions and separate depth horizons shows subhorizontal plunge of r3 with trends NE –

SW to NNW – SSE. The direction of r3 from the NRA data set is rotated 20j clockwise and 14j counterclockwise with respect to the results from the works of Delouis et al. (1993) and Plenefisch and Bonjer (1997), respectively. Additionally, r1 and r2 are found in a vertical plane (exceptions are the r1 trend for MRA and r2 trend for 15 – 22 km) comparable to results from Delouis et al. (1993). However, the trend from the present study is rotated 15– 20j clockwise. Considering that Delouis et al. (1993) only use events < 9-km depths, the cylindrical shape of their stress tensor with r1 = r2 agrees well with our results for the upper crust, where the magnitudes of maximum and

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medium principal stress are similar (Fig. 17). This result cannot be extended over the entire northern Rhine area due to the limited depth range of available earthquake data. The directions for r1 and r2 from Plenefisch and Bonjer (1997) are within the range of values from this study. Their values are closest to the results for the MRA and the 6 –9-km data set. This

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result makes sense as 10 of their 19 events for the northern Rhine Graben data set have depths less than 12 km, and the majority of the events are located in the MRA subregion or in the northern part of the Upper Rhine Graben. The change of stress regime with depth for the northern Rhine area is opposite to the results from the

Fig. 19. Orientation of major horizontal stress directions from the inversion of earthquake fault plane solutions in context with the main tectonic features of the northern part of the Central European rift system. Stress orientations for the northern Alpine foreland (NAF) and the Upper Rhine Graben (URG) are from Plenefisch and Bonjer (1997), for the central western region (CWR) from Delouis et al. (1993), and for the Rhenish Massif (RHS), the Lower Rhine Embayment (LRE) and the Hohe Venn area (HVA) from this study. Abbreviations: CNSG = Central North Sea Graben, RVG = Roer Valley Graben, HED = Hessian Depression, SWJ = Swabian Jura, BRG = Bresse Graben. Tectonic features are modified after Mayer et al. (1997) and Van den Berg (1994).

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upper Rhine Graben (Plenefisch and Bonjer, 1997). If the earthquake distribution in both regions represents the stress tensor well enough to detect changes with depth, which seems likely given the results shown here, the stress regime between the southern part of the Upper Rhine Graben is significantly different from the northern Rhine area. The composition of rock changes where the Upper Rhine Graben approaches the Rhenish Massif. Consequently, the response of the rock to stress is different. The rocks of the southern basement react tectonically competent. These rocks are replaced in the Rhenish Massif by incompetently reacting folded Devonian and Lower Carboniferous rocks with 5- to 10-km thickness (Baumann and Illies, 1983). These rocks are able to consume stress by ductile behavior and show rifting only at higher deformation rates as in the Neuwied Basin (Schreiber and Rotsch, 1998). The change from the tendency to uplift in the Rhenish Massif (Meyer and Stets, 2002) to subsidence in the Lower Rhine Embayment is also accompanied by modifications of the mechanical properties of the crust (Baumann and Illies, 1983). Here, the seismogenic part of the crust is influenced by the Brabant Massif and responds tectonically more competently due to strain hardening. The Rhenish Massif acts as a buffer zone for the stress in the shallow crust between the two sections of the Rhine rift system. The extensional stress regime in the shallow crust can be interpreted as a local effect overlaying the regional trend towards a strike-slip regime and is more pronounced in the deeper parts of the crust. The directions of principal stresses in both parts of the Rhine rift system are compatible; differences exist only in the magnitudes of the principal stresses. These findings also explain the ambiguity between extensional and strike-slip regime found for the northern Rhine area in previous studies (e.g. Mu¨ller et al., 1992; Delouis et al., 1993; Plenefisch and Bonjer, 1997). Combining all events from NRA should result in a mixture of strike-slip and extensional regime: prevalence for one or the other is controlled by event depth and geographic distribution. The HVA shows a strike-slip regime while the neighboring LRE subregion is extensional. The observed change in stress field has a strong depthdependent component, making it difficult to define clear borders between subregions. With the complex

geologic and tectonic situation at the borders between the Brabant Massif, Hohe Venn, and the western part of the Rur Graben, a transition zone between the two regimes is proposed. The two minima in the distribution of the angle of misfit for the MRA subregion indicate a mixing of the two stress regimes. In addition to a change with depth, a difference in the local stress regime in the parts west and east of the Rhine River within the Rhenish Massif as mentioned by Schreiber and Rotsch (1998) might be observable. In their model of a Cenozoic clockwise block rotation of the eastern part of the Rhenish Massif, they propose some strike-slip faulting west of the Rhine River. This result might be an explanation for the second minimum for MRA, and the directions of the faults in their model (ca. N110jE –N140jE) are not in contrast to the results shown here. The significant difference in uplift during the last 0.8 Ma in the two blocks east and west of the Rhine River as described by Meyer and Stets (2002) is an additional argument for local stress changes. At the present time, the number of wellrecorded events in the Rhenish Massif is not sufficient to resolve this ambiguity. Fig. 19 relates stress inversion results based on fault plane solutions to the geological and tectonic structure of Central Europe. Stress conditions in Central Europe are mainly governed by the northwards directed compressive push of the African plate through the Adriatic plate. Results from this study confirm a counterclockwise rotation of the horizontal stresses proposed by Delouis et al. (1993) and Bonjer (1997) with increasing distance from the Alps towards northern and western directions. The stress field in the Rhenish Massif and the Hohe Venn area indicates a strike-slip regime and the subvertical r1 axis in the Lower Rhine Embayment indicates a normal faulting regime.

Acknowledgements I thank all organizations and individuals who provided phase data to the BENS database since 1975. I highly appreciate the many discussions with S.K. Reamer and her improving suggestions for the manuscript. My thanks also goes to T. Plenefisch for the fruitful discussions. The paper benefited a lot from critical comments and very helpful suggestions

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from K.-P. Bonjer, B. Delouis, and H. Thybo. I thank J.W. Gephard for providing the FMSI code. K. Weber assisted with the preparation of several figures.

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