Image‐warping waveform tomography

Abstract

ABSTRACTImaging the change in physical parameters in the subsurface requires an estimate of the long wavelength components of the same parameters in order to reconstruct the kinematics of the waves propagating in the subsurface. One can reconstruct the model by matching the recorded data with modeled waveforms extrapolated in a trial model of the medium. Alternatively, assuming a trial model, one can obtain a set of images of the reflectors from a number of seismic experiments and match the locations of the imaged interfaces. Apparent displacements between migrated images contain information about the velocity model and can be used for velocity analysis. A number of methods are available to characterize the displacement between images; in this paper, we compare shot‐domain differential semblance (image difference), penalized local correlations, and image‐warping. We show that the image‐warping vector field is a more reliable tool for estimating displacements between migrated images and leads to a more robust velocity analysis procedure. By using image‐warping, we can redefine the differential semblance optimization problem with an objective function that is more robust against cycle‐skipping than the direct image difference. We propose an approach that has straightforward implementation and reduced computational cost compared with the conventional adjoint‐state method calculations. We also discuss the weakness of migration velocity analysis in the migrated‐shot domain in the case of highly refractive media, when the Born modelling operator is far from being unitary and thus its adjoint (migration) operator poorly approximates the inverse.