Absolute Acoustic Impedance Inversion Based on Reflectivity Estimated by Image Domain Least Squares Migration

Abstract

Summary Instead of solving nonlinear FWI, the acoustic impedance (AI) model can be divided into two parts for linear inversion. One is the smooth background, and the other is the reflectivity. Assuming the background AI model is obtained, true-amplitude and broadband reflectivity can be estimated by solving least-squares migration (LSM). We can calculate the corresponding broadband AI, and then the background AI is merged to get the absolute AI. In this paper, we firstly solve the image domain LSM (IDLSM) for true-amplitude and broadband reflectivity inversion. Then the absolute AI model is inverted with the estimated reflectivity and the given the background AI. For IDLSM, we approximate the Hessian matrix with non-stationary matching filters. The image deblurring problem is solved with the sparse (L1 norm) and total variation (TV) regularization. With the estimated reflectivity and given background impedance, we solve a constrained optimization problem with combined first and second order TV regularizations for absolute AI model inversion. Numerical examples on Marmousi model illustrate that the IDLSM results solved by the proposed method have both more balanced amplitudes and higher resolution than conventional migration images. Absolute AI model can be inverted with the estimated reflectivity and given background impedance.