**5. Conclusions**

We have introduced a more rigorous form of definition of fractional derivative to calculate the fractional time derivative of the viscoasoustic wave equation, which is more accurate and simpler than the other nearly constant-*Q* methods for describing the propagation of viscoasoustic wave. The rigorous form is the limit of the original definition when time step approaching zero. We discretize the rigorous form and bring it into the fractional time derivative wave equation to obtain the explicit expression of viscoelastic wave extrapolation. The computation time of the new method is merely about 20% of the original method at the same memory length. Some numerical examples demonstrate that the solution calculated by the new method is more accurate and stable in the uniform model or the large contrast velocity and *Q* model. By the new method, we can choose a smaller memory length at an acceptable accuracy; thereby, we can save memory resources and computation time. For the wavefield simulation of gas hydrate layer, White theory is selected to establish velocity and quality factor models, and then the fractional wave equation is used to simulate the propagation of seismic waves in the hydrate model. Finally, the connection between the elastic parameters and content of each component of the rock in the hydrate layer, the seismic wave speed, attenuation characteristics, and the law of seismic wave propagation are established. The above contents provide theoretical foundation for identifying gas hydrate and estimating hydrate content by seismic exploration.

**Author Contributions:** Y.W. (Yanfei Wang) designed the study. Y.N. and Y.W. (Yanfei Wang) conducted experiments. Y.W. (Yanfei Wang), Y.N. and Y.W. (Yibo Wang) wrote the paper. All authors contributed to synthetic data interpretation and provided significant input to the final manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Original Innovation Program of CAS (grant no. ZDBS-LY-DQC003), the Key Research Program of the Institute of Geology & Geophysics, CAS (grant no. IGGCAS-201903), and the National Key R & D Program of the Ministry of Science and Technology of China (grant nos. 2018YFC0603500 and 2018YFC1504203).

**Acknowledgments:** We are grateful to four reviewers' important questions and suggestions which make an improvement of our paper.

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