Introduction to a Two‐Way Beam Wave Method and Its Applications in Seismic Imaging

Abstract Ray theory gives a high‐frequency asymptotic solution of the wave equation, which has been widely used in the seismic study because of its high computational efficiency and good physical insights for elementary waves. However, the fundamental high‐frequency assumption makes it difficult to accurately simulate the finite‐frequency effect of wave propagations. On the other hand, the Gaussian beam, as one of the advanced ray‐based methods, overcomes the amplitude singularity problem near the caustics by introducing a complex‐valued paraxial approximation. But Gaussian beams only use the velocity and up to second‐order velocity derivative of central rays and thus does not accurately simulate the response of heterogeneity away from the rays. To bridge the gap between the ray theory and wave‐equation methods, we present a two‐way beam wave method and apply it to seismic imaging. A fan of central rays are first shot to extract local ray‐centered model parameters in the global Cartesian coordinates. Then, a finite‐difference method is used to solve the acoustic wave equation in the ray‐centered coordinates to simulate wave propagations near the central rays. The beam wave method can accurately simulate the response of the velocity heterogeneities in the ray tubes and therefore produces more accurate wavefields. In addition, we discretize the ray‐centered wave equation onto a non‐orthogonal grid, which considerably reduces the computational cost. We apply the two‐way beam wave method in seismic imaging and develop a beam wave reverse‐time migration. It inherits the advantages of both ray‐based and wave equation migrations, and produces clear images for complicated structures with fewer artifacts than traditional imaging methods.