The Study of Elastic Symmetry and Anisotropy of Elastic Body Waves In Gneiss

Abstract

SUMMARY This paper describes a method for determining the effective elastic constants of anisotropic rocks from the results of ultrasonic measurements of the phase velocity of elastic body waves with arbitrary directions of the wave normal in the absence of a priori information on the texture symmetry. For estimating the regular and fluctuating components of the effective tensor of elastic constants the method requires the measurement of phase velocities along nine directions in a sample having the form of a cuborhombododecahedron. The rock symmetry category is determined beforehand from the symmetry of the acoustic tensor, and a standard coordinate system is chosen along eigenvectors of the latter. Rules for selecting the standard acoustic coordinate system for rocks of any symmetry have been formulated. The initial approximation of elastic constants is found from exact equations connecting the elastic constants and the acoustic tensor components, as well as from equations connecting the elastic constants in the working and auxiliary coordinate systems. The fluctuational components of measured values of effective phase velocities are smoothed using the convolution property of the acoustic tensor. The mean elastic constants are calculated from a set of equations, which includes convolutions of the elastic tensor and a linearized set of equations with elastic displacement vectors. The proposed method has been applied to the results of ultrasonic measurements of a twice-deformed gneiss sample from the Lodogian series of the Baltic Shield. Experimental findings conform to triclinic symmetry.