Rapid modeling of the 2011 Mw 9.0 Tohoku-oki earthquake with seismogeodesy

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1 GEOPHYSICAL RESEARCH LETTERS, VOL. 4, , doi:1.12/grl.559, 213 Rapid modeling of the 211 Mw 9. Tohoku-oki earthquake with seismogeodesy Diego Melgar, 1 Brendan W. Crowell, 1 Yehuda Bock, 1 and Jennifer S. Haase 1 Received 22 April 213; accepted 24 May 213; published 18 June 213. [1] Rapid characterization of finite fault geometry and slip for large earthquakes is important for mitigation of seismic and tsunamigenic hazards. Saturation of near-source weak motion and problematic integration of strong-motion data into displacements make this difficult in real time. Combining GPS and accelerometer data to estimate seismogeodetic displacement waveforms overcomes these limitations by providing mm-level three-dimensional accuracy and improved estimation of coseismic deformation compared to GPS-only methods. We leverage collocated GPS and accelerometer data from the 211 Mw 9. Tohoku-oki, Japan earthquake by replaying them in simulated real-time mode. Using a novel approach to account for fault finiteness, we generate an accurate centroid moment tensor solution independently of any constraint on the slab geometry followed by a finite fault slip model. The replay of GPS and seismic data demonstrates that robust models could have been made available within 3 min of earthquake initiation. Citation: Melgar, D., B. W. Crowell, Y. Bock, and J. S. Haase (213), Rapid modeling of the 211 Mw 9. Tohoku-oki earthquake with seismogeodesy, Geophys. Res. Lett., 4, , doi:1.12/grl Introduction [2] The need for more accurate and rapid estimates of the characteristics of large earthquakes has been poignantly illustrated by actual responses to recent great tsunamigenic earthquakes in Sumatra, Chile, and Japan, which relied on traditional seismic methods [e.g., Lay and Kanamori, 211; Hoshiba et al., 211; Cardenas-Jiron, 212]. Broadband seismometers saturate near the source and so magnitude estimation relies on teleseismic waves recorded much later at distant seismic stations [Kanamori and Rivera, 28]. To overcome this limitation, seismic stations are augmented with strong-motion instruments. However, a double integration is required to convert accelerations into displacements, which is unreliable at low frequencies because tilts of the instruments are indistinguishable from translations and any errors are amplified in the integration [Boore and Bommer, 25; Emore et al., 27]. Subjective correction algorithms are available but require the full waveform, and Additional supporting information may be found in the online version of this article. 1 Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA. Corresponding author: D. Melgar, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA, USA. (dmelgarm@ucsd.edu) 213. American Geophysical Union. All Rights Reserved /13/1.12/grl.559 the permanent deformation that accompanies large earthquakes may be filtered out or not estimated correctly in the process [Melgar et al., 213]. [3] The state of the art in seismic monitoring is best illustrated in Japan, which has the world s most advanced earthquake and tsunami early warning system. During the 211 Mw 9. Tohoku-oki earthquake, the system operated as designed [Hoshiba et al., 211] and alerted residents up to a minute in advance that strong ground shaking was imminent. However, early estimates of earthquake magnitude from the Japan Meteorological Agency (JMA) were too low by 1 2 orders of magnitude; an estimate of M 7.2 was determined after 3 s and revised to M 8. by 17 s [Hoshiba et al., 211]. It took 2 min for a reliable estimate of magnitude to be made teleseismically through the W phase method [Duputel et al., 211], which is unable to use near-source data of great earthquakes due to violation of the point source assumption. This requires waiting for long period (1 1 s) seismic waves to propagate to more distant stations. Other real time waveform inversion algorithms which rely on local strong motion data near the source require specific assumptions on source geometry to render the problem tractable and investigate only a limited range of the most dangerous scenario faulting sources [Guillhem et al., 212]. The first tsunami waves arrived near Sendai within 3 min of the main shock, with the early estimates of wave heights underestimated by several meters [Ozaki, 211]. Many of the coastal towns possess seawalls that can protect the residents from moderate tsunamis, but they could not protect against such large waves. A more accurate estimate of wave heights could have resulted from a better estimate of the size and geometry of the earthquake source. Japan also possesses the largest real-time GPS network; the GEONET operated by the Geospatial Information Authority of Japan (GSI) [Miyazaki et al., 1998] with over 12 stations. Real-time GPS can rapidly provide estimates of permanent deformation and considerably reduce the delay time for obtaining source information for large earthquakes [e.g., Crowell et al., 212; Ohta et al., 212; Wright et al., 212; O Toole et al., 213; Hoechner et al., 213], even in regions with low station density such as the great 24 Mw 9.2 Sumatra-Andaman earthquake and tsunami [Blewitt et al., 26]. However, operational early warning systems including the one in Japan have not yet incorporated GPS data into the determination of earthquake magnitude [e.g., Allen et al., 29]. Although GPS observations of megathrust events are limited to on-shore data which limit the resolution of modeled slip close to the trench, the along-strike variations of displacement still make it possible to discern important features of the source for large events, in particular rupture length that control earthquake size. [4] GPS data are significantly noisier than accelerometer data but provide improved resolution at the lower frequencies, 2963

