S-wave attenuation in northeastern Sonora, Mexico, near the faults that ruptured during the earthquake of 3 May 1887 Mw 7.5
© Villalobos-Escobar and Castro; licensee Springer. 2014
Received: 12 September 2014
Accepted: 11 December 2014
Published: 17 December 2014
We used a new data set of relocated earthquakes recorded by the Seismic Network of Northeastern Sonora, Mexico (RESNES) to characterize the attenuation of S-waves in the fault zone of the 1887 Sonora earthquake (M w 7.5). We determined spectral attenuation functions for hypocentral distances (r) between 10 and 140 km using a nonparametric approach and found that in this fault zone the spectral amplitudes decay slower with distance at low frequencies (f < 4 Hz) compared to those reported in previous studies in the region using more distant recordings. The attenuation functions obtained for 23 frequencies (0.4 ≤ f ≤ 63.1 Hz) permit us estimating the average quality factor Q S = (141 ± 1.1 )f(0.74 ± 0.04) and a geometrical spreading term G(r) = 1/r0.21. The values of Q estimated for S-wave paths traveling along the fault system that rupture during the 1887 event, in the north–south direction, are considerably lower than the average Q estimated using source-station paths from multiple stations and directions. These results indicate that near the fault zone S waves attenuate considerably more than at regional scale, particularly at low frequencies. This may be the result of strong scattering near the faults due to the fractured upper crust and higher intrinsic attenuation due to stress concentration near the faults.
KeywordsSeismic attenuation Geometrical spreading Sonora Mexico
On May 3, 1887, a mayor seismic event (M w = 7.5) took place on northeastern Sonora (Mexico), destroying the town on Bavispe and its surroundings (Aguilera, 1888). This event, as well as most northern Mexico, is located south of the Basin and Range province (Suter and Contreras, 2002), and generated the longest recorded normal fault surface rupture (101.8 km) in historic time (Suter, 2006).
The Red Sísmica del Noreste de Sonora (RESNES) was installed in 2002 to monitor the seismicity related with the Basin and Range normal faults of northeastern Sonora (Castro et al., 2002; Romero et al., 2004). The seismic instruments of the RESNES array consist of Kinemetrics digital recorders (model K2) with internal Episensors that record the three components of ground acceleration, sampled at 200 samples per second, and an external short-period seismometer (model L4C) to record the vertical ground velocity. All stations are autonomous and have a GPS built-in timing system (Castro et al., 2010).
Since the occurrence of the major event in 1887, several studies have been made, including contemporary field studies (Goodfellow, 1888; Aguilera, 1888), studies of intensity and attenuation (DuBois and Smith, 1980; Sbar and DuBois, 1984; Bakun, 2006; Castro et al., 2008; Castro et al., 2009), regional seismotectonics (Suter and Contreras, 2002), geomorphology (Bull and Pearthree, 1988; Pearthree et al., 1990) and microseimicity (Natali and Sbar 1982). Condori (2006) and Castro et al. (2008) studied the spectral amplitude decay of body waves with hypocentral distance and proposed local and regional attenuation curves to characterize the attenuation near the fault zone and at distances beyond 100 km from the center of the network.
An important element to evaluate seismic hazard is the attenuation, particularly to estimate the intensity of ground-motion at different epicentral distances. Thus, the quality factor Q and the geometrical spreading are key parameters for ground-motion predictions and for seismic hazard analysis. We use in this article a new and more complete data set to study in more detail the seismic attenuation near the fault zone. This new data set is composed by earthquakes relocated by Castro et al. (2010) near the faults that rupture during the 1887 event. We also compare results from previous studies of spectral attenuation in the Sonora region with our new results and with results from other studies within the Basin and Range province.
List of earthquakes used in the attenuation analysis
Attenuation functions using a nonparametric method
Where U i (f, r) is a datum from event i recorded at hypocentral distance r at a frequency f, S i (f) is a scalar that depends on the size of the i th event at a frequency f. A(f, r) is the empirically determined attenuation function that describes the distance decay trend. We assume that A(f, r) implicity contains the effect of both the geometrical spreading and the quality factor Q, but we do not limit their behavior to a predetermined parametrical function, instead, we constrain A(f, r) to decay smoothly with distance. The basis of the smooth decaying restriction lies on the principle that the inelastic properties in the crust tend to decrease the amplitudes gradually with distance and that undulations may be related to other factors such as site and wave propagation effects that would reflect on the residuals when solving equation (1) (Castro et al., 1990; Castro et al., 2008).
