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Frequency-magnitude relationship and Poisson's ratio in the Pyrenees, in relation to earthquake distribution
1Letter Section1
Tectonophysics, 215 (1992) 363-369
Elsevier Science Publishers B.V., Amsterdam
Frequency-magnitude relationship and Poisson’s ratio in the Pyrenees, in relation to earthquake distribution Jacques-Duclos
Njike-Kassala a, Annie Souriau a, Jeannine Gagnepain-Beyneix Louis Martel a and Marcel Vadell a
b,
a OMP/ GRGS, 14 Avenue Edouard Belin, 31400 Toulouse, France ’ IPG, 4 Place Jussieu, 75252 Paris Ceder 0.5, France
(Received July 1,1992; revised version accepted July 29,1992)
ABSTRACT Njike-Kassala, J.-D., Souriau, A., Gagnepain-Beset, J., Martel, L. and Vadeil, M., 1992. Fr~uen~-magnitude ship and Poisson’s ratio in the Pyrenees, in relation to earthquake distribution. ~ecro~p~y~~c~, 21.5: 363-369.
relation-
An attempt is made to relate the seismic&y pattern along the Pyrenean range to the regional variations of the Poisson’s ratio and to the b-value of the frequency-magnitude relationship. No obvious relation is found with the Poisson’s ratio. For the b-parameter, a tendency is observed for lower values in the western Pyrenees, where seismic& is concentrated along well defined faults, whereas higher values are observed in the regions of diffuse seismicity to the east. It is suggested that the b-variations reflect the fractal nature of faulting, as proposed by others.
Introduction The Pyrenean range, which results from the collision between the Eurasian and Iberian plates, exhibits rather simple structural features (e.g., Choukroune, 1992), with a nearly cylindrical symmetry. It is bordered to the north by a major fault, the North Pyrenean Fault (NPF), which strikes E-W along the whole range and is considered to be the boundary between the two plates. This fault coincides with a Moho jump of lo-15 km, the crust being thicker on the Iberian side (Gallart et al., 1981). Despite this apparently simple structural scheme, the seismic&y distribution is rather complex. Systematic epicenter locations have been made since 1962 by the Laboratoire de Detection Geophysique, and refined locations have been obtained later from specific networks (Olivera et al., 1986; Gagnepain-Beyueix et al., 1992). They show that, in the western
Correspondexe to: A. Souriau, OMP/GRGS, Edouard Belin, 31400 Toulouse, France. HO-1951/92/$05.~
14 Avenue
part, the seismicity is generally concentrated along the NPF, whereas in the eastern part it is more diffuse and not specifically related to identified faults (Figs. 1 and 2). This paper is an attempt to relate the change in the style of seismicity along the range to various parameters describing the properties and behaviour of the crust. We analyse in particular the regional variations of the Poisson’s ratio, which is related to the mechanical properties of the crust, and those of the b-parameter of the frequencymagnitude relationship, which gives information on the state of stress and the nature of faulting. Data used Three sets of data have been used: (1) A survey of the global seismicity in France has been made by the Laboratoire de Detection Geophysique of the Commissariat a 1’Energie Atomique (LDG/CEA) since 1962. Only one station of the LDG network has been located in the Pyrenees (since 1976). The accuracy in epicenter locations for the Pyrenean events is therefore
0 1992 - Elsevier Science Publishers B.V. All rights reserved
J.-D.
364
rather poor (up to 10 km error) and small earthquakes (magnitudes less than 2) can generally not be located. IIowever, this very homogeneous series is the longest (29 years) and consequently the most representative record of the permanent seismic activity. (2) An array was set up by the Institut de Physique du Globe de Paris in the western Pyrenees (in the seismic region of Arette) in 1978. It has allowed to obtain a very accurate picture of the local seismicity, including most of the events of magnitude > 0.5 occurring within the array (Gagnepain-Beyneix, 1987). (3) Since the end of 1988, a network of 10 stations has been set up in the French eastern and central Pyrenees by the Observatoire MidiPyrCnCes (OMP), in complement to a network set up on the Iberian side by the Servei Geologic de Catalunya (SGC), providing a refined image of the seismicity in that part of the range (Fig. 1). For these three series of data, the magnitudes have been estimated from signal duration, but with different scaling. The LDG series is scaled by comparison to well d~umented European earthquakes, whereas the Arette series is scaled by reference to local events. For the OMP data, magnitudes are poorly reliable, because the signal may be troncated for its transmission through the satellite Meteosat.
NJIKE-KASSALA
ET AL.
