P- and S-wavefield simulations using both the first- and second-order separated wave equations through a high-order staggered grid finite-difference method |
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| Authors: | Chao-ying Bai Xin Wang Cai-xia Wang |
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| Institution: | 1. Department of Geophysics, College of Geology Engineering and Geomatics, Chang’an University, Xi’an, 710054, China
2. Institute of Computing Geophysics, Chang’an University, Xi’an, 710054, China
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| Abstract: | In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equations. In this study, we compare two kinds of such wave equations: the first-order (velocity–stress) and the second-order (displacement–stress) separate elastic wave equations, with the first-order (velocity–stress) and the second-order (displacement–stress) full (or mixed) elastic wave equations using a high-order staggered grid finite-difference method. Comparisons are given of wavefield snapshots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corresponding first-order or second-order full elastic wave equations. These mixed equations are computationally slightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-component processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements. |
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| Keywords: | Finite-difference method Staggered grid First-order separate elastic wave equation Second-order separate elastic wave equation Multiple arrival tracking |
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