Rapid calculation of a Centroid Moment Tensor and waveheight predictions around the north Pacific for the 2011 off the Pacific coast of Tohoku Earthquake
 Jascha Polet^{1} and
 Hong Kie Thio^{2}Email author
https://doi.org/10.5047/eps.2011.05.005
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2011
Received: 5 April 2011
Accepted: 7 May 2011
Published: 27 September 2011
Abstract
We present the results of a near realtime determination of a Centroid Moment Tensor for the 2011 Tohoku quake and the subsequent rapid prediction of Pacific coast tsunami waveheights based on these CMT parameters. Initial manual CMT results for this event were obtained within 23 minutes of origin time and fully automatic results were distributed by Email within 33 minutes. The mechanism, depth and moment magnitude were all well constrained, as was indicated by a bootstrapping analysis. Using an existing library of tsunami Green’s functions, we computed predicted waveheights in the north Pacific for several scenarios of the Tohoku earthquake that are consistent with the CMT solution. Overall, these predicted waveheights correspond well with preliminary observations around the Pacific Rim. The predictions for North America were sent out three and a half hours after the origin time of the earthquake, but this system has the potential to provide these predictions within minutes after receiving the CMT solution.
Key words
1. rCMT
The rCMT (research CMT) system computes fully automated Centroid Moment Tensors (CMTs) for large worldwide earthquakes using long period surface waves and is currently operational at the National Earthquake Information Center (NEIC) of the United States Geological Survey (USGS) in research/evaluation mode. One of the missions of the USGS NEIC is to rapidly determine the location and size of all destructive earthquakes worldwide and to immediately disseminate this information to concerned national and international agencies, scientists, and the general public. The rCMT system’s main purpose is to calculate very rapid reliable moment magnitude estimates and mechanisms for earthquakes greater than 7.0 without the requirement of a human operator, in order to help assess the appropriate level of NEIC response after a large global earthquake, both in terms of the needed response staff and the level of urgency in generating and reviewing derived data products such as PAGER (Earle et al., 2009) and ShakeMap (Wald et al., 2003) that provide impact estimates. The method used to compute the CMTs is based on Dziewonski et al. (1981), as also used by the Global CMT group, but input waveforms are filtered to 130 to 330 s. We calculate excitation kernels for 6 independent components of the moment tensors generated by summation of normal modes. A synthetic seismogram is a linear combination of these six traces and the goal of the inversion is to find the weights that give the best agreement between the observed and synthetic seismograms. A least squares condition leads to an initial estimate of the moment tensor. In the full CMT inversion, the initial, hypocentral, parameters (location/origin time) are then perturbed in subsequent iterations. More information about the basic inversion methodology may be found in Kawakatsu (1989) and Polet and Kanamori (1995). An Email list is used to distribute these rCMT solutions, (http:// geohazards.cr.usgs.gov/mailman/listinfo/researchcmt).

The effect of 3D heterogeneity is minimized, so 1D mode synthetics, involving only relatively few normal modes, can be used. The synthetics can thus be computed very quickly.

The directivity effects are limited for events with magnitude < 8.5, so a point source approximation is appropriate.

Large aftershocks can still be analyzed, in cases where body wave techniques suffer from interference effects from the mainshock surface waves.

Surface waves need to travel some distance before they are fully developed and closein stations may be clipped, so we do not use stations at distances less than 10° from the earthquake.

Long period surface wave inversions for very shallow dipslip sources are illconditioned, such that moment and dip are difficult to resolve independently (e.g. Kanamori and Given, 1981).
The rCMT method uses data with a similar period range as the Wphase moment tensor (Hayes et al., 2009), also in use at the NEIC, but its input signal is dominated by the surface waves, which arrive later and are of higher amplitude. Therefore, the rCMT requires a longer time window, but can also determine CMTs for large aftershocks, when the body wave signal (and thus the Wphase) may still be buried by the surface waves from a previous large event, such as some of the large aftershocks in the first day after the Tohoku mainshock. These methods also differ in the use of an inversion for centroid location (in the case of rCMT) as compared to the Wphase grid search approach.
2. rCMT Results for the Tohoku Earthquake
3. Rapid Prediction of Offshore Waveheights
We have developed a method for Probabilistic Tsunami Hazard Analysis (PTHA) (Thio et al., 2010) based on the summation of subfault tsunami Green’s functions for subduction zones along the Pacific Rim. The library of Green’s functions that was developed for this purpose also enables us to quickly compute offshore waveheights for earthquake scenarios, including the recent Tohoku event.
The underlying principle for this approach is the linear behaviour of tsunami waves in deep water. This enables us to deconstruct a tsunami that is generated by an earthquake into a sum of individual tsunami waveforms (Green’s functions) from a set of subfaults that adequately describes any significant earthquake rupture. By precomputing and storing the tsunami waveforms at points along the coast, as generated by each subfault for a unit slip (1 m), we can efficiently synthesize tsunami waveforms for any slip distribution by summing the individual subfault tsunami waveforms (weighted by their slip). The same principle is used in the inversion of tsunami waves for earthquake rupture (e.g. Satake, 1995) as well as the NOAA Shortterm Inundation Forecast for Tsunamis (SIFT, Gica et al., 2008) system. The database of Green’s functions was originally developed for PTHA studies, for which the desired location of the waveheights was offshore at depth of 5–30 m. These waveheights might therefore slightly underpredict the actual shoreline waveheights.
The efficiency of this method enables us to quickly generate a suite of tsunami waveheight predictions from possible scenarios that are consistent with the initial moment tensor solution, within minutes after receiving it. In this case, we sent out the waveheight predictions 3 1/2 hours after of the origin time. Had the system been automated, or even streamlined, the waveheight predictions could have been sent within minutes of completion of the rCMT solution. Therefore, the rCMT timelines for the Tohoku earthquake illustrate the potential for determining tsunami height estimates within 30 minutes after large global earthquakes (although of course this time also depends on the GSN station coverage near the earthquake) and thus for regional tsunami warning.
4. Conclusion and Discussion
The automated rCMT system provided an accurate estimate of the magnitude and mechanism of the 2011 Tohoku earthquake within 35 minutes of the earthquake origin time. By combining the automated rCMT procedure with tsunami Green’s function summation techniques, we were able to rapidly predict tsunami waveheights along the Northern Pacific Rim, even though the tsunami calculation has not been automated yet. Due to the use of precomputed Green’s functions, the range of solutions that may be computed in a very short period of time is large, and a next step is to incorporate variability based on the rCMT bootstrapping results. We are also considering the use of a set of scenarios with heterogeneous slip, based on a systematic analysis of rupture models of previous megathrust earthquakes. These enhancements will provide a distribution of expected maximum waveheights, which can be updated and refined as more constraints on the rupture model or observed waveheight data become available.
Declarations
Acknowledgments
We thank two anonymous reviewers and Gavin Hayes for their helpful suggestions to improve this manuscript. The rCMT part of this project was supported by the US Geological Survey. We would also like to thank Paul Earle at the NEIC for his help with rCMT.
Authors’ Affiliations
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