Seismic profiles north of the NPF have given even higher values (V 4 0.29 to 0.32; Daignieres et al., 1981), which have been ascribed either to water infiltration, or to the presence of magmatic intrusions in the upper crust (Daignieres, 1982). The same method was used with the OMP/SGC data to determine the Poisson’s ratio in the central and eastern Pyrenees. A regionalization was performed (Fig. l), considering only the paths nearly fully contained in a given region. In a first stage, we verified that there was no significant difference in Poisson’s ratios on both sides of the NPF. The values obtained were Y = 0.248 + 0.05 (2% error bar) on the Iberian side, and v = 0.256 + 0.010 on the French side. Three regions, including the main seismic units, were then considered (Fig. 1): one including the Bigorre Fault (region B), one including the Maladeta and Andone Massifs (region C), and the last one including the Tet and Tech fault system (region D). The results are summarized in Figure 1. They do not reveal strong variations in the Poisson’s ratio, which is close to the standard value 0.25, A slightly higher value is obtained for the Tet and Tech fault system, suggesting the presence of a more ductile crust. This may, perhaps, partly explain the surprisingly low seismicity in a region of strong tectonic activity, e.g., the fast surrection of the Canigou Massif (Fourniguet and Lenotre, 1987).
Poisson’s ratio The frequency-magnitude
The Poisson’s ratio v is directly related to the P and S seismic velocity ratio K (K = V,/V,). It may provide information on the mechanical properties of a structure, differing from those of a perfectly elastic medium. Its variations depend on the nature of the rock, on temperature and pressure, and on the presence of partial melting or fluid inclusions (e.g., Nur, 1971). Standard vaiues for v are 0.25 (crust) and 0.28 (upper mantle), but values ranging from 0.23 to 0.30 are often reported in the literature. In the western Pyrenees, a determination of the Poisson’s ratio has been made previously, using the Wadati method, with the data of the Arette array (Gagnepain-Beyneix, 1987). A rather high value was found (V = 0.27; Fig. 1, region A).
relationship
A Iinear relationship, log N = a - b M, known as the Gutenberg and Richter law, has been empirically established between the frequency occurrence of earthquakes N with magnitudes higher than M, and the value of M. Experimental results have shown that b may vary with seismic region. Moreover, b generally decreases with increasing focal depth. Laboratory experiments have revealed that the frequency-magnitude relationship is also valid for microfractures produced during rock deformation (Mogi, 1962), and that the b-value depends primarily on stress (Scholz, 1968). The validity of this relationship, changing scale from microcracks to earthquakes, is not yet fully understood; however, an interest-
FREQUENCY-MAGNITUDE
365
RELATIONSHIP AND POISSON’S RATIO IN THE PYRENEES
1
S. France: _--0
Station
IS
’ OM P V Arei te l LD( A SG TEA
Events Md=2 Md=3 Md=40
Fig. 1. Determination reported (OMP/SGC
v = 0.260
001 ^^ .
v = 0.256
f
0.010 0
----0 0
N. Iberia:
v = 0.246
f 0.005
,
of the Poisson’s ratio in different seismic units of the Pyrenees. The seismicity for the years 1989-1991 is data and Arette array data), as well as the stations used in this study. Also indicated are the major faults: North Pyrenean Fault (NPF), Bigorre Fault (BF), and the Tet and Tech Faults.
ing consequence of this result is the possibility to infer regional or temporal variations of the state of stress from the variations of the b-parameter, decreasing values being related to increasing stresses. A possible physical explanation of the b-dependence on stress invokes the predominance of occurrence of small earthquakes on preexisting cracks, as a result of low stress, whereas, as a result of increasing stress, new cracks may be generated, giving rise to earthquakes which are statistically larger. The b-dependence to stress field may also reflect the competition for energy release, between either a few large faults (giving low b-values) or a great number of small faults (giving larger b-values). The geometrical properties of the fault system, in relation to the fractal dimensions of the fault, may also be at the origin of the b-variations (e.g., Aki, 1981). The regional variations of b have been studied in the Pyrenees using the very homogeneous series of the LDG (Fig. 2). Most of the earthquakes are shallow (depth < 10 km); only a small number of deeper earthquakes (10 to 30 km depth) have been recorded in the western Pyrenees. Figure 2 shows the regions which have been considered for the determination of b. They only include natural seismicity, except for region 1 in which most events are induced by gas pumping.
