Generalized least‐squares DSR migration using a common angle imaging condition

Abstract

Pre-stack wavefield propagators based on generalized phase-shift operators produce accurate depth images of complex geological structures. The standard imaging condition for pre-stack Double-Square-Root (DSR) migration extracts the zero time wavefield at zero offset, resulting in a single depth image. In least-squares (LS) Kirchhoff migration a smoothing constraint along the offset direction in the common reflection point (CRP) domain has been proposed to mitigate artifacts resulting from incompletely and/or coarsely sampled data. In order to make this regularization approach available to least-squares phase-shift migration techniques the common angle imaging condition (CAI) is employed. This imaging condition extracts the zero time wavefield at a set of constant offset ray parameters. This allows for an efficient computation of CAI gathers and the introduction of a ray parameter dependent smoothing in LS migration. The wavefield propagators for modeling and migration used in the LS inversion are based on the split-step approximation of the Square-Root operator. They can be improved by utilizing a multiple reference velocity approach.

Wave-Equation Angle-Domain Hessian

“…Prucha et al (2000) and Kuehl and Sacchi (2001) propose smoothing the image in the offset ray parameter dimension, which is equivalent to the same procedure in the reflection angle dimension. This idea can be generalize to include the azimuth dimension.…”

“…Valenciano et al (2005b) define the zero subsurface-offset Hessian by using the adjoint of the zero subsurface-offset migration as the modeling operator L. Then the zero-offset inverse image can be estimated as the solution of a non-stationary least-squares filtering problem, by means of a conjugate gradient algorithm (Valenciano et al, 2005b,a). But, from the results reported by Prucha et al (2000), Kuehl and Sacchi (2001), and Valenciano et al (2005a), regularization in the reflection angle dimension is necessary to stabilize the wave-equation inversion problem.…”

“…The definition of the wave-equation angle-domain Hessian allows the angle-domain regularization required to stabilize the wave equation inversion problem (Prucha et al, 2000;Kuehl and Sacchi, 2001). It also allows to obtain a prestack inverse image, adding the possibility of doing amplitude vs. angle (AVA) analysis for reservoir characterization.…”

Imaging by target-oriented wave-equation inversion

“…Seismic imaging (migration) operators are non-unitary (Claerbout, 1992) because they depend on: (1) the seismic experiment acquisition geometry (Nemeth et al, 1999;Duquet and Marfurt, 1999;Ronen and Liner, 2000), (2) the complex subsurface geometry (Prucha et al, 2000;Kuehl and Sacchi, 2001), and (3) the bandlimited characteristics of the seismic data (Chavent and Plessix, 1999). Often, they produce images with reflectors correctly positioned but with biased amplitudes.…”

Regularized least‐squares inversion for 3‐D subsalt imaging

“…This regularization can take many forms. In this abstract, we will discuss two possibilities: geophysical regularization in which amplitudes are regularized along reflection angles for every point in the subsurface (Prucha and Biondi, 2002;Kuehl and Sacchi, 2001) and dual stacked image regularization in which two images of the same subsurface volume with different illumination patterns are used to regularize each other (Clapp, 2003).…”