Three-dimensional, nonlinear, asymptotic seismic inversion

Agur G.J. Sevink? G?erard C. Hermany

June 13, 1995

Abstract

One of the difficulties associated with 3D nonlinear seismic inverse problems is the huge computational size. A pragmatic way to reduce the computational effort is to first estimate a background model and subsequently linearize the problem around this background model. This approach is taken in seismic imaging methods (like Born inversion). These methods are efficient but are, in general, not accurate for those cases, where the estimate of the background model is inaccurate and for 3D data that is measured using an acquisition geometry with large gaps.

Nonlinear iterative inverse scattering methods can be used to resolve this kind of problems but are extremely compute intensive. We propose an iterative scheme consisting of two nested loops for an alternate estimation of background and contrast parameters. For the inner loop for determining the contrast, high-frequency asymptotic methods are used for both computing the data misfit function and accelerating the rate of convergence by means of preconditioning. As a preconditioner, the Born inversion operator is used.

We have applied the method to simulated data for a typical 3D acquisition geometry. On one hand, the iterative method employed in the inner loop is shown to be less sensitive to sampling problems (due to gaps in acquisition) than Born inversion. On the other hand, the rate of convergence of the preconditioned iterative (PK) scheme, important for the total computational effort, is accelerated significantly when compared to conjugate-gradient and other well-established iterative methods. We have found that the nonlinear iterative method, with our PK scheme as inner loop, appears to be capable of resolving both background and contrast parameters after only a few iterations.

Physics Abstracts Classification: 02.60, 03.40K, 43.25, 91.30

1 Introduction

The objective of seismic inverse scattering is the determination of subsurface parameters from seismic wavefield measurements. This type of inverse problems has been studied by many authors (see [19] and references therein), and is complicated severely by the fact

?Faculty of Technical Mathematics and Computer Science, Delft University of Technology yFaculty of Technical Mathematics and Computer Science, Delft University of Technology