Numerical results demonstrate that the one-way wave equation modeling scheme exhibits sufficient accuracy in terms of primary reflected waves in comparison with the two-way wave equation scheme. The computational cost is greatly reduced by employing the one-way wave equation scheme. Moreover, only a rough velocity model is needed for implementing the one-way wave equation scheme in seismic modeling. Since the one-way wave equation modeling scheme can be considered as the inverse depth migration, we can use the current depth migration schemes and its codes. Accounting for both accuracy and computational efficiency, we use the explicit short extrapolation operator scheme in a complicated medium layer and the split step Fourier operators in a simple medium layer during depth extrapolations. Reflected coefficients are obtained by considering its variation with incident angles in the scheme.
The 3‐D wave equation prestack depth migration is one of the most important steps in the structure imaging and the inversion of elastic parameters of complex medium. It is very difficult to deal with for the implement of this technique relates not only to the innovation of the wavefield extrapolation theory but also large scale calculation. This paper is to get the result of the experiment and completely realize the 3‐D symplectic wave equation prestack depth migration of SEG/EAGE Salt and Overthrust model. We discuss in detail the imaging ability of our symplectic 3‐D prestack depth migration software system with complex geologic structures including the following topics: 1) The choice of imaging parameters , the effect on the migration result of the seismic wavelet and comparison between 2‐D and 3‐D prestack depth migration result of the Salt model. 2) The presentation of the impulse response of the Overthrust model. 3) The imaging result of the two international models indicates that our software system accommodate great transversal velocity variation and have ability of imaging complex geologic structures.
We propose a wave equation based migration scheme for imaging the steep dipping structures with 3-D sparsely sampled dataset, especially sparsely sampled in the crossline direction. The scheme is developed based on the hybrid domain (wavenumber and space) wave equation based migration methods. The problem for imaging the steep dipping structures can be solved by applying anti-alias one-way propagator together with filling zero traces into the original sparsely sampled data (to generate dataset with a sufficient sampling). The proposed scheme overcomes a main difficulty when applying wave equation based migration methods to the field data. As a result, good imaging can be obtained for complex structures by using wave equation based migration methods. The proposed scheme is demonstrated by 2-D Marmousi dataset and 3-D field data. The proposed scheme will be much helpful to the current 3-D dataset.
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