| Citation: | Chengli Liu, Yong Zheng, Xiong Xiong. Focal mechanism and rupture process of the 2012 Mw 7.0 Santa Isabel, Mexico earthquake inverted by teleseismic data. Journal of Earth Science, 2015, 26(3): 384-390. doi: 10.1007/s12583-014-0503-x
|
As one of the most earthquake-prone countries in the world, Mexico is located in the conjunction among three large tectonic plates: the Pacific, America and Antarctica plates. The Gulf of California is an active rift between the Pacific and North American plates (Lizarralde et al., 2007; Larson et al., 1968). The west of the gulf, including Mexico's Baja California Peninsula, is still moving northwestward the Pacific Plate at about ~45–47 mm per year (Plattner et al., 2007; Dixon et al., 2000) (Fig. 1). Here, the Pacific and North American plates grind past each other and generated strike-slip faulting, connecting to the California's San Andreas fault (González-Fernández et al., 2005; Nagy and Stock, 2000). In the past, this relative plate motion pulled Baja California away from the coast and formed the Gulf of California, which might be accountable for earthquakes happened in the Gulf of California region (Reichle et al., 1976; Molnar, 1973). The relative motion among these crustal plates caused frequent moderate earthquakes in Mexico and adjacent regions recently (Castro et al., 2011; Hauksson et al., 2011; Ortega and Quintanar, 2010).
The ground shaking produced by large earthquakes is one of the greatest natural hazards on the Earth. Thus, when earthquakes, especially large earthquakes (Mw > 7.0) occur, quick estimation of the source parameters and rupture process is crucial in predicting the damage of the earthquake and thus offering the first aid treatment in earthquake-stricken areas (Ji et al., 2004; Dreger and Kaverina, 2000; Wald et al., 1999a, b).
On April 12, 2012, an Mw 7.0 earthquake occurred in Santa Isabel of the Gulf of California. In order to understand the rupture process and the seismogenic structure of this earthquake, we investigated the point source mechanism by a means of cut and paste (CAP) approach. Based on the obtained source parameters, we inverted the rupture process of the main shock using the finite-fault inversion method (Ji et al., 2002a, b; Hartzell and Hearon, 1983). Our inversion is based on teleseismic body waveforms downloaded from Incorporated Research Institutions for Seismology (IRIS) data center due to lack of direct observation in the near field.
The purpose of this study is to discuss the source parameters and slip pattern, and provide a reference model for the further studies on stress distribution and its significance for future seismic activity under the impact of the Mw 7.0 Santa Isabel Earthquake.
After the main shock, the source parameters from various earthquake observation agencies differentiate from one another (Table 1). The traditional cut and paste (CAP) method therefore is employed to invert point source parameters indicated by the teleseismic P and SH waveforms downloaded from IRIS (Fig. 2). This method applies a direct grid search through all possible solutions to detect the global minimum of misfits between the observations and the synthetics, allowing time shifts between portion of seismograms and synthetics. The synthetic displacement for a double couple source could be written as
|
s(t)=M03∑i=0Ai(ϕ−θ,δ,λ)Gi(h,Δ,t) |
| Source | Depth (km) | Node plan Ⅰ | Node plan Ⅱ |
| GCMT | 14.1 | 41/89/0 | 311/90/179 |
| USGS body-wave | 20 | 333/74/177 | 64/88/16 |
| USGS W phase | 11 | 135/68/175 | 227/86/22 |
| This study | 13 | 37/90/-9 | 127/81/-180 |
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here, $i$ =1, 2, 3 corresponds to three fundamental faults (i.e., vertical strike-slip, vertical dip-slip, and 45° dip-slip), ${G_i}\left({h, \varDelta, t} \right)$ are the Green's functions, ${A_i}$ are the radiation coefficients, $\phi $ is the station azimuth, $\varDelta $ is the distance, ${M_0}$ is the scalar moment, and the $h$ $\theta $, $\delta $ and $\lambda $ are the depth, strike, dip and rake of the point source we want to determine. They are estimated by fitting the data in L2 norm with time shifts allowed between seismograms and synthetics to get the maximum cross-correlation coefficients (Zhu and Helmberger, 1996).
