A Rayleigh wave back-projection method applied to the 2011 Tohoku earthquake

GEOPHYSICAL RESEARCH LETTERS, VOL. 39,, doi:10.1029/2011gl050183, 2012 A Rayleigh wave back-projection method applied to the 2011 Tohoku earthquake Daniel Roten, 1,2 Hiroe Miyake, 1 and Kazuki Koketsu 1 Received 31 October 2011; revised 14 December 2011; accepted 14 December 2011; published 18 January 2012. [1] We study the rupture process of the 2011 Tohoku megathrust by analyzing 384 regional strong-motion records using a novel back-projection method for Rayleigh waves with periods between 13 and 100 s. The proposed approach is based on isolating the signal at the selected period with a continuous wavelet transform, and generating the stack using arrival times predicted from detailed fundamental mode Rayleigh wave group velocity maps. We verify the method by back-projecting synthetic time series representing a point source off the coast of Tohoku, which we generate with a 3D finite difference method and a mesh based on the Japan Integrated Velocity Structure Model. Application of the method to K-NET/KiK-net records of the M w 9.1 Tohoku earthquake reveals several Rayleigh wave emitters, which we attribute to different stages of rupture. Stage 1 is characterized by slow rupture down-dip from the hypocenter. The onset of stage 2 is marked by energetic Rayleigh waves emitted from the region between the JMA hypocenter and the trench within 60 s after hypocentral time. During stage 3 the rupture propagates bilaterally towards the north and south at rupture velocities between 3 and 3.5 km s 1, reaching Iwate-oki 65 s and Ibaraki-oki 105 s after nucleation. In contrast to short-period backprojections from teleseismic P-waves, which place radiation sources below the Honshu coastline, Rayleigh wave emitters identified from our long-period back-projection are located 50 100 km west of the trench. This result supports the interpretation of frequency-dependent seismic wave radiation as suggested in previous studies. Citation: Roten, D., H. Miyake, and K. Koketsu (2012), A Rayleigh wave back-projection method applied to the 2011 Tohoku earthquake, Geophys. Res. Lett., 39,, doi:10.1029/2011gl050183. 1. Introduction [2] The M w 9.1 Tohoku earthquake of March 11, 2011, was the greatest event ever recorded in Japan. It resulted in strong shaking across northeastern Honshu and a devastating tsunami, causing massive destruction and approximately 20,000 fatalities. [3] The Tohoku megathrust provided more data than any other earthquake in the history of seismology, and it has been studied using a variety of methods. Waveform inversions using long-period teleseismic P-wave records or regional strong motion data suggest that the slip reached values between 40 and 60 m off Miyagi prefecture [e.g., 1 Earthquake Research Institute, University of Tokyo, Tokyo, Japan. 2 Now at Swiss Seismological Service, ETH Zurich, Zurich, Switzerland. Copyright 2012 by the American Geophysical Union. 0094-8276/12/2011GL050183 Ammon et al., 2011; Koper et al., 2011; Lay et al., 2011; Yagi and Fukahata, 2011; Yoshida et al., 2011]. Static coseismic slip models obtained from inversion of onshore and offshore GPS data are characterized by a slip maximum of 35 50 m in the same general location [e.g., Pollitz et al., 2011; Simons et al., 2011]. However, these studies vary significantly in the placement of maximum slip; Ammon et al. [2011] and Simons et al. [2011] report the largest slip near the JMA hypocenter and a drop-off in slip towards the trench, while Lay et al. [2011], Yagi and Fukahata [2011], Yoshida et al. [2011] and Pollitz et al. [2011] obtain the largest slip close to the trench. Tsunami waveform inversions using records from coastal tide gauges, offshore wave gauges and bottom-pressure transducers are also placing the maximum slip close to the trench off Miyagi prefecture [e.g., Fujii et al., 2011]. To reconcile these differences a joint inversion of teleseismic, local strong motion and geodetic data was performed by Koketsu et al. [2011]. [4] Back-projections (BP) of short-period (1 s) P-wave arrivals recorded on US and EU arrays, on the other hand, are pointing towards radiation sources downdip from the hypocenter beneath the Honshu coastline [e.g., Meng et al., 2011; Wang and Mori, 2011]. It has been suggested that these differences may be explained by frequency-dependent variations in seismic wave radiation, with the long-period energy originating far offshore from the shallow part of the rupture and the short-period energy