High-order recursive convolution method for viscoacoustic wave modeling

An accurate and efficient modeling method is critical for studying seismic wave propagation, which is essential for full-waveform inversion. High-order temporal numerical methods can significantly improve the performance of viscoacoustic wave modeling, particularly in computational accuracy and efficiency. A high-order recursive convolution (RC) method is presented based on the staggered Adams-Bashforth time-stepping scheme derived from Taylor series expansion. This method can achieve arbitrary order by retaining a varying number of terms for calculating the temporal convolutions involved in viscoacoustic wave modeling. Theoretical analysis demonstrates that our high-order RC method achieves superior accuracy in viscoacoustic wave modeling. Furthermore, it outperforms the conventional high-order auxiliary differential equation (ADE) method in terms of memory cost and runtime. Numerical tests conducted in 1D and 2D settings verify the efficiency of our method. For instance, in a 2D scenario with a 1000 × 1000 grid, the fourth-order RC method reduces computation time by 27% and memory usage by 12% compared with the fourth-order ADE method while maintaining the same accuracy level. In addition, simulations using the Marmousi model confirm the accuracy and applicability of the high-order RC method for heterogeneous models.