In order to avoid the influence caused by seismic point source approximation, both the P and SH waveforms (Fig. 3) were band-pass filtered with relative low frequency band of 0.01–0.07 Hz. We obtained a strike of 37°/127°, dip of 90°/81°, rake of -9°/-180°, the moment magnitude of 7.06, and a depth of about 13 km (Fig. 4a), suggesting a pure strike-slip event. The synthetics generated by the preferred point source mechanism fit the data well for all stations. Growing evidence shows that the rupture duration is crucial for the focal mechanism inversion of moderate magnitude earthquakes (Mw > 6.0). In order to minimize the uncertainty of rupture duration time, we, based on the half duration provided by GCMT, moved the time from 8 to 16 s to get the best duration time with minimum fit error. When we fixed the focal depth at 13 km, the minimum misfit error occurred in the duration time of 12 s (Fig. 4b).
Nineteen teleseismic P waveforms and eighteen SH waveforms of the Mw 7.0 Santa Isabel Earthquake are available from (IRIS) data center, with good signal-to-noise ratio and well azimuthally distribution (Table 3) for analysis. The seismograms are band-pass filtered with frequency band of 0.005–1 Hz. We choose the location (28.79°N, -113.142°E), origin time: 2012/04/12 07:15:48.62 (GMT time) provided by the National Earthquake Information Center (NEIC).
In order to determine the space and time distribution of rupture process, we carried out the waveform inversion in the wavelet domain using finite fault inversion approach, and then searched for global optimal solutions using a simulated annealing method (Ji et al., 2003). Based on the tectonic setting, aftershock distribution and source parameters from our result, we choose the fault plane which consists of a single rupture plane have a size of 85.5 km along strike and 24 km down dip, with the strike and dip angles of 127° and 81°, respectively. The depth of hypocenter is 13 km; the whole fault plane is divided into 152 subfaults with the spatial dimension of 4.5 km by 3.0 km.
During the inversion, slip amplitude varies from 0 to 6 m, and rake angle changes from 150° to 210° with an interval of 2°. The average rupture velocity ranges from 1.5 to 2.5 km/s with an interval of 0.1 km/s. The rise time in the inversion model varies from 1.0 to 7.6 s with time step of 0.6 s. During the inversion process, the seismograms are band-pass filtered with frequency band of 0.005–2 Hz, which basically contains the main frequency band of the energy carried by these seismograms. We use a 1D layered velocity model (Table 2) interpolated from Crust2.0 (Bassin et al., 2000) to approximate the structure in the source region and treat the teleseismic station sites as on a half-space.
| NO. | Depth (km) | Vp (km·s-1) | Vs (km·s-1) | ρ (kg·m-3) |
| 1 | 1.0 | 2.1 | 1.0 | 2 100.0 |
| 2 | 7.0 | 6.0 | 3.4 | 2 700.0 |
| 3 | 7.0 | 6.6 | 3.7 | 2 900.0 |
| 4 | 7.0 | 7.2 | 4.0 | 3 050.0 |
| 5 | Half-space | 8.2 | 4.7 | 4 000.0 |
| Note: the velocity model is interpolated from Crust2.0. | ||||
DownLoad:
CSV
| Stations | Lat (°) | Lon (°) | Az (°) | Distance (°) |
| KBS | 11.938 5 | 78.915 4 | 9.824 7 | 68.133 2 |
