*2.4. Principle of Combined Compact Difference Scheme*

The combined compact difference (CCD) to suppress the numerical dispersion caused by the spatial step size are enclosed in this paper to solve the problem of low SH shear wave velocity; the formula is as follows [35,36]:

$$\begin{cases} \begin{aligned} a\_1(f\_{i+1}' + f\_{i-1}') + f\_i' + hb\_1(f\_{i+1}'' - f\_{i-1}'') &= \frac{1}{h} \sum\_{m=1}^n c\_m(f\_{i+m} - f\_{i-m})\\ \frac{1}{h} a\_2(f\_{i+1}' - f\_{i-1}') + f\_i'' + b\_2(f\_{i+1}'' + f\_{i-1}'') &= \frac{1}{h^2} \sum\_{m=1}^n d\_m(f\_{i+m} - 2f\_i + f\_{i-m}) \end{aligned} \end{cases} \tag{2}$$

In Equation (2), *h* is the grid spacing, *a*, *b*, *c*, *d* are the difference coefficient matrices; *f* is the function value of node *i*; *f <sup>i</sup>* and *f <sup>i</sup>* represent the first- and second-order derivatives of node *i*, respectively; *fi*+*m*, *fi*−*<sup>m</sup>* represent the function values of node *i* successively m nodes forward and m nodes backward; *f <sup>i</sup>*+1, *<sup>f</sup> <sup>i</sup>*−<sup>1</sup> represent the first-order derivatives of node *i* successively one node forward and one node backward, respectively; *f <sup>i</sup>*+1, *f i*−1 represent the second derivative of *i* node one node forward and one node backward. The wave field of the SH shear wave can be simulated with the above method applied to the numerical simulation of SH shear wave propagation under the condition of a twodimensional medium.

In this paper, we use the three-point sixth order format of Equation (2) for the SH shear wave reverse time migration, that is, Formula (3).

$$\begin{cases} \frac{7}{16} \left( f\_{i+1}' + f\_{i-1}' \right) + f\_i' - \frac{h}{16} \left( f\_{i+1}'' - f\_{i-1}'' \right) = \frac{15}{16h} (f\_{i+1} - f\_{i-1})\\ \frac{9}{8h} \left( f\_{i+1}' - f\_{i-1}' \right) + f\_i'' - \frac{1}{8} \left( f\_{i+1}'' + f\_{i-1}'' \right) = \frac{3}{h^2} (f\_{i+1} - 2f\_i + f\_{i-1}) \end{cases} \tag{3}$$
