Stress induced elastic anisotropy of the Etnean basalt: Theoretical and laboratory examination

Abstract

A theory, the stress-sensitivity approach, has been developed, which relates the elastic moduli of anisotropic rocks to the stress tensor and pore pressure for an arbitrary symmetry of the applied load. The theory explains the stress-induced changes of seismic velocities in terms of stress-induced changes of the pore space geometry. The stress dependent anisotropy is described in terms of Thomsen’s anisotropy parameters, g and d. To test the theory we analyze the laboratory (high frequency) results of deformation of an isotropically crack damaged dry lava flow basalt from Mt. Etna volcano. The theory states that, under an anisotropic (i.e. axisymmetric triaxial) load and in the case of an initially isotropic rock, (1) the anisotropy parameters are linear functions of the stress exponentials (i. e. exponential functions of principal stress components) and (2) the ratio of these anisotropy parameters as a function of the stress is constant. In order to verify these relationships, the stress exponentials and the anisotropy parameters based on the measured velocities are computed as well as the expected ratio of the Thomsen’s parameters. Our experimental results are in very good agreement with the theoretically predicted relations.