Real Earth media is anelastic, which affects both kinematics and dynamics of propagating waves. Waves are attenuated and dispersed. If anelastic effects are neglected, inversion and migration can yield erroneous results. The anelastic effects, on propagating waves, in real rocks can be well described by a viscoelastic model. Hence, viscoelastic wave propagation simulation is a well suited base for a realistic inversion algorithm derived through the adjoint state technique. We have developed a finite-difference simulator to model wave propagation in viscoelastic media. The viscoelastic scheme is only slightly more expensive than analogous elastic schemes. This thesis also presents a method for modeling of constant Q as a function of frequency based on an explicit closed formula for calculation of the parameter fields. The τ-p (intercept time-slowness) domain permits economical modeling and inversion of 3-D wave propagation in layered media.