Numeric implementation of wave-equation migration velocity analysis operators

Conclusions

The wave-equation MVA operator discussed in this paper, can be implemented in various imaging frameworks, e.g. zero-offset (exploding reflector), survey-sinking or shot-record. In all cases, the forward and adjoint operators follow similar patterns involving combinations of scattering, imaging and extrapolation. The forward and adjoint operators share common elements and can be implemented in the mixed space-wavenumber domain, similarly to the implementation of the wavefield extrapolation operators.

The real challenges in using wave-based MVA are two-fold. First, the image perturbations need to be generated by techniques that do not compare image features that are too far from one-another, which is a property partially addressed by techniques based on differential semblance. Second, the cost of the wave-equation MVA operator is large, therefore a feasible implementation requires clever numeric implementation, e.g. by frequency decimation similarly to the approach taken in waveform inversion.

The examples shown in this paper illustrate the main characteristics of the various wave-equation MVA operators, i.e. stability during back-projection in background models with sharp velocity variation (e.g. salt), natural ability to characterize multi-pathing and wide area of sensitivity which is commensurate with the frequency band of the recorded data.

Numeric implementation of wave-equation migration velocity analysis operators