Determination of near-surface attenuation, with κ parameter, to obtain the seismic moment, stress drop, source dimension and seismic energy for microearthquakes in the Granada Basin (Southern Spain)

Physics of the Earth and Planetary Interiors 141 (2004) 9–26

Determination of near-surface attenuation, with κ parameter, to obtain the seismic moment, stress drop, source dimension and seismic energy for microearthquakes in the Granada Basin (Southern Spain) J.M. Garc´ıa Garc´ıa∗ , M.D. Romacho, A. Jiménez Department of Applied Physics, University of Almer´ıa, 04120 Almer´ıa, Spain Received 24 March 2003; received in revised form 4 August 2003; accepted 28 August 2003

Abstract A set of 43 microearthquakes of the Granada Basin with magnitude duration MD from 1.4 to 3.5, have been spectrally analysed. The digital data used in this study was recorded by two short-period digital seismic network, five permanent stations using Andalusian Seismic Network (Red S´ısmica de Andaluc´ıa, RSA) and three stations of a portable digital seismic network (Red S´ısmica Portátil, RSP). The displacement spectra for P- and S-waves were analysed with Brune’s [J. Geophys. Res. 75 (1970) 4997; J. Geophys. Res. 76 (1971) 5002] source model and the spectra parameters were determined by Snoke’s model. To correct spectra from path attenuation coda-Q was used. For the spectra correction from near-surface attenuation κ parameter was calculated, obtaining it from acceleration spectra. The values of κ parameter range from 0.01 to 0.04 s for P-waves and from 0.006 to 0.04 s to S-waves. Once the spectra of these attenuation effects was corrected, we obtained the seismic moments that range from 5.45 × 1017 dyne cm to 1.53 × 1020 dyne cm. The source radii are between 0.13 and 0.39 km. The seismic energy ranges from 7.17 × 103 J to 1.13 × 108 J. The stress drop values were below 4 bars. The scaling relations between seismic moment and stress drop indicated decreasing stress drop with decreasing seismic moment. © 2003 Elsevier B.V. All rights reserved. Keywords: Microearthquakes; Source parameters; κ parameter; Scaling law; Stress drop; Granada Basin

1. Introduction The Granada Basin is bounded to the north and to the west by Subbetic domain materials, mainly Jurassic and Cretaceous carbonate sedimentary series belonging to the Subiberic paleomarge. The south and east sides are bounded by the Alpujarrides units of the ∗ Corresponding author. Tel.: +34-950-015911; fax: +34-950-015477. E-mail addresses: [email protected] (J.M. Garc´ıa Garc´ıa), [email protected] (M.D. Romacho), [email protected] (A. Jim´enez).

Alborán domain. The edges of both domains are covered by Neogene and Quaternary filling on the basin (de Miguel et al., 1992). The crust reaches 42 km towards the northeastern borders of the zone under study and becomes as thin as 14 km towards the south beneath the Alborán Sea (Banda et al., 1983). The P-wave average velocity in the Betic Cordillera varies from 6.0 to 6.3 km s−1 . Three fundamental sets of large faults oriented N70–100E, N120–150E and N10–70E, respectively, are present in the zone (Vidal, 1986; Peña et al., 1993). These faults are produced by the collision between the Euroasian and the African plates in

0031-9201/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.pepi.2003.08.006

10

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

the westernmost Mediterranean producing the greatest magnitude earthquakes in the area. The epicentral distributions show that the seismic activity trends mainly in N40–60W and N20–30E, orientations well correlated with existing faults in this region (Buforn et al., 1988; de Miguel et al., 1989; Morales et al., 1990; Henares and López, 2001). The Central zone of the Betics has a high level of seismic activity. In the Granada Basin, the earthquakes of 1431, 1806 and 1884 generated ground motions that reached intensity IX (MSK scale). In the present century two earthquakes have generated intensity VIII, the events of 1910 (Santa Fé) and 1956 (Albolote). The main seismic activity of the Central Betic region is shallow, but there is a significant number of subcrustal events with depths down to 120 km (mainly in the south of Málaga) and there is also a very deep and rare seismic activity shown by the 1954, 1973, 1990 and 1993 earthquakes with depths around 630–650 km. The Andalusian Seismic Network (Red S´ısmica de Andaluc´ıa, RSA) has permitted (since 1983) the analysis of several thousands of microearthquakes of the Granada Basin (Alguacil et al., 1990). The spectral analysis for the determination of source parameters, for microearthquakes and small earthquakes recorded with a local seismic network, has been widely used by different authors following Brune’s (1970, 1971) and Boatwright’s (1980) models and methods (see Garc´ıa, 1995; Garc´ıa et al., 1996). In this study we present a data set of source parameters and the scaling relations among them for microearthquakes occurred in the Granada Basin. To make the correction of the displacement spectra for near-surface attenuation we modeled the sharp decay at high frequency of acceleration spectra, observed for different authors (Anderson and Hough, 1984; Margaris and Boore, 1998) with the diminution function, D(f) = e−πrf/Q(f)v e−πκf

(1)

where r is the hypocentral distance, f the frequency and Q(f) the quality factor. The path-dependent part of the diminution is controlled by the function Q(f). According to Anderson and Hough (1984), a quantity, κ, was used to parameterize the slope of the high-frequency band. In its ac-

tion on the seismic spectrum, κ may be compared with t∗ , but is only equal to t∗ if we consider a ω-square source model and a frequency independent total Q (e.g. Hough et al., 1988; Hough, 2001). In this study the κ parameter was determined for eight stations located in the Granada Basin, sited on hard bedrock, and we have investigated the distance dependence and the magnitude dependence on that parameter. The corrected spectra were used to compute the seismic moment, the source radius and the stress drop, assuming a ω−2 Brune source model. 2. Data The digital data used in this work were recorded by short-period seismic stations, five permanent using the RSA (Andalusian Seismic Network) and three portable ones using the RSP (Portable Digital Seismic Network), located around the Granada Basin. All stations were in a low noise environment and the geophones used had vertical component with 1 Hz natural-frequency (Kinemetrics Ranger SS-1 or Mark L-4C). The signals were radio-telemetered to the Central Recording Station at the Andalusian Institute of Geophysics. Each channel signal was filtered to avoid aliasing with a 30 Hz seven-pole Butterworth low-pass filter and converted to digital form at a frequency of 100 Hz with a resolution of 12 bits. The overall response is flat to ground velocity between 1 and 30 Hz, the lower limit being imposed by the seismometer and the higher one by the cut-off frequency of the anti-alias low-pass filter. The station sites, on hard bedrock (Morales et al., 1990), combined with the electronic characteristics of the instruments ensure a practical dynamic range of 66–72 dB (Alguacil et al., 1990). Since the stations are in hard bedrock the site effects will be minimized. A data set consisting of 43 events (Fig. 1, Table 1), which occurred between 1989 and 1990, was selected on the basis of a good signal to noise ratio, accurate epicentral location and sufficient separation between P and S phases. The recordings affected by saturation effects and other problems were discarded. The duration magnitude (MD ) of the selected events, ranged between 1.4 and 3.5, was estimated according to the formulae given by de Miguel et al. (1988) (MD = (1.67 ± 0.11) log t − (0.43 ± 0.19) for MD ≤ 3.1 and

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

11

Fig. 1. Map including the epicenters of the 43 analyzed events; the size of the symbol ( ) is proportional to the magnitude. ( ) Represents the seismic stations.

