Integrated seismic source model of the 2015 Gorkha, Nepal, earthquake
Abstract
We compared spatiotemporal slip‐rate and high‐frequency (around 1 Hz) radiation distributions from teleseismic P wave data to infer the seismic rupture process of the 2015 Gorkha, Nepal, earthquake. For these estimates, we applied a novel waveform inversion formulation that mitigates the effect of Green's functions uncertainty and a hybrid backprojection method that mitigates contamination by depth phases. Our model showed that the dynamic rupture front propagated eastward from the hypocenter at 3.0 km/s and triggered a large‐slip event centered about 50 km to the east. It also showed that the large‐slip event included a rapid rupture acceleration event and an irregular deceleration of rupture propagation before the rupture termination. Heterogeneity of the stress drop or fracture energy in the eastern part of the rupture area, where aftershock activity was high, inhibited rupture growth. High‐frequency radiation sources tended to be in the deeper part of the large‐slip area, which suggests that heterogeneity of the stress drop or fracture energy there may have contributed to the damage in and around Kathmandu.
1 Introduction
On 25 April 2015, Kathmandu, Nepal, was struck by a large thrust earthquake. According to the U.S. Geological Survey (USGS) (http://earthquake.usgs.gov; last accessed, 13 May 2015), the origin time of this earthquake was 25 April 2015 at 06:11:26 (UTC); its epicenter was at 28.147°N, 84.708°E; and its hypocentral depth was 15 km. Many large earthquakes have occurred in the past near Kathmandu [Bilham et al., 2001], where the India and Eurasia plates are converging at about 1.8 cm/yr [Ader et al., 2012]. The aftershock distribution (USGS epicenters) and the focal mechanism, shown in Figure 1, indicate that the 2015 Gorkha earthquake occurred on a low‐angle fault plane and that the slip vector is consistent with the tectonic stress field in the source region.
The estimation of slip‐rate (dislocation speed on the fault plane) distributions of large earthquakes from their seismic waveforms provides the broad features of the seismic source process [e.g., Hartzell and Heaton, 1983; Beroza and Spudich, 1988]. Because rapid acceleration and deceleration of a dynamic rupture generate high‐frequency seismic waves [e.g., Madariaga, 1977; Bernard and Madariaga, 1984; Spudich and Frazer, 1984], to comprehend fully the evolution of the rupture process during a large earthquake, it is necessary to construct a spatiotemporal slip‐rate distribution that can explain the high‐frequency components. However, it is difficult to estimate the slip‐rate distribution including the high‐frequency components by waveform inversion because of the uncertainty of the Green's functions [e.g., Zeng et al., 1993; Nakahara, 2008].
In this study, we used the newly developed inversion [Yagi and Fukahata, 2011] and hybrid backprojection (HBP) [Yagi et al., 2012] methods to estimate the slip‐rate distribution and high‐frequency radiation (around 1 Hz) related to rapid acceleration and deceleration of a dynamic rupture, respectively, of the 2015 Gorkha earthquake from teleseismic P wave data. We compared the high‐frequency radiation event and the slip‐rate distribution and then constructed an integrated source model that we used to infer the detailed dynamic rupture process during this earthquake.
2 Data and Method
We applied the waveform inversion and HBP methods to teleseismic body waves. For both analyses, we used teleseismic P wave data of the 2015 Gorkha earthquake recorded by 52 broadband seismograph stations (Figure 2a). We manually picked the first P wave arrival times and then shifted the observed waveforms accordingly (Figure 2b). We also removed the seismograph response from the original waveforms to convert them into velocity waveforms with sampling intervals of 0.8 s and 0.05 s for the inversion and HBP analyses, respectively. We selected data sampling intervals for inversion in order to stably obtain the inverse data covariance matrix and to maximize the data information. In the inversion analysis, we applied a 0.001–0.36 Hz Butterworth band‐pass filter before resampling to mitigate the aliasing effect and low‐frequency noise. In the HBP analysis, we applied a 0.5–2.0 Hz Butterworth band‐pass filter to estimate the high‐frequency radiation source.
Since the first pioneering studies of the finite fault modeling [e.g., Olson and Apsel, 1982; Hartzell and Heaton, 1983], waveform inversion has been used to estimate the spatiotemporal slip‐rate distribution, but estimates often differ even for the same earthquake [e.g., Beresnev, 2003]. In general, it is not possible to calculate the true Green's functions for large earthquakes, so the use of Green's functions with limited accuracy is an unavoidable problem in seismic source inversion. Yagi and Fukahata [2011] proposed a new method of mitigating the effect of the uncertainty of the Green's functions by using the data covariance matrix and demonstrated the advantages of the new method by applying it to both a synthetic and a real data set. In this study, by applying the method of Yagi and Fukahata [2011], we objectively determined the smoothness of the slip‐rate distribution from the observed data by using Akaike's Bayesian information criterion [e.g., Akaike, 1980; Yabuki and Matsu'ura, 1992].
