Optimized Chebyshev Fourier migration: A wide-angle dual-domain method for media with strong velocity contrasts

Abstract

A wide-angle propagator is essential when imaging complex media with strong lateral velocity contrasts in one-way wave-equation migration. We have developed a dual-domain one-way propagator using truncated Chebyshev polynomials and a globally optimized scheme. Our method increases the accuracy of the expanded square-root operator by adding two high-order terms to the traditional split-step Fourier propagator. First, we approximate the square-root operator using Taylor expansion around the reference background velocity. Then, we apply the first-kind Chebyshev polynomials to economize the results of the Taylor expansion. Finally, we optimize the constant coefficients using the globally optimized scheme, which are fixed and feasible for arbitrary velocity models. Theoretical analysis and nu-merical experiments have demonstrated that the method has veryhigh accuracy and exceeds the unoptimized Fourier finite-difference propagator for the entire range of practical velocity contrasts. The accurate propagation angle of the method is always about 60° under the relative error of 1% for complex media with weak, moderate, and even strong lateral velocity contrasts. The method allows us to handle wide-angle propagations and strong lateral velocity contrast simultaneously by using Fourier transform alone. Only four 2D Fourier transforms are required for each step of 3D wavefield extrapolation, and the computing cost is similar to that of the Fourier finite-difference method. Compared with the finite-difference method, our method has no two-way splitting error (i.e., azimuthal-anisotropy error) for 3D cases and almost no numerical dispersion for coarse grids. In addition, it has strong potential to be accelerated when an enhanced fast Fourier transform algorithm emerges.