MD = (2.99 ± 0.14) log t − (3.25 ± 0.33) for MD > 3.1) which are based on the duration, t, of the seismogram. The location accuracy relied upon a very good reading of the first P- and S-wave arrivals and the relatively large number of stations used. Eighty percent of the events were registered at least on seven stations

and 60% on nine or more. Most of the events have depths of less than 20 km (generally between 9 and 16 km), and only three events have depths between 40 and 60 km. The hypocentral distances are typically less than 100 km. It should be noted that the impulsive P- and S-wave arrivals are characteristic to all selected events.

12

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

Table 1 Locational parameters, with depth in km, and duration magnitude N

Date

Latitude

Longitude

Depth

Magnitude

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

03 01 03 15 19 21 21 02 08 14 22 11 19 23 25 04 25 21 27 29 23 03 08 19 09 13 28 28 25 28 30 12 19 23 29 07 04 11 18 12 14 28 28

37.212 37.031 37.013 37.001 37.045 37.101 37.084 37.240 37.056 37.025 37.102 36.982 37.019 37.052 37.050 37.218 36.828 37.079 37.111 36.866 37.114 37.111 36.972 37.221 37.052 37.017 36.905 36.644 37.102 37.156 37.158 37.103 37.143 36.705 36.985 36.773 37.256 37.041 36.978 6.994 37.012 37.047 36.839

−3.648 −3.839 −3.983 −4.037 −3.925 −3.836 −3.828 −3.633 −3.931 −4.081 −3.602 −4.015 −3.690 −4.060 −4.038 −3.726 −4.112 −3.594 −3.784 −3.901 −3.860 −3.618 −3.718 −4.023 −3.650 −3.921 −3.978 −3.515 −3.547 −4.028 −4.033 −3.947 −4.321 −4.138 −3.760 −3.832 −3.014 −3.928 −3.767 −3.742 −3.695 −3.998 −3.948

12.0 12.3 14.0 15.5 11.6 14.2 11.7 20.2 14.6 7.2 15.3 14.4 12.6 12.1 12.1 8.4 44.2 13.9 12.4 56.1 9.1 9.9 14.0 10.1 11.8 14.9 11.0 4.6 15.0 12.7 12.7 10.9 9.3 0.7 11.0 7.9 10.4 9.0 10.5 10.0 11.3 13.9 60.1

2.6 2.1 1.9 2.1 1.4 2.2 2.1 3.0 2.5 1.8 2.6 2.4 3.5 1.7 3.0 2.7 2.9 3.3 2.4 2.7 2.5 2.3 3.3 2.8 3.4 1.9 2.2 2.4 2.2 2.5 2.3 2.3 2.0 2.5 2.2 2.5 2.7 1.9 1.8 2.0 3.2 2.7 2.5

January 1989 February 1989 February 1989 February 1989 February 1989 February 1989 February 1989 March 1989 March 1989 March 1989 April 1989 June 1989 July 1989 July 1989 July 1989 September 1989 September 1989 October 1989 October 1989 October 1989 October 1990 February 1990 February 1990 February 1990 May 1990 May 1990 May 1990 May 1990 June 1990 June 1990 June 1990 July 1990 July 1990 July 1990 July 1990 August 1990 September 1990 September 1990 September 1990 October 1990 October 1990 October 1990 October 1990

3. Method of analysis All the spectra studied, from P- and S-wave, were calculated using a fast Fourier transform. First, the signal was base-line corrected by removing the mean. The time series were windowed from the start of each

phase by using a both ends 10 percent cosine taper. Signal windows of varying lengths were tested in order to select a length that would avoid contamination from other phases and maintain the resolution and stability of the spectra. The spectra were subsequently corrected for instrumental response.

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

To estimate earthquake source parameters from amplitude spectra, several corrections of observed spectra are needed. The observed velocity spectrum X(f, R) at a distance R may be described as, X(f, R) = I(f) · G(R) · D(f) · S(f)

(2)

where f is the frequency (Hz), I(f) the recording instrument transfer function, D(f) the diminution function, G(R) corrects for the attenuation of body waves due to geometrical spreading, and S(f) is the amplitude source spectrum. The observed spectra, once corrected for instrumental response, need to be corrected for geometrical spreading, attenuation and site response. The term G(R) corrects the amplitude decay of ground motion due to geometrical spreading and it is assumed to be 1/R, since all the spectra are recorded at distances less than 100 km and we use body waves (e.g. Singh et al., 1982; Hermann, 1985; Ordaz and Singh, 1992). This is the value that corresponds to an earth medium with constant velocity. However, when we consider a velocity increase with depth and/or strong lateral inhomogeneities, which modify the wavefront geometry, the term R−1 can change to R−n with n > 1. Ibáñez et al. (1993), using data from 11 earthquakes which occurred in Southern Spain, applied two methods to estimate the geometrical spreading factor n, one to S-waves and other to coda waves. They obtained that n, for S-waves, proves to be slightly frequency dependent, increasing linearly with frequency. 3.1. The κ parameter The path-dependent part of the diminution applied to the spectra was e+πft/Q(f) , with Q(f) being the quality factor and t the travel-time. The coda-Q values, Qc , were used instead of the Q(S) values, based on the observations of Aki (1980), Savage (1987) and Herráiz and Espinosa (1987). The Qc values calculated for the Granada Basin by Ibáñez et al. (1991), Qc = Q0 f n , with Q0 = 80–120 and n = 0.6–0.8, have been employed. The ratio of Q(S)/Q(P) includes both depth and frequency dependence and varies with frequency because of the frequency-dependent component of Q (Hough and Anderson, 1988). Since separation of attenuation and site response from the source spectrum is usually ambiguous, we assume that S(f) has the shape of Brune’s model (1970).

13

Deviations from this shape at frequencies higher than the source corner frequency are modeled as site attenuation effects using the empirical parameter κ of Anderson and Hough (1984). Variations in the spectral shape not accounted for by the attenuation parameter are interpreted as site effects (Humphrey and Anderson, 1994). Several studies have found that apparent corner frequencies of microearthquakes are significantly higher for borehole instruments than for seismometers located on the surface (Hauksson et al., 1987; Frankel and Wennerberg, 1989). This observation supports the inference of other studies that substantial attenuation occurs in the near-surface rocks, producing the corner frequencies of microearthquakes determined from surface recording. The attenuation of seismic waves near the site is commonly accounted for by e−πκf (Anderson and Hough, 1984; Bindi et al., 2001). To obtain the κ parameter at each station we used the acceleration spectrum (obtained by multiplying the velocity spectrum by jω), already corrected for attenuation along the path and plotted in a semi-logarithmic diagram, to choose the frequency interval where the high frequencies decay. As is indicated by Hough et al. (1988), the frequency bands were firstly chosen visually for each spectrum to be above the corner frequency and below a frequency at which the spectrum is dominated by noise. After that, the slope of the asymptotic spectral decay was estimated by least squares linear regression to that part of the spectrum (Garc´ıa et al., 1996; Garc´ıa, 1995). The κ parameter ranges, for all the stations, roughly from 0.01 to 0.04 s for P-waves and from 0.006 to 0.04 s for S-waves. Thus, we find an average κ of 0.02 s with no systematic differentiation of κ values between the different analyzed stations, which are similar to the value reported by Castro et al. (1990) for Guerrero, México zone and by Hough et al. (1999) at the Coso Geothermal Field, California. In Fig. 2b, we show an earthquake displacement spectrum (P-wave for the event 11 recorded at Loja station) before and after the κ correction, together with its best fit spectrum. In Table 2 we report the obtained values of κ for all the stations considered and the frequency range selected. Small values of κ are found corresponding to stations placed on hard rock. The expected increase versus hypocentral distance (see Anderson and Hough, 1984) is not observed for these data (Fig. 3) because

14

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

Fig. 2. (a) Observed seismogram at LOJ station of the event 11. The vertical lines indicate the onset of P- and S-waves. (b) Displacement spectra for the P-wave of this record.

