Iterative asymptotic inversion in the acoustic approximation

Abstract

We propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation. For this purpose, we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods. The different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image. In the linearized inversion, we use the background velocity model obtained by velocity analysis. We determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model. Because the inverse operator is not exact, and because the source and station distribution is limited, the first iteration of our asymptotic inversion technique is not exact. We improve the images by an iterative procedure. Since the background velocity does not change between iterations. There is no need to retrace rays, and the same ray quantities are used in the iterations. For this reason our method is very fast and efficient. The results of the inversion demonstrate that iterations improve the spatial resolution of the model images since they mainly contribute to the increase in the short wavelength contents of the final image. A synthetic example with one‐dimensional (1-D) velocity background illustrates the main features of the inversion method. An example with two‐dimensional (2-D) heterogeneous background demonstrates our ability to handle multiple arrivals and a nearly perfect reconstruction of a flat horizon once the perturbations above it are known. Finally, we consider a seismic section taken from the Oseberg oil field in the North Sea off Norway. We show that the iterative asymptotic inversion is a reasonable and accurate alternative to methods based on finite differences. We also demonstrate that we are able to handle an important amount of data with presently available computers.

Efficient calculation of partial derivative wavefield using reciprocity for seismic imaging and inversion

“…The off-diagonal elements of the approximate Hessian matrix are the zero-lag values of the crosscorrelation of the partial derivative wavefields. In the high-frequency limit and for models having relatively smooth impedance variation, the approximate Hessian matrix is diagonally dominant (Pratt et al, 1998;Gray, 1997;Lambaré et al, 1992;Jin et al, 1992). Lambaré et al (1992) show that for uniformly sampled data around a scattering point, the Hessian matrix can be approximated as a delta function (diagonal element of the Hessian matrix).…”

Asymptotic pseudounitary stacking operators

“…In the more common case, the forward operator is strictly defined by the physics of a problem. In this case, we can include asymptotic inversion in the iterative least-squares inversion by means of preconditioning Lambaré et al, 1992). The linear preconditioning operator should transform the forward stackingtype operator to the form (24) with the weighting function (28).…”

Iterative estimation of reflectivity and image texture: Least-squares migration with an empirical Bayes approach

“…This approach to imaging is conventionally referred to as least-squares migration (LSM). Early treatments of this approach can be found in LeBras and Clayton (1988) and Lambare et al (1992). This paper will deal mainly with Kirchhoff-based LSM , which uses a ray-theoretic-based forward-modeling operator; its derivation and application are discussed in Nemeth et al (1999) and Duquet et al (2000).…”