Some of these regions have an important overlap, in particular regions 2 and 4. Region 2’ is a subset of region 2. Typical examples of frequency-magnitude curves are shown on Figure 3. The deficit of small earthquakes with respect to the linear relationship is due to the poor detection of the earthquakes with magnitudes less than 2.5. The irregular shape of the curves at the highest magnitudes reflects the fact that the time interval considered (29 years) is less than the time recurrence of the strongest earthquakes. For the determination of the b-coefficient, only the nearly rectilinear part of each curve between two magnitudes Mmin and M,, has been considered, and b has been obtained from a least square fit. The error bars on b have been directly estimated by varying Mmin and M,,,, by k 0.1, they are generally close to 0.1. The comparison of the b-values obtained for regions 2, 2’ and 4 provides a good test of the stability of the results. The results are summarized in Figure 2b. Except for region 1, b is close to 1.1 everywhere, a value similar to that obtained for the world seismicity (Aki, 1981). A slightly lower value (b = 0.96) is obtained in region 3 (Navarra), southwest of the range. By contrast, there is a tendency for higher b-values in regions 8 and 9 (b = 1.21 and 1.23, respectively), on both sides of the eastern end of the Pyrenees.
J.-D. NJIKE-KASSALA ET AL.
366
-1
-2
b-values I
/
/
/
I’
/
1
0
n
1
2
j
3
a.
f
8:
b. Fig. 2. Determination
of regional variations of b with the LDG data. (a) Seismicity for the years (1962-1991) and regions considered. (b) Results.
Comments on the regional variations of b
Ma@tude
Fig. 3. Two examples of frequency-magnitude relationships obtained in two regions of the Pyrenees (see Figure 2 for locations). Data from LDG.
Despite the smah range of the b-variations along the Pyrenean range, some particularities may possibly be related to tectonic features or to physical properties of the crust. (1) The higher value obtained in region 1 (b = 1.44) suggests that the stress field, induced by the gag pumping and responsible for the seismicity in this region, is lower than the stress field responsi-
FREQUENCY-MAGNITUDE
RELATIONSHIP AND POISSON’S RATIO IN THE PYRENEES
ble for the seismicity of tectonic origin along the range. Part of the stress field may be released by aseismic slip. A detailed study of the b-variations in this region, in relation to stress history, has been carried out by Volant et al. (1992). (2) It is interesting to check whether the bvariations obtained along the range may be due to a variation of the mean focal depth. Only regions 2 and 4 exhibit focal depths higher than 10 km. Because the focal depths are poorly reliable in the LDG file, we have used for comparison the data of the Arette array, and limited the investigated area to that covered by this array (Fig. 4). The results (Table 1) show that, as expected, b decreases with increasing depth. Due to different magnitude scaling, LDG and Arette data do not lead exactly to the same &-values, but the b-variations with depth are the same. It is clear from Table 1 that the significant proportion of earthquakes with focal depths of > 5 km contributes to decrease the mean b-value; on the other hand, the error bars obtained with the less homogeneous, whole data sets are larger. (3) Coming back to the LDG data (Fig. 21, the lowest value is obtained in region 3, where the seismic&y is concentrated in a small area near Pamplona (Olivera and Gallart, 1987). A low
367
value is also obtained in the Arette region (b = 1.01, see Table l), where the seismicity is concentrated in a narrow strip along the NPF. Even lower values have been reported during earthquakes sequences in this region (Gallart et al., 1985). In region 4, the seismici~ is very complex (see the more accurate picture given by Fig. 0, because of the intersection of the Bigorre Fault with the NPF. In region 5, whith also a low b-value, an accurate mapping of epicenter locations has been possible only for the last 3 years, using the OMP/SGC data (Fig. 1). They indicate a tendency for a concentration of events along a strip oriented N115E along the Maladeta Massif; however, there is also a diffuse seismicity present between this strip and the NPF. The highest b-values are obtained in regions 8 and 9, where the seismic&y is very diffuse. For comparison we have computed the b-value in Britanny, a region of low tectonic activity where the seismicity is also diffuse. The data also come from the LDG file, and are then homogeneous with the Pyrenean data for the magnitudes. The value obtained, b = 1.25 f 0.05, is similar to those in regions 8 and 9. These higher values in regions of diffuse seismic&y suggest the presence of a lower stress field than in the regions where seis-
Fig. 4. Seismic& obtained in the western Fyrenees with the Arette array for the period 1978-1991. The rectangle is the region investigated for the dete~ination of the &-variations with depth.
J.-D. NJIKE-KASSALA ET AL.
