Elastic wave-mode separation for TTI media

Marmousi II model

My second model (Figure 12) uses an elastic anisotropic version of the Marmousi II model (Bourgeois et al., 1991). In the modified model, $V_{P0}$ is taken from the original model (Figure 12(a)), the $V_{P0}/ V_{S0}$ ratio ranges from 2 to 2.5, (Figure 12(b)), and the density $\rho$ is taken from the original model (Figure 12(c)). The parameter $\epsilon$ and $\delta$ are derived from the density model $\rho$ with the relations of $\epsilon=0.25\rho-0.3$ and $\epsilon=0.125\rho-0.1$ , respectively. The parameter $\epsilon$ ranges from $0.13$ to $0.36$ Figure 12(d), and parameter $\delta$ ranges from $0.11$ to $0.24$ Figure 12(e). These anisotropy parameters are obtained by assuming linear relationships to the velocity models, and therefore, they both follow the structure of the model. Figure 12(f) represents the local dips obtained from the density model using plane wave destruction filters (Fomel, 2002). The dip model is used to simulate the wavefields and also used to construct TTI separators. A displacement source oriented at 45$^\circ$ to the vertical direction and located at coordinates $x=11$  km and $z=1$  km is used to simulate the elastic anisotropic wavefield.

Figure 13(a) presents one snapshot of the simulated elastic wavefields using the anisotropic model shown in Figure 12. Figures 13(b), fig:vA-wom, and fig:pA-wom demonstrate the separation using conventional divergence and curl operators, VTI filters, and correct TTI filters, respectively. The VTI filters are constructed assuming zero tilt throughout the model, and the TTI filters are constructed with the dips used for modeling. As expected, the conventional divergence and curl operators fail at locations where anisotropy is strong. For example, in Figure 13(b) at coordinates $x=12.0$  km and $z=1.0$  km strong S-wave residual exists, and at coordinates $x=13.0$  km and $z=1.5$  km strong P-wave residual exists. VTI separators fail at locations where the dip is large. For example, in Figures 13(c) at coordinates $x=10.0$  km and $z=1.2$  km, strong S-wave residual exist. However, even for this complicated model, separation using TTI separators is effective at locations where medium parameters change rapidly.

vp,vs,rx,epsilon,delta,nu
Figure 12. Anisotropic elastic Marmousi II model with (a) $V_{P0}$ , (b) $V_{S0}$ , (c) density, (d) $\epsilon$ , (e) $\delta$ , and (f) local tilt angle $\nu$ .

uA-wom,iA-wom,vA-wom,pA-wom
Figure 13. (a) A snapshot of the vertical and horizontal displacement wavefield simulated for model shown in Figure 12. Panels (b) to (c) are the P- and SV-wave separation using $\nabla \cdot {}$ and $\nabla \times {}$ , VTI separators and TTI separators, respectively. The separation is incomplete in panels (b) and (c) where the model is strongly anisotropic and where the model tilt is large, respectively. Panel (d) shows the best separation among all.

Elastic wave-mode separation for TTI media