Wave-equation-based image warping

In seismic processing and reservoir characterization, we often need to measure relative displacements between different realizations of data. Over the years, many methods have been developed using different measures of similarity. Such alignment or warping methods are often effective signal or image processing tools. However, none of the available methods are directly driven by the physics of seismic imaging. We have found that a seismic image can be considered as a field governed by the wave equation. We visualized different image realizations as snapshots of the wavefield at different times, and these conveyed the required displacements or time shifts. By formulating the problem in a physical context, we obtained displacements that honored the directionality of the wave propagation. For example, 4D time shifts on migrated stacks were obtained in a direction normal to the reflectors. We have computed these shifts in an inverted finite-difference scheme. To overcome limitations of the two-way wave equation in this application, we factorized it to its one-way counterparts. The method was demonstrated on synthetic and real data sets.