368 TABLE 1 Determination Depth range
of the b-coefficient as a function of focal depth in the Arette region Arette array data
LDG data Number of data
b
Error on b
O-5 km 5-10 km >I0 km
134 56 66
1.09 0.92 0.91
0.06 0.08 0.09
All the data
200
1.01
0.12
micity is more concentrated, of faulting.
or a different nature
Discussion and conclusion We have seen that the general features of the seismicity along the Pyrenees are poorly related to the geographic variations of the Poisson’s ratio. Except for the region of induced seismicity, the results obtained for the b-parameter show a weak but general tendency for lower values (b = 1.0) in regions of concentrated seismicity, and higher values (b = 1.25) in regions of diffuse seismic&y. This is in good agreement with the model proposed by Aki (1981) in terms of fractal dimension of the fault: b = 1 corresponds to a fractal dimension of the fault of 2, i.e. a well defined fault plane. This is the case for the Arette earthquakes, for which the fault planes have been well identified thanks to the local array (GagnepainBeyneix, 1987). By contrast, b = 1.5 corresponds to a fractal dimension of 3, which represents the filling up of the volume with fault planes. High b-values in the forelands of the eastern Pyrenees correspond to earthquakes occurring in a multiplicity of sites which are not related to identified faults, without coherent geographic distribution nor coherency in the focal solutions (Nicolas et al., 1990). Therefore, an explanation invoking the geometrical properties of faulting seems appropriate, but a variation of the stress field along the range, and the possibility of stress release by aseismic slip, may also contribute to the global distribution of the seismicity. Particularly in the eastern Pyrenees, a slightly higher value of the Poisson’s ratio may favor aseismic deformation.
b
Error on b
497 423 225
1.01 0.82 0.82
0.04 0.04 0.07
1091
0.89
0.13
Number of data
Acknowledgements We thank B. Massinon and the staff of the Laboratoire de Detection Geophysique for making their data file available to us. We also thank C. Olivera and the Servei Geologic de Catalunya for their cooperation in hypocenter determinations. References Aki, K., 1981. A probabilistic synthesis of precursory phenomena. In: D.W. Simpson and P.G. Richards (Editors), ~rthquake Prediction. Am. Geophys. Union, Maurice Ewing Ser., 4, pp. 566-574. Choukroune, P., 1992. Tectonic evolution of the Pyrenees. Ann. Rev. Earth Planet. Sci., 20: 143-158. Daignieres, M., 1982. Les Pyrenees: une chaine intra~ntinentale sur un grand decrochement? Elements de r6ponses geophysiques. Thesis, Univ. Montpellier. Daignieres, M., Gallart, J. and Banda, E., 1981. Lateral variation of the crust in the Noah-~renean Zone. Ann. Geophys., 37: 435-456. Fourniguet, J. and Lenotre, N., 1987. Comparaison de nivellements dans les Pyre&es. BRGM, Orleans, Rep. No. 103. Gagnepain-Beyne~, J., 1987. Etude expirimentale des tremblements de Terre. Exemple de la region d’Arette (France). Thesis, Univ. Paris 7, 140 pp. Gagnepain-Beyneix, J., Massinon, B., Olivera, C. and Martinez-Solares, J.M., 1992. Seismicid de la chaine des Pyrenees et de ses avants-pays. In: Synthise Geologique des Pyre&es. BRGM, Orleans, in press. Gallart, J., Banda, E. and Daignibres, M., 1981. Crustal structure of the Paleozoic Axial Zone of the Pyrenees and transition to the North Pyrenean Zone. Ann. GCophys.. 37: 457-480. Gallart, J., Daignibres, M., Gagnepain-Beyneix, J. and Hirn, A., 1985. Relationship between deep structure and seismicity in western Pyrenees. Arm. Geophys., 3: 239- 248. Mogi, K., 1962. Study of the elastic shocks caused by the fracture of heterogeneous materials and its relation to
FREQUENCY-MAGNITUDE
RELATIONSHIP AND POISSON’S RATIO IN THE PYRENEES
earthquakes phenomena. Bull. Earthquake Res. Inst., 40: 125-173. Nicolas, M., Santoire, J.P. and Delpech, P.Y., 1990. Intraplate seismicity: new seismotectonic data in Western Europe. Tectonophysics, 179: 27-53. Nur, A., 1971. Viscous phase in rocks and the low velocity zone. J. Geophys. Res., 76: 1270-1277. Olivera, C. and Gallart, J., 1987. Sismicidad de la region de Navarra (Pireneos Occidentales). Rev. Geofis., 43: 221234. Olivera, C., Gallart, J., Goula, X. and Banda, E., 1986.
369
Recent activity and seismotectonics of the Eastern Pyrenees. Tectonophysics, 129: 367-380. Scholz, C., 1968. The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes. Bull. Seismol. Sot. Am., 58: 399-415. Volant, Ph., Grasso, J.R., Chatelain, J.L. and Frogneux, M., 1992. b-value, aseismic deformation and brittle failure within an isolated geologic object: evidence for a dome structure loaded by fluid extraction. Geophys. Res. Lett., 19: 1149-1152.
