THE WASSERSTEIN-FISHER-RAO METRIC FOR WAVEFORM BASED EARTHQUAKE LOCATION

doi:10.4208/jcm.2109-m2021-0045

In this paper, we apply the Wasserstein-Fisher-Rao (WFR) metric from the unbalanced optimal transport theory to the earthquake location problem. Compared with the quadratic Wasserstein (W₂) metric from the classical optimal transport theory, the advantage of this method is that it retains the important amplitude information as a new constraint, which avoids the problem of the degeneration of the optimization objective function near the real earthquake hypocenter and origin time. As a result, the deviation of the global minimum of the optimization objective function based on the WFR metric from the true solution can be much smaller than the results based on the W₂ metric when there exists strong data noise. Thus, we develop an accurate earthquake location method under strong data noise. Many numerical experiments verify our conclusions.

Key words: The Wasserstein-Fisher-Rao metric, The quadratic Wasserstein metric, Inverse theory, Waveform inversion, Earthquake location

CLC Number:

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THE WASSERSTEIN-FISHER-RAO METRIC FOR WAVEFORM BASED EARTHQUAKE LOCATION

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