Research on the differential coefficient least-squares optimization method of reverse time migration in acoustic-reflected S-wave imaging logging

The numerical dispersion phenomenon in the finite-difference forward modeling simulations of the wave equation significantly affects the imaging accuracy in acoustic reflection logging. This issue is particularly pronounced in the reverse time migration (RTM) method used for shear-wave (S-wave) logging imaging. This not only affects imaging accuracy but also introduces ambiguities in the interpretation of logging results. To address this challenge, this study proposes the use of a least-squares difference coefficient optimization algorithm aiming to suppress the numerical dispersion phenomenon in the RTM of S-wave reflection imaging logging. By optimizing the difference coefficients, the high-precision finite-difference algorithm serves as an effective operator for both forward and backward RTM processes. This approach is instrumental in eliminating migration illusions, which are often caused by numerical dispersion. The effectiveness of this optimized algorithm is demonstrated through numerical results, which indicate that it can achieve more accurate forward imaging results across various conditions, including high- and low-velocity strata, and is effective in both large and small spatial grids. The results of processing real data demonstrate that numerical dispersion optimization effectively reduces migration artifacts and diminishes ambiguities in logging interpretations. This optimization offers crucial technical support to the RTM method, enhancing its capability for accurately modeling and imaging S-wave reflections.