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 - <p style="text-align: justify;">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.</p>