Research on Band-limited Local Plane Wave Propagator and Imaging Method in TI Medium

Traditional ray-based seismic wave propagators, under the infinite frequency assumption, are widely used in seismic wave propagation and imaging due to its efficiency and flexibility. Seismic wave is a typical band-limited signal; consequently, the high-frequency ray theory is difficult to accurately describe the propagation characteristics of the band-limited signals, and it cannot avoid ray shading zones and caustics. As for wave equation based operators, even though they can propagate band-limited waves accurately, they are computationally demanding. In this study, under the framework of traditional ray theory, a seismic wave propagator applicable to transverse anisotropic medium is proposed, which is based on the local plane wave assumption. The proposed band-limited local plane wave propagator not only preserves the advantages of conventional ray-based propagators but also propagates band-limited waves accurately. To be detailed, a band-limited Snell's Law is constructed by solving the Kirchhoff boundary integral in a local plane, which is perpendicular to the central ray. Then band-limited rays are traced following the band-limited Snell's Law, and equivalent ray parameters are calculated by averaging local plane wave parameters. Physically, band-limited Snell's Law depicts that the directions of band-limited wavefields with maximum energy rays in the first Fresnel zone. Finally, the band-limited beam migration method in TI medium is developed by combining the paraxial beams with the band-limited central rays. Numerical experiments show that the local plane wave propagator can enhance the illumination in shadow zone and the imaging qualities of complex structures, such as rugose salt boundaries. Compared to conventional beam migration, our method generates better angle domain common imaging gathers (ADCIGs).