**5. Conclusions**

In this paper, we proposed a fourth-order time difference solution for the shear-wave equation using the supercompact difference scheme and the combined supercompact difference scheme. We carried out a detailed comparison of their accuracy in numerical simulations and reverse-time migrations. Thus, we reached the following conclusions:

The combined compact difference scheme (CCD) has the characteristics of low numerical dispersion, high stability, and simulation accuracy. It is suitable for the numerical simulation of the seismic wavefield with large space and time steps. It provides an effective method for simulating shear-wave propagation and implementing shear-wave reverse-time migration.

The combined supercompact difference scheme (CSCD) is extended and optimized from the combined compact difference scheme (CCD). Compared with its prototype, the supercompact difference scheme, the combined supercompact difference scheme further suppresses the numerical dispersion caused by the increase in spatial step length and is suitable for numerical simulation with even larger spatial step length.

Finally, we carried out the reverse-time migration imaging of the Marmousi model of shear-wave velocity under isotropic conditions. The combined supercompact difference scheme (CSCD) yields the best shear-wave imaging results of the Marmousi model when compared with the other methods. These results reveal the potential for further extending the supercompact difference scheme and the combined supercompact difference scheme forward simulation of shear waves in complex media such as two-dimensional or threedimensional anisotropic media and viscoelastic media. It is worth highlighting that the method presented in this paper is restricted to isotropic media at the moment. However, these results reveal the potential for further extending the supercompact difference scheme and the combined supercompact difference scheme forward simulation of shear-wave in complex media such as two-dimensional or three-dimensional anisotropic or viscoelastic media. Of course, the method in this paper also has its limitations, such as low computational efficiency, making it very challenging to apply to three-dimensional media, which is also the focus of our subsequent research.

**Author Contributions:** Conceptualization, C.Z.; Funding acquisition, X.L.; Formal analysis, W.Y.; Investigation, C.Z.; Methodology, C.Z., X.L. and P.S.; Project administration, W.W., X.L. and P.S.; Resources, W.Y.; Software, C.Z. and W.Y.; Supervision, P.S.; Validation, W.W.; Visualization, C.Z.; Writing—original draft, C.Z.; Writing—review & editing, W.W. and X.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** The study is supported by the Science and Technology Research and Development Project of CNPC (2021DJ3506) and (2021ZG03) and R&D Department of China National Petroleum Corporation (Investigations on fundamental experiments and advanced theoretical methods in geophysical prospecting applications, 2022DQ0604-02).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

