An efficient short memory algorithm for the propagation of viscoacoustic waves in heterogeneous media

The time-fractional viscoacoustic wave equation has important applications in geological exploration, where it quantifies the attenuation and velocity dispersion of waves as they propagate through real Earth media. However, due to the existence of Fractional-derivatives stress-strain relations with less than one Caputo fractional derivative and the inhomogeneity of the Earth's materials, there are great challenges in maintaining both numerical accuracy and efficiency. To address these challenges, we propose an Efficient Short-Time Memory Algorithm (ESMA) scheme to efficiently solve problems associated with heterogeneous earth media. By localising the singular kernel in the fractional-order stress-strain relation and introducing an auxiliary function, the storage length of the historical variables is converted from the full historical wavefield record to an M-layer auxiliary function. Our scheme can effectively handle attenuating models with complex geometries. Several numerical examples are developed to test the feasibility and accuracy of the ESMA scheme