Strainprox: Seismic Time-Strain Inversion with Proximal Solvers

Abstract

This paper introduces a novel methodology, called StrainProx, for direct time-strain inversion of time-lapse seismic data, grounded in convex optimization theory. A synthetic example is first designed to illustrate the limitations of state-of-the-art time-shift and time-strain inversion algorithms, and motivate the design choices of the proposed approach; specifically, we show that directly inverting seismic data for time strains yields more robust estimates than differentiating inverted time shifts; finally, integrating the estimated time strains produces time shifts that are more reliable than those obtained by inverting seismic data for time shifts. Due to the band-limited nature of seismic data, the estimated time strains lack low and high frequencies, leading to unclear boundary delineation and side lobes. By combining Total Variation (TV) regularization with a segmentation term into a Joint Inversion and Segmentation (JIS) optimization framework, we produce estimates that strike a balance between reduced global error, minimal background leakage, and precise recovery of the anomaly geometry. The effectiveness of the proposed method is further validated on the Sleipner field dataset. Our results demonstrate that JIS can resolve a structurally consistent and geologically interpretable time-strain field.