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Datong Zhou1, Jing Chen1, Hao Wu1, Dinghui Yang1, Lingyun Qiu2,3   

  1. 1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
    2. Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China;
    3. Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China
  • Received:2020-02-11 Revised:2021-05-17 Published:2023-03-14
  • Contact: Hao Wu,
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871297, 11971258, U1839206), the National Key Research and Development Program of China on Monitoring, Early Warning and Prevention of Major Natural Disaster (Grant No. 2017YFC1500301), and Tsinghua University Initiative Scientific Research Program. The authors are indebted to Prof. Y. Brenier for his helpful discussions.

Datong Zhou, Jing Chen, Hao Wu, Dinghui Yang, Lingyun Qiu. THE WASSERSTEIN-FISHER-RAO METRIC FOR WAVEFORM BASED EARTHQUAKE LOCATION[J]. Journal of Computational Mathematics, 2023, 41(3): 437-458.

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.

CLC Number: 

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