Elastic wave-mode separation for VTI media |
Figure shows one snapshot of the modeled elastic anisotropic wavefields using the model shown in Figure 14. Figure illustrates the separation of the anisotropic elastic wavefields using the and operators, and Figure illustrates the separation using my pseudo derivative operators. Figure shows the residual of unseparated P and S wave modes, such as at coordinates km and km in the qP panel and at km and km in the qS panel. The residual of S waves in the qP panel of Figure is very significant because of strong reflections from the salt bottom. This extensive residual can be harmful to under-salt elastic or even acoustic migration, if not removed completely. In contrast, Figure shows the qP and qS modes better separated, demonstrating the effectiveness of the anisotropic pseudo derivative operators constructed using the local medium parameters. These wavefields composed of well separated qP and qS modes are essential to producing clean seismic images.
In order to test the separation with a homogeneous assumption of anisotropy in the model, I show in Figure the separation with and in the domain. This separation assumes a model with homogeneous anisotropy. The separation shows that there is still residual in the separated panels. Although the residual is much weaker compared to separating using an isotropic model, it is still visible at locations such as at coordinates km and km, and km and km in the qP panel and at km and km in the qS panel.
vp,vs,ro,epsilon,delta
Figure 14. A Sigsbee 2A model in which (a) is the P wave velocity (taken from the original Sigsbee 2A model (Paffenholz et al., 2002) ), (b) is the S wave velocity, where ratio ranges from to , (c) is the density ranging from g/cm to g/cm , (d) is the parameter ranging from to , and (e) is the parameter ranging from 0 to in the rest of the model. |
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Figure 15. Anisotropic wavefield modeled with a vertical point force source at km and km for the model shown in Figure 14. |
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Figure 16. Anisotropic qP and qS modes separated using and for the vertical and horizontal components of the elastic wavefields shown in Figure . Residuals are obvious at places such as at coordinates km and km in the qP panel and at km and km in the qS panel. |
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Figure 17. Anisotropic qP and qS modes separated using pseudo derivative operators for the vertical and horizontal components of the elastic wavefields shown in Figure . They show better separation of qP and qS modes. |
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Figure 18. Anisotropic qP and qS modes separated in the domain for the vertical and horizontal components of the elastic wavefields shown in Figure . The separation assumes and throughout the model. The separation is incomplete. Residuals are still visible at places such at coordinates km and km, and km and km in the qP panel and at km and km in the qS panel. |
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Elastic wave-mode separation for VTI media |