The main assumptions of the model described by equation (1) are that A(f, 0) = 1.0, because at r = 0 there is not attenuation and the spectral amplitudes are fully governed by the source term S i (f). The model assumes that the shape of the attenuation function is the same for all the sources, for a given frequency, regardless of the size of the event (Castro et al., 1990; Castro et al., 2008). Thus, the source factor S i (f) shifts upwards or downwards the attenuation function depending on the magnitude of the event without modifying its shape. One major advantage of this last assumption is that the observed amplitudes of events recorded at different distances at a given frequency complement each other and permits to define the attenuation function at a wider distance range.
Where w1 and w2 are weighting factors provided as input to constrain a1 = 0 at r = 0, and to weight the second derivate, for smoothing purposes, respectively. The weighting factor w1 forces the attenuation function to cross the origin. We tested diverse values of the weighting factors and discretized the hypocentral distances at different intervals in order to achieve the expected monotonic and smooth decay of the attenuation function without losing the characteristic trend of the data.
The quality factor Q using a homogeneous attenuation model
Where 1/r b represents the effect of geometric spreading, N is a normalization distance and the exponential function accounts for the amplitude decrease due to total Q (intrinsic plus scattering). The normalization distance N is a reference distance that is chosen as close to the source as the data permits. Note that (r – N) in equation (4) is the S-wave path distance length where Q takes effect to normalize the spectral amplitudes at the reference distance. The parameter υ is the average S-wave velocity (3.4 km/sec), based on the crustal structure reported by Harder and Keller (2000) for this region. This model has a crustal thickness of 35 km and consists of three layers: the uppermost layer is one km thick and has a S-wave velocity of 2.86 km/s; the second layer has a thickness of 21 km and a velocity of 3.3 km/s; and the third layer, that represents the lower crust, has a thickness of 13 km and a velocity of 3.88 km/s. Different values of N, between 1 and 20 km, were tested to evaluate the influence of this parameter in the geometric spreading behavior.
Where d i = log A(f,r i ) – logN is the normalized amplitude at distance r i , m i = -πf(r i -N)loge/υ, υ = 3.4 km/s is the average S-wave velocity and c i = -log(r i ). 1/Q and b are estimated by solving equation (5) with a least-squares inversion scheme.
Results and discussion
The spectral amplitudes modeled with equation (1) describe the S-wave attenuation in northeastern Sonora, in the region close to the rupture zone of the 1887 (M W = 7.5) earthquake. We determined 23 spectral attenuation functions that represent the decay of the S-wave energy for discrete frequencies defined between 0.4 and 63.1 Hz. Figure 6 shows a sample of these attenuation functions and the observed spectral amplitudes for both horizontal (black circles) and vertical (open circles) components. We observe that spectral amplitudes at low frequencies (up to 5.0 Hz) tend to attenuate less with hypocentral distance than amplitudes at higher frequencies. Figure 7 compares the observed spectral amplitudes (circles) from a M L = 3.5 earthquake (event 9 in Table 1) with the nonparametric attenuation functions (dashed lines) scaled with the corresponding values of S i (f) (equation (1)) resulting from solving equation (2). We also plotted in Figure 7A(f, r) for S i (f) = 1(solid lines) as a reference to show that for a given frequency the shape of the attenuation function is the same regardless of the event size. In other words, the rate of decay of the spectral amplitudes with distance is assumed to be the same for all the events.
To evaluate the effect of site conditions of the recoding stations, we calculated spectral attenuation functions separately for both vertical and horizontal ground-motion components using the whole distance range (Figure 6). Under the assumption that the vertical component of acceleration is less susceptible to site-amplification effects, a comparison of the attenuation functions obtained using the vertical component provides a reference to evaluate the effect of local site response on the attenuation functions determined with the horizontal components. We found no substantial differences between the observed spectral data or between the calculated attenuation functions (Figure 6).
Estimates of Q
Values of Q (Figure9) estimated at different frequencies using N = 1 and b = 0.21 in equation ( 4) with the RMS values reported by the inversion process
Although the model they used to describe the sources of attenuation involve a term that accounts for the near-surface attenuation, their Q-frequency relation (equation (7)) follows the general trend of Q obtained in this study (circles in Figure 9). However, between 0.63 Hz and 4.0 Hz equation (7) underestimates the values of Q here determined (Figure 9). The data sets used in previous studies (Castro et al., 2008, 2009) and that used in this paper have important differences. First, we used a greater number of events located in the epicentral area of the 3 May 1887 M W 7.5 earthquake; second, we used hypocenters relocated by Castro et al. (2010) and the precise locations guarantee a better control on the source-station distances; third, the volume sampled by the source-station paths in this paper follows the strike of the faults closer than previous studies.
follows a similar trend of our Q estimates. The parameter b depends on the hypocentral distance, and for distances greater than 50 km has values below the theoretical value of one.
