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Volume 41, Issue 3
The Wasserstein-Fisher-Rao Metric for Waveform Based Earthquake Location

Datong Zhou, Jing Chen, Hao Wu, Dinghui Yang & Lingyun Qiu

DOI: 10.4208/jcm.2109-m2021-0045

J. Comp. Math., 41 (2023), pp. 437-457.

Published online: 2023-02

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  • Abstract

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 ($W_2$) 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 $W_2$ 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.

  • Keywords

The Wasserstein-Fisher-Rao metric, The quadratic Wasserstein metric, Inverse theory, Waveform inversion, Earthquake location.

  • AMS Subject Headings

65K10, 86C08, 86A15, 86A22

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zdt14@mails.tsinghua.edu.cn (Datong Zhou)

jing-che16@mails.tsinghua.edu.cn (Jing Chen)

hwu@tsinghua.edu.cn (Hao Wu)

ydh@mail.tsinghua.edu.cn (Dinghui Yang)

lyqiu@tsinghua.edu.cn (Lingyun Qiu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-437, author = {Zhou , DatongChen , JingWu , HaoYang , Dinghui and Qiu , Lingyun}, title = {The Wasserstein-Fisher-Rao Metric for Waveform Based Earthquake Location}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {3}, pages = {437--457}, abstract = {

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 ($W_2$) 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 $W_2$ 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2109-m2021-0045}, url = {http://global-sci.org/intro/article_detail/jcm/21392.html} }
TY - JOUR T1 - The Wasserstein-Fisher-Rao Metric for Waveform Based Earthquake Location AU - Zhou , Datong AU - Chen , Jing AU - Wu , Hao AU - Yang , Dinghui AU - Qiu , Lingyun JO - Journal of Computational Mathematics VL - 3 SP - 437 EP - 457 PY - 2023 DA - 2023/02 SN - 41 DO - http://doi.org/10.4208/jcm.2109-m2021-0045 UR - https://global-sci.org/intro/article_detail/jcm/21392.html KW - The Wasserstein-Fisher-Rao metric, The quadratic Wasserstein metric, Inverse theory, Waveform inversion, Earthquake location. AB -

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 ($W_2$) 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 $W_2$ 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.

Datong Zhou, Jing Chen, Hao Wu, Dinghui Yang & Lingyun Qiu. (2023). The Wasserstein-Fisher-Rao Metric for Waveform Based Earthquake Location. Journal of Computational Mathematics. 41 (3). 437-457. doi:10.4208/jcm.2109-m2021-0045
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