Tectonophysics, 215 (1992) 363-369
Elsevier Science Publishers B.V., Amsterdam
Frequency-magnitude relationship and Poisson’s ratio in the Pyrenees, in relation to earthquake distribution Jacques-Duclos
Njike-Kassala a, Annie Souriau a, Jeannine Gagnepain-Beyneix Louis Martel a and Marcel Vadell a
b,
a OMP/ GRGS, 14 Avenue Edouard Belin, 31400 Toulouse, France ’ IPG, 4 Place Jussieu, 75252 Paris Ceder 0.5, France
(Received July 1,1992; revised version accepted July 29,1992)
ABSTRACT Njike-Kassala, J.-D., Souriau, A., Gagnepain-Beset, J., Martel, L. and Vadeil, M., 1992. Fr~uen~-magnitude ship and Poisson’s ratio in the Pyrenees, in relation to earthquake distribution. ~ecro~p~y~~c~, 21.5: 363-369.
relation-
An attempt is made to relate the seismic&y pattern along the Pyrenean range to the regional variations of the Poisson’s ratio and to the b-value of the frequency-magnitude relationship. No obvious relation is found with the Poisson’s ratio. For the b-parameter, a tendency is observed for lower values in the western Pyrenees, where seismic& is concentrated along well defined faults, whereas higher values are observed in the regions of diffuse seismicity to the east. It is suggested that the b-variations reflect the fractal nature of faulting, as proposed by others.
Introduction The Pyrenean range, which results from the collision between the Eurasian and Iberian plates, exhibits rather simple structural features (e.g., Choukroune, 1992), with a nearly cylindrical symmetry. It is bordered to the north by a major fault, the North Pyrenean Fault (NPF), which strikes E-W along the whole range and is considered to be the boundary between the two plates. This fault coincides with a Moho jump of lo-15 km, the crust being thicker on the Iberian side (Gallart et al., 1981). Despite this apparently simple structural scheme, the seismic&y distribution is rather complex. Systematic epicenter locations have been made since 1962 by the Laboratoire de Detection Geophysique, and refined locations have been obtained later from specific networks (Olivera et al., 1986; Gagnepain-Beyueix et al., 1992). They show that, in the western
Correspondexe to: A. Souriau, OMP/GRGS, Edouard Belin, 31400 Toulouse, France. HO-1951/92/$05.~
14 Avenue
part, the seismicity is generally concentrated along the NPF, whereas in the eastern part it is more diffuse and not specifically related to identified faults (Figs. 1 and 2). This paper is an attempt to relate the change in the style of seismicity along the range to various parameters describing the properties and behaviour of the crust. We analyse in particular the regional variations of the Poisson’s ratio, which is related to the mechanical properties of the crust, and those of the b-parameter of the frequencymagnitude relationship, which gives information on the state of stress and the nature of faulting. Data used Three sets of data have been used: (1) A survey of the global seismicity in France has been made by the Laboratoire de Detection Geophysique of the Commissariat a 1’Energie Atomique (LDG/CEA) since 1962. Only one station of the LDG network has been located in the Pyrenees (since 1976). The accuracy in epicenter locations for the Pyrenean events is therefore
0 1992 - Elsevier Science Publishers B.V. All rights reserved
J.-D.
364
rather poor (up to 10 km error) and small earthquakes (magnitudes less than 2) can generally not be located. IIowever, this very homogeneous series is the longest (29 years) and consequently the most representative record of the permanent seismic activity. (2) An array was set up by the Institut de Physique du Globe de Paris in the western Pyrenees (in the seismic region of Arette) in 1978. It has allowed to obtain a very accurate picture of the local seismicity, including most of the events of magnitude > 0.5 occurring within the array (Gagnepain-Beyneix, 1987). (3) Since the end of 1988, a network of 10 stations has been set up in the French eastern and central Pyrenees by the Observatoire MidiPyrCnCes (OMP), in complement to a network set up on the Iberian side by the Servei Geologic de Catalunya (SGC), providing a refined image of the seismicity in that part of the range (Fig. 1). For these three series of data, the magnitudes have been estimated from signal duration, but with different scaling. The LDG series is scaled by comparison to well d~umented European earthquakes, whereas the Arette series is scaled by reference to local events. For the OMP data, magnitudes are poorly reliable, because the signal may be troncated for its transmission through the satellite Meteosat.
NJIKE-KASSALA
ET AL.
