Model-based analysis of seismic data, now recognized as a key to a better understanding of images of subsurface structure, began in the 1960s. But these models were inflexible, primarily due to hardware and software limitations, and generally were simple homogeneous isotropic horizontal layers—i.e., with only vertical velocity variations.

Various corrections to these models were quickly introduced to compensate for layer dips. However, many corrections were a posteriori, at various stages of the processing, without consulting the original model. Such approaches may be dangerous because we may lose control of the physics of the problem and end up with data about...

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