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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 secondorder(displacement–stress) separate elastic wave equations, with the first-order(velocity–stress) and the secondorder(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 computationallyslightly 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.
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. in this study, we compare two kinds of such wave equations: the first- order (velocity-stress) and second (displacement-stress) separate elastic wave equations with a first-order (velocity-stress) and second order The 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, regar dless 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 filed calculated using the corresponding first- order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that who achieve achieve P- and S-wavefields which can be used to test the efficacy of wave The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.