Seismic profiles north of the NPF have given even higher values (V 4 0.29 to 0.32; Daignieres et al., 1981), which have been ascribed either to water infiltration, or to the presence of magmatic intrusions in the upper crust (Daignieres, 1982). The same method was used with the OMP/SGC data to determine the Poisson’s ratio in the central and eastern Pyrenees. A regionalization was performed (Fig. l), considering only the paths nearly fully contained in a given region. In a first stage, we verified that there was no significant difference in Poisson’s ratios on both sides of the NPF. The values obtained were Y = 0.248 + 0.05 (2% error bar) on the Iberian side, and v = 0.256 + 0.010 on the French side. Three regions, including the main seismic units, were then considered (Fig. 1): one including the Bigorre Fault (region B), one including the Maladeta and Andone Massifs (region C), and the last one including the Tet and Tech fault system (region D). The results are summarized in Figure 1. They do not reveal strong variations in the Poisson’s ratio, which is close to the standard value 0.25, A slightly higher value is obtained for the Tet and Tech fault system, suggesting the presence of a more ductile crust. This may, perhaps, partly explain the surprisingly low seismicity in a region of strong tectonic activity, e.g., the fast surrection of the Canigou Massif (Fourniguet and Lenotre, 1987).
Poisson’s ratio The frequency-magnitude
The Poisson’s ratio v is directly related to the P and S seismic velocity ratio K (K = V,/V,). It may provide information on the mechanical properties of a structure, differing from those of a perfectly elastic medium. Its variations depend on the nature of the rock, on temperature and pressure, and on the presence of partial melting or fluid inclusions (e.g., Nur, 1971). Standard vaiues for v are 0.25 (crust) and 0.28 (upper mantle), but values ranging from 0.23 to 0.30 are often reported in the literature. In the western Pyrenees, a determination of the Poisson’s ratio has been made previously, using the Wadati method, with the data of the Arette array (Gagnepain-Beyneix, 1987). A rather high value was found (V = 0.27; Fig. 1, region A).
relationship
A Iinear relationship, log N = a - b M, known as the Gutenberg and Richter law, has been empirically established between the frequency occurrence of earthquakes N with magnitudes higher than M, and the value of M. Experimental results have shown that b may vary with seismic region. Moreover, b generally decreases with increasing focal depth. Laboratory experiments have revealed that the frequency-magnitude relationship is also valid for microfractures produced during rock deformation (Mogi, 1962), and that the b-value depends primarily on stress (Scholz, 1968). The validity of this relationship, changing scale from microcracks to earthquakes, is not yet fully understood; however, an interest-
FREQUENCY-MAGNITUDE
365
RELATIONSHIP AND POISSON’S RATIO IN THE PYRENEES
1
S. France: _--0
Station
IS
’ OM P V Arei te l LD( A SG TEA
Events Md=2 Md=3 Md=40
Fig. 1. Determination reported (OMP/SGC
v = 0.260
001 ^^ .
v = 0.256
f
0.010 0
----0 0
N. Iberia:
v = 0.246
f 0.005
,
of the Poisson’s ratio in different seismic units of the Pyrenees. The seismicity for the years 1989-1991 is data and Arette array data), as well as the stations used in this study. Also indicated are the major faults: North Pyrenean Fault (NPF), Bigorre Fault (BF), and the Tet and Tech Faults.
ing consequence of this result is the possibility to infer regional or temporal variations of the state of stress from the variations of the b-parameter, decreasing values being related to increasing stresses. A possible physical explanation of the b-dependence on stress invokes the predominance of occurrence of small earthquakes on preexisting cracks, as a result of low stress, whereas, as a result of increasing stress, new cracks may be generated, giving rise to earthquakes which are statistically larger. The b-dependence to stress field may also reflect the competition for energy release, between either a few large faults (giving low b-values) or a great number of small faults (giving larger b-values). The geometrical properties of the fault system, in relation to the fractal dimensions of the fault, may also be at the origin of the b-variations (e.g., Aki, 1981). The regional variations of b have been studied in the Pyrenees using the very homogeneous series of the LDG (Fig. 2). Most of the earthquakes are shallow (depth < 10 km); only a small number of deeper earthquakes (10 to 30 km depth) have been recorded in the western Pyrenees. Figure 2 shows the regions which have been considered for the determination of b. They only include natural seismicity, except for region 1 in which most events are induced by gas pumping.
