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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.

Zhou , DatongChen , JingWu , HaoYang , Dinghui and Qiu , Lingyun. (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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