Modeling the variability of seismic properties of frozen multiphase media depending on temperature

A three-phase model of a deformable porous medium saturated with a mixture of liquid and gas is presented. The derivation of the model is based on the theory of Hyperbolic Thermodynamically Compatible systems (HTC) applied to a mixture of solid, liquid and gas. The resulting governing equations are hyperbolic and satisfy the laws of thermodynamics (energy conservation and entropy growth). Based on the formulated nonlinear model, governing equations for modeling the propagation of small amplitude seismic waves are obtained. These equations have been used to study the variability of wave fields caused by temperature changes in geological media with porous structures saturated with a mixture of liquid and gas. Numerical examples are presented to illustrate the peculiarities of wave propagation in media of varying porosity and different ratios of liquid and gas fractions. The finite difference scheme on staggered grids has been used for the numerical solution.