# Numerical Modeling of Scholte Wave in Acoustic-Elastic Coupled TTI Anisotropic Media
## 4 Numerical Experiments
### 2D Two-Layer Acoustic-Elastic Coupled Model  
First, we design a two-layer acoustic-elastic coupled model, where the upper and lower layer are fluid and TTI solid (Figure 3). The size of the model is 2 km \(\times\) 2 km. The grid spacing is \(\Delta x=\Delta z=5\) m. The lower layer is described by the Thomsen parameters: \(V_{P0}=2.0\) km/s, \(V_{S0}=1.1\) km/s, \(\epsilon=0.2\) and \(\delta=-0.05\). The density of the lower layer is \(\rho_{S}=1.5\) gcm\({}^{-3}\). The acoustic velocity and density in the fluid are \(V_{f}=1.5\) km/s and \(\rho_{f}=1.0\) gcm\({}^{-3}\), respectively. A point source with 30 Hz wavelet is located at x = 1.0 km and z = 0.97 km. The polar angle of the TTI symmetry axis is \(\theta=30^{\circ}\). The temporal step for the staggered-grid finite-difference method is \(\Delta t=0.5\) ms. Figure 3 shows that wavefield includes reflected/transmitted waves, head waves, and the Scholte wave. The numerical calculation is stable, and the expected arrivals are reconstructed. The kinematics of the wavefield propagating is distorted by anisotropy in solid. Comparing our algorithm with the result of the spectral element method (Figure 4), with the same parameters and sampling time, we can find that the result of the spectral element method brings into correspondence with Figure 3, which indicates the accuracy of our algorithm. Then, the calculation time and memory of the two methods were evaluated on a single node, with each method requiring 0.5 s (Table 1). We can find that the calculation time and memory of SEM are much greater than FD. In return, SEM typically provides higher accuracy than FD. However, the accuracy of the finite difference method is also acceptable, and the computational cost is much lower. We select a point (x = 1.75 km, z = 1.0 km) on the fluid-solid interface in the two-layer acoustic-elastic coupled model. During wave propagation, the Scholte wave could pass through this point. Therefore, we have drawn the vibration curve of the Scholte wave propagating from left to right to this point (Figure 5). It can be seen that the vibration direction of the Scholte wave is counterclockwise, and the shape of the curve approaches an irregular ellipse. Compared to the horizontal direction, the Scholte wave has much larger amplitudes in the vertical direction. And it has stronger amplitudes in the water \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Time (s)** & **Memory (G)** \\ \hline FD & 418.26 & 0.24 \\ SEM & 3769.98 & 1.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison table of calculation costs. Figure 3: Snapshots of particle-velocity components (**a**) \(v_{x}\) and (**b**) \(v_{z}\) at \(t=0.5\) s. The red line denotes the fluid-solid interface. layer (\(z<0\)) in the vertical direction and propagates along the fluid-solid interface, with weak vertical propagation. Then, we take the Thomsen parameters \(\epsilon=0.2\), \(\delta=-0.05\), and the polar angle \(\theta=30^{\circ}\) as the initial values. We select four sets of Thomsen parameters along with a set of initial values, and test the arrival time for Scholte wave on this point at different polar angles (Figure 6). When the parameter values are initial (blue), the curve as a whole is close to sinusoidal, with variations at extreme values. It has quasi periodicity, but there is a maximum value around \(\theta=45^{\circ}\). We vary the values of the Thomsen parameters and test the arrival time for the Scholte wave on this point at different polar angles again. We can find that the overall trend is consistent across all curves. Without modifying the experimental parameters such as velocity and density, we find that \(\epsilon\) (purple and green) has a greater effect on the arrival time of the Scholte wave than \(\delta\) (red and yellow) in Figure 6, and there is still a peak around \(\theta=45^{\circ}\). Changing the value of \(\delta\) makes the maximum disappear.