Migration velocity analysis is carried out by analysing the residual moveout and amplitude variations in common image point gathers (CIGs) parametrized by scattering angle and azimuth. The misfit criterion in the analysis is of the differential-semblance type. By using angles to parametrize the imaging we are able to handle and exploit data with multiple arrivals, although artefacts may occur in the CIGs and need to be suppressed.
The CIGs are generated by angle migration, an approach based on the generalized Radon transform (GRT) inversion, and they provide multiple images of reflectors in the subsurface for a range of scattering angles and azimuths. Within the differential semblance applied to these CIGs, we compensate for amplitude versus angle (AVA) effects. Thus, using a correct background velocity model, the CIGs should have no residual moveout nor amplitude variation with angles, and the differential semblance should vanish. If the velocity model is incorrect, however, the events in the CIGs will appear at different depths for different angles and the amplitude along the events will be non-uniform. A standard, gradient-based optimization scheme is employed to develop a velocity updating procedure. The model update is formed by backprojecting the differential semblance misfits through ray perturbation kernels, within a GRT inverse. The GRT inverse acts on the data, subject to a shift in accordance with ray perturbation theory.
The performance of our algorithm is demonstrated with two synthetic data examples using isotropic elastic models. The first one allows velocity variation with depth only. In the second one, we reconstruct a low-velocity lens in the model that gives rise to multipathing. The velocity model parametrization is based upon the eigentensor decomposition of the stiffness tensor and makes use of B-splines.