CMT inversion

INTRODUCTION

This inversion model aims of simplified the earthquake source inversion process by GPS static data. I further test the stability and efficiency of this inversion process.

The March 27 M_w6.0 Nantou earthquake, or 0327 Nantou earthquake, the June 2 M_w6.3 Nantou earthquake, or 0602 Nantou earthquake and the October 31 M_w6.3 Ruisui earthquake are in this model testing.

METHOD

In contrast to the traditional dislocation model, the model parameters in CMT inversion could be significant reduced to M(m_ij,x_k), where m_ij are the 6-linear independent terms of moment tensor, are the x_k3-dimensional source location. With total 9 parameters, we could simply reveal the earthquake properties, including the moment magnitude, earthquake location, and the focal mechanism. Considering our stations are close enough to the seismic source, our observations could be represented by following Stoles equation:

Notice that this equation simplifies the contribution of dynamic wave (e.g. P and S-wave) and the rupture properties (e.g. rupture speed) with assumes that the time after earthquake origin t>tc , where tc is the sum of rupture duration and the maximum transition time between source and observation. That is, when t>tc , we can eliminate all the dynamic effects of source, which usually hard to determine and make the calculation more complex in near-field. Without dynamic behavior and the time information, this equation could simply represent the pure permanent displacements on surface and directly reveals the "final" moment release of earthquake source.

The inversion matrix, G[j * i] where j and i represents the number of observations and the index of moment tensor, respectively. Index k denotes the typical E/N/U-component in observations.

Given a source location, the Green's function can easily be extracted by the frequency-wavenumber method. (see, Zhu, L., & Rivera, L. A. (2002). A note on the dynamic and static displacements from a point source in multilayered media. Geophysical Journal International, 148(3), 619-627.) However, the source location is unknown, thus, we should test all the "possible" location of the source and compare all the misfit of the solutions. The best solution would be the point where has minimum misfit.

DATA

Total 18-cGPS stations for Nantou earthquakes and 22 stations for Ruisui earthquake are selected to evaluate coseismic/permanent displacements.

All stations (1 Hz/30 sec & and 20 Hz band cGPS) in this research

Time series for Nantou events (shows East component only)

Furthermore, high-rate GPS solutions are clearly observed the dynamic displacements for Ruisui earthquake, which include the body wave and permanent displacement.

RESULTS

(1)GPS daily solution

Comparing GPS-based inversion and the results from GCMT and CWB, which evaluating focal mechanism by broadband far-field data and strong motion data, respectively.

Red beach balls show the GPS-based inversion model for three events. Gray lines indicate the confidence interval for fault plane of 95%, red shadows denote the best solution (minimum misfit) of all solutions.

Furthermore, high rate GPS inversion successfully evaluate a stable solution with only 10 sec after earthquake occurred, showing the power of GPS-based inversion and strengthen the concept of earthquake early warning (EEW) or tsunami early warning. This model also overcomes the near-field clipping problem in velocity instrument and the drifting problem in accelerometer, and could provide the true displacements in near field, which is important for earthquake property study. Take Ruisui earthquake for example, the inversion results indicate the asperity of this earthquake was generated <10-sec, which could provide a great constrain for finite source inversion.

(2)GPS high-rate(1 Hz) solution

MORE WORKS

M6.8 Chungkung earthquake, Taiwan.

Aug. 24, 2014 California earthquake

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