Generalized recursive convolution method for viscoelastic wave modelling

Seismic wavefield forward modeling in viscoelastic media is fundamental for both data processing and interpretation in seismic exploration. We develop a generalized recursive convolution method to accurately calculate the temporal convolutions, which are required by the constitutive relationship for anelasticity rather than solving many auxiliary partial differential equations of memory variables. The new method is based on a Taylor series expansion of the temporal convolution and is very competitive with the widely-used memory variable method and the conventional recursive convolution methods. We conduct theoretical and numerical comparisons of the new method with the common leapfrog time-stepping memory variable method and other traditional recursive convolution methods. Our numerical examples verify the accuracy of the new method for viscoacoustic and viscoelastic wave modeling.