1887
Volume 36 Number 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Numerical wavefield extrapolation represents the backbone of any algorithm for depth migration pre‐ or post‐stack. For such depth imaging techniques to yield reliable and interpretable results, the underlying wavefield extrapolation algorithm must propagate the waves through inhomogeneous media with a minimum of numerically induced distortion, over a range of frequencies and angles of propagation.

A review of finite‐difference (FD) approximations to the acoustic one‐way wave equation in the space‐frequency domain is presented. A straightforward generalization of the conventional FD formulation leads to an algorithm where the wavefield is continued downwards with space‐variant symmetric convolutional operators. The operators can be precomputed and made accessible in tables such that the ratio between the temporal frequency and the local velocity is used to determine the correct operator at each grid point during the downward continuation.

Convolutional operators are designed to fit the desired dispersion relation over a range of frequencies and angles of propagation such that the resulting numerical distortion is minimized. The optimization is constrained to ensure that evanescent energy and waves propagating at angles higher than the maximum design angle are attenuated in each extrapolation step. The resulting operators may be viewed as optimally truncated and bandlimited spatial versions of the familiar phase shift operator. They are unconditionally stable and can be applied explicitly. This results in a simple wave propagation algorithm, eminently suited for implementation on pipelined computers and on large parallel computing systems.

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2006-04-27
2020-04-04
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