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26 Table 2 κ parameter used, for all the stations, to correct the spectra; number of events for each station and the used frequency range Stations

Number of events

κ (s)

f (Hz)

APN LOJ PHE SMO TEJ HAC RES TOR

9 28 34 17 31 5 12 8

0.019 0.038 0.035 0.073 0.016 0.032 0.019 0.024

13–23 14–23 15–23 14–24 16–23 14–23 17–24 14–23

P wave - PHE station kappa (sec)

0.15 0.10 0.05 0.00 0

10

20

30

40

50

60

70

80

hypocentral distance (km)

Fig. 3. κ vs. hypocentral distance.

S wave - PHE station kappa (sec)

0.08 0.06 0.04 0.02 0.00 0.5

1.0

1.5

2.0

2.5

1991) being the value that we have adopted in this work. 3.2. The spectral parameters Following Brune’s source model, the usual spectral parameters, low frequency level Ω0 and corner frequency fc of the displacement spectra have been used to find out the source parameters. The Snoke’s method (Snoke, 1987), which avoids problems associated with the visual determination of fc , uses two independent parameters, the low frequency plateau Ω0 and the energy flux J. Ω0 is calculated by visual inspection of the displacement spectrum, whereas J is the integral of the square of the ground velocity of either P- or S-waves given by,
∞ 2 |ωU(ω)|2 df = (Ω0 ω1 )2 f1 J =2 3 0
f2 +2 |ωU(ω)|2 df + 2|ω2 U(ω2 )|2 f2 (3) f1

of the lack of information for distances greater than some 50 km and because of the large fluctuations. Also the κ parameter displayed no apparent dependence on earthquake magnitude (Fig. 4). This result is similar to that obtained by other authors (e.g. Rovelli et al., 1988; Margaris and Boore, 1998). In general, the P-wave κ found for this procedure at any particular site are about the same as the S-waves values determined from that site. From several hundred earthquakes occurred within the San Andreas fault system, Abercrombie and Leary (1993) obtained Q(P) ≈ 2Q(S)near the surface. A curve fitting the spectral ratios of surface and downhole recordings was used. This result is similar to those found in studies of Q in the mantle where Q(P) = 9/4Q(S) (Anderson et al., 1965; Castro et al.,

0.0

15

3.0

3.5

where U(ω) is the far-field displacement in the frequency domain. The values f1 and f2 have been estimated assuming a constant spectral amplitude for f < f1 and f−2 fall-off for f > f2 being ωi = 2πfi . The corner frequency fc is given by, 1/3  J (4) fc = 2π3 Ω02 The Snoke’s method provides results less sensitive to the distortion of the spectra due to site effects that could invalidate the measure of the corner frequency (Bindi et al., 2001). It should be noted that, as pointed out by Di Bona and Rovelli (1988), the measurement of the corner frequency computed by the Snoke method is less affected by errors due to the limited frequency band analyzed. We also tried Andrews’ formulae (Andrews, 1986) to obtain Ω0 and fc parameters. Andrews used two spectral parameters, J—same as above; and K—which depends on the cumulative squared displacement,
∞ |U(ω)|2 df = 2 |U(ω1 )|2 f1 K=2 0

duration magnitude

Fig. 4. κ vs. duration magnitude for the S-wave at PHE station.

+2




f2

f1

|U(ω)|2 df +

2 |U(ω2 )|2 f2 3

(5)

16

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

In the application of Andrews’ method in this study the correction terms proposed by Snoke (1987) for the K parameter have been used. The corner frequencies automatically estimated by Snoke’s formula were very similar to those obtained by Andrews’ formula, but the Snoke’s frequencies appeared to fit closer to the values visually determined in a set of spectra with exhibiting distinct fc . Ω0 values obtained by the two methods were very similar. Consequently, only the values determined using Snoke’s method were retained to calculate the source parameters. Average values for Ω0 and fc from both P- and S-waves were obtained for each one of the 43 events analysed. Between four and six records obtained from the RSA stations were used for each earthquake. The fc (P) and fc (S) values are in the ranges 4.3–14.0 and 3.5–11.4 Hz, respectively. The P-wave corner frequencies fc (P) are on average 51% greater than S-wave corner frequencies fc (S), and the mean ratio fc (P)/fc (S) is 1.3. This observation supports the presence of a corner frequency shift even when attenuation is accounted for, which is in agreement with others studies (e.g. Hanks, 1981; Fletcher and Boatwright, 1991; Abercrombie, 1995).

the compressional wave velocity, 6 km/s (Zappone et al., 2000); R is the hypocentral distance; Ω0 is the low-frequency level for the S (or P-wave); Rθ ,ϕ is the radiation pattern coefficient for the S (or P-wave). Since the focal mechanism could not be determined, the rms averages of radiation coefficients Rθ,ϕ (P) = 0.52 and Rθ,ϕ (S) = 0.63 were used (Boore and Boatwright, 1984). Our data correspond to small earthquakes, so the solution for the fault plane is not unique, either by the first impulses technique or by calculating the moment tensor. Since the stations have good azimutal coverage, the use of averaged values is adequate. The F factor was included in order to consider the wave amplification of the free surface. An average value of 1 was estimated for F coefficient (Garc´ıa et al., 1996), following Aki and Richards (1980), for the angles of incidence observed. However, small changes in F do not alter significantly the calculated values for the moment and the energy. The estimation of the radiated seismic energy Es of S-wave (or P-wave) was computed by (Boatwright and Fletcher, 1984), Es =

3.3. The source parameters We analyzed the spectra according to Brune’s (1970, 1971) fault model for the average far-field spectrum from a circular dislocation. The following equations were used to calculate the seismic moment M0 (a source parameter independent of the dynamics of the rupture process), the source radius r, and the stress drop σ (represents the difference between the initial tectonic stress and the final stress across a fault after the earthquake is over), M0 (dyne-cm) =

4πρc3 R Ω0 F Rθ,ϕ

 1/3 Ω02 2.34c r (km) = = 2.34c 2πfc 4J

(6)

(7)

4πρcR2 J (F Rθ,ϕ )2

(9)

The apparent stress σ a was calculated following Wyss (1970), σa = µ

Es M0

(10)

where µ is the shear modulus (3 × 1010 N/m2 ) and Es the total radiated energy. For each event, the average values for seismic moment, source radius, stress drop and seismic energy were computed. Calculations were made using P- and S-wave data separately as well as combined. The average values are estimated (Archuleta et al., 1982) as,   Ns 1  x¯ = antilog log xi (11) Ns i=1

