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 utilizing different similarity measuring techniques. Such alignment or warping methods are often effective signal or image processing tools. However, a survey of available methods shows that none are directly driven by the physics of seismic imaging. We show that a seismic image can be considered a field governed by the wave equation. We visualize different image realizations as snapshots of the wavefield at different times, and these give us the required displacements or time-shifts. By formulating the problem in a physical context, displacement vectors are obtained that honor the directionality of the wave propagation. For example, 4D time-shifts are obtained in a direction normal to the reflectors. We compute these shifts in an inverted finite-difference scheme. To overcome limitations of the two-way wave equation, we factorize it to its one-way counterparts. The method is demonstrated on synthetic and real datasets.