Theoretical bounds on the adiabatic compressibility of rocks

Upper and lower bounds on the adiabatic bulk modulus are calculated using energy principles for two cases. In the high-frequency case, deformation is adiabatic on the scale of a single grain, and temperature may vary from grain to grain. Bounds are found to be given by the Voigt and Reuss averages of the components of the adiabatic stiffness and compliance tensors. At lower frequencies, deformation is adiabatic overall, but temperature of adjacent grains has sufficient time to reach an equilibrium value. Bounds at high frequencies for olivine at room temperature are found to be nearly equal numerically to the low-frequency bounds.