Salt reconstruction in full-waveform inversion using topology optimization techniques

Abstract

Summary With the increasing advances in the oil and gas industry, seismic imaging near or under salt structures has become an important point in deep-water exploration. Detailed velocity models of these areas are particularly interesting not only to characterize hydrocarbon reservoirs but also to identify potential sites for hydrogen and carbon dioxide storage in offshore salt caverns. Thus, we study the Full Waveform Inversion (FWI) for the salt reconstruction in acoustic media with constant density considering the time-harmonic wave propagation in a Finite Element formulation using the Topology Optimization (TO) method. This problem is challenging due to the strong velocity contrast between salt bodies and the sedimentary background, in addition to the lack of low-frequency data and the inherent ill-posedness of the inverse problem. In this context, we incorporate techniques from the TO field, usually used in design applications, to overcome or reduce these known problems. We initially defined the squared slowness as a combination of two fields, one related to the salt shape and the other to the background. An interpolation rule based on the Solid Isotropic Material with Penalization (SIMP) method, combined with filtering and projection schemes, is used to find the shape of the salt bodies with increased sharpness interfaces. A Helmholtz-type filter is applied to modify the gradient aimed to regularize the problem and provide a more stable way for the salt shape to evolve during the inversion process. In particular, we demonstrate that the proposed approach may be relevant for reconstructing media with salt bodies when a suitable starting model is unavailable, and sharp interfaces are required. In addition, we present inversion results from synthetic data generated by a variable density model to demonstrate the approach capability when subjected to a reconstruction application.