# Numerical Modeling of Scholte Wave in Acoustic-Elastic Coupled TTI Anisotropic Media
## 4 Numerical Experiments
### 3D Two-Layer Acoustic-Elastic Coupled Model  
Second, we designed a 3D two-layer acoustic-elastic coupled model, where the upper and lower layer are fluid and TTI solid, respectively. The size of the model is \(1\) km \(\times\) 1 km \(\times\) 1 km. The grid spacing is \(\Delta x=\Delta z=5\) m. The lower layer is defined by the Thomsen parameters: \(V_{P0}=2.0\) km/s, \(V_{S0}=1.1\) km/s, and the Thomsen parameters are \(\varepsilon=0.2\), \(\delta=-0.05\), and \(\gamma=0.1\). 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 \(\mathrm{x}=0.5\) km, \(\mathrm{y}=0.5\) km, and \(\mathrm{z}=0.48\) km. The polar angle of the TTI symmetry axis is \(\theta=45^{\circ}\). The temporal step for the staggered-grid finite-difference method is \(\Delta t=0.5\) ms. We take observation lines as shown in Figure 8 and obtain the snapshots of different observation lines by numerical calculation (Figure 9). The parameter \(\varphi\) is the orientation of the observation line. Figure 9 shows that the wavefield snapshot includes the reflected/transmitted P wave, S wave, head wave, and the Scholte wave on the four tangent planes across the source projection point.  
Figure 8: The orientation of the observation line. \(\varphi\) denotes the orientation of the observation line. The points are used to test the arrival time of the Scholte wave.  
Figure 6: Arrival time of the Scholte wave with a different polar angle.  
However, the velocity difference of the Scholte wave in different directions is not obvious. We set the polar angle \(\theta\) to \(0^{\circ}\), \(45^{\circ}\), and \(90^{\circ}\) to characterize the Scholte wave at the fluid-solid interface, respectively (Figure 10). We find that the velocity difference of the Scholte wave is obvious when the polar angle \(\theta=90^{\circ}\) (HTI); when the polar angle \(\theta=0^{\circ}\) (VTI), there is no velocity difference of the Scholte wave in different directions. The direct  
Figure 9: Snapshots of the components (**left**) \(v_{x}\), (**centre**) \(v_{y}\), and (**right**) \(v_{z}\) at \(t=0.25\) s. The red line denotes the fluid-solid interface. The plane of parameter \(\varphi=0^{\circ}\) is XOZ plane, and the plane of parameter \(\varphi=90^{\circ}\) is YOZ plane. The Thomsen parameters are \(\varepsilon=0.2\), \(\delta=-0.05\), and \(\gamma=0.1\).  
wave propagates in the isotropic water layer, and the reflection and transmission occur at the fluid-solid interface; the direct wave is circular.  
We select four points on the fluid-solid interface (Figure 8) and record the time of Scholte waves arriving at the four points (Figure 11). The shape of the arrival time curve of the Scholte wave at point A is basically consistent with Figure 6; the peak at \(\theta=45^{\circ}\) disappears. The curve of point B is basically symmetric about \(\theta=0^{\circ}\). The curve of point C is close to the curve of point A. The curve of point D is close to the curve of point B. Figure 11 shows that the velocity of the Scholte wave at point B is positively related to the polar angle. When the polar angle \(\theta=0^{\circ}\), the curves intersect at one point. Scholte waves have the same velocity.  
In this section, we apply the algorithm to a 3D homogeneous acoustic-elastic coupled model. We find that there is a difference in the velocity of Scholte waves when the polar angle \(\theta\) changes. The curve of the Scholte wave arrival time has different motion trends with the change of polar angle \(\theta\) in different orientations.  
Figure 10: Snapshots of the components (**left**) \(v_{x}\), (**centre**) \(v_{y}\), and (**right**) \(v_{z}\) on the fluid-solid interface at \(t=0.25\) s. The Thomsen parameters are \(\varepsilon=0.2\), \(\delta=-0.05\) and \(\gamma=0.1\).