We developed a new method to invert surface wave dispersion data directly for 3-D variations of shear wave speed, that is, without the intermediate step of phase or group velocity maps, using frequency-dependent ray tracing. Our method takes into consideration the off-great-circle path effect of short period surface waves and the spatial correlation of adjacent nodes, compared to conventional two-step methods. The application to Taipei Basin show its robustness by imaging the low shear velocity zone related to the basin, which is very important for ground motion simulation and thus hazard mitigation (Fang et al., 2015). Code is available at my GitHub site.

Seismic body and surface wave data have complementary strengths in constraining the velocity structure, with body and surface wave data sensitive to deep compression and shallow shear wave velocity, respectively. Based on the direct inversion of surface wave data, we proposed to jointly invert both body and surface wave data to better constrain the Vp and Vs structure, and thus Vp/Vs ratio, which can put more tight constraint on the lithology, partial melting, porosity and so on (Fang et al., 2016).

Velocity model can be downloaded here. Code is available upon request.

Depth phases are important to obtain the depth of earthquakes. In this study, we apply the auto-correlation technique to extract depth-phase signals using tele-seismic data with magnitude goes down to Mw4.0. This leads to better constraints on the depth of intermediate-depth earthquakes as well as the Vp/Vs ratio near the source region.

Earthquake rupture process can be constrained by tracking the high frequency radiation using back projection (BP) method. However, it is nontrivial to choose a window length using frequency domain based BP method, since large window length leads to low time resolution, whereas short window may cause signal leaking. Taking advantages of the multi-scale resolution of wavelet transform, we developed a wavelet-based method to image the rupture process of large earthquakes. We apply the method to the 2011 Tohoku earthquake and find structure controlled radiation distribution, with radiation sources mostly limited in high wavespeed (velocity weakening) region and little radiation in low wavespeed (velocity strengthening) region (Fang et al., 2018).

Seismic inverse problems, including seismic tomography, are mostly intrinsically both over and under-determined and need to incorporate a pri-ori information, via regularization terms, to obtain physically plausible results. The subjective regularization terms, such as damping and smoothing, are usually chosen subjectively and could lead to bias in the results. Assuming the velocity model is located in a certain low dimension subspace, which is post pri-ori information from trans-dimensional tomography, we directly solve the inverse problem in the low-dimensional subspaces, which are formed by Possion Voronoi cells. We validate this method by applying it to the southern California plate boundary region by imaging the along-strike variation, which is not clearly seen using conventional method. More importantly, this method allows us to roughly estimate the uncertainty, which is critical in geological interpretation. The method is very efficient and can be extended to global tomography, where trans-dimensional tomography is still computation prohibitive (Fang et al., 2019). Code is available at my GitHub site.