Optimized Pseudo-Padé Fourier Migrator in Terms of Propagation Angles

Cong Tang,Jianping Huang,Li-Yun Fu,Qingqing Li,Wenyong Pan

doi:10.1109/access.2020.2973042

Abstract

A wide-angle Fourier migrator is proposed to more accurately image complex media with strong lateral velocity contrasts. The broadband wave-equation migrator is developed based on the pseudo-Pade approximation, where the Pade coefficients are independent of spatial coordinates, leading to a pure Fourier transform-based matching solution for one-way wavefield extrapolation. We use genetic algorithms to estimate the constant Pade coefficients more accurately than is feasible with conventional least-squares methods. Because of the global features of pure Fourier migrators, we present an angle-partitioning optimization scheme with dip focusing to improve the performance of the Fourier migrator for super-wide-angle waves and strong velocity contrasts. The wavefield gradient is used to calculate propagation angles during dual-domain wavefield extrapolation. Particular attention is paid to the first-order optimized pseudo-Pade Fourier (OPF1) migrator, which significantly improves the split-step Fourier (SSF) method for strong lateral variations at the cost of one additional Fourier transform in each step. Wavefield extrapolation based on the OPF1 method actually constitutes linear interpolation in the wavenumber domain between two split-step terms. We benchmark the OPF1 migrator with other typical migrators based on the exact dispersion equation. Numerical experiments with impulse responses, the SEG/EAGE salt model and 3D field data demonstrate the excellent performance and efficiency of seismic imaging with the OPF1 migrator.

Highlights

Fourier wave-equation migration is a rapidly developing area of research because of its computational efficiency in commercial applications
One of the key issues associated with Fourier migrators in handling wide-angle waves and lateral velocity variations simultaneously is the global features of the Fourier transform; this issue has led to the acknowledgement that velocity variations, propagation angles, and imaging accuracies are closely related at a variety of scales
Both relative phase-error analyses and numerical experiments demonstrate that the OPF1 method can image steep dips for almost all velocity contrasts

Summary

INTRODUCTION

Fourier wave-equation migration is a rapidly developing area of research because of its computational efficiency in commercial applications. For high-contrast media with wide angles, the most appropriate approach may be the Rytov approximation [8] or separation-of-variables [9] screen propagators These dual-domain propagators are generally formulated by the first-order approximation of the square-root operator, whereas higher-order approximations enhance the imaging accuracy but require additional Fourier transforms at each step, which considerably increases the computational time, especially for immense 3D cases. The Padé approximation, an efficient rational function, has been used to construct various hybrid Fourier matching solutions for one-way propagation problems in high-contrast media; the corresponding migrators include the Padé FD migrator [19], the split-step Padé propagator [20], and the FFD migrator [10] These rational approximations to the square-root operator lead to variable Padé coefficients as functions of the corresponding spatial coordinates and require an additional implicit FD implementation. Wavefield extrapolation by (6) under condition (10) will be unconditionally stable

OPTIMIZATION OF COEFFICIENTS BY GENETIC ALGORITHMS

OPTIMIZATION BY ANGLE PARTITIONING

DISCUSSION AND CONCLUSION