ABSTRACT
This chapter describes the non-linear field in the context of equilibrium thermodynamics. It considers the equations of motion, boundary conditions, Raleigh wave, body waves and the reflection transmission problem for a composite medium composed of elastic components. The chapter shows that the interpretation of the wave numbers representing the direction of propagation and the attenuation of the waves in elasticity theory is not correct for composite media. When two or more elastic solids interact at the pore scale, their coupled interactions at the pore scale must be accounted for when describing deformations at much larger scales. What is observed is that not only are two coupled equations of motion obtained but a new dynamic variable and associated equation is obtained that describes how their volume fractions change in time. This differs substantially from standard seismic analyses which present slight deviations from elasticity.
