On the computation of wavenumber integrals in phase-shift migration of common-offset sections

Xinxiang Li and Gary F. Margrave


The evaluation of wavenumber integrals often occurs in migration and modelling algorithms in exploration seismology. The integrals over offset-wavenumbers in phase-shift migration of common-offset sections are the specific case analysed in this paper. The accurate algorithm is numerically simple and easy to implement, but it is computationally very time consuming.

Two approximation methods to compute the offset-wavenumber integrals are discussed in this paper. The first method is the stationary-phase method, which is very often used to evaluate the offset-wavenumber integrals. The second method is called the trapezoidal Filon method, which has been known in synthetic seismogram theory for decades.

Numerical results from these two methods suggest that the stationary-phase method has high accuracy when the wavefield extrapolation depth step-size is not very small relative to the source-receiver offsets of the input common-offset sections. The trapezoidal Filon method, on the other hand, is more suitable in the evaluation of offset-wavenumber integrals when the offsets are large relative to the depth step-size.

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