Acoustic nonlinearities in earth solids

Abstract

Nonlinear elastic response in earth solids is a robust and representative physical characteristic. In this lecture the evidence leading to this conclusion is presented by providing an overview of theoretical and experimental developments in the domain. Illustrated measurements include those of nonlinear response in rock from a variety of dynamical wave experiments. The evidence leads to a pattern of unifying behavior. Nonlinear elasticity in earth solids is large relative to most materials; hysteresis and ‘‘discrete’’ memory play an important role in nonlinear properties of earth solids; nonlinear response is evident over a large frequency interval (dc to several MHz at least); and nonlinear response is significant, as is commonly appreciated, at large static and dynamic strain levels, but also at small strains where this behavior and the manifestations of this behavior are commonly disregarded. Recently, the methodology for extracting the nonlinear coefficients for a material have been proposed. Some theoretical models of structural nonlinearity of solid media and of wave propagation in such media are also described.