Some of these regions have an important overlap, in particular regions 2 and 4. Region 2’ is a subset of region 2. Typical examples of frequency-magnitude curves are shown on Figure 3. The deficit of small earthquakes with respect to the linear relationship is due to the poor detection of the earthquakes with magnitudes less than 2.5. The irregular shape of the curves at the highest magnitudes reflects the fact that the time interval considered (29 years) is less than the time recurrence of the strongest earthquakes. For the determination of the b-coefficient, only the nearly rectilinear part of each curve between two magnitudes Mmin and M,, has been considered, and b has been obtained from a least square fit. The error bars on b have been directly estimated by varying Mmin and M,,,, by k 0.1, they are generally close to 0.1. The comparison of the b-values obtained for regions 2, 2’ and 4 provides a good test of the stability of the results. The results are summarized in Figure 2b. Except for region 1, b is close to 1.1 everywhere, a value similar to that obtained for the world seismicity (Aki, 1981). A slightly lower value (b = 0.96) is obtained in region 3 (Navarra), southwest of the range. By contrast, there is a tendency for higher b-values in regions 8 and 9 (b = 1.21 and 1.23, respectively), on both sides of the eastern end of the Pyrenees.
J.-D. NJIKE-KASSALA ET AL.
366
-1
-2
b-values I
/
/
/
I’
/
1
0
n
1
2
j
3
a.
f
8:
b. Fig. 2. Determination
of regional variations of b with the LDG data. (a) Seismicity for the years (1962-1991) and regions considered. (b) Results.
Comments on the regional variations of b
Ma@tude
Fig. 3. Two examples of frequency-magnitude relationships obtained in two regions of the Pyrenees (see Figure 2 for locations). Data from LDG.
Despite the smah range of the b-variations along the Pyrenean range, some particularities may possibly be related to tectonic features or to physical properties of the crust. (1) The higher value obtained in region 1 (b = 1.44) suggests that the stress field, induced by the gag pumping and responsible for the seismicity in this region, is lower than the stress field responsi-
FREQUENCY-MAGNITUDE
RELATIONSHIP AND POISSON’S RATIO IN THE PYRENEES
ble for the seismicity of tectonic origin along the range. Part of the stress field may be released by aseismic slip. A detailed study of the b-variations in this region, in relation to stress history, has been carried out by Volant et al. (1992). (2) It is interesting to check whether the bvariations obtained along the range may be due to a variation of the mean focal depth. Only regions 2 and 4 exhibit focal depths higher than 10 km. Because the focal depths are poorly reliable in the LDG file, we have used for comparison the data of the Arette array, and limited the investigated area to that covered by this array (Fig. 4). The results (Table 1) show that, as expected, b decreases with increasing depth. Due to different magnitude scaling, LDG and Arette data do not lead exactly to the same &-values, but the b-variations with depth are the same. It is clear from Table 1 that the significant proportion of earthquakes with focal depths of > 5 km contributes to decrease the mean b-value; on the other hand, the error bars obtained with the less homogeneous, whole data sets are larger. (3) Coming back to the LDG data (Fig. 21, the lowest value is obtained in region 3, where the seismic&y is concentrated in a small area near Pamplona (Olivera and Gallart, 1987). A low
367
value is also obtained in the Arette region (b = 1.01, see Table l), where the seismicity is concentrated in a narrow strip along the NPF. Even lower values have been reported during earthquakes sequences in this region (Gallart et al., 1985). In region 4, the seismici~ is very complex (see the more accurate picture given by Fig. 0, because of the intersection of the Bigorre Fault with the NPF. In region 5, whith also a low b-value, an accurate mapping of epicenter locations has been possible only for the last 3 years, using the OMP/SGC data (Fig. 1). They indicate a tendency for a concentration of events along a strip oriented N115E along the Maladeta Massif; however, there is also a diffuse seismicity present between this strip and the NPF. The highest b-values are obtained in regions 8 and 9, where the seismic&y is very diffuse. For comparison we have computed the b-value in Britanny, a region of low tectonic activity where the seismicity is also diffuse. The data also come from the LDG file, and are then homogeneous with the Pyrenean data for the magnitudes. The value obtained, b = 1.25 f 0.05, is similar to those in regions 8 and 9. These higher values in regions of diffuse seismic&y suggest the presence of a lower stress field than in the regions where seis-
Fig. 4. Seismic& obtained in the western Fyrenees with the Arette array for the period 1978-1991. The rectangle is the region investigated for the dete~ination of the &-variations with depth.
J.-D. NJIKE-KASSALA ET AL.