7M0 σ (bar) = 16r 3

(8)

where ρ is the density, here 2.7 g/cm3 ; c represents either the shear wave velocity, 3.46 km/s, or

where Ns is the number of stations used. One reason is that the errors associated with Ω0 and r are log-normally distributed. The standard deviation of the logarithm, S.D. (log x¯ ), is estimated by calculating the

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

variance of the individual logarithms about the mean logarithm,  1/2 Ns 1  S.D. (log x¯ ) = (12) [log xi − log x¯ ]2 Ns − 1

Mo(P) (dyne-cm)

1,00E+21

i=1

and a multiplicative error factor, Ex, were calculated as, Ex = antilog(S.D.(log x¯ ))

1,00E+20 1,00E+19 1,00E+18 1,00E+17 1,00E+ 1,00E+ 1,00E+ 1,00E+ 1,00E+ 17 18 19 20 21

(13)

Table 3 shows the average values (from P and S data) of M0 , r, σ, σ a , Es , with its multiplicative error factors. The seismic moments M0 for P-waves range from 5.45 × 1017 to 1.53 × 1020 dyne-cm and for S-wave from 4.40×1019 to1.91×1020 dyne-cm. Fig. 5 presents the relationships between P- and S-wave results for M0 . The logarithmic average M0 (S)/M0 (P) is 0.9. The agreement between seismic moments from Pand S-waves provides enough confidence that the radiation pattern correction was adequate and also that the technique for evaluating the low-frequency level on the seismic spectrum was correctly applied, because they were determined from different sets of spectral values (Fletcher and Boatwright, 1991). The source radii range from 0.1 to 0.4 km with an average value of the multiplicative error factor of 2.3. The mean ratio r(P)/r(S) was found to be around 1.3, indicating that the empirical relation suggested by

17

Mo(S) (dyne-cm)

Fig. 5. Correlation between P- and S-waves results for M0 . The straight line represents a least squares linear fit.

Hanks and Wyss (1972) for P-waves is appropriated for in this study (Fig. 6). The total seismic energy varies from 7.17 × 103 to 1.13 × 108 J with an average value of the multiplicative error factor for the total data set of 1.7. The correlation between the total P- and S-wave energies is shown in Fig. 7, where the lines of equal energy ratio Es (P)/Es (S) have been indicated. For about 81.4% of the events, the S-wave to P-wave energy ratio ranges from about 0.1–1. It is remarkable that the mean Es (S) to Es (P) ratio was 5.5, similar to that found by Fletcher and Boatwright (1991) and almost half that of Boatwright et al. (1991).

0.6 0.5

r(P) (km)

0.4 r(P)/r(S)=1 0.3 0.2 0.1 0.0 0

0.1

0.2

0.3

0.4

0.5

r(S) (km)

Fig. 6. Correlation between P- and S-waves results for r. The straight line represents a least square linear fit. The dashed line indicates a ratio equal to 1.

18

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

Table 3 Average values (from P and S waves) of M0 , r, σ, σ a , Es , with its multiplicative error factors N

M0

EM0

r

Er

σ

E σ

σa

Eσ a

Es

EEs

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

5.99E+18 2.89E+18 7.37E+17 4.31E+18 5.45E+17 2.24E+18 1.73E+18 2.20E+19 7.21E+18 2.61E+18 2.22E+19 6.86E+18 1.53E+20 2.35E+1B 2.51E+19 1.72E+19 4.00E+19 7.33E+19 8.66E+18 1.82E+19 1.29E+19 1.03E+19 4.22E+19 9.81E+18 1.31E+20 3.73E+18 9.00E+18 3.91E+19 8.07E+18 1.45E+19 1.21E+19 9.67E+18 1.09E+19 3.11E+19 7.07E+18 2.60E+19 8.67E+19 4.60E+18 2.96E+18 4.46E+18 1.10E+20 2.16E+19 1.39E+19

2.13 1.28 1.63 1.53 1.29 2.07 2.15 1.39 1.63 1.65 2.35 1.13 1.51 1.55 1.24 1.82 1.67 1.82 1.42 1.87 1.42 1.27 1.37 1.42 2.03 1.73 138 1.43 1.75 1.60 1.58 1.61 1.91 1.29 1.19 1.39 1.57 1.46 1.39 1.90 1.25 1.70 1.90

0.31 0.18 0.13 0.19 0.17 0.16 0.20 0.33 0.25 0.17 0.28 0.19 0.32 0.14 0.24 0.24 0.37 0.30 0.20 0.44 0.20 0.25 0.31 0.20 0.37 0.14 0.23 0.17 0.23 2.00 0.22 0.27 0.24 0.32 0.16 0.23 0.27 0.15 0.16 0.14 0.39 0.28 0.26

1.06 1.17 1.78 1.42 1.47 1.63 2.02 1.80 2.44 2.21 2.32 2.83 2.31 3.12 3.22 2.41 1.95 2.23 2.10 2.25 2.32 2.69 2.62 2.40 2.37 2.12 2.56 3.35 2.47 2.33 2.41 2.70 2.69 2.71 3.19 2.76 3.58 2.68 3.45 3.22 4.14 2.41 2.92

0.09 0.20 0.13 0.26 0.05 0.24 0.10 0.28 0.22 0.22 0.43 0.41 2.09 0.35 0.84 0.56 0.34 1.18 0.46 0.10 0.71 0.29 0.60 0.55 1.18 0.56 0.32 3.57 0.28 0.57 0.52 0.22 0.36 0.42 0.79 0.94 1.96 0.58 0.29 0.67 0.83 0.43 0.34

2.49 1.76 3.74 2.38 2.68 1.15 3.18 1.90 4.19 1.79 3.32 1.65 3.31 2.08 2.44 2.68 2.00 3.65 2.06 2.24 2.28 2.10 1.96 3.26 1.96 2.66 1.69 2.82 2.36 2.27 2.47 2.19 1.75 2.19 1.63 1.84 3.17 1.66 1.62 1.62 3.06 2.68 3.25

0.16 0.18 0.11 0.19 0.04 0.20 0.09 0.29 0.20 0.17 0.70 0.51 2.12 0.31 0.72 0.78 0.30 1.43 0.41 0.08 0.50 0.27 0.43 0.45 2.59 0.40 0.22 6.41 0.39 0.37 0.36 0.17 0.25 0.35 0.61 0.59 1.78 0.43 0.25 0.48 0.68 0.37 0.21

4.65 1.74 2.94 2.97 2.48 3.01 3.91 2.27 3.19 2.11 6.00 2.04 2.83 2.04 2.25 3.59 3.02 3.20 2.49 3.33 2.17 1.89 2.04 3.00 3.38 3.04 2.31 3.29 2.93 2.55 2.54 3.16 3.36 2.12 1.52 1.76 2.69 2.09 1.53 2.63 2.89 4.31 4.59

3.11E+05 1.73E+05 2.67E+04 2.74E+05 7.17E 03 1.48E+05 4.89E+04 2.14E+06 4.87E+05 1.49E+05 5.20E+06 1.17E+06 1.08E+08 2.41E+05 5.98E+06 4.47E+06 3.93E+06 3.50E+07 1.19E+06 4.53E+05 2.16E+06 9.13E+05 5.98E+06 1.46E+06 1.13E+08 4.95E+05 6.66E+05 8.34E+07 1.04E+06 1.84E+06 1.45E+06 5.54E+05 9.13E+05 3.67E+06 1.44E+06 5.11E+06 5.15E+07 6.57E+05 2.44E+05 7.14E+05 2.51E+07 2.68E+06 9.85E+05

2.18 1.37 1.80 1.94 1.93 1.46 1.82 1.63 1.96 1.28 2.56 1.81 1.87 1.31 1.81 1.97 1.81 1.76 1.75 1.78 1.53 1.49 1.49 2.11 1.67 1.76 1.67 2.30 1.67 1.59 1.61 1.97 1.75 1.64 1.27 1.27 1.71 1.43 1.10 1.39 2.32 2.53 2.41

N: event number; M0 : average seismic moment (D cm); EM0 : multiplicative error factor for M0 ; r: average source radius (km); Er: multiplicative error factor for r; σ: average stress drop (bar); E σ: multiplicative error factor for σ; σ a : average apparent stress (bar); Eσ a : multiplicative error factor for σ a ; Es : average seismic energy (J); EEs : multiplicative error factor for Es .