Since it was proposed by pioneering early work [Ishii et al., 2005; Krüger and Ohrnberger, 2005], the backprojection (BP) method has been widely used to estimate the spatiotemporal distribution of the high‐frequency radiation source. The clear advantage of BP is that it makes possible to obtain the high‐frequency radiation without the theoretical Green's functions. Many researchers have developed BP analysis methods [e.g., Xu et al., 2009; Meng et al., 2011; Haney, 2014; Kennett et al., 2014a], but the timing of the subevents estimated by the BP methods can be distorted by the effects of reflected phases (e.g., pP and sP phases) [Yagi et al., 2012]. As a result, it is quite difficult to reliably compare the distribution of subevents obtained by BP and the spatiotemporal slip‐rate distributions inferred by waveform inversion. To avoid the distortion effects of reflected phases, we applied the HBP method developed by Yagi et al. [2012]. The HBP method uses the Green's functions to mitigate the effect of reflected phases, and the HBP result can thus be compared to the slip‐rate distribution obtained by the waveform inversion [Okuwaki et al., 2014].
In both analyses, we assumed the CRUST 1.0 structure model [Laske et al., 2013] for the near‐source region and then calculated the theoretical Green's functions by using the program of Kikuchi and Kanamori [1991]. We adopted the USGS hypocenter (28.147°N, 84.708°E; depth 15 km) as the rupture start point and inferred the fault plane (strike 285°, dip 10°) from the aftershock distribution and the global centroid moment tensor (GCMT) solution (http://www.globalcmt.org; last accessed, 13 May 2015). The fault area used for the analyses was 168 km × 96 km, with grid intervals of 8 km and 2 km for the inversion and HBP analyses, respectively.
For the inversion analysis, we represented the slip‐rate function on each fault patch as linear B splines (maximum length = 28 s, grid interval = 0.8 s) and assumed a slip rate of zero from 60 s after the initial break. Because the HBP result can be used to constrain the dynamic rupture‐front velocity [Okuwaki et al., 2014], for the inversion analysis we assumed a maximum rupture‐front velocity of 3.0 km/s on the basis of a preliminary HBP result.
For the HBP analysis, we applied nonlinear Nth root stacking [Muirhead and Datt, 1976] to improve the signal‐to‐noise ratio and adopted N = 3.5. The rake angle was set to 95° on the basis of a preliminary inversion result.
3 Results
Figure 1 shows a map view of the total slip distribution along with the aftershock distribution and the moment‐rate function for the 2015 Gorkha earthquake. The rupture area extended eastward from the epicenter, and the effective rupture area was approximately 120 km long and 80 km wide (see Figure S1 in the supporting information). The largest Mw 7.3 aftershock (27.837°N, 86.077°E, as determined by the USGS) occurred on 12 May 2015 on the east side of the main shock rupture area (Figure 1). An area of large slip, in which the maximum slip was about 7.5 m, was centered about 50 km east of the epicenter. The total seismic moment was 9.1 × 1020 Nm (Mw = 7.9), which is similar to the GCMT solution of 7.8 × 1020 Nm.
Figure 3a shows snapshots of the slip‐rate distribution and high‐frequency radiation sources at each time step. The spatiotemporal slip‐rate distribution shows that the main rupture started 19 s after the initial break in the western part of the large‐slip area and the slip rate accelerated until about 30 s after the initial break. At about 40 s, the slip rate decreased along the dynamic rupture front and the rupture‐front speed decelerated with time. The slip had ceased about 50 s after the initial break. As shown in Figure 1, the total moment release rate increased gradually for 24 s to 3.6 × 1019 Nm/s, and the maximum rate of 3.7 × 1019 Nm/s was reached at 35 s. The inverted slip‐rate distribution could well reproduce the characteristics of the observed waveforms (see Figure S2).
The distribution of high‐frequency radiation sources shows that a strong high‐frequency event, which was excited near the hypocenter immediately after the initial break, propagated eastward with a rupture‐front velocity of about 3.0 km/s until about 30 s. Then, moderate high‐frequency radiation continued to propagate eastward until about 50 s. The large high‐frequency radiation sources tended to be distributed on the deeper side of the assumed fault plane.
Both inversion and HBP results show that the rupture propagated unilaterally eastward from the hypocenter. This characteristic of the rupture process can be expected from the main shock waveform (Figure 2c), which became relatively broader toward the west and relatively shorter toward the east.
