Finite Difference Pre-Stack Depth Migration of One-Way Wave Equation in Isotropic Visco-Acoustic Media of a Ray-Centered Coordinate System

Abstract

In seismic exploration, obtaining accurate bandwidth of the reflected signal is essential for determining seismic resolution. A portion of the stored energy is attenuated during signal propagation, narrowing the received seismic signal bandwidth. Therefore, compensating the energy attenuation is important for improving the seismic resolution. The current method of compensating absorption and attenuation based on a single channel can only compensate the post-stack data (self-exciting and self-receiving), whereas in practice, seismic waves do not propagate along the self-exciting and self-receiving seismic wave path; the propagation path is complex. The absorption and attenuation depend on the propagation path. The primary methods used for Q-compensation along the propagation paths are one-way wave extrapolation in the Cartesian coordinate system and Gaussian beam Q-compensation migration in the ray-centered coordinate system. However, the large angle limits the one-way wave method, and the Gaussian beam method refers to the high-frequency approximation solution of the two-way wave equation. Therefore, a 15-degree equation in the ray-centered coordinate system is proposed. Seismic waves extrapolate along the ray, which compensates the absorption and attenuation along the real propagation path. The 15-degree equation in the ray-centered coordinate system does not perform high-frequency approximation in the ray beam and has no large angle limit, facilitating the accurate description of local wavefields in the ray beam.