Estimating quartz fabrics from piezoelectric measurements

An aggregate of piezoelectric minerals may itself be piezoelectric if the minerals are suitably aligned. Thus quartz-bearing rocks may be piezoelectric, since quartz is one such mineral. It has been shown that some rocks do possess this effect, termed a piezoelectric fabric (Bishop, 1981). The type of piezoelectric fabric may be determined by matching experimental data to theoretical models of piezoelectric fabrics. These theoretical models of pure quartz aggregates are derived by considering the symmetry of the preferred crystallographic directions of the aggregate grains. From the symmetry, the piezoelectric matrix of the model may be determined. The best-fitting model and the orientation of its fabric is obtained by equating the experimental data to each model in turn. For each model, the best fitting fabric orientation is determined by using an inversion routine. If the experimental data are due to a piezoelectric fabric and not to some random or nonpolar distribution of grains, the fabric type (c-axis point maximum or large-circle girdle) and its orientation with respect to the specimen may be determined. The positions and polarities of the quartz a-axes are also specified. A statistical examination of results from a quartz-mylonite shows that the problem of piezoelectric model fitting is well posed, in that the Eulerian angles that specify the fabric orientation are fairly independent important parameters and a sufficiently close fit of the model to the data can be obtained to determine the fabric.