*3.4. Comparison of Spatial Dispersion Suppression Effect*

As the shear wave has the characteristics of low propagation speed, a one-dimensional low-speed homogeneous medium is constructed below. The velocity of the homogeneous medium model is 1000 m/s, the excitation position is located in the center of the model, and the source is a 10 Hz Rayleigh wavelet. Different space steps are set with a time step of 1 ms, the seismic records of 6 s are recorded, and the results are shown in Figures 3–5. As shown in Figure 3, the traditional CFD scheme has numerical dispersion when the gird size is 9 m, and the dispersion increased substantially when the step increases to 10 m (Figure 5). In contrast, as shown in Figure 4, the corresponding seismic record calculated with the

CCD scheme shows no numerical dispersion, and there is still no numerical dispersion when the gird size increases by 10 m (Figure 5).

**Figure 3.** (**a**) CFD is used to simulate the numerical simulation of seismic records in the 1D homogeneous medium model, Δx = 9 m; (**b**) CCD is used to simulate the numerical simulation of seismic records in the 1D homogeneous medium model, Δx = 9 m.

**Figure 4.** *Cont*.

**Figure 4.** (**a**) CFD is used to simulate the numerical simulation of seismic records in the 1D homogeneous medium model, Δx = 10 m; (**b**) CCD is used to simulate the numerical simulation of seismic records in the 1D homogeneous medium model, Δx = 10 m.

**Figure 5.** (**a**) CCD is used to simulate the numerical simulation of seismic records in the 1D homogeneous medium model, Δx = 15 m; (**b**) CSCD is used to simulate the numerical simulation of seismic records in the 1D homogeneous medium model, Δx = 15 m.

Figure 5a,b compare the numerical dispersion between the CCD and CSCD schemes when the step increases to 15 m. As shown in Figure 5a, at the speed of 1000 m/s, when the gird size continues to increase to 15 m, the CCD scheme shows dispersion, while the CSCD scheme shows no numerical dispersion at the same step. This confirms that the CSCD scheme improves the compactness of the CCD scheme and can better suppress the numerical dispersion so that a coarser grid may be used in the numerical simulation.