| DAG | -18.655 0 | 76.771 3 | 14.901 5 | 63.228 6 |
| SFJD | -50.620 8 | 66.996 1 | 25.832 6 | 53.147 8 |
| MUD | 9.173 3 | 56.455 0 | 28.276 6 | 82.067 0 |
| KHC | 13.578 2 | 49.131 0 | 31.775 2 | 89.050 9 |
| SSB | 4.542 0 | 45.279 0 | 38.759 4 | 87.053 8 |
| PVAQ | -7.717 3 | 37.403 7 | 50.519 4 | 84.035 7 |
| FRNY | -73.588 3 | 44.835 0 | 52.003 4 | 35.094 3 |
| KSCT | -73.484 3 | 41.726 1 | 57.366 5 | 34.558 9 |
| FDF | -61.143 0 | 14.735 0 | 94.765 7 | 49.910 4 |
| SDV | -70.634 0 | 8.883 9 | 107.800 0 | 44.526 2 |
| SAML | -63.183 1 | -8.948 9 | 120.199 0 | 61.060 4 |
| OTAV | -78.450 8 | 0.237 6 | 124.445 0 | 43.639 3 |
| PEL | -70.674 9 | -33.143 6 | 143.809 0 | 73.589 1 |
| PLCA | -70.550 8 | -40.732 8 | 148.482 0 | 79.650 9 |
| PPTF | -149.565 0 | -17.589 6 | 221.894 0 | 58.011 5 |
| NIUE | -169.927 0 | -19.076 3 | 236.018 0 | 72.599 0 |
| MSVF | 178.053 0 | -17.744 8 | 244.126 0 | 80.951 7 |
| KNTN | -171.719 0 | -2.774 4 | 251.108 0 | 64.276 4 |
| KIP | -158.011 0 | 21.420 0 | 270.202 0 | 41.099 9 |
| CBIJ | 142.184 0 | 27.095 7 | 300.396 0 | 88.921 3 |
| INU | 137.029 0 | 35.350 0 | 309.701 0 | 88.134 9 |
| PET | 158.650 0 | 53.023 3 | 318.832 0 | 66.522 6 |
| FALS | -163.417 0 | 54.856 4 | 320.479 0 | 44.336 2 |
| MDJ | 129.591 0 | 44.617 0 | 320.540 0 | 87.239 7 |
| HIA | 119.741 0 | 49.270 4 | 328.510 0 | 89.135 8 |
| PMR | -149.131 0 | 61.592 2 | 334.360 0 | 40.499 5 |
| FYU | -145.234 0 | 66.565 7 | 341.690 0 | 42.562 8 |
| BILL | 166.453 0 | 68.065 3 | 334.692 0 | 60.067 8 |
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CSV
Based on the source parameters described in the Table 1, we obtain the rupture process of the Santa Isabel earthquake constrained by teleseismic body-waves. The inverted results show that the model with the source parameters determined by this study fits the data batter than others (Table 4), The inverted slip history based on the source parameters of our study is shown in Fig. 5a. The synthetic waveforms fit the data quite well (Fig. 6), only on station KIP and KNTN have some misfits in the P wave segments, which may be caused by local structures under the stations or induced by the fault complexities. View from our inversion results, however, these effects do not seem to dominate the entire records.
| Source | Misfit |
| GCMT | 0.232 6 |
| USGS body-wave | 0.261 8 |
| USGS W phase | 0.189 5 |
| This study | 0.186 0 |
DownLoad:
CSV
The rupture model shows the main shock is dominated by pure strike slip motions. Although there are weak dip-slip components in the south end of the rupture plane, which may be artificial result because of the boundary effect. Compared to the cases with higher or lower rupture velocity, the fit to seismic waveforms are pretty well for the case where rupture velocity is fixed to 2.0 km/s. The total seismic moment is 3.98×1019 N·m, and most of the moment released at the first 25 s after the onsets of the rupture (Fig. 5b). Overall, most of the slip occurred at depths less than 13 km and the main rupture asperity is located in 20–40 km southeast of hypocenter, with strike slip amplitude up to 3.57 m. However, there are no significant slip components distributed around the hypocenter.
