A stable approach for Q-compensated viscoelastic reverse time migration using excitation amplitude imaging condition

Abstract

The earth [Formula: see text] filtering causes poor illumination of the subsurface. Compensating for the attenuated amplitude and distorted phase is crucial during elastic reverse time migration (ERTM) to improve the imaging quality. Conventional [Formula: see text]-compensated ERTM ([Formula: see text]-ERTM) methods tend to boost the attenuated energy to inverse the [Formula: see text] effects. These methods usually suffer from severe numerical instability because of the unlimited amplification of the high-frequency noise. Low-pass filtering is generally used to stabilize the process, however, at the expense of precision. We have developed a stable compensation approach in this paper. Based on the decoupled fractional Laplacians viscoelastic wave equation, two compensation operators are obtained by extrapolating wavefield in the dispersion-only and viscoelastic media. Because no explicit amplification is included, these two operators are absolutely stable for implementation. To improve the division morbidity for calculating the compensation operators, we use the excitation amplitude criterion and embed the operators into a vector-based [Formula: see text]-compensated excitation amplitude imaging condition. With the derived imaging condition, we could compensate for the absorption accurately without needing to concern the stability issue. The [Formula: see text]-ERTM results for noise-free data are carried out over a simple layered model and a more realistic Marmousi model with an attenuating area to verify the feasibility of the proposed approach. The migration results for noisy data from the Marmousi model further prove that the proposed method performs better fidelity, adaptability, and antinoise performance compared with conventional compensation method with low-pass filtering.