2 Up (m) East (m) North (m) a b JMA 3 s M w 7.2 c JMA 17 s M w 8. GPS GPS+Accelerometer CMT and Slip Inversion 157 s M w NEIC W Phase ~2 min M w 9. d P Wave e P Wave N E U N E U Displacement (mm) Velocity (mm/s) Velocity (m/s).1..1 P Wave f S Wave Time After Origin (s) Figure 1. Typical near-source broadband displacement and velocity waveforms from seismogeodesy. The (a) north, (b) east and (c) up broadband displacements for GEONET GPS station 914 (black circles) and K-NET accelerometer MYG3, 155 km from the JMA hypocenter (location shown in Figure 2). The 1 Hz seismogeodetic solution is shown by the solid lines; the 1 Hz GPS-only solution is shown by circles. The time is seconds from 5:46:18.12 UTC on 11 March 211. Magnitude estimates from the NEIC and JMA are shown in Figure 1b and from the seismogeodetic methods in Figure 1c. (d) The combined displacements for the three components for the first 5 s after the P wave arrival at 24.7 s. We remove a cubic fit from each of the components to clearly show details of the P wave arrival. (e) The combined velocities for the first 5 s after the P wave arrival. (f) The north velocity (solid line) and displacement (dashed line) records up to 9 s after the earthquake start showing the locations of the P and S wave arrivals and the progression of dynamic and static slips Displacement (m) including the static displacement [Melgar et al., 213]. One can combine accelerometer data and GPS displacements to obtain more accurate displacements and velocities in real time, in particular in the critical vertical component [Bock et al., 211]. As with GPS, displacement waveforms can be obtained close to the source without clipping. However, compared to GPS alone, the precision is improved such that small-scale features including P waves are visible in the displacement and velocity records (Figure 1). [5] We use data from collocated regional GPS and accelerometer stations during the 211 Mw 9. Tohoku-oki, Japan earthquake and replay them in simulated real-time mode to estimate broadband displacement and velocity waveforms. We demonstrate the ability to account for fault finiteness by generating an accurate centroid moment tensor solution independently of any constraint on the slab geometry followed by a finite fault slip model. These abilities provide distinct advantages for mitigating earthquake and tsunami hazards. 2. Data [6] We start with data from 785 GEONET GPS stations throughout Honshu and Hokkaido Islands. The GPS phase and pseudorange data are processed in a simulated real-time mode to estimate displacement waveforms using instantaneous relative positioning, where the network is subdivided using Delaunay triangulation, and the data from each triangle are processed independently. Station positions are then referenced to GEONET station 848 on the northern tip of Hokkaido Island, 9 km northwest of the hypocenter. The first waves arrive about 2 3 s after earthquake onset. We then, as described in Bock et al. [211], combine the GPS displacements with data from 138 accelerometers in the K-NET and KiK-net networks operated by Japan s National Research Institute for Earth Science and Disaster Prevention (NIED) [Aoi et al. 24] that are within 1.5 km of a GPS station; we refer to the resulting displacement and velocity waveforms as seismogeodetic. The displacements contain an unprecedented view of the progression of dynamic ground motion to the final static offsets (Figure 1) from, for example, a collocated GPS instrument (GEONET 914) and strong-motion accelerometer (K-NET MYG3) about 155 km northwest of the 211 Mw 9. Tohoku-oki epicenter (Figure 2). 3. Rapid Source Modeling 3.1. Line-Source CMT Solutions [7] Rapid earthquake response is predicated on discerning the geometry and location of the seismic source. Two recent events illustrate that one cannot simply assume that all large 2964

3 MELGAR ET AL.: RAPID MODELING WITH SEISMOGEODESY GPS/Accelerometer station fastcmt inversion node fastcmt moment release Direction of slip 44 fastcmt GCMT km km Slip(m) 1 ΔSlip(m) Seismogeodesy - GPS Figure 2. (a) fastcmt and slip inversion results. Green circles are the point sources superimposed to compute the line source of CMT solutions, the final averaged solution shown as fastcmt, and the Global CMT solution (GCMT) shown for comparison. The inset shows the moment release from the line source as a function of distance along fault. Shown along the fault interface with 1 km depth contours from the Slab 1. model [Hayes et al., 212] is the result of the slip inversion; the blue lines represent the direction of slip. The triangles indicate the locations of all the GPS/accelerometer stations used for computing the slip