Preliminary Investigation of Wavefield Depth Extrapolation by Two-Way Wave Equations

Abstract

Most of the wavefield downward continuation migration approaches are relying on one-way wave equations, which move the seismic energy always in one direction along depth. The one-way downward continuation migrations only use the primaries for imaging and do not treat secondary reflections recorded on the surface correctly. In this paper, we investigate wavefield depth extrapolators based on the full acoustic wave equations, which can propagate wave components to opposite directions. Several two-way wavefield downward continuation propagators are numerically tested in this study. Recursively implementing of the depth extrapolator makes it necessary and important to eliminate the unstable wave modes, that is, evanescent waves. For the laterally varying velocity media, distinction between the propagating and evanescent wave mode is less clear. We demonstrate that the spatially localized two-way beamlet propagator is an effective way to remove the evanescent waves while maintain the propagating mode in laterally inhomogeneous media.

Two-way wave equation-based depth migration using one-way propagators on a bilayer sensor seismic acquisition system

“…We think that the root cause lies in the decomposition of the two-way wave equation. Kosloff and Baysal (1983), Sandberg and Beylkin (2009), and Wu et al (2012) investigate wavefield extrapolation based on the full wave equation using the wavefield and its derivatives at the surface, and Pan (2015) tries to apply the wavefield and the ratio of the wavefield to its derivative to perform a two-way wave-equation migration.…”