Elastic wave-mode separation for TTI media |
Figure 11(a) shows the vertical and horizontal components of one snapshot of the simulated elastic anisotropic wavefield; Figure 11(b) shows the separation into P- and S-modes using divergence and curl operators; Figure 11(c) shows the separation into qP and qS modes using VTI filters, i.e., assuming zero tilt throughout the model; and Figure 11(d) shows the separation obtained with the TTI operators constructed using the local medium parameters with correct tilts. The isotropic separation shown in Figure 11(b) is incomplete; for example, at km and km, and at km and km, residuals for direct P and S arrivals are visible in the qP and qS panels, respectively. A comparison of Figures 11(c) and fig:pA indicates that the spatially-varying derivative operators with correct tilts successfully separate the elastic wavefields into qP and qS modes, while the VTI operators only work in the part of the model that is locally VTI.
vp,vs,ro,epsilon,delta,aoppos
Figure 9. A fold model with parameters (a) , (b) , (c) density, (d) , (e) , and (f) tilt angle . The dots in panel (f) correspond to the locations of the anisotropic operators shown in Figure 10. |
---|
rop
Figure 10. The TTI wave-mode separation filters projected to local symmetry axes and their orthogonal directions. Here, I use in equation 12 to taper the polarization vector components before the Fourier transform. The filters correspond to the intersections of , , km and , , km for the model shown in Figure 9. The locations of these operators are also shown by the dots in Figure 9(f). |
---|
uA,pI,pV,pA
Figure 11. (a) A snapshot of the anisotropic wavefield simulated with a vertical point displacement source at km and km for the model shown in Figure 9. Panels (b) to (d) are the anisotropic qP and qS modes separated using isotropic, VTI, 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 |