368 TABLE 1 Determination Depth range
of the b-coefficient as a function of focal depth in the Arette region Arette array data
LDG data Number of data
b
Error on b
O-5 km 5-10 km >I0 km
134 56 66
1.09 0.92 0.91
0.06 0.08 0.09
All the data
200
1.01
0.12
micity is more concentrated, of faulting.
or a different nature
Discussion and conclusion We have seen that the general features of the seismicity along the Pyrenees are poorly related to the geographic variations of the Poisson’s ratio. Except for the region of induced seismicity, the results obtained for the b-parameter show a weak but general tendency for lower values (b = 1.0) in regions of concentrated seismicity, and higher values (b = 1.25) in regions of diffuse seismic&y. This is in good agreement with the model proposed by Aki (1981) in terms of fractal dimension of the fault: b = 1 corresponds to a fractal dimension of the fault of 2, i.e. a well defined fault plane. This is the case for the Arette earthquakes, for which the fault planes have been well identified thanks to the local array (GagnepainBeyneix, 1987). By contrast, b = 1.5 corresponds to a fractal dimension of 3, which represents the filling up of the volume with fault planes. High b-values in the forelands of the eastern Pyrenees correspond to earthquakes occurring in a multiplicity of sites which are not related to identified faults, without coherent geographic distribution nor coherency in the focal solutions (Nicolas et al., 1990). Therefore, an explanation invoking the geometrical properties of faulting seems appropriate, but a variation of the stress field along the range, and the possibility of stress release by aseismic slip, may also contribute to the global distribution of the seismicity. Particularly in the eastern Pyrenees, a slightly higher value of the Poisson’s ratio may favor aseismic deformation.
b
Error on b
497 423 225
1.01 0.82 0.82
0.04 0.04 0.07
1091
0.89
0.13
Number of data
Acknowledgements We thank B. Massinon and the staff of the Laboratoire de Detection Geophysique for making their data file available to us. We also thank C. Olivera and the Servei Geologic de Catalunya for their cooperation in hypocenter determinations. References Aki, K., 1981. A probabilistic synthesis of precursory phenomena. In: D.W. Simpson and P.G. Richards (Editors), ~rthquake Prediction. Am. Geophys. Union, Maurice Ewing Ser., 4, pp. 566-574. Choukroune, P., 1992. Tectonic evolution of the Pyrenees. Ann. Rev. Earth Planet. Sci., 20: 143-158. Daignieres, M., 1982. Les Pyrenees: une chaine intra~ntinentale sur un grand decrochement? Elements de r6ponses geophysiques. Thesis, Univ. Montpellier. Daignieres, M., Gallart, J. and Banda, E., 1981. Lateral variation of the crust in the Noah-~renean Zone. Ann. Geophys., 37: 435-456. Fourniguet, J. and Lenotre, N., 1987. Comparaison de nivellements dans les Pyre&es. BRGM, Orleans, Rep. No. 103. Gagnepain-Beyne~, J., 1987. Etude expirimentale des tremblements de Terre. Exemple de la region d’Arette (France). Thesis, Univ. Paris 7, 140 pp. Gagnepain-Beyneix, J., Massinon, B., Olivera, C. and Martinez-Solares, J.M., 1992. Seismicid de la chaine des Pyrenees et de ses avants-pays. In: Synthise Geologique des Pyre&es. BRGM, Orleans, in press. Gallart, J., Banda, E. and Daignibres, M., 1981. Crustal structure of the Paleozoic Axial Zone of the Pyrenees and transition to the North Pyrenean Zone. Ann. GCophys.. 37: 457-480. Gallart, J., Daignibres, M., Gagnepain-Beyneix, J. and Hirn, A., 1985. Relationship between deep structure and seismicity in western Pyrenees. Arm. Geophys., 3: 239- 248. Mogi, K., 1962. Study of the elastic shocks caused by the fracture of heterogeneous materials and its relation to
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RELATIONSHIP AND POISSON’S RATIO IN THE PYRENEES
earthquakes phenomena. Bull. Earthquake Res. Inst., 40: 125-173. Nicolas, M., Santoire, J.P. and Delpech, P.Y., 1990. Intraplate seismicity: new seismotectonic data in Western Europe. Tectonophysics, 179: 27-53. Nur, A., 1971. Viscous phase in rocks and the low velocity zone. J. Geophys. Res., 76: 1270-1277. Olivera, C. and Gallart, J., 1987. Sismicidad de la region de Navarra (Pireneos Occidentales). Rev. Geofis., 43: 221234. Olivera, C., Gallart, J., Goula, X. and Banda, E., 1986.
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Recent activity and seismotectonics of the Eastern Pyrenees. Tectonophysics, 129: 367-380. Scholz, C., 1968. The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes. Bull. Seismol. Sot. Am., 58: 399-415. Volant, Ph., Grasso, J.R., Chatelain, J.L. and Frogneux, M., 1992. b-value, aseismic deformation and brittle failure within an isolated geologic object: evidence for a dome structure loaded by fluid extraction. Geophys. Res. Lett., 19: 1149-1152.