@Article{NMTMA-16-2,
author = {Wu, Hao and Zhengyang, Li and Yijia, Tang and Jing, Chen and Wu, Hao},
title = {On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {2},
pages = {277--297},
abstract = {<p style="text-align: justify;">The quadratic Wasserstein metric has shown its power in comparing probability densities. It is successfully applied in waveform inversion by generating objective functions robust to cycle skipping and insensitive to data noise. As an alternative approach that converts seismic signals to probability densities, the squaring
scaling method has good convexity and thus is worth exploring. In this work, we
apply the quadratic Wasserstein metric with squaring scaling to regional seismic tomography. However, there may be interference between different seismic phases in
a broad time window. The squaring scaling distorts the signal by magnifying the
unbalance of the mass of different seismic phases and also breaks the linear superposition property. As a result, illegal mass transportation between different seismic
phases will occur when comparing signals using the quadratic Wasserstein metric.
Furthermore, it gives inaccurate Fréchet derivative, which in turn affects the inversion results. By combining the prior seismic knowledge of clear seismic phase separation and carefully designing the normalization method, we overcome the above
problems. Therefore, we develop a robust and efficient inversion method based on
optimal transport theory to reveal subsurface velocity structures. Several numerical
experiments are conducted to verify our method.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0111},
url = {https://global-sci.com/article/90207/on-quadratic-wasserstein-metric-with-squaring-scaling-for-seismic-velocity-inversion}
}