inversion and CMT solution. The two large triangles represent the fixed GPS station (848, red) and the GPS/accelerometer pair (914/MYG3, blue) shown in Figure 1. (b) Difference between slip inversions computed using the seismogeodetic displacements compared to the inversion carried out using the GPS-only derived displacements. Red indicates more slip with the seismogeodetic solution, and blue indicates more slip with the GPS-only solution. earthquakes in a subduction setting rupture the megathrust. The Mw 8.6 event off Sumatra, Indonesia, on 11 April 212 [Satriano et al., 212] was a predominantly strike-slip event and the Mw 8.1 Samoa event on 29 September 29 was a normal faulting, outer-rise type event that produced a tsunami with 189 fatalities [Okal et al., 21]. Therefore, our first step is to estimate a CMT solution for the earthquake to determine the style of faulting (e.g., strike, dip, and rake) and magnitude. Near real-time waveform inversion CMT algorithms [e.g., Dreger, 23] are usually based on regional velocity recordings that clip in the near field of high magnitude events or acceleration recordings which are difficult to integrate to displacements in real time. [8] Using the seismogeodetic displacements from the 138 collocated GPS and accelerometer stations, we employ the fastcmt algorithm, which uses a trailing variance technique, to quickly determine final static offsets from high-rate data [Melgar et al., 212] at 157 s after rupture initiation and invert for the moment tensor. Note that the rupture duration has previously been determined to be ~18 s [Shao et al., 211]. We first assumed a point source approximation. However, it yielded a solution with an unreasonably high magnitude (> 9.5) and poorly located centroid due to the fact that the spatial extent of slip is too large [Guillhem et al., 212]. To account for source finiteness, we extend the fastcmt algorithm to a linear geometry by superposition of point sources. This is straightforward because static deformation modeling has no temporal dependence. We invert for several moment tensors (MTs) at predefined points along the line source, and perform a grid search for the proper line azimuth and spatial location. We assume that the Green s functions (GFs) are predetermined at inversion nodes on a.1 by.1 by 2 km in depth grid to cover all of Japan with the same strategy as originally described in Melgar et al. [212]. The line source length is 7 with 3 point sources; in practice, these values must be chosen a priori according to the observational goals of a particular network. We then solve the minimization problem minfkwgm Wd k þ lklmkg; (1) where m is the source model, G the GFs, L the smoothness matrix, l the smoothing parameter, and W the data weights computed as the inverse of standard deviation of 6 s of pre-event noise. It must be noted that W is different for GPS-only and seismogeodetic solutions. For GPS-only displacements, the computed weight is smaller for the noisier vertical direction estimate than for the seismogeodetic displacements, where after combination with accelerometer data, the noise in the vertical direction is significantly reduced. The inversion scheme is L1-norm minimizing with first order Tikhonov smoothing for the five deviatoric MT components. This regularization is applied to each of the five components of the MT with regard to the same component of the neighboring MTs along the line direction. Thus, sharp variations in a particular component of the MT 2965

4 between neighboring point sources are penalized. We also experimented with L 2 inversions but found that they yielded results that were too smooth and did not bracket the main asperity; as in Melgar et al. [212], we find L 1 -norm minimization more favorable. The procedure to determine the line location and azimuth and the critical smoothing parameter l in (1) is discussed in the supporting information (Figure fs1). The final inversion yields a variance reduction [Melgar et al., 212] of 84% with the GPS data alone and a slight improvement to 86% with the seismogeodetic displacement data. We contend that this marginal improvement is in part due to the one-dimensional nature of the line source, which does not account for along dip variations in moment release. [9] Next, we compute the weighted average of all individual moment tensors over the line source and place the average moment tensor at the location of mean moment release to obtain a single CMT estimate (Figure 2). Note that no a priori information is required on the fault geometry and no assumption that the source is confined to the slab. The process is computationally simple and automatable. For this earthquake we obtain a magnitude of 9., average strike, dip, and rake of 24,3, and 95, respectively, with a source extent of 34 km along strike. The trailing variance technique produces final static offset estimates at 157 s after rupture initiation; our line source CMT solution is then available within several seconds. As a comparison, the USGS ShakeMap and PAGER products were initially released based on point sources [Hayes et al., 211]. The alerts were later updated to a finite fault source after 2 h and 42 min, significantly extending the length of affected coastline [Hayes et al., 211]. Our line source CMT found the correct