Attenuation in the north–south direction
To evaluate the attenuation of S waves in the north–south direction, along the strike of the faults that ruptured during the 1887, we calculated attenuation functions using data from the same site to avoid the possible influence of site amplification effects. We selected station OAX (Figure 1) for having the largest amount of records and for being located inside the fault zone. We formed a dataset with horizontal spectral records of OAX from 33 events with magnitudes between 1.0 and 3.5 that occurred in the 20–90 km distance range from the station. We determined attenuation functions for the same frequencies and procedure (equation 1) as before, and then we used them to estimate b and Q with equation (4).
while b is weakly dependent of frequency, having a value close to 1.4 for the whole frequency band analyzed (1.3–63.1 Hz).
Some studies of body wave attenuation shows that the coefficient b associated with the geometrical spreading is more complex than b = 1 and they attribute this to complex velocity structures (Ibáñez et al.,1993; Olafsson et al., 1998; Castro et al., 1999; Akıncı et al., 2006; Padhy, 2009). Ou and Herrmann (1990) found that G(r) may depend upon source depth in layered structures, while Burger et al., (1987) remarked the importance of post-critical reflections from mid-lower crustal velocity discontinuities and the Moho in controlling amplitudes in certain distance ranges. Chapman and Godbee (2012) found values of the geometrical spreading in eastern North-America up to r -4 for the vertical components and up to r -1.5 for the horizontal components, which exceeds notably the theoretical standards for body waves. In our case, we are finding similar values of the parameter b (for N = 20), for the OAX data set, to those reported by Chapman and Godbee (2012) for the horizontal components (Figure 10). Malagnini et al., (2002) introduced a slightly frequency-dependent geometrical spreading to model ground motion in northeastern Italy, a region where the attenuation parameters vary considerably. Akıncı et al. (2006) proposed geometric spreading functions that are frequency dependent on a stepped way for frequencies below and above 1.0 Hz and for a different range of distances in the Marmara (Turkey) region. The results obtained in this paper (Figures 8 and 10) show that b is weakly dependent of frequency and that there are certainly other factors, beyond simple theoretical models, to fully account for all the processes affecting the attenuation of S-waves in the Sonora region.
Summary and conclusions
We used precise hypocenter locations from local events to find nonparametric spectral attenuation functions for the region that ruptured with the M w = 7.5 1887 earthquake of Sonora. The attenuation functions determined decay more slowly with hypocentral distance at low frequencies (f < 4 Hz) than results reported previously in the area using more distant recordings. Consequently the Q-frequency relation (eq. (7)) obtained by Castro et al. (2008) tends to underestimate Q between 0.63 and 4.0 Hz. The values of Q estimated for the S-waves (Figure 9) show a clear dependence of Q with the frequency, and agree with the models proposed by Castro et al. (2008) for the region, and with the values of Q calculated by Jeon and Herrmann (2004) for the Basin and Range Province in the state of Utah (USA).
The values of Q estimated with station OAX (eq. (9) and Figure 10) for S-wave paths traveling along the strike of the fault system located near the rupture of the 1887 event, in the north–south direction, are considerably lower than the average Q estimated using source-station paths from multiple stations and directions (eq. (6) and Figure 9). These results indicate that near the fault zone S waves attenuate considerably more than at regional scale, particularly at low frequencies. For instance, at 0.5 Hz Q in the north–south direction, along the strike of the faults (eq. (9)), is 10.5 times smaller than the average Q (eq. (6)). This may be the result of strong scattering near the faults due to the fractured upper crust and higher intrinsic attenuation due to stress concentration near the faults.
The geometric spreading models found have weak frequency dependence (Figures 8 and 10) and can be approximated as G(r) = 1/r0.21 for the average Q. This spreading function predicts slower amplitude decay with hypocentral distance than the r- 1 theoretical model of body waves.
We acknowledge CONACYT for providing the scholarship for the first author (GV) and for the research funding through the project CB-2011-165401-F. We thank Luis Inzunza, Arturo Perez-Vertti and Antonio Mendoza for technical support and assistance during the operation of the seismic network. Shri Krishna Singh, José M. Romo and Luis Munguía provided us useful information, encouraging discussions and valuable comments.
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