originating from deeper parts [e.g., Koper et al., 2011; Ide et al., 2011]. [5] However, inversions of geodetic or seismological data have difficulties in resolving the up-dip extent of the rupture [Lay et al., 2011]. Array BP techniques are complementing traditional finite source inversions due to their robustness and independence from assumed Green s functions or restrictive source parameterizations. Therefore, it would be desirable to extend BPs to longer periods to confirm the near-trench location of long-period radiators. In this work we address this problem by introducing a BP of Rayleigh waves at periods between 13 and 100 s using K-NET and KiK-net data. 2. Back-Projections at Teleseismic, Regional and Local Distances [6] In BP studies, seismic sources are identified by stacking waveforms along predicted travel-times for an assumed grid of source locations. The central requirement is that the selected phase represents the arrival with the highest amplitude. BPs from teleseismic data are using P-wave arrivals [e.g., Krüger and Ohrnberger, 2005; Ishii et al., 2005], which offers a time window of up to 10 minutes to track the rupture without interference from the more energetic S-waves. At local distance, where the delay between P- and S-wave arrivals amounts only to a few seconds, S-wave 1of6

Figure 1. (a) Frequency B-spline wavelet employed for continuous wavelet transform at (left) a period of 20 s and (right) its corresponding magnitude spectrum. (b) CWT envelopes for T = 13 s computed from simulated U-D velocities of 14 stations along a NE-SW cross-section through southern Honshu (as shown on inset map). Numbers below station names show epicentral distance. Letters above the envelopes indicate the expected arrival time of S-waves and Rayleigh waves (LR) for a period of 13 seconds. arrivals may be used [e.g., Allmann and Shearer, 2007]. This approach is successful because most phases have either smaller amplitude than S or have not yet fully developed at local distance. [7] However, the method breaks down at epicentral distances exceeding about 150 km, where the refracted phases (such as Sb or Sn), which usually have small amplitude, arrive ahead of the direct Sg phase [Kao and Shan, 2004]. This is the case for the 2011 Tohoku earthquake, where the vast majority of K-NET and KiK-net stations are outside the 150 km radius from the epicenter. Furthermore, the crustal phase Lg (a wave group caused by superposition of multiple S-wave reverberations inside the whole crust), which carries substantial energy, arrives just a few seconds after S [Furumura and Kennett, 2001]. For this reason we decided against using the S-wave first arrival for the BP, as it does not represent the phase with the highest amplitude. Instead, we aim to perform a BP using surface waves, as they contain more energy than other phases at regional distance. 3. Method [8] Since surface waves are dispersive, we propose to extract the signal at the period of interest T using a continuous wavelet transform: wt k ðs; t Þ ¼ p 1 ffiffi s Z x k ðþy t t t dt: s ð1þ 2of6

[10] Since wt k is complex and contains both the phase and the amplitude of the signal, coherent phases will be amplified and incoherent phases will be canceled out, as is the case when stacking in the time domain. d m,k is the traveltime of the analyzed phase from source k to receiver m; itis dependent on the scale s in the case of dispersive surface waves. d m,k is derived from the Rayleigh wave fundamental mode group velocity at the analyzed period (Figure S1 in the auxiliary material), which is computed from the Japan Integrated Velocity Structure Model (JIVSM) [Koketsu et al., 2008]. 1 p m,k is a taper dependent on source-receiver distance, which helps to reduce migration artifacts [Allmann and Shearer, 2007]. w m,k denotes an azimuthal weighting factor which compensates for the irregular station distribution: 1 w m;k ¼ XN i¼1 1 jj m;i J m;k j DJ ð4þ for jj m;i J m;k j < DJ; where J m,k is the azimuth of the path between source m and station k. Azimuthal weighting works by reducing the weight of a station depending on the number of other stations that have a similar azimuth to the assumed source m, and is controlled by the azimuthal taper DJ. Figure 2. Results of Rayleigh wave back-projection at T = 13 s applied to radial-component synthetic time series of a point source. Color maps show the stack amplitude for different times, with t = 0 corresponding to the true hypocentral time. The amplitude was normalized to the maximum amplitude encountered