fault orientation without any a priori information. The initial W-phase CMT inversion found a strike of 23 inconsistent with slab geometry in the area, which delayed the rapid finite fault inversion and ultimately required realignment to the Slab1. geometry [Hayes et al., 212]. Thus, the resulting source extent of 34 km derived from the extended CMT approach is sufficiently close to the final extent and orientation of slip to infer that it would have been of value for guiding the initial release of hazard maps Static Slip Inversion [1] After receiving information on the style of faulting and the centroid from the finite line source fastcmt analysis and determining that it is a thrust event close to the slab, we invert for static slip using the same coseismic offsets and data weights W as in the CMT modeling. For the static slip inversion, we first locate the closest fault segment from the Slab1. model [Hayes et al., 212] to the line source. The fault is then subdivided into 5 km 2 segments, accounting for 3-D geometry of the slab and ensuring all subfaults are quadrangles [Romano et al., 212]. GFs are computed for a homogeneous half-space [Okada, 1985]. We use Laplacian smoothness as L in equation (1). As in the fastcmt solution, an optimal smoothing parameter l * is determined from the maximum curvature of the L-curve (see supporting information, Figure fs2). We constrain the edges and bottom of the fault to zero to avoid non-physical slip distributions in the model (i.e., step-function motion at the edges). The fault segments at the trench are left freely slipping to accommodate shallow slip. The inverse problem is solved by minimizing the L 2 -norm in equation (1). This solution takes several seconds to complete after the line-source CMT solution becomes available. [11] Our model indicates a moment magnitude of 8.9, a slip patch that is roughly 34 km along-strike and 155 km along-dip, and maximum slip of 27 m located near the center of the fastcmt location at 14 km depth. Using seafloor geodetic measurements of displacement outboard of the trench that were surveyed up to a month after the earthquake, static slip inversions produced final estimates of maximum slip closer to 5 m [Sato et al., 211]. However, seafloor geodetic measurements are currently not available in real time and would include some amount of postseismic deformation, so our model is indicative of a realistic real-time scenario using just land-based seismogeodetic data. A joint inversion using far-field seafloor pressure gauge data and GPS offsets was able to produce a maximum slip of 5 m [Simons et al., 211] and could possibly be available in real time in the future, although seafloor pressure gauge data in the near-field records the superposition of seafloor motion and water column changes that may be difficult to separate in real time (D. Chadwell, personal communication, 213). It is, of course, possible to obtain models with higher amounts of slip by reducing the smoothing, but these are not selected under the automated operator-independent L-curve criterion we present here (Figure fs1, fs2). The moment release from the line source fastcmt overlain upon the slip distribution in Figure 2a shows that the slip distribution is bounded by the line source moment release along strike, indicating that both methods independently agree on the spatial extent of slip. The dip of the fastcmt solution (3 ) is larger than the average dip for the slab in the region (~15 ), possibly because of the unmodeled along-dip dimension. This demonstrates the importance of having both the CMT modeling and slip inversion to independently validate results and guide automated response. We also perform the line-source fastcmt approach and slip inversion just using the GPS data for the same stations to investigate any improvements with seismogeodetic data (Figure fs3 in the supporting information). We find that vertical bias (median difference of 18 mm) in the GPS-only slip inversion solution leads to far more deep slip and significantly less shallow slip than the seismogeodetic solution (Figure 2b) and a 4 difference in the average rake (84 for combined data and 88 for GPS-only data). This is due to the improved precision in the vertical offset estimates from seismogeodetic data and greater weights assigned to the improved vertical channel in the inversion, yielding improved along-dip model resolution. The seismogeodetic inversion provides an improved slip inversion. 4. Timeline of Event Analysis From Seismogeodetic Data [12] Streaming data in real time using radio and internet telemetry has a latency of.4 1. s. Baseline positioning is parallelizable because it depends on groups of only three sites and an epoch-by-epoch network adjustment; it requires 1 2s. The seismogeodetic Kalman filter adds another second to the latency. Further improvements in speed and efficiency can be obtained using precise point positioning with ambiguity resolution [Geng et al., 213]. The computation to estimate seismogeodetic waveforms is insignificant compared to source inversion time. 2966

