Conclusions

In this paper, we investigate the limits of the Born approximation when applied to wave-equation migration velocity analysis. Experimentally we find that the Born approximation is only valid for small slowness anomalies, on the order of $1-2\%$ of the background slowness for an anomaly of the shape and size used in the example in this paper. These numbers, however, are model dependent, because we have to consider both the magnitude and size of the anomaly: a small anomaly of large magnitude can have a similar effect as a large anomaly of small magnitude.

Moving beyond the Born approximation involves one of the two solutions: we can either artificially create image perturbations that are compliant with this approximation Sava and Biondi (2001), or we can improve the WEMVA operator to better handle the non-linearity in the image perturbations, as presented in this paper.

We propose two improved versions of the WEMVA operator which are more appropriate for the case of large/strong slowness anomalies. Our new operators involve linearizations using bilinear and implicit approximations to the exponential function. With the new operators, we not only improve accuracy but we also maintain stability of the inversion scheme at much higher values of the slowness anomalies, even in the order of $25\%$ of the background.

Finally, we note that our new operators come at a cost which is practically no different than the cost of the Born-linearized operator, while improving its accuracy and stability.