High-order kernels for Riemannian Wavefield Extrapolation

High-order kernels for Riemannian Wavefield Extrapolation

Paul Sava (Colorado School of Mines)

Sergey Fomel (University of Texas at Austin)

psava@mines.edu, sergey.fomel@beg.utexas.edu

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Abstract:

Riemannian wavefield extrapolation (RWE) is a technique for one-way extrapolation of acoustic waves. RWE generalizes wavefield extrapolation by downward continuation by considering coordinate systems different from conventional Cartesian. Coordinate systems can conform with the extrapolated wavefield, with the velocity model or with the acquisition geometry.

When coordinate systems conform with the propagated wavefield, extrapolation can be done accurately using low-order kernels. However, in complex media or in cases the coordinate systems do not conform with the propagating wavefields, low order kernels are not accurate enough and need to be replaced by more accurate, higher order kernels. Since RWE is based on factorization of an acoustic wave-equation, higher order kernels can be constructed using methods analogous with the one employed for factorization of the acoustic wave-equation in Cartesian coordinates. Thus, we can construct space-domain finite-differences as well as mixed-domain techniques for extrapolation.

High-order RWE kernels improve the accuracy of extrapolation, particularly when the Riemannian coordinate systems does not match closely the general direction of wave propagation.

High-order kernels for Riemannian Wavefield Extrapolation