An Investigation of Causality for Biot Models by Using Kramers-Krönig Relations

Abstract

Kramers-Kronig integrals for the index of refraction are evaluated numerically to establish causality requirements between phase velocity and attenuation. Accuracy of numerical integrations is checked using a causal Biot (poro-elastic) model. A poroviscoelastic Biot model is developed for acoustic wave propagation in porous media, and it is demonstrated that the new model satisfies the causality principle. Non-causality of a Biot model with a slightly inelastic frame assumption is analyzed for different types of marine sediments. Acoustic pulse propagation in marine sediments is also formulated for poro-viscoelastic and slightly nonlinear Biot models, and resulting pulse shapes are compared.