Least-Squares Reverse Time Migration in Imaging Domain Based on Global Space-Varying Deconvolution

Bo Li,Yingzhe Bai,Chen Xiang,Minao Sun

doi:10.3390/app12052361

Abstract

The classical least-squares migration (LSM) translates seismic imaging into a data-fitting optimization problem to obtain high-resolution images. However, the classical LSM is highly dependent on the precision of seismic wavelet and velocity models, and thus it suffers from an unstable convergence and excessive computational costs. In this paper, we propose a new LSM method in the imaging domain. It selects a spatial-varying point spread function to approximate the accurate Hessian operator and uses a high-dimensional spatial deconvolution algorithm to replace the common-used iterative inversion. To keep a balance between the inversion precision and the computational efficiency, this method is implemented based on the strategy of regional division, and the point spread function is computed using only one-time demigration/migration and inverted individually in each region. Numerical experiments reveal the differences in the spatial variation of point spread functions and highlight the importance to use a space-varying deconvolution algorithm. A 3D field case in Northwest China can demonstrate the effectiveness of this method on improving spatial resolution and providing better characterizations for small-scale fracture and cave units of carbonate reservoirs.

Highlights

High-resolution seismic imaging is a critical tool to acquire information on underground structures from observed seismic data [1,2]
Point spread function (PSF) from one scattering point is consistent with a row of elements in the Hessian matrix, which physically describes the impact of single-point-scattered energy on underground media, including local illumination characteristics of the observation geometry, the space variation in velocity model, and the band-limiting effect in seismic wavelet and received data [32,33]
Equation (8) shows that the point spread function is exactly the image of the scattered wave radiated from the scattering point, which has a limited distribution in the space

Summary

Introduction

High-resolution seismic imaging is a critical tool to acquire information on underground structures from observed seismic data [1,2]. Point spread function (PSF) from one scattering point is consistent with a row of elements in the Hessian matrix, which physically describes the impact of single-point-scattered energy on underground media, including local illumination characteristics of the observation geometry, the space variation in velocity model, and the band-limiting effect in seismic wavelet and received data [32,33] These approximations for Hessian in imaging domain LSM can be used as preconditioners for the data domain LSM, which, after multiple iterations, can more quickly approximate the real reflection coefficient [34,35,36,37].

The Global Space-Varying Point Spread Function

Global Space-Varying Deconvolution