during the back-projection; numbers in the lower right corner indicate the maximum stack amplitude during each snapshot. The yellow star shows the true epicenter of the point source. In the above expression, x k (t) represents the velocity time series at station k, y* is the conjugate complex of the wavelet and s is termed scale. For the wavelet y we chose a frequency B-spline [e.g., Gao and Yan, 2010]: y B ðþ¼ t p ffiffiffi f b t p f b sin c e i2pfct ; ð2þ p where f b is the bandwidth parameter, f c the wavelet center frequency and p 2 an integer parameter. We chose f c =1Hz to make the scale s in equation 1 equivalent with the analyzed period T, and we used f b = 2 Hz and p = 2. Figure 1a shows a frequency B-spline scaled with a factor of 20, which was employed to calculate the CWT at a period of 20 s. [9] For the mth source location, the CWTs are summed up over all stations N to make the stack as a function of time t: S m ðs; t Þ ¼ XN k¼1 2 wt k s; t þ d m;k wm;k p m;k : ð3þ 4. Verification and Validation [11] We verified the proposed method by back-projecting synthetic time series representing a point source off the coast of Tohoku, using the location of the M w 7.2 foreshock of March 9. Synthetic data were obtained by running a 3D finite difference (FD) simulation [Olsen et al., 2006] on a 1575 2825 630 km 3 mesh representing the JIVSM. We used a spatial step of 400 m, a time step of 0.02 seconds, and a minimum shear-wave velocity of 1 km s 1. With this configuration, frequencies of up to 0.5 Hz can be simulated using at least five points per wavelength. We generated synthetics for all the 809 locations that recorded the M w 9.1 event. [12] Figure 1b shows CWT envelopes for T = 13 s computed from the simulated U-D velocities at 14 stations located along a NE-SW cross-section through southern Honshu. The passage of the Rayleigh wave is clearly visible by a distinct peak in the CWT envelope at each station. At this period, the wavefield is entirely dominated by Rayleigh waves. We performed the BP on radial-component CWTs using a grid of 3,686 assumed sources with 10 km spacing, covering the area from the trench to 100 km inland. Figure 2b shows the stack amplitude for the hypocentral time (t = 0 s). The location of the maximum array output is very close to the source used for the FD simulation. For t = 20 s (Figure 2a), the array produces a ghost peak located 50 km ESE of the true hypocenter. Similarly, a ghost peak is visible closer to the shore at t = 20 s (Figure 2c). These ghost peaks are consequences of the limited azimuthal distribution provided by the K-NET/ KiK-net array. However, the array yields the highest stack amplitude for the true source time and location. We experimented with different azimuthal weightings and distance taperings to reduce these artifacts, and found that an azimuthal taper of DJ = 25 helps to reduce ghost peaks. However, azimuthal weighting generates artifacts for sources located within the array. We addressed this problem by 1 Auxiliary materials are available in the HTML. doi:10.1029/ 2011GL050183. 3of6

Figure 3. Same as Figure 2, but showing BP results at T = 20 s for the Tohoku earthquake. The yellow star shows the JMA epicenter, and t = 0 corresponds to the JMA hypocentral time. setting the distance-dependent taper p m,k to zero for stations located within 100 km from a source. Conversely, azimuthal weighting alleviates the need for tapering off stations at distance from an assumed source. Additionally, we excluded 425 stations located on thick sedimentary deposits from the back-projection to reduce problems related to reverberations of surface waves in deep basins. Figure 2 shows the remaining 384 stations employed for the BP. While these measures help to reduce ghost peaks, they can not be entirely eliminated. Any point source will still be represented by a peak migrating approximately from ESE to WNW, which means that K-NET/KiK-net array provides better resolution is the along-trench direction than in the dip direction. [13] Figure S2 of the auxiliary material shows the theoretical array response function for the 384 employed stations and the JMA epicenter of the M w 9.1 event. In Figure S3 we show the results of a validation against recorded seismograms of an M w 6.5 aftershock, using an array of 284 K-NET/ KiK-net stations. A further verification was performed with synthetic seismograms representing a finite source, which we obtained by simulating a rupture propagating southwards (Figure S4 and Movie S1 of the auxiliary material). 