A Sonic Method for petrographic analysis

Abstract

A sonic method as a tool for detecting and describing preferred crystallographic orientation has been proposed by Bennett (1972). The Q ellipsoid is a theoretical surface whose magnitude for any direction is the sum of the squares of the three seismic wave phase velocities for that direction. The orientation of the ellipsoid relative to the sample is controlled by crystal orientation and structural effects of the sample. For completely isotropic samples the Q surface is a sphere; for anisotropic samples the Q surface is ellipsoidal. Sample homogeneity is testable by the closeness of fit of the velocity data to the ellipsoidal surface. In this respect, crystal aggregates can be considered to behave as elastic long-wave equivalents to single crystals. The baraboo quartzite, a Grenville marble, and a plastically deformed granite boulder are analyzed according to the Q ellipsoid technique. Optical analysis is performed on the quartzite and marble. The oriented optical indicatrixes for the individually measured crystals are summed, an ellipsoidal surface characterizing the preferred crystal orientation direction of the sample thus being produced. For the quartzite, which is nearly isotropic, the optical surface and the sonic surface closely coincide. This situation is evidence that the sonic orientation accurately reflects the subtle crystallographic orientation. The marble displays a strong crystallographic orientation, as well as a pronounced micaceous layering. The orientation of the Q ellipsoid reflects the net effect of this structural fabric and the crystallographic fabric. The granitic boulder was plastically deformed into an ellipsoidal shape. The shape axes and the Q ellipsoid axes closely coincide, the indication being that the Q ellipsoid technique may be useful in describing regional tectonic forces.