Real earth media disperse and attenuate propagating mechanical waves.
This anelastic behavior can be described well by a viscoelastic model.
We have developed a finite-difference simulator to model wave propaga
tion in viscoelastic media. The finite-difference method was chosen in
favor of other methods for several reasons. Finite-difference codes a
re more portable than, for example, pseudospectral codes. Moreover, fi
nite-difference schemes provide a convenient environment in which to d
efine complicated boundaries. A staggered scheme of second-order accur
acy in time and fourth-order accuracy in space appears to be optimally
efficient. Because of intrinsic dispersion, no fixed grid points per
wavelength rule can be given; instead, we present tables, which enable
a choice of grid parameters for a given level of accuracy. Since the
scheme models energy absorption, natural and efficient absorbing bound
aries may be implemented merely by changing the parameters near the gr
id boundary. The visoelastic scheme is only marginally more expensive
than analogous elastic schemes. The efficient implementation of absorb
ing boundaries may therefore be a good reason for also using the visco
elastic scheme in purely elastic simulations. We illustrate our method
and the importance of accurately modeling anelastic media through 2-D
and 3-D examples from shallow marine environments.