4 Discussion and Conclusion
Our HBP result clearly indicates that the dynamic rupture front propagated mainly eastward with a rupture‐front velocity of about 3.0 km/s. In contrast, the BP results automatically produced by the Incorporated Research Institutions for Seismology (IRIS) indicate that the rupture‐front velocity was about 2.0 km/s (http://www.iris.edu; last accessed, 13 May 2015). The timing of subevents estimated by BP methods can be distorted by the effects of reflected phases [Yagi et al., 2012], and such distortion may have contributed to this discrepancy between the HBP and the IRIS BP results. To clarify the reason for the discrepancy, we performed a conventional BP analysis of the 2015 Gorkha earthquake in which we adopted the same data and fault model as for our HBP analysis. The high‐frequency distributions estimated by HBP and BP methods are compared in Figure 4. The BP image shows that the rupture propagated eastward, and the gross rupture pattern obtained by the BP method is consistent with that obtained by the HBP method. On the other hand, we can identify a time delay in the high‐frequency radiation distribution in the BP result compared with the HBP result. Fukahata et al. [2014] predicted that a reflected phase (e.g., the sP phase) would cause a time delay in the BP image, and previous studies that employed the HBP method have detected a similar time delay in BP images [Yagi et al., 2012; Okuwaki et al., 2014]. In the BP analysis, an sP phase with larger amplitude than the direct P phase in reverse faulting was projected onto the fault plane and produced the slow rupture velocity in the present case. These results show that the BP method can be a strong and suitable tool for tracking a high‐frequency rupture and deriving the rupture pattern of a large earthquake, while the HBP method is an appropriate tool for estimating a plausible high‐frequency radiation distribution that can be compared to the slip‐rate distribution.
Integration of the slip rate and high‐frequency radiation source (Figures 3 and 4a) showed that the high‐frequency radiation source tends to be concentrated along the dynamic rupture front. This tendency, which has been reported previously [Okuwaki et al., 2014], indicates that the HBP analysis method is useful for constraining the assumed maximum rupture‐front velocity in the seismic source inversion. Numerical studies have shown that the high‐frequency component is generated by rapid changes of slip rate or rupture velocity or both [e.g., Madariaga, 1977; Bernard and Madariaga, 1984; Spudich and Frazer, 1984]. The strong high‐frequency event between 13 s and 18 s corresponds to a rapid acceleration of the slip rate or rupture‐front velocity and may trigger a large‐slip event. A similar high‐frequency event was detected at the breakpoint of asperities in the case of the 2010 Mw 8.8 Chile earthquake [Okuwaki et al., 2014]. In contrast, the moderate high‐frequency event between 37 s and 48 s corresponds to an irregular deceleration of the slip‐rate and rupture‐front velocity estimated by the waveform inversion where a high density of aftershock activity was detected. In general, the irregular deceleration of rupture is related to a heterogeneous distribution of the stress drop or fracture energy [e.g., Okuwaki et al., 2014]. Such heterogeneity might have impeded the dynamic rupture propagation and contributed to the aftershock activity in this region.
As shown in Figure 3, the deeper part of the large‐slip area generated the high‐frequency components. A similar pattern has been reported for great earthquakes in subduction zones [Koper et al., 2011; Lay et al., 2012]. Spatial changes in the slip rate or rupture‐front velocity generate high‐frequency components [e.g., Spudich and Frazer, 1984], and such discontinuities might be caused by an abrupt spatial change of fracture energy or stress drop [e.g., Husseini, 1975; Fukuyama and Madariaga, 1998]. The depth variation of the slip rate and high‐frequency radiation is related to the heterogeneous distribution of fracture energy or stress level, and our result suggests that the heterogeneous distribution of fracture energy or stress level in the deeper part of the large‐slip area caused the strong ground motion and thus contributed to the damage in and around Kathmandu.
The HBP image seems to be somewhat spiky compared to other BP images (e.g., the BP image by IRIS). In general, the spatial resolution becomes high with the broad spread azimuth of stations [e.g., Walker et al., 2005; Kennett et al., 2014b], and this tendency was observed in our previous work [Okuwaki et al., 2014]. The high‐frequency radiation is related to the complex rupture process, and the spiky HBP image reflects the rapid rupture acceleration and deceleration during the earthquake.
In this study, we integrated a high‐frequency radiation event into the slip‐rate distribution and found that the integrated seismic source model was useful not only for understanding the acceleration and deceleration of dynamic rupture during a large earthquake but also for understanding the heterogeneity of fracture energy or stress level along the fault plane.
Acknowledgments
We thank two anonymous reviewers and the Editor Michael Wysession for their helpful comments. We also thank Bogdan Enescu for the valuable discussions. We used the CMT solution estimated by the GCMT project and hypocenter information estimated by the USGS. Waveform data observed by the Canadian National Seismograph Network, Czech Regional Seismic Network, GEOFON, GEOSCOPE, the Global Seismograph Network (GSN–IRIS/IDA and GSN–IRIS/USGS), the Global Telemetered Seismograph Network (USAF/USGS), the MEDNET Project, the New China Digital Seismograph Network, Pacific21, and the United States National Seismic Network were downloaded through IRIS. Topography data are from the Geographic Information Network of Alaska. This work was supported by JSPS KAKENHI grant 24310133. Figures were created with Seismic Analysis Code and Generic Mapping Tools [Wessel and Smith, 1998].
The Editor thanks an anonymous reviewer for assisting in the evaluation of this paper.
