  In many applications, and in particular in seismology, realistic propagation
media disperse and attenuate waves. This dissipative behavior can be taken into
account by using a viscoacoustic propagation model, which incorporates a
complex and frequency-dependent viscoacoustic modulus in the constitutive
relation. The main difficulty then lies in finding an efficient way to
discretize the constitutive equation as it becomes a convolution integral in
the time domain. To overcome this difficulty the usual approach consists in
approximating the viscoacoustic modulus by a low-order rational function of
frequency. We use here such an approximation and show how it can be
incorporated in the velocity-pressure formulation for viscoacoustic waves. This
formulation is coupled with the fictitious domain method which permit us to
model efficiently diffraction by objects of complicated geometry and with the
Perfectly Matched Layer Model which allows us to model wave propagation in
unbounded domains. The space discretization of the problem is based on a mixed
finite element method and for the discretization in time a 2nd order centered
finite difference scheme is employed. Several numerical examples illustrate the
efficiency of the method.