5 [13] Based upon the aforementioned approach and our application to the Tohoku-oki event, we propose the following timeline of effective warnings for an improved seismogeodetic earthquake early warning and rapid response system. The origin time and hypocenter are calculated from first detections of P waves at a subset of seismic or seismogeodetic instruments using existing methodologies. For the Tohoku-oki data set, the time of arrival of P waves at the first stations is 24 s after earthquake initiation. Line-source CMT solutions are initiated based on the displacements exceeding a threshold [Melgar et al., 212] and thus independently confirm, rather than rely on, the seismic network hypocenter. The line-source CMT solutions computed from the coseismic offsets by 157 s after rupture initiation determine an initial magnitude, location, and style of faulting and provide rough constraints on the lateral extent of moment release; the duration of the Tohoku-oki earthquake rupture was ~18 s [Shao et al., 211]. From the line source CMT solutions, we are able to determine an appropriate section of fault to perform a heterogeneous static slip inversion. The slip inversion can run immediately after the CMT computation, so a full heterogeneous slip distribution is determined within seconds of the CMT solution; for this event, the static slip inversion is available within 3 min. [14] After the slip inversion, obvious next steps would include ingestion into ShakeMap, PAGER maps, tsunami forward modeling to ascertain near-field inundation models [Ohta et al., 212], kinematic slip inversions, and further analysis of aftershocks and postseismic deformation. 5. Discussion [15] The success of our approach is predicated on the satisfactory solution of an inverse problem for which the critical determination of the smoothing parameter typically requires operator decision-making. Our simple algorithm (supporting information) adds minimal computational overhead to guide the determination of this critical parameter without human interaction. [16] Rapid earthquake response clearly benefits from nearsource high-density networks that are currently available in Japan and the Western U.S. Even in regions with low station density and proximity such as the great 24 Mw 9.2 Sumatra-Andaman earthquake, important information on the earthquake source can be derived with GPS data alone [Blewitt et al., 26]. Earlier studies have shown that seismogeodesy can significantly improve rapid characterization of finite fault geometry even for networks with sparser station distribution and less favorable geometry [e.g., Bock et al., 211]. For the Tohoku-oki earthquake, model resolution in the along-dip direction is significantly improved with seismogeodetic offset estimates; this is critical for accurate tsunami modeling since it directly impacts vertical seafloor deformation estimates. [17] Considering the review of the sequence of events at the USGS National Earthquake Information Center (NEIC) [Hayes et al., 211], there are several stages where the independent information provided by the seismogeodetic time series could have been helpful for a great event such as Tohoku-oki. Both the NEIC and the Pacific Tsunami Warning Center obtained preliminary teleseismic locations and mechanisms within 5 min of the origin time, but the first public release was delayed until 9.7 min. Independent confirmation of the source size would provide confidence for releasing information earlier. The first two versions of ShakeMap and PAGER alerts were released with the affected areas based on point sources. They were updated to a finite fault source, significantly extending the length of affected coastline after 2 h and 42 min. Our line source fastcmt and slip inversion solutions reproduce the main features of the rupture, approximately 34 km long with average slip of 15 m over the main source region. Early access to this information, which in addition had the correct fault orientation of 24 as opposed to 23 for the rapid finite fault inversion based on the W-phase fault orientation, could provide confidence for earlier release of the finite fault Global ShakeMap. Full integration and combination of GPS into seismic monitoring is essential for a hazard system that is more robust than either traditional seismic or geodetic monitoring alone. Because the fastcmt algorithm does not require assumptions about the fault geometry, it is also applicable to source regions outside subduction zones. The ability to produce seismogeodetic displacement and velocity time series in real time implies that the delay for calculating near real-time kinematic rupture models can also be significantly reduced in the future. [18] Acknowledgments. We would like to thank NIED for access to K-NET and KiK-net accelerometer data and GSI for GEONET GPS data. Suggestions provided by Rob Clayton, Sharon Kedar, and Tim Melbourne are appreciated. We thank two reviewers and the Associate Editor for their feedback. This paper was funded by NASA Grants NNX9AI67G, NNX12AK24G, and NNX12AN55H (Melgar fellowship) and SCEC award All codes used in this study are open source and available at github.com/dmelgarm. [19] The Editor thanks two anonymous reviewers for assistance evaluating this manuscript. References Allen, R. M., P. Gasparini, O. Kamigaichi, and M. Bose (29), The status of earthquake early warning around the world: An introductory overview, Seismol. Res. Lett., 8, , doi:1.1785/gssrl Aoi, S., K. 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