Generalized anelastic asymptotic ray theory

This paper deals with dispersion and attenuation of body waves in a wide range of materials representing realistic rock structures. The time-domain asymptotic ray theory is applied to a new generalized coordinate-free wave equation with an arbitrary tensor relaxation function. This function describes any general viscosity that can occur in 3D anisotropic and laterally inhomogeneous media of practical interest. Perfect elasticity and existing anelastic models (linear viscoelasticity, power-law models, Biot’s fluid flow, thermoelasticity, etc.) are considered as special cases. A ray-series solution is obtained for both the principal and additional components. This solution is suitable for the analysis of anelasticity problems involving propagation of evanescent waves provided that the causality principle is respected. Accuracy of the principal component is numerically tested.