Adaptive phase-ray wavefield extrapolation

Jeff Shragge and Paul Sava

jeff@sep.stanford.edu, paul@sep.stanford.edu

ABSTRACT

Riemannian wavefield extrapolation (RWE) is a generalization of downward continuation to coordinate systems that closely conform to the orientation of extrapolated wavefields. If the coordinate system overturns, so does the computed wavefield, despite being extrapolated with a one-way solution to the acoustic wave-equation. This allows for accurate imaging of structures of arbitrarily steep dips with simple operators equivalent to standard $15^\circ$extrapolators. An obvious question for RWE is which is an optimal coordinate system for a given velocity model. One option is to compute ray coordinates as a solution to the wide-band eikonal equation in a smoothed velocity model. However, this solution ignores the natural variability and frequency dependence of wavepaths in cases of complicated velocity models, for example under salt bodies. The solution advocated in this paper is a recursive bootstrap procedure where a frequency-dependent coordinate system is computed on-the-fly at every step from the gradient of the monochromatic wavefield phase of the preceding few steps, coupled with standard RWE.