VISCOELASTIC PROPERTIES OF THE STANDARD LINEAR SOLID*

Abstract

ABSTRACT This study is an attempt to find a phenomenological model which will behave in a manner similar to that of common earth materials in regard to the dependence of attenuation and phase velocity on frequency. An analysis of two commonly employed rheological models, Maxwell's and Kelvin‐Voigt's and their variants, is presented indicating that these models are too simple to conform phenomenologically to the behavior of rocks. It is shown that a linear combination of the Maxwell and Kelvin‐Voigt models, known as the standard linear solid, comes closer to giving an adequate description of the behavior of some earth materials, than either one of the two models. A method of determining the viscoelastic constants of a solid is presented provided that its attenuation and dispersion curves are known. The viscoelastic constants (relaxation times and/or viscosity coefficients) of the solid are determined by superimposing the experimental curves on master curves, and reading the constants off the theoretical curves. An analysis of published experimental data is presented, indicating that the present model is capable of accounting for at least some attenuation and dispersion phenomena.