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The expression for forms the basis for a one-way extrapolation operator that can be used to propagate wavefields on generalized coordinate meshes. This requires that a wavefield at step (i.e., ) be propagated to the next step (i.e., ) according to
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(32) |

The back-projection of residuals required for waveform inversion can be implemented easily according to the adjoint process of equation 32,

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(33) |

Note that the coefficients above are spatially variant which requires employing a typical approach (e.g. split-step Fourier, FFD or phase-screens) for developing a mixed domain exponential operators. This study uses the split-step Fourier approach detailed in Shragge (2006a) using the extrapolation wavenumber defined by equation 31.

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Stanford Exploration Project

1/16/2007