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.
Highlights
Downward continuation migration calculates the wavefield at greater depth based on the existing wavefield at the shallower depth
The one-way downward continuation migrations only use the primaries for imaging and do not treat secondary reflections recorded on the surface correctly
We investigate wavefield depth extrapolators based on the full acoustic wave equations, which can propagate wave components to opposite directions
Summary
Downward continuation migration calculates the wavefield at greater depth based on the existing wavefield at the shallower depth. The wavefield can be downward continued recursively from surface to target depth These algorithms have the flexibility of migrating the seismic data sequentially in depth and frequency, which leads to substantial reduction of both computational and memory requirements. To assure the numerical stability, Kosloff and Baysal suggested using the cutoff filter adjusted to the maximum velocity at each depth [3] Such a strategy discarded certain propagating waves generated by the steeply dipping events, resulting in poor imaging of these structures. We derive the two-way beamlet propagator for the local background velocity by using LCB transform and test wave propagation and post stack imaging in the lateral high contrast velocity surroundings
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