Using the teleseismic P and SH waveforms we first obtained the best point source mechanism of Mw 7.0 Santa Isabel, Mexico, Earthquake, which is 37°/127°, 90°/81°, -9°/-180° for strike, dip and rake respectively, based on the tectonic setting and aftershock distribution, the fault plane with the strike of 127°, dip of 81° is identified; and then we inverted the slip model by teleseismic waveforms, using the source parameters from different agencies, the result shows that the model with the source parameters determined by this study fits the data batter than others, the rupture initiates at a depth of 13 km and propagates southeastwards with a relatively low speed, about 1.8 km/s on average. The maximum slip occurs at 20-40 km southeast of the hypocenter, with the peak slip of 3.57 m and the total of seismic moment of whole fault is 3.98×1019 N·m. Compared with our rupture model and the PGA distribution of strong motion (USGS, http://earthquake.usgs.gov/earthquakes/shakemap/global/shake/c00091a1/), there are some differences between these two images. In PGA map, the region with big amplitude of ground motion is located near the hypocenter of the earthquake, while in our result the big asperity of strike slip is located are ~30 km from the hypocenter. This difference may due to following reasons: (1) The earthquake occurred inside of the sea, it is impossible to pick out strong motion information in the area close to the rupture, which will blur the distribution in the surrounding inland areas; (2) lacking of near field measurements, which will lower the resolution of inverted rupture model; (3) the accurate hypocenter location and the geometry of fault model are two essential pre-conditions of the inversion. In our model, a single flat rupture fault is applied, which may be too simple to obtain the detailed rupture process of the earthquake. But anyway, the good consistence between the synthetic seismograms and observed data, and the consistence between the distribution of aftershocks and the inversion result give us confidence that the inversion result is reasonable and reliable.
The source parameters are of importance to the slip model inversion, although we can obtain properly good slip model of this earthquake even with the simplest assumption. However, further work is still needed to improve the resolution and accuracy of the rupture process, because the actual rupture process of an earthquake is usually more complicated than the inversion results. The difference between the distribution of inverted rupture model and the distribution of PGA is an evidence for the effect of lacking near field measurement. So, more detailed datasets are needed to constrain the fault geometry (Li et al., 2011; Wei et al., 2011; Simons et al., 2002) and rupture process, especially the near field observations (e.g., InSAR, GPS, strong motion data). If the slip amplitudes are not constrained by near-field geodetic data, the trade-off between rupture velocity and slip amplitudes would become vague. However, after the earthquake, only the teleseismic waveforms of the global IRIS network is available online, at present we can only provide the rupture model based on the teleseismic data. In the near future, if enough field observations and more geodetic data are available, a better result should be expected.