5. Back-Projection of Tohoku Earthquake [14] We applied the procedure described above to 384 K-NET/KiK-net records of the M w 9.1 Tohoku earthquake of March 11. Figure 3a shows the stack amplitude at t = 10 s (relative to 14:46:18 JST) for a period of 20 s. A local maximum in the array output occurs just SW of the JMA epicenter (yellow star in Figure 3), indicating the first stage of rupture (stage 1). However, larger amplitudes are obtained near the trench, which represent artifacts related to the second stage of rupture (stage 2). At t = 33 s (Figure 3b), two distinct peaks are visible NE and SE of the JMA epicenter. The southern peak provides the maximum array output after 33 s at (143.25 E, 37.66 N), while the northern peak reaches its maximum at t = 39 s (Figure 3c). At this time two more ghost peaks emerge, representing the third stage of rupture (stage 3). The signal to the north peaks at t = 61 s off Iwate prefecture (Figure 3d), and the southern segment of stage 3 produces the maximum amplitude at t = 124 s in the Fukushima-oki region (Figure 3e). Movie S2 in the auxiliary material shows the entire sequence of images in 1 s intervals. [15] We repeated the procedure for periods of 13, 30, 50, and 100 s. From the resulting BP images we identified Rayleigh wave emitters based on the assumption that each ESE-WNW migrating peak represents a stationary emitter, and that the true location and time of each emitter coincides with the location and time where the migrating peak reaches its maximum. The results are summarized in Figure 4a and Table S1. For T = 30 s two emitters related to stage 2 were identified, with the first subevent located close to the trench in the Miyagi-oki region at t = 38 s, and the second subevent close to the JMA epicenter at t = 55 s. At periods of 50 s and 100 s, stage 2 is only represented as a single broad peak in BP images due to the longer wavelengths. However, the southern segment of stage 3 is clearly visible at all the analyzed periods. (Figure S5 in the auxiliary material shows stack amplitudes obtained for T = 50 s.) [16] BPs performed at periods of 30 100 s are resolving one emitter associated with the southern segment of stage 3, located 50 km from the trench and 100 km off southern 4of6

Figure 4. (a) Rayleigh wave emitters identified from BP of radial-component seismograms of the Tohoku earthquake using periods of 100 s (triangles), 50 s (diamonds), 30 s (squares), 20 s (hexagons), and 13 s (spheres). Symbol colors indicate source time relative to the JMA hypocentral time, and symbol sizes (defined as the diameter of circumscribed circle) reflect stack amplitude. The yellow star shows the JMA epicenter. The location of the Japan trench along the identified emitters is indicated by the dark red front. (b) Rupture time versus epicentral distance of Rayleigh wave emitters. Fukushima prefecture (Figure S2 b, Figure 4a). Additionally, at 20 and 13 s a further source is identified below the shoreline in the Fukushima-oki region, which was activated between 120 and 130 s after nucleation. Stage 1 and the northern segment of stage 3 are not identified at periods above 30 s. 6. Discussion and Conclusions [17] The spatial and temporal distribution of the identified Rayleigh wave emitters allows us to create a coarse picture of the rupture process and estimate rupture velocities (Figure 4a and 4b). During the initial stage the rupture was propagating down-dip at 2 3.5 km s 1. This stage must have been accompanied by an up-dip component as well, which initiated stage 2 of rupture after approximately 35 s. The onset of stage 2 is marked by radiation of long-period surface waves within 50 100 km of the trench at the height of northern and southern Miyagi-oki (38.5 N and 37.75 N, respectively). The rupture was then propagating down-dip from the trench, releasing energetic Rayleigh waves from near the hypocentral area between 40 and 60 s after initiation. This stage of rupture produces the highest amplitudes in the BP images. We also observe propagation towards the north during stage 3, accompanied by release of Rayleigh waves with periods of 30 s or less off southern Iwate prefecture (39.25 N). The rupture reaches Fukushima-oki between 85 and 105 s after nucleation. Rupture velocities during the bilateral propagation between stages 2 and 3 are in the range of 3 to 3.5 km s 1 (Figure 4b). [18] Stage 3 of rupture was followed by a down-dip component, accompanied by radiation of shorter-periods signals ( 20 s) below the shoreline off Fukushima-oki. The