A fast and accurate elastic reverse-time migration method based on decoupled elastic wave equations

Abstract

The extrapolation and decomposition of different mode waves are very important to efficiently obtain multi-wave depth images for elastic reverse-time migration (ERTM). To achieve this goal successfully, we firstly develop an efficient and accurate staggered-grid finite-difference method (SFDM) based on decoupled elastic wave equations. This developed SFDM uses two sets of difference operator lengths for decoupled elastic wave equations to respectively perform the extrapolation of decoupled P- and S-wavefields and employs the least squares (LS) to minimize the objective functions respectively constructed from the time-space dispersion equations of P- and S-waves to generate their corresponding difference coefficients. This developed method can theoretically be regarded as the optimal SFDM based on least squares (LSSFDM), and it can provide the high-precision separated wavefields of different mode waves simultaneously and reduce the computing time effectively for elastic wave modeling under the given accuracy requirements. The modeling results of different models illustrate that our developed LSSFDM based on decoupled elastic wave equations can generate the decomposed P- and S-wavefields and suppress their numerical dispersions effectively. Secondly, we present a fast and accurate ERTM method based on this developed LSSFDM to successfully achieve the multi-wave imaging results, including PP, PS, SP and SS images. The ERTM examples of different models demonstrate that our ERTM based on this developed LSSFDM can accurately obtain the high-precision depth images of multimode waves and effectively reduce the computing time of wavefield extrapolation.