ACKNOWLEDGMENTS: This study was supported by the National Natural Science Foundation of China (Nos. 41422401, 41174086, 41104027) and the Excellent Young Scientist Grant of National Science Foundation of Hubei Province (No. 2012FFA026). We thank two anonymous reviewers for their helpful comments and constructive suggestions. The data are downloaded from IRIS. All figures were generated by using the open-source Generic Mapping Tools software (Wessel and Smith, 1991).| Bassin, C., Laske, G., Masters, G., 2000. The Current Limits of Resolution for Surface Wave Tomography in North America. Eos, Transactions American Geophysical Union, 81: F897. http://igppweb.ucsd.edu/~gabi/crust2.html |
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| 1. | G.E. Hilley, R.M. Sare, F. Aron, et al. Coexisting seismic behavior of transform faults revealed by high-resolution bathymetry. Geology, 2020, 48(4): 379. doi:10.1130/G46663.1 | |
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Figures(6) / Tables(4)
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Chengli Liu, Yong Zheng, Xiong Xiong. Focal mechanism and rupture process of the 2012 Mw 7.0 Santa Isabel, Mexico earthquake inverted by teleseismic data. Journal of Earth Science, 2015, 26(3): 384-390. doi: 10.1007/s12583-014-0503-x
| Source | Depth (km) | Node plan Ⅰ | Node plan Ⅱ |
| GCMT | 14.1 | 41/89/0 | 311/90/179 |
| USGS body-wave | 20 | 333/74/177 | 64/88/16 |
| USGS W phase | 11 | 135/68/175 | 227/86/22 |
| This study | 13 | 37/90/-9 | 127/81/-180 |
DownLoad:
CSV
| NO. | Depth (km) | Vp (km·s-1) | Vs (km·s-1) | ρ (kg·m-3) |
| 1 | 1.0 | 2.1 | 1.0 | 2 100.0 |
| 2 | 7.0 | 6.0 | 3.4 | 2 700.0 |
| 3 | 7.0 | 6.6 | 3.7 | 2 900.0 |
| 4 | 7.0 | 7.2 | 4.0 | 3 050.0 |
| 5 | Half-space | 8.2 | 4.7 | 4 000.0 |
| Note: the velocity model is interpolated from Crust2.0. | ||||
DownLoad:
CSV
| Stations | Lat (°) | Lon (°) | Az (°) | Distance (°) |
| KBS | 11.938 5 | 78.915 4 | 9.824 7 | 68.133 2 |
| DAG | -18.655 0 | 76.771 3 | 14.901 5 | 63.228 6 |
| SFJD | -50.620 8 | 66.996 1 | 25.832 6 | 53.147 8 |
| MUD | 9.173 3 | 56.455 0 | 28.276 6 | 82.067 0 |
| KHC | 13.578 2 | 49.131 0 | 31.775 2 | 89.050 9 |
| SSB | 4.542 0 | 45.279 0 | 38.759 4 | 87.053 8 |
| PVAQ | -7.717 3 | 37.403 7 | 50.519 4 | 84.035 7 |
| FRNY | -73.588 3 | 44.835 0 | 52.003 4 | 35.094 3 |
| KSCT | -73.484 3 | 41.726 1 | 57.366 5 | 34.558 9 |
| FDF | -61.143 0 | 14.735 0 | 94.765 7 | 49.910 4 |
| SDV | -70.634 0 | 8.883 9 | 107.800 0 | 44.526 2 |
| SAML | -63.183 1 | -8.948 9 | 120.199 0 | 61.060 4 |
| OTAV | -78.450 8 | 0.237 6 | 124.445 0 | 43.639 3 |
| PEL | -70.674 9 | -33.143 6 | 143.809 0 | 73.589 1 |
| PLCA | -70.550 8 | -40.732 8 | 148.482 0 | 79.650 9 |
| PPTF | -149.565 0 | -17.589 6 | 221.894 0 | 58.011 5 |
| NIUE | -169.927 0 | -19.076 3 | 236.018 0 | 72.599 0 |
| MSVF | 178.053 0 | -17.744 8 | 244.126 0 | 80.951 7 |
