Wave Equation Prestack Depth Migration Method in 3D VTI Media

Abstract

Based on the 3‐D dispersion equation for the transversely isotropic media with a vertical symmetry axis (VTI), we proposed one‐way operators in the wavenumber‐space domain such that the terms that contain spatial coordinates and the terms that contain wavenumbers are separated. The coefficients in one‐way operators are determined using an optimization scheme for more accurately matching to the exact phase‐shift operator with a wide‐angle. The resulting 3‐D VTI wave equation prestack migration algorithm can accommodate a wide range of anisotropy rather than the weak anisotropy. For its practical aspects, we also present a frequency‐dependent varying‐step depth extrapolation scheme for reducing the computational cost of wavefield depth extrapolation and an anti‐alias one‐way propagator aiming at imaging the steep dipping structures with 3‐D sparsely sampling dataset in 3‐D VTI media. The proposed 3‐D VTI wave equation prestack migration scheme is demonstrated by SEG 2‐D Hess VTI dataset and a 3‐D migration impulse response with its layout resulting from the 3‐D field data.