Three-dimensional, nonlinear, asymptotic seismic inversion

Abstract

One of the difficulties associated with three-dimensional (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 (such as 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 are measured using an acquisition geometry with large gaps. Nonlinear iterative inverse scattering methods can be used to resolve this kind of problem but are extremely computer intensive. We propose an iterative scheme consisting of two alternate 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 the 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 iterative preconditioned Krylov (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.