Robust Frequency Domain Full-Waveform Inversion via HV-Geometry

Conventional frequency-domain full-waveform inversion (FWI) is typically implemented with an L2 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 (dHV), inspired by optimal transport theory, which compares signals based on horizontal and vertical changes without requiring the normalization of data. We implement dHV 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 dHV outperforms the L2 and Wasserstein metrics in scenarios with limited prior model information and high noise while robustly improving inversion results on clinical USCT data.