Full Waveform Inversion using modified Softplus Objective Function

Abstract:

The full waveform inversion (FWI) method is for updating the physical properties of the subsurface so that the objective function of the residuals of the modeled and observed data is minimized. Generally, and are used as the objective function to perform FWI. In the case of , there is robustness in the outlier of the residuals, but there are difficulties in approaching the solution. In the case , it responds sensitively to the outliers of the residuals, but the answer is quickly accessible.

Bube and Langan (1997) proposed a hybrid norm with characteristics like l2-norm when the residual is small and l1-norm when the residual is large. The Softplus function, which is mainly used as an activation function in machine learning, has similar characteristics to hybrid norm. In this study, we tried to use the Softplus function as the objective function. When Softplus is used as an objective function, there is a problem that the objective function value becomes smaller as the negative value of the residual becomes larger. This problem is corrected and applied to the FWI objective function.

ACKNOWLEDGMENTS

This research was supported by the Basic Research Project (20-3313) of the Korea Institute of Geoscience and Mineral Resources(KIGAM) funded by the Ministry of Science, ICT and Future Planning of Korea, and the Korea Institute of Energy Technology Evaluation and Planning (KETEP) with a grant funded by the Ministry of Trade, Industry and Energy, Republic of Korea (No. 20182510102470).