| KNTN | -171.719 0 | -2.774 4 | 251.108 0 | 64.276 4 |
| KIP | -158.011 0 | 21.420 0 | 270.202 0 | 41.099 9 |
| CBIJ | 142.184 0 | 27.095 7 | 300.396 0 | 88.921 3 |
| INU | 137.029 0 | 35.350 0 | 309.701 0 | 88.134 9 |
| PET | 158.650 0 | 53.023 3 | 318.832 0 | 66.522 6 |
| FALS | -163.417 0 | 54.856 4 | 320.479 0 | 44.336 2 |
| MDJ | 129.591 0 | 44.617 0 | 320.540 0 | 87.239 7 |
| HIA | 119.741 0 | 49.270 4 | 328.510 0 | 89.135 8 |
| PMR | -149.131 0 | 61.592 2 | 334.360 0 | 40.499 5 |
| FYU | -145.234 0 | 66.565 7 | 341.690 0 | 42.562 8 |
| BILL | 166.453 0 | 68.065 3 | 334.692 0 | 60.067 8 |
DownLoad:
CSV
| Source | Misfit |
| GCMT | 0.232 6 |
| USGS body-wave | 0.261 8 |
| USGS W phase | 0.189 5 |
| This study | 0.186 0 |
DownLoad:
CSV
| Source | Depth (km) | Node plan Ⅰ | Node plan Ⅱ |
| GCMT | 14.1 | 41/89/0 | 311/90/179 |
| USGS body-wave | 20 | 333/74/177 | 64/88/16 |
| USGS W phase | 11 | 135/68/175 | 227/86/22 |
| This study | 13 | 37/90/-9 | 127/81/-180 |
| NO. | Depth (km) | Vp (km·s-1) | Vs (km·s-1) | ρ (kg·m-3) |
| 1 | 1.0 | 2.1 | 1.0 | 2 100.0 |
| 2 | 7.0 | 6.0 | 3.4 | 2 700.0 |
| 3 | 7.0 | 6.6 | 3.7 | 2 900.0 |
| 4 | 7.0 | 7.2 | 4.0 | 3 050.0 |
| 5 | Half-space | 8.2 | 4.7 | 4 000.0 |
| Note: the velocity model is interpolated from Crust2.0. | ||||
| Stations | Lat (°) | Lon (°) | Az (°) | Distance (°) |
| KBS | 11.938 5 | 78.915 4 | 9.824 7 | 68.133 2 |
| DAG | -18.655 0 | 76.771 3 | 14.901 5 | 63.228 6 |
| SFJD | -50.620 8 | 66.996 1 | 25.832 6 | 53.147 8 |
| MUD | 9.173 3 | 56.455 0 | 28.276 6 | 82.067 0 |
| KHC | 13.578 2 | 49.131 0 | 31.775 2 | 89.050 9 |
| SSB | 4.542 0 | 45.279 0 | 38.759 4 | 87.053 8 |
| PVAQ | -7.717 3 | 37.403 7 | 50.519 4 | 84.035 7 |
| FRNY | -73.588 3 | 44.835 0 | 52.003 4 | 35.094 3 |
| KSCT | -73.484 3 | 41.726 1 | 57.366 5 | 34.558 9 |
| FDF | -61.143 0 | 14.735 0 | 94.765 7 | 49.910 4 |
| SDV | -70.634 0 | 8.883 9 | 107.800 0 | 44.526 2 |
| SAML | -63.183 1 | -8.948 9 | 120.199 0 | 61.060 4 |
| OTAV | -78.450 8 | 0.237 6 | 124.445 0 | 43.639 3 |
| PEL | -70.674 9 | -33.143 6 | 143.809 0 | 73.589 1 |
| PLCA | -70.550 8 | -40.732 8 | 148.482 0 | 79.650 9 |
| PPTF | -149.565 0 | -17.589 6 | 221.894 0 | 58.011 5 |
| NIUE | -169.927 0 | -19.076 3 | 236.018 0 | 72.599 0 |
| MSVF | 178.053 0 | -17.744 8 | 244.126 0 | 80.951 7 |
| KNTN | -171.719 0 | -2.774 4 | 251.108 0 | 64.276 4 |
| KIP | -158.011 0 | 21.420 0 | 270.202 0 | 41.099 9 |
| CBIJ | 142.184 0 | 27.095 7 | 300.396 0 | 88.921 3 |
| INU | 137.029 0 | 35.350 0 | 309.701 0 | 88.134 9 |
| PET | 158.650 0 | 53.023 3 | 318.832 0 | 66.522 6 |
| FALS | -163.417 0 | 54.856 4 | 320.479 0 | 44.336 2 |
| MDJ | 129.591 0 | 44.617 0 | 320.540 0 | 87.239 7 |
| HIA | 119.741 0 | 49.270 4 | 328.510 0 | 89.135 8 |
| PMR | -149.131 0 | 61.592 2 | 334.360 0 | 40.499 5 |
| FYU | -145.234 0 | 66.565 7 | 341.690 0 | 42.562 8 |
| BILL | 166.453 0 | 68.065 3 | 334.692 0 | 60.067 8 |
| Source | Misfit |
| GCMT | 0.232 6 |
| USGS body-wave | 0.261 8 |
| USGS W phase | 0.189 5 |
| This study | 0.186 0 |
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