Tariq A. Alkhalifah, KAUST

KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

May 7-8, 2011

King Abdullah University of Science and Technology (KAUST)

Thuwal, Kingdom of Saudi Arabia

Time Extrapolation of the Double-Square-Root Equation: Prestack Exploding Reflector Modeling and Migration

Unlike prestack imaging using the conventional wave equation, which requires an integral based imaging condition, imaging using the double square (DSR) equation avoids that requirement and thus provides an explicit relation between the imaging operator and medium parameters. Thus, while most of the modern seismic imaging methods perform imaging by separating input data into parts (shot gathers), we develop a formulation that is able to incorporate all available data at once while numerically propagating the recorded multidimensional wavefield backward in time. While computationally extensive, this approach has the potential of generating accurate images, free of artifacts associated with conventional approaches. However, DSR suffers from an inherent singularity when waves travel horizontally. We explain this singularity, show its extent, and the limits on offset and dip treated because of this singularity. Our analysis covers both laterally homogeneous and inhomogeneous media, and thus, we show the behavior for lateral inhomogeneous media is different. A numerical extrapolation shows the evolution of the wavefield in the prestack domain using a prestack exploding reflector modeling experiment.