Introduction

Migration velocity analysis based on downward-continuation methods, commonly referred to as wave-equation migration velocity analysis (WEMVA), is a promising technique which has become an active area of research over the recent years Biondi and Sava (1999); Sava and Biondi (2000, 2001). The main idea of WEMVA is to use downward-continuation operators not only for migration, but also for migration velocity analysis. This is in contrast with other techniques which use downward-continuation for migration but traveltime-based techniques for migration velocity analysis Clapp (2001); Liu et al. (2001); Mosher et al. (2001).

The main benefits of WEMVA are identical to the benefits of downward-continuation migration methods versus the more common Kirchhoff methods. Among these benefits, the most important are the accurate handling of complex wavefields, characterized by multipathing, and the band-limited nature of the imaging process, which can handle sharp velocity variations much better than traveltime-based methods Woodward (1992). The areas of complex geology are those where WEMVA is expected to provide the largest benefits.

The problem with WEMVA is that, in its simplest form, it is based on the Born approximation of the wavefield in the perturbation region. This leads to severe limitations of the magnitude and size of the anomalies that can be resolved, which means that, in principle, it cannot operate successfully in the regions of high complexity where it is needed most.

The limitations imposed by the Born approximation can be partially circumvented by special ways of creating the image perturbation in connection with residual migration Sava and Biondi (2001). This process of creating Born-compliant image perturbations is not the ideal strategy, since it closely links a highly accurate method, wavefield-continuation, to a less accurate method, Stolt residual migration.

In this paper, we introduce a new method of linearization designed to overcome the limitations imposed by the Born approximation. Our method is based on linearizations of the exponential function containing the slowness perturbation using more accurate approximations than Born linearization. The resulting operator is more accurate and also more stable in areas of high contrast, at a cost that is practically identical to the one of the Born linearized operator.

This paper is organized as follows: in the next two sections we review the theory of downward-continuation and wave-equation MVA using the Born approximation; then, we introduce the new operators and analyze their meaning in the general context of non-linear optimization; and finally, we present a synthetic example that demonstrates the features of our new method.