An elastic modeling algorithm for a 2D stratified medium is introduced. The technique uses phase shift extrapolation in depth for wavefield propagation and the explicit Zoeppritz equations for reflection, transmission and mode conversion. All possible multiples and mode conversions may be computed by cascading each horizontal wavenumber though a computation grid similar to that used in 1D seismograms.
As an initial test, we have implemented the algorithm in the 1D acoustic case and compared its results to the conventional technique (time domain method). The time domain method is so named because it resamples the depth model into layers of equal travel time. Since our method does not resample the model, we expect its results to be more theoretically correct. We used four synthetic models, two of a constant velocity and two of a constant density, from two typical impedance cases: step model and random model. Our algorithm and the time domain algorithm are equivalent for constant velocity but can give quite different results in other cases. For variable velocity models our algorithm generates results which meet theoretical expectations for both primaries and multiples but which differ in details from results of the time domain method. We also compared the two methods on real Blackfoot 08-08 well log data. Both algorithms produce a series of spectral notches due to the effects of the Mannville coals though the seismograms themselves are very different.
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