We have developed a finite difference simulator to model wave propagation in viscoelastic media. The finite difference method was chosen in favor of other methods for several reasons. Finite difference codes are more portable than pseudo spectral codes for instance. Moreover, finite difference schemes provide a convenient environment in which to define complicated boundaries. Several finite difference schemes for viscoelastic wave propagation are thoroughly investigated with convergence tests, dispersion and stability analyses.
Seismic waves attenuate and disperse while propagating through the earth.
These anelastic effects can be large, and can adversely affect the results of imaging and inversion if neglected. Two dimensional viscoacoustics provides a reasonably realistic model for multidimensional simulation and inversion in the presence of attenuation and dispersion. The adjoint state method leads to an effective algorithm for linear least squares inversion of short wavelength model components. However the nonreversibility of the viscoacoustic system complicates its efficient implementation, as fields must be accessed in both forward and backward order in time during the adjoint state calculation. For 2D examples of dimensions typical of exploration seismology these fields are far to large too store in fast memory.