Numerical modeling of transient seismic fields in viscoelastic media based on the Laguerre spectral method

The wave propagation in real media can be described within the framework of the theory of linear viscoelasticity. The presence of convolutional integral in Boltzmann' superposition principle poses the main difficulties in implementing the direct numerical methods in time domain. The paper presents an efficient algorithm, based on the application of the spectral Laguerre method for approximation of temporal derivatives as applied to the problem of seismic wave propagation in the heterogeneous viscoelastic medium.