Elastic wave-mode separation for TTI media

3D TTI model

I use a homogeneous TTI model to illustrate the separation of P-, SV-, and SH-modes. The model has parameters $V_{P0}=3.5$  km/s, $V_{S0}=1.75$  km/s, $\rho=2.0$  g/cm$^3$ , $\epsilon=0.4$ , $\delta=0.1$ , $\gamma=0.0$ , $\nu=30^\circ$ , and $\alpha=45^\circ$ . Figure 14 shows a snapshot of the elastic wavefields in the $z$ , $x$ , and $y$ directions. A displacement source located at the center of the model and oriented at tilt 45$^\circ$ and azimuth 45$^\circ$ is used to excite the wavefield. Figure 15 shows successfully separated P-, SV-, and SH-modes. In this model, the parameter $\gamma$ , which characterizes the anisotropy of SH-mode, is set to zero so that the SH-mode propagation is isotropic. For this homogeneous model, a spherical wavefront in the SH-panel indicates successful separation of SV- and SH-modes.

Because this model is homogeneous, the separation is implemented in the wavenumber domain to reduce computation cost. For heterogeneous models, 3D non-stationary filtering is necessary to separate different wave-modes. I do not perform wave-mode separation in 3D heterogeneous models because of the high computational cost, which will be discussed in more detail in the following section.

we3d-0,we3d-1,we3d-2
Figure 14. A snapshot of the elastic wavefield in the $z$ , $x$ and $y$ directions for a 3D VTI model. The model has parameters $V_{P0}=3.5$  km/s, $V_{S0}=1.75$  km/s, $\rho=2.0$  g/cm$^3$ , $\epsilon=0.4$ , $\delta=0.1$ , and $\gamma=0.0$ . 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.

P,SH,SV
Figure 15. Separated P-, SV- and SH-wave-modes for the elastic wavefields shown in Figure 14. P, SV, and SH are well separated from each other.

Elastic wave-mode separation for TTI media