  Members of a wide class of geomaterials are known to display complex and
fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range
of bulk strains, down to surprisingly low values, e.g., 10^{-7}. In this paper
we investigate two sandstones, Berea and Fontainebleau, and characterize their
behavior under the influence of very small external forces via carefully
controlled resonant bar experiments. By reducing environmental effects due to
temperature and humidity variations, we are able to systematically and
reproducibly study dynamical behavior at strains as low as 10^{-9}. Our study
establishes the existence of two strain thresholds, the first, epsilon_L, below
which the material is essentially linear, and the second, epsilon_M, below
which the material is nonlinear but where quasiequilibrium thermodynamics still
applies as evidenced by the success of Landau theory and a simple macroscopic
description based on the Duffing oscillator. At strains above epsilon_M the
behavior becomes truly nonequilibrium -- as demonstrated by the existence of
material conditioning -- and Landau theory no longer applies. The main focus of
this paper is the study of the region below the second threshold, but we also
comment on how our work clarifies and resolves previous experimental conflicts,
as well as suggest new directions of research.
