Wasserstein Distance (W2) Gradient-based Multi-Point-Source (MPS) Inversion

In seismology, a misfit function is commonly used to quantify the similarity between recorded and model-predicted waveforms. In comparison with the L2 norm, the Wasserstein distance (W2 norm) mitigates the “cycle skipping” problem and offers a more effective waveform similarity measurement for optimization purposes. The W2 norm avoids local minima and enables efficient gradient-based methods to be adopted in waveform inversions. In this study, we develop an algorithm based on W2 norm for multi-point-source models of large earthquakes. We employ Basin Hopping and L-BFGS-B for global and local optimizations, respectively, to invert for the locations, times, moments, and focal mechanisms of multiple point sources to describe the rupture processes of large earthquakes.We develop a novel method that combines W2 and L2 norms to avoid non-uniqueness and enhance the robustness and accuracy of the inversion process. Comprehensive synthetic tests are conducted to demonstrate the good performance in waveform fitting accuracy, computational efficiency, and inversion stability for multi-point-source parameters. Application to the 2016 Mw 7.0 Kumamoto earthquake shows promising results in effectively balancing accuracy and computational demands while characterizing the event's complex rupture process. Our inversion method provides a rapid and effective multi-point-source inversion tool that can deliver reliable constraints on earthquake rupture processes.