Robust Frequency Domain Full-Waveform Inversion via HV-Geometry

TL;DR

This paper introduces the HV metric for frequency-domain full-waveform inversion, effectively addressing cycle skipping and noise sensitivity issues by leveraging optimal transport concepts without data normalization.

Contribution

The novel HV metric is proposed for frequency-domain FWI, improving robustness and accuracy over traditional $L^2$ and Wasserstein metrics in noisy and limited prior scenarios.

Findings

HV metric outperforms $L^2$ and Wasserstein metrics in synthetic tests.

HV metric enhances inversion robustness with high noise levels.

Effective in seismic and ultrasound imaging applications.

Abstract

Conventional frequency-domain full-waveform inversion (FWI) is typically implemented with an $L^2$ misfit function, which suffers from challenges such as cycle skipping and sensitivity to noise. While the Wasserstein metric has proven effective in addressing these issues in time-domain FWI, its applicability in frequency-domain FWI is limited due to the complex-valued nature of the data and reduced transport-like dependency on wave speed. To mitigate these challenges, we introduce the HV metric ($d_{\text{HV}}$), inspired by optimal transport theory, which compares signals based on horizontal and vertical changes without requiring the normalization of data. We implement $d_{\text{HV}}$ as the misfit function in frequency-domain FWI and evaluate its performance on synthetic and real-world datasets from seismic imaging and ultrasound computed tomography (USCT). Numerical experiments demonstrate that $d_{\text{HV}}$ outperforms the $L^2$ and Wasserstein metrics in scenarios with limited prior model information and high noise while robustly improving inversion results on clinical USCT data.