The stress drop range from 0.05 to 3.6 bars with an averaged error factor of 1.7. In Fig. 8a the stress drop for P- and S-waves is plotted. The ratio between S- and P-waves stress-drop values shows some scatter

but is centered around a value of 0.4 (Fig. 8b). The histogram of σ(P)/σ(S) suggest a tendency towards a ratio of 0.5 (Fig. 8c). Hough et al. (1999) obtained, at the Coso Geothermal Field, California, an average

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

19

1,0E+09 1,0E+08

Es(P) (J)

1,0E+07 1,0E+06 1,0E+05 1,0E+04 1,0E+03

1 0.1

1,0E+02

0.01

1,0E+01 1,0E+03 1,0E+04 1,0E+05 1,0E+06 1,0E+07 1,0E+08 1,0E+09 Es(S) (J) Fig. 7. P-wave energy Es (P) vs. S-wave energy Es (S). The lines indicate the ratio Es (P)/Es (S) constant.

ratio of 1.05 ± 0.58, considering all the data of small (M from 0.4 to 1.3) earthquakes. The influence that uncertainties in the model parameters can have on the estimates of stress release has been extensively discussed (the calculated corner frequency can lead to large errors in determining static stress drops, which depend on the cube of the corner frequency according to the Brune (1970) model). Nevertheless, apparent stress is model independent because it is obtained directly from seismic energy and seismic moment and they are only very slightly influenced by the source geometry. Also the definition of apparent stress does not require any high frequency decay assumption. However, it is important to consider that the attenuation, radiation pattern and free surface corrections can all influence the evaluation of seismic energy and therefore apparent stress. Zúñiga et al. (1987) discuss the advantages obtained from the use of the Brune stress drop and the apparent stress simultaneously. The apparent stress ranges from 0.04 to 6.4 bars with an error factor of 2.2 (Eσ a was estimated from the product EM0 × EEs ). A plot of the apparent stress versus stress drop is included in Fig. 9. The least squares linear fit to these data gives, log σa (P, S) = (1.07 ± 0.05) log σ − (0.02 ± 0.02) (14) with a correlation coefficient of 0.95. Zúñiga (1993) proposed, to investigate possible variations in stress drop mechanism, the use of the

parameter ε, defined as, σ σ 1 − σ2 or ε= σ1 − σ f σa + (σ/2)

(15)

where σ 1 and σ 2 are initial and final stresses. σ f is the frictional stress and σ a and σ as mentioned before. This ratio is adequate to differentiate between “frictional overshoot” (the final stress reaches a value less than the frictional stress on the fault or σa < σ/2 with ε > 1) and “partial stress drop” (the final stress is greater than the frictional stress on the fault or σa > σ/2 with ε < 1). In Fig. 9 we compare the estimates of the Brune and apparent stress parameters for all the analyzed earthquakes. It is noted the apparent stress exhibits similar values than the Brune stress (on average 0.95 times). One value for ε of 0.6 has been obtained; thus, these results favor a partial stress release. 3.4. Scaling laws The scaling laws are important to define the relationship between earthquake size (seismic moment or magnitude), fault dimensions and stress drop. If how source parameters scale for large earthquakes is known, we can predict the accelerations from large earthquakes using data from smaller shocks (Frankel, 1981). Whereas the magnitude scales suffer severe intrinsic limitations, such as saturation and discrepancies between scales, the seismic moment (a measure of earthquake size defined in terms of parameters of the double-couple shear dislocation source model) can

20

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

be estimated from the recordings of all suitable seismographs (Bakun, 1984). For that, it is usual to find empirical formulae relating the seismic moment to the magnitude. These expressions fit to a linear relation between log M0 and duration magnitude. In Fig. 10 we have plotted log M0 against the duration magnitude MD . The seismic moments have been estimated from P- and S-waves, or both. A least squares fit to

all data yields, log M0 (P, S) = (1.02 ± 0.09)MD + (16.56 ± 0.22) (16) with a correlation coefficient of 0.87. Similar relations were obtained for M0 (P) and M0 (S) both of which were found to have slopes 1.02 and 1.10, respectively.

S-stress drop (bar)

10

1

0,1

0,01 0,01

0,1

(a)

1

10

100

P-stress drop (bar)

ratio of P- to S-wave stress drop

2.5

2

1.5

1

0.5

0 17.5

(b)

18

18.5

19

19.5

20

20.5

LogMo

Fig. 8. (a) P-wave stress drop vs. S-wave stress drop. The line indicates the linear least squares fit. (b) Ratio P- to S-wave stress drop vs. log(M0 ). (c) Histogram of ratio of P- to S-wave stress drop results.

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

25

Number

20

15

10

5

0 0,5

(c)

1

1,5

Ratio of P- to S- wave stress drop

2

Fig. 8. (Continued ).

Numerous microearthquakes source studies have shown an apparent scaling breakdown for earthquakes magnitudes less than 3 (e.g. Fletcher et al., 1986; Fletcher et al., 1987). The fundamental questions are whether the inferred scaling breakdown is a site effect or a property of the earthquake source. Some studies predict an apparent breakdown at low magnitudes and other ones conclude that scaling breakdown

reflects an attenuation effect. The model presented by Anderson (1986) describes that there is a trade off between the site and path attenuation parameters and the corner frequency at low magnitudes. The spectral decay parameter, κ, has the feature than it seems to be primarily an effect caused by subsurface geological structure near the site because it is only a weak function of distance (Anderson and Hough, 1984). The scale invariance of the seismic rupture process is equivalent to the observation that the ratio of seismic moment to event radius is a power law with exponent 3 and the earthquakes have a constant stress drop. In contrast, a marked decrease of stress drop with decreasing moment seems to be a scaling relation for small earthquakes with seismic moment smaller than about 1020 dyne-cm (e.g. Archuleta, 1986; Dysart et al., 1988). This means that there is evidence for breakdown in constant stress drop scaling. In that case, it seems that the events have a minimum source dimension of a few hundred meters (Archuleta et al., 1982; Aki, 1987, Abercrombie and Leary, 1993) or a nucleation patch too small to be detected (Abercrombie et al., 1995). The resolution of source parameters with decreasing magnitude is a fundamental interest in the derivation of earthquake scaling relationships and the determination of the stress drops of local earthquakes (Ichinose et al., 1997).

