SSIM-FWI: Full Waveform Inversion based on Multi-scale Structural Similarity Index Measure

Abstract

Full waveform inversion (FWI) is a high-resolution seismic inversion technique popularly used in oil and gas exploration. Traditional FWI employs the l2 norm measurement to minimize the misfit between observed and predicted seismic data. However, when the background velocity is inaccurate or the seismic data lacks lowfrequency components, the conventional FWI suffers from cycle skipping, leading to inaccurate inversion results. To address this issue, we introduce a multi-scale structural similarity index measure (SSIM) objective function for FWI.We also incorporate anisotropic total variation regularization with the lp quasi-norm (ATpV) to further improve the accuracy of FWI. Multi-scale SSIM extracts multi-scale structural features of seismic data in both time and space dimensions. These features can reduce the risk of cycle skipping and improve the stability of FWI. Additionally, ATpV applies structural constraints to the velocity gradients, which helps suppress artifacts and preserve the sharp boundaries of geological formations. We propose to use the automatic differentiation (AD) to efficiently and stably optimize this novelly introduced FWI objective function. Both synthetic and field seismic data demonstrate that the proposed method accurately characterizes complex subsurface velocity structures, even when the background velocity is crude, the data lacks low-frequency components, or contains noise.