distribution of identified subevents suggest that the earthquake ruptured at least 400 km along the trench (Figure 4a). [19] These rupture characteristics are, in general, in agreement with results of finite source inversions, which place the maximum slip near the epicentral area [e.g., Koketsu et al., 2011; Ammon et al., 2011; Simons et al., 2011]. The overall progression of the rupture, with a weak initial stage, a strong stage 2 and bilateral rupture during stage 3, is also consistent with other studies [e.g., Yoshida et al., 2011; Yagi and Fukahata, 2011; Koketsu et al., 2011]. However, these studies report the peak moment release between 60 80 s after nucleation, while our Rayleigh wave BP images yield the highest amplitudes between 33 and 55 s after nucleation, depending on the analyzed period. Similarly, our BP results suggest rupture velocities of 3 3.5 km s 1 during the bilateral stage, while Koketsu et al. [2011] and Yagi and Fukahata [2011] report only 2.5 km s 1. BPs performed at 50 100 s suggest that the energy radiated during stage 3 amounts to 36 56% of the amount released during stage 2 (Table S1). Such a strong contribution from the southern segment has not been reported by long-period finite fault inversions. This discrepancy may be explained by a source directivity effect, which could amplify the array output for sources in the south, as we observed for the verification with a finite source (Figure S3). [20] In contrast to BP studies performed at periods of 1 to 10 s [e.g., Meng et al., 2011; Simons et al., 2011; Koper et al., 2011; Wang and Mori, 2011], which located sources mainly at the down-dip edge of the fault, emitters identified from our long-period BP are mostly located within about 100 km of the trench. This result supports the interpretation of frequency-dependent seismic wave radiation suggested by Koper et al. [2011] and Ide et al. [2011]. An exception to this rule is represented by the source in the Fukushima-oki region at (141.0 E, 36.6 N) (Figure 4a), which we identified from BPs at periods of 13 and 20 s between 116 and 124 s after nucleation. This source was also identified in the high-frequency BP of Meng et al. [2011], and directly observed in strong-motion records by Simons et al. [2011]. 5of6

[21] In conclusion, the Rayleigh wave BP method proposed in this study provides a simple and robust way to characterize the key features of the megathrust event. It only requires a group velocity map and does not depend on a source parameterization. It is computationally inexpensive, and BP images can be generated within a few minutes if the travel times for a grid of assumed sources have been precomputed. Since this type of BP does not depend on teleseismic data, it could potentially be applied for a rapid analysis of offshore events within minutes after their detection. The obvious disadvantage of the method lies in the rather low temporal and spatial resolution due to the long periods and wavelengths of the analyzed phases. A further problem consists in the apparent migration of sources, which reduces resolution in the along-dip direction. These artifacts are a consequence of the limited azimuthal coverage of the K-NET/KiK-net array, which also poses a challenge to other source characterization methods. [22] Acknowledgments. This research was supported by a short-term fellowship for foreign researchers (to D. Roten) from the Japanese Society for the Promotion of Science (PE10061). The authors are grateful to NIED for providing K-NET and KiK-net strong motion data. We used hypocenters determined by JMA. Maps shown in this article were generated with GMT [Wessel and Smith, 1998]. We used the AWP-ODC [e.g., Olsen et al., 2006; Cui et al., 2010] FD code to produce synthetic time series. The 3D FD simulations were run on the Cray XT5 Monta Rosa of the Swiss National Supercomputing Centre. We used the gpdc tool of the geopsy software package for the computation of group velocities. We thank two anonymous reviewers for their valuable suggestions, which helped to improve the manuscript. 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Irikura (2011), Source process of the 2011 off the Pacific coast of Tohoku earthquake inferred from waveform inversion with long-period strong-motion records, Earth Planets Space, 63, 577 582. K. Koketsu and H. Miyake, Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo, 113-0032, Japan. D. Roten, Swiss Seismological Service, ETH Zurich, Sonneggstr. 5, CH-8092 Zurich, Switzerland. (daniel.roten@sed.ethz.ch) 6of6