Apparent Stress (bar)

10

1

0,1

0,01 0,01

21

0,1

1 Static Stress Drop (bar)

Fig. 9. Apparent stress vs. stress drop and the least squares line fit.

10

22

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26 1,0E+21

Mo (dyne cm)

1,0E+20

1,0E+19

1,0E+18

1,0E+17 1,0

1,5

2,0

2,5

3,0

3,5

4,0

Duration Magnitude MD Fig. 10. Plot of the seismic moment M0 , as determined from P- and S-waves, against duration magnitude MD . The straight line represents the least squares fit to the data. Average error for M0 is represented at the bottom.

The relation between M0 and static stress drop σ is shown in Fig. 11. Linear least squares fit through the data gives, log M0 (P, S) = (1.10 ± 0.17) log σ + (19.47 ± 0.09)

(17)

with a correlation coefficient of 0.72. Haar et al. (1984) observed that the stress drops increase with seismic moment up to 1020 dyne-cm (suggesting a slope of 1.6) when they calculated the source parameters of 48 events in the north-central Arkansas swarm from January 1982 to December 1983.

Seismic Moment (dyne cm)

1,0E+21

1,0E+20

1,0E+19

1,0E+18

1,0E+17 0,01

0,1

1

10

Static Stress Drop (bar)

Fig. 11. Relation between seismic moment M0 and static stress drop, calculated from P- and S-waves. The straight line is the best fit to the data. Averaged error bars are represented at the bottom.

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

23

Seismic Moment (dyne cm)

1,0E+21 1 bar 1,0E+20 0.1 bar 1,0E+19

1,0E+18

1,0E+17 0,1

1 Radius (km)

Fig. 12. Seismic moment M0 plotted as function of source radius r, determined from P- and S-waves. The straight lines are contours of constant stress drop. The errors bars are represented at the bottom.

Seismic Moment (dyne cm)

1,0E+22

0.1 bar

1,0E+21

1 bar

1,0E+20 1,0E+19 1,0E+18 1,0E+17 1,0E+16 1,0E+03 1,0E+04 1,0E+05 1,0E+06 1,0E+07 1,0E+08 1,0E+09 Seismic Energy (J)

Fig. 13. Total seismic energy Es vs. seismic moment M0 evaluated from P-and S-waves. The lines of constant apparent stress show the range of energy variation for a given seismic moment. Also averaged errors are represented at the bottom.

In Fig. 12, M0 is plotted versus source radius r and lines of constant apparent stress drop are also indicated. The relation obtained for M0 (P, S) versus r is, log M0 (P, S) = (3.28 ± 0.43)log r + (21.15 ± 0.28)

(18)

with a rather low correlation coefficient of 0.76. The slope slightly greater than three is observed. A constant stress drop is commonly accepted for large and moderate earthquakes. Figs. 11 and 12 and also formulae 17 and 18 indicate that our data are close to the limit where decreasing σ with decreasing M0 begins. This observation implies either a breakdown

in the similarity of rupture processes for small earthquakes or incompletely accounted attenuation effects. The values of the total seismic energy are plotted against the average seismic moment in Fig. 13. The values are bounded by lines of constant apparent stress to show that energy can vary for a given seismic moment. 4. Conclusions We have examined 319 spectra of 43 selected microearthquakes for both P- and S-waves. The κ parameter ranges, for all the stations, roughly from

24

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

0.01 to 0.04 s for P-waves and from 0.006 to 0.04 s for S-waves. Small values of κ are found corresponding to stations placed on hard rock. Fluctuations were found to be randomly distributed, with no dependence on magnitude. The expected increase of κ versus hypocentral distance is not evident for these data, possibly due to the lack of information for distances greater than some 50 km and also the large fluctuations. Measurement uncertainties and high variability among the geomorphologic features of the station sites are probably responsible for the observed dispersion. The determined corner frequencies range from 4 to 12.6 Hz with a P- to S-wave ratio of 1.35, which agrees with values found in the literature (e.g. Fletcher and Boatwright, 1991). The objective determination of Snoke’s J parameter allowed for more direct determination of Brune’s stress drop σ, because σ is linearly related to J (instead of estimating σ by the third power of fc ). The seismic moment M0 from either P- or S-waves estimation ranged from 5.45 × 1017 to 1.53 × 1020 dyne-cm, values commonly obtained for earthquakes with similar magnitudes. The M0 (P) to M0 (S) ratio of 1.1 indicates that Snoke’s technique, the radiation pattern and free surface corrections applied to the data were right. The source radius was found to range from approximately 0.13–0.40 km. The source sizes estimated from P-waves were slightly greater than those estimated from S-waves, by a ratio of about 1.3. The seismic energy, which ranged from 7.17×103 to 1.13×108 J, showed large variation with respect to the seismic moment. The seismic energy values obtained for S-waves were greater than the values for P-waves and for 81.4% of the events its ratio was found to be between 0.1 and 1.0. As indicated above about seismic moment, the seismic energy could be slightly affected if different constant values of F and Rθ ,ϕ are applied, but the Es values would only differ in a constant. A similar comment could be made regarding the stress release and the apparent stress parameters, which are related to M0 and Es , respectively. One interesting result of this work is the low stress release estimates obtained for this tectonic area. Most of the stress drop values were below 4 bar, a result similar to those obtained for small earthquakes in other tectonic settings (e.g. Fletcher et al., 1986; Dysart et al., 1988; Abercrombie et al., 1995; Hough and

Kanamori, 2002). Although high values of stress drop correspond to the higher seismic moment values, a large proportion of the events (88%) had stress drops between 0.14 and 1 bar. Based on the applied corrections, it is believed by the authors that the stress release estimates outline a characteristic of the region. However, it could still be possible that the κ parameter correction was not large enough to remove the near site and other attenuation effects in the spectra, mainly as the smaller events for which such kind of effects has a great influence in the record. For these reasons, a decreasing stress drop with a decreasing seismic moment is not entirely conclusive. The apparent stress values estimated were similar to the stress drops, σa = 1.07σ; this point out to a partial stress release. Moreover, a low and partial stress drops might occur when the fault locks itself soon after the rupture is over or when the stress release is not uniform and coherent over the whole fault plane (Brune et al., 1986). The obtained moment–radius relations suggest a breakdown of similarity for the microearthquakes in the Granada Basin. Similar results were obtained in other tectonic regions using coda waves (e.g. Chouet et al., 1978; Rautian and Khalturin, 1978). It should be underlined that all the correlations obtained should not be extrapolated without caution outside our magnitude range (MD 1.4–3.5, Mw 1.2–2.7).

Acknowledgements The authors want to thank F. Vidal, J.M. Mart´ınMarfil, A. Posadas and F. Luzón, colleagues of the Andalusian Institute of Geophysics, whose comments and useful discussions at the various stages of this study led to an improvement of the work. We wish to express our sincere thanks to the professor Dr. Aki for his critical reading of this paper, helpful revision and useful recommendations to improve it. The comments of an anonymous reviewer helped to improve the original article. This work was partially supported by CICYT, Spain, under Grant REN2002-04198-C02-02/RIES, by the European Community with FEDER, by the research team of Geof´ısica Aplicada (RNM194) of Junta de Andaluc´ıa, by the Andalusian Institute of Geophysics and the University of Almer´ıa.

