Regularized least‐squares inversion for 3‐D subsalt imaging

Abstract

SUMMARYObtaining seismic images of the subsurface near and beneath salt is very difficult due to seismic energy that is lost by propagating outside of the survey area or becoming evanescent at salt boundaries (poor illumination). We demonstrate an iterative regularized least-squares inversion for imaging that helps to compensate for illumination problems. We show the use of a regularization operator that acts to regularize amplitudes along reflection angles (or equivalent offset ray parameters) to compensate for the sudden, large amplitude changes caused by poor illumination. This regularization operator has the effect of filling in the gaps created in the reflection angle range due to the lost seismic energy. We discuss the use of this regularization operator in an iterative least-squares inversion scheme to improve imaging for a poorly illuminated 3-D seismic dataset. We introduce a new type of joint inversion problem that will allows us to simultaneously invert two or more datasets. For this iterative inversion scheme, we design a different regularization operator that allows us to share illumination information between images created from the different datasets involved. This regularized inversion allows us to create images that share the illumination information from the different datasets.

Numerical tests on generalized diffraction tomography

“…Here we would like to discuss the relationship between the resolving kernel derived in this paper and the Hessian matrix in least-square inversion because they are closely related to each other. In the leastsquare inversion (Beylkin, 1985;Chavent and Plessix, 1999;Clapp et al, 2005;Hu et al, 2001;Kuhl and Sacchi, 2003;Lailly, 1983;Plessix and Mulder, 2004;Pratt et al, 1998;Rickett, 2003;Tarantola, 1984a;ten Kroode et al, 1994;Valenciano et al, 2005Valenciano et al, , 2006, which is based on the minimizing the misfit function using adjoint operator in the Hessian matrix, the backpropagation operator is defined as the gradient of the least-square error function, and the Hessian matrix is the second derivative of the error function (Plessix and Mulder, 2004). There are several differences between the formula of the resolving kernel and that of Hessian matrix.…”

Failure and opportunity: environmental groups in US climate change policy

“…He rejected the idea that environmentalism needs to be redefined and rejected calls for the death of current environmentalism as nihilistic and counterproductive. Along similar lines, Phil Clapp (2005), head of the National Environmental Trust, argued that while environmentalists should regularly reassess their strategy, climate change is unfolding along the exact same trajectory that other major environmental statutes have followed over the past 30 years:…”

Fast Single-Step Least-Squares Reverse-Time Imaging via Adaptive Matching Filters in Beams

“…[10] first proposed the concept of the least-squares migration (LSM), which afterward catches the wide attention from academia and industry. LSM is first applied to Kirchhoff migration [11], [12], and then phase-shift migration [13], [14] and one-way wave-equation migration [15], [16], and now RTM. Here, we mainly focus on LSRTM.…”