**Fractional Time Derivative Seismic Wave Equation Modeling for Natural Gas Hydrate**

**Yanfei Wang 1,2,3,\*, Yaxin Ning 1,2,3 and Yibo Wang 1,3**


Received: 1 October 2020; Accepted: 3 November 2020; Published: 12 November 2020

**Abstract:** Simulation of the seismic wave propagation in natural gas hydrate (NGH) is of grea<sup>t</sup> importance. To finely portray the propagation of seismic wave in NGH, attenuation properties of the earth's medium which causes reduced amplitude and dispersion need to be considered. The traditional viscoacoustic wave equations described by integer-order derivatives can only nearly describe the seismic attenuation. Differently, the fractional time derivative seismic wave-equation, which was rigorously derived from the Kjartansson's constant-*Q* model, could be used to accurately describe the attenuation behavior in realistic media. We propose a new fractional finite-difference method, which is more accurate and faster with the short memory length. Numerical experiments are performed to show the feasibility of the proposed simulation scheme for NGH, which will be useful for next stage of seismic imaging of NGH.

**Keywords:** natural gas hydrate; seismic modeling; fractional derivatives; numerical simulation