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

References Abercrombie, R.E., 1995. Earthquake source scaling relationships from −1 to 5 ML using seismograms recorded at 2.5-km depth. J. Geophys. Res. 100, 24015–24036. Abercrombie, R.E., Leary, P.C., 1993. Source parameters of small earthquakes recorded at 2.5 km depth, Cajon Pass, southern California: implications for earthquake scaling. Geophys. Res. Lett. 20, 1511–1514. Abercrombie, R.E., Main, I.G., Douglas, A., Burton, P.W., 1995. The nucleation and rupture process of the 1981 Gulf of Corinth earthquakes from deconvolved broad-band. Geophys. J. Int. 120, 393–405. Aki, K., 1980. Scattering and attenuation of shear waves in the lithosphere. J. Geophys. Res. 85, 6496–6504. Aki, K., 1987. Magnitude-frequency relation for small earthquakes: a clue to the origin of fmax of large earthquakes. J. Geophys. Res. 92, 1349–1355. Aki, K., Richards, P.G., 1980. Quantitative Seismology: Theory and Methods, vols. 1 and 2. Freeman, San Francisco, CA. Alguacil, G., Guirao, J.M., Gómez, F., Vidal, F., de Miguel, F., 1990. Red S´ısmica de Andaluc´ıa (RSA): a digital PC-Based seismic Network. Cahiers du Centre Européen de Géodynamique et de Séismologie 1, 19–27. Anderson, J.G., 1986. Implication of attenuation for studies of the earthquake source. In: Das, S., Boatwright, J., Scholz, C.H. (Eds.), Earthquake Source Mechanics, Maurice Ewing Series 6. American Geophysical Union, Washington, DC, pp. 311–318. Anderson, D.L., Ben-Menahem, A., Archambeau, C.B., 1965. Attenuation of seismic energy in the upper mantle. J. Geophys. Res. 70, 1441–1448. Anderson, J.G., Hough, S.E., 1984. A model for the shape of the Fourier amplitude spectrum of acceleration at high frequencies. Bull. Seism. Soc. Am. 74, 1969–1993. Andrews, D.J., 1986. Objective determination of source parameters and similarity of earthquakes at different size. In: Das, S., Boatwright, J., Scholz, C.H. (Eds.), Earthquake Source Mechanics, Proceedings of the 5th Maurice Ewing Symposium. American Geophysical Union, Washington, DC, pp. 259–267. Archuleta, R.J., 1986. Downhole recordings of seismic radiation. In: Das, S., Boatwright, J., Scholz, C.H. (Eds.), Earthquake Source Mechanics, Proceedings of the 5th Maurice Ewing Symposium. American Geophysical Union, Washington, DC, pp. 319–329. Archuleta, R., Cranswick, E., Mueller, C., Spudich, P., 1982. Source parameters of the 1980 Mammoth Lakes, California, earthquake sequence. J. Geophys. Res. 87, 4595–4607. Bakun, W.H., 1984. Seismic moments, local magnitudes, and coda duration magnitudes for earthquakes in central California. Bull. Seism. Soc. Am. 74, 439–458. Banda, E., Ud´ıas, A., Mueller, S., Mezcua, J., Boloix, M., Gallart, J., Aparicio, A., 1983. Crustal structure beneath Spain from deep seismic sounding experiments. Phys. Earth Planet. Inter. 31, 277–280. Bindi, D., Spallarossa, D., Augliera, P., Cattaneo, M., 2001. Source parameters estimated from aftershocks of the 1997 Umbria-Marche (Italy) seismic sequence. Bull. Seism. Soc. Am. 91, 448–455.

25

Boatwright, J., 1980. A spectral theory for circular seismic sources simple estimates of source dimension, dynamic stress drop, and radiated seismic energy. Bull. Seism. Soc. Am. 70, 1–26. Boatwright, J., Fletcher, J.B., 1984. The partition of radiated energy between P and S waves. Bull. Seism. Soc. Am. 74, 361–376. Boatwright, J., Fletcher, J.B., Fumal, T.E., 1991. A general inversion scheme for source, site, and propagation characteristics using multiply recorded sets of moderate-sized earthquakes. Bull. Seism. Soc. Am. 81, 1754–1782. Boore, D.M., Boatwright, J., 1984. Average body-wave radiation coefficients. Bull. Seism. Soc. Am. 74, 1615–1621. Brune, J.N., 1970. Tectonic stress and the spectra of seismic shear waves from earthquakes. J. Geophys. Res. 75, 4997–5009. Brune, J.N., 1971. Correction (to Brune (1970)). J. Geophys. Res. 76, 5002. Brune, J.N., Fletcher, J., Vernon, F., Haar, L., Hanks, T., Berger, J., 1986. Low stress-drop earthquakes in the light of new data from the Anza, California telemetered digital array. In: Das, S., Boatwright, J., Scholz, C.H. (Eds.), Earthquake Source Mechanics, Proceedings of the 5th Maurice Ewing Symposium. American Geophysical Union, Washington, DC, pp. 237–245. Buforn, E., Ud´ıas, A., Mezcua, J., 1988. Seismicity and focal mechanisms in South Spain. Bull. Seism. Soc. Am. 78, 2008– 2024. Castro, R.R., Anderson, J.G., Singh, S.K., 1990. Site response, attenuation and source spectra of S waves along the Guerrero, Mexico, subduction zone. Bull. Seism. Soc. Am. 80, 1481– 1503. Castro, R.R., Anderson, J.G., Brune, J.N., 1991. Origin of high P/S spectral ratios from the Guerrero accelerograph array. Bull. Seism. Soc. Am. 81, 2268–2288. Chouet, B., Aki, K., Tsujirua, M., 1978. Regional variation of the scaling law of earthquake source spectra. Bull. Seism. Soc. Am. 68, 59–79. Di Bona, M., Rovelli, A., 1988. Effects of the bandwidth limitation on stress drops estimated from integral of the ground motion. Bull. Seism. Soc. Am. 78, 1818–1825. Dysart, P.S., Snoke, J.A., Sacks, I.S., 1988. Source parameters and scaling relations for small earthquakes in the Matsushiro region, southwest Honshu, Japan. Bull. Seism. Soc. Am. 78, 571–589. Fletcher, J.B., Boatwright, J., 1991. Source parameters of Loma Prieta aftershocks and wave propagation characteristics along the San Francisco Peninsula from a joint inversion of digital seismograms. Bull. Seism. Soc. Am. 81, 1783–1812. Fletcher, J.B., Haar, L.C., Vernon, F.L., Brune, J.N., Hanks, T.C., Berger, J., 1986. The effects of attenuation on the scaling of source parameters for earthquakes at Anza, California. In: Das, S., Boatwright, J., Scholz, C.H. (Eds.), Earthquake Source Mechanics, Proceedings 5th Maurice Ewing Symposium. American Geophysical Union, Washington, DC, pp. 331–338. Fletcher, J., Haar, L., Hanks, T., Baker, L., Vernon, F., Berger, J., Brune, J., 1987. The digital array at Anza, California: processing and initial interpretation of source parameters. J. Geophys. Res. 92, 369–382. Frankel, A., 1981. Source parameters and scaling relationships of small earthquakes in the northeastern Caribbean. Bull. Seism. Soc. Am. 71, 1173–1190.

