A discrete representation of a heterogeneous viscoelastic medium for the finite-difference modelling of seismic wave propagation

The accuracy and efficiency of numerical simulations of seismic wave propagation and earthquake ground motion in realistic models strongly depend on discrete grid representation of the material heterogeneity and attenuation. We present a generalization of the orthorhombic representation of the elastic medium to the viscoelastic medium to make it possible to account for a realistic attenuation in a heterogeneous viscoelastic medium with material interfaces. An interface is represented by an averaged orthorhombic medium with rheology of the Generalized Maxwell body (GMB-EK, equivalent to the Generalized Zener body). The representation is important for the possibility of applying one explicit finite-difference scheme to all interior grid points (points not lying on a grid border) no matter what their positions are with respect to the material interface. This is one of the key factors of the computational efficiency of the finite-difference modelling. Smooth or discontinuous heterogeneity of the medium is accounted for only by values of the effective (i.e. representing reasonably averaged medium) grid moduli and densities. Accuracy of modelling thus very much depends on how the medium heterogeneity is represented/averaged. We numerically demonstrate accuracy of the developed orthorhombic representation. The orthorhombic representation neither changes the structure of calculating stress-tensor components nor increases the number of arithmetic operations compared to a smooth weakly heterogeneous viscoelastic medium. It is applicable to the velocity-stress, displacement-stress and displacement FD schemes on staggered, partly staggered, Lebedev and collocated grids. We also present an optimal procedure for a joint determination of the relaxation frequencies and anelastic coefficients.