Abstract
The mathematical formulations of the wave propagation problem in a linear viscoelastic solid are reviewed from the point of view of constitutive equations and the theory of linear physical systems. Various general results from the theory of propagating singular surfaces and from the mathematical theory of hyperbolic equations are applied to the analysis of the wave propagation process. The impulse responses of three viscoelastic media are analyzed by use of asymptotic methods. The three material models are the standard linear solid, the standard linear solid with a continuous spectrum of relaxation times, and the power law solid. The standard linear solid with a continuous spectrum of relaxation times and the power law solid have a nearly constant quality factor, Q, over the seismic frequency band. The impulse responses of these two viscoelastic solids are compared. The results show significant and discernible features in the wave profile. It is concluded that differentiation of the models can be made by comparing wave shapes and that a complete knowledge of Q over the entire frequency range is required to determine the wave propagation problem when initiated by an impulsive process. 11 figures, 1 table.
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