26

J.M. Garc´ıa Garc´ıa et al. / Physics of the Earth and Planetary Interiors 141 (2004) 9–26

Frankel, A., Wennerberg, L., 1989. Microearthquake spectra from the Anza, California, seismic network: site response and source scaling. Bull. Seism. Soc. Am. 79, 581–609. Garc´ıa, J.M., 1995. Caracter´ısticas espectrales y de fuente de terremotos y microterremotos de Andaluc´ıa Oriental. Ph.D. Thesis. University of Granada Press, Granada. Garc´ıa, J.M., Vidal, F., Romacho, M.D., Mart´ın-Marfil, J.M., Posadas, A., Luzón, F., 1996. Seismic source parameters for microearthquakes and small earthquakes of the Granada basin (Southern Spain). Tectonophysics 261, 51–66. Haar, L.C., Fletcher, J.B., Mueller, C.S., 1984. The 1982 Enola, Arkansas, swarm and scaling of ground motion in the eastern United States. Bull. Seism. Soc. Am. 74, 2463–2482. Hanks, T.C., 1981. The corner frequency shift, earthquake source models and Q. Bull. Seism. Soc. Am. 71, 597–612. Hanks, T.C., Wyss, M., 1972. The use of body-wave spectra in the determination of seismic-source parameters. Bull. Seism. Soc. Am. 62, 561–589. Hauksson, E., Teng, T., Henyey, T.L., 1987. Results from a 1500 m deep, three-level downhole seismometer array: site response, low Q values, and fmax . Seism. Soc. Am. 77, 1883– 1904. Henares, J., López, C., 2001. Catálogo de mecanismos focales del área Ibero-Mogreb´ı. University of Granada Press, Granada. Hermann, R.B., 1985. An extension of random vibration theory estimates of strong ground motion to large distances. Bull. Seism. Soc. Am. 75, 1447–1453. Herráiz, M., Espinosa, A.F., 1987. Coda waves: a review. Pure Appl. Geophys. 125, 499–577. Hough, S.E., 2001. Triggered earthquakes and the 1811–1812 New Madrid, central U.S., earthquake sequence. Bull. Seism. Soc. Am. 91, 1574–1581. Hough, S.E., Anderson, J.G., 1988. High-frequency spectra observed at Anza, California: implications for Q structure. Bull. Seism. Soc. Am. 78, 692–707. Hough, S.E., Anderson, J.G., Brune, J., Vernon, F., Berger, J., Fletcher, J., Haar, L., Hanks, T., Baker, L., 1988. Attenuation near Anza, California. Bull. Seism. Soc. Am. 78, 672–691. Hough, S.E., Kanamori, H., 2002. Source properties of earthquakes near the Salton Sea triggered by the 16 October 1999 M 7.1 Hector Mine, California, earthquake. Bull. Seism. Soc. Am. 92, 1281–1289. Hough, S.E., Lees, J., Monastero, F., 1999. Attenuation and source properties at the Coso geothermal region, California. Bull. Seism. Soc. Am. 89, 1606–1619. Humphrey, J., Anderson, J.G., 1994. Seismic source parameters from the Guerrero subduction zone. Bull. Seism. Soc. Am. 84, 1754–1769. Ibáñez, J.M., de Miguel, F., Alguacil, G., Morales, J., Vidal, F., del Pezzo, E., Posadas, A.M., 1991. Coda Q analysis of the digital data in the Central Betics. Rev. de Geof´ısica 47, 59–74. Ibáñez, J.M., del Pezzo, E., Alguacil, G., de Miguel, F., Morales, J., de Martino, S., Sabbarese, C., Posadas, A.M., 1993. Geometrical spreading function for short-period S and coda waves recorded in southern Spain. Phys. Earth Planet. Inter. 80, 25–36.

Ichinose, G.A., Smith, K.D., Anderson, J.G., 1997. Source parameters of the 15 November 1995 Border Town, Nevada, earthquake sequence. Bull. Seism. Soc. Am. 87, 652–667. Margaris, B.N., Boore, D.M., 1998. Determination of σ and κ0 from response spectra of large earthquakes in Greece. Bull. Seism. Soc. Am. 88, 170–182. de Miguel, F., Alguacil, G., Vidal, F., 1988. Una escala de magnitud a partir de la duración para terremotos del sur de España. Rev. de Geof´ısica 44, 75–86. de Miguel, F., Ibáñez, J.M., Alguacil, G., Canas, J.A., Vidal, F., Morales, J., Peña, J.A., Posadas, A.M., Luzón, F., 1992. 1–18 Hz Lg attenuation in the Granada Basin (southern Spain). Geophys. J. Int. 111, 270–280. de Miguel, F., Vidal, F., Alguacil, G., Guirao, J.M., 1989. Spacial and energetic trends of the microearthquakes activity in the Central Betics. Geodinámica Acta 3, 87–94. Morales, J., Vidal, F., de Miguel, F., Alguacil, G., Posadas, A.M., Ibáñez, J.M., Guzman, A., Guirao, J.M., 1990. Basement structure of the Granada Basin, Betic Cordillera (southern Spain). Tectonophysics 177, 337–348. Ordaz, M., Singh, S.K., 1992. Source spectra and spectral attenuation of seismic waves from Mexican earthquakes, and evidence of amplification in the hill zone of Mexico City. Bull. Seism. Soc. Am. 82, 24–43. Peña, J.A., Vidal, F., Posadas, A.M., Morales, J., Alguacil, G., de Miguel, F., Ibáñez, J.M., Romacho, M.D., López-Linares, A., 1993. Space clustering properties of the Betic-Alboran earthquakes in the period 1962–1989. Tectonophysics 221, 125– 134. Rautian, T.G., Khalturin, V.I., 1978. The use of the coda for determination of the earthquake source spectrum. Bull. Seism. Soc. Am. 68, 923–948. Rovelli, A., Bonamassa, O., Cocco, M., Di Bona, M., Mazza, S., 1988. Scaling laws and spectral parameters of the ground motion in active extensional areas in Italy. Bull. Seism. Soc. Am. 78, 530–560. Savage, M.K., 1987. Spectral properties of Hawaiian microearthquakes: source, site, and attenuation effects. Ph.D. Thesis. The University of Wisconsin, Madison. Singh, S.K., Apsel, R.J., Fried, J., Brune, J.N., 1982. Spectral attenuation of SH waves along the imperial fault. Bull. Seism. Soc. Am. 72, 2003–2016. Snoke, J.A., 1987. Stable determination of (Brune) stress drops. Bull. Seism. Soc. Am. 77, 530–538. Vidal, F., 1986. Sismotectónica de la región Béticas—Mar de Alborán. Ph.D. Thesis. University of Granada Press, Granada. Wyss, M., 1970. Stress estimates for South American shallow and deep earthquakes. J. Geophys. Res. 75, 1529–1544. Zappone, A., Fernández, M., Garc´ıa-Dueñas, V., Burlini, L., 2000. Laboratory measurements of seismic P-wave velocities on rocks from the Betic chain (southern Iberian Peninsula). Tectonophysics 317, 259–272. Zúñiga, F.R., 1993. Frictional overshoot and partial stress drop. Which one? Bull. Seism. Soc. Am. 83, 939–944. Zúñiga, F.R., Wyss, M., Wilson, M.E., 1987. Apparent stresses, stress drops, and amplitude ratios of earthquakes preceding and following the 1975 Hawaii MS = 7.2 main shock. Bull. Seism. Soc. Am. 77, 69–96.