New numerical schemes for time-domain seismic wave modeling in viscoelastic media

To avoid extensive computation of convolution, common time-domain viscoelastic wave modelling often applies either fractional derivatives or solve many auxiliary partial differential equations of memory variables. Basing on the general Zener model, we found that the memory variables or the convolutions can be directly calculated in a semi-analytic manner, which results in recursive formulas for efficient computations of the convolutions. The formulas show that the computations only require the two wavefields at the time interval, and the accuracies only depend on the time step, and the wavefields at the time interval, nothing related to the time-stepping schemes to solve the partial differential equations of the memory variables. Applying the semi-analytic formulas, new sets of the 1^st- and 2^nd-order viscoelastic wave equations are established and shown the similar forms to the elastic cases except for the extra 'body-source' terms.