Abstract: Compared with the integer derivative, the fractional differential operator can describe a complex mechanical and physical process with historical dependence and spatial global correlation more succinctly. But the computational complexity and the storage capacity of the numerical simulation of fractional wave equations will increase, especially for the simulation of long or large computational domains. In this paper, three kinds of calculation methods are given:global memory method, short-term memory method, and adaptive memory method. These three methods were applied to the simulation of the fractional-order wave propagation equations in a vicious fluid-saturated vicious two-phase VTI medium. Comparing the simulation accuracy, calculation time and memory usage of the three methods, we found that although the short-term memory method could adjust the calculation time and memory by setting the short-term memory length, the shorter the short-term memory length, the worse the accuracy. On the premise of ensuring accuracy, the adaptive memory method is a compromise between the short-term memory and the global memory methods in terms of calculation time and memory occupation. In the process of forward modeling, not only should the model be closer to the actual underground media, but also the selected numerical algorithm needs to balance the calculation time, the calculated storage capacity, and the precision. This method provides a reference for the follow-up forward modeling and the development of the new fractional numerical algorithm.

Key words: fractional temporal derivative, short-term memory method, adaptive memory method, viscoelasticity, two-phase medium