Elastic anisotropy estimation from laboratory measurements of velocity and polarization of quasi-P-waves using laser interferometry

Abstract

A new method for conducting laboratory measurements of the velocities and polarizations of compressional and shear waves in rock samples uses a laser Doppler interferometer (LDI). LDI can measure the particle velocity of a small (0.03 mm2) element of the surface of the sample along the direction of the laser beam. By measuring the particle velocity of the same surface element in three linearly independent directions and then transforming those velocities to Cartesian coordinates, three orthogonal components of the particle-velocity vector are obtained. Thus, LDI can be used as a localized three-component (3C) receiver of ultrasonic waves, and, together with a piezoelectric transducer as a source, it can simulate a 3C seismic experiment in the laboratory. Performing such 3C measurements at various locations on the surface of the sample produces a 3C seismogram, which can be used to separate the P-wave and two S-waves and to find the polarizations and traveltimes of those waves. Then, the elasticity tensor of the medium can be obtained by minimizing the misfit between measured and predicted polarizations and traveltimes. Computation of the polarizations and traveltimes of body waves inside a sample with a given elasticity tensor is based on the Christoffel equation. The predicted polarizations on the surface then are obtained using the anisotropic Zoeppritz equations. The type of velocity measured (phase or group velocity) depends on the acquisition geometry and the material properties. This is taken into account in the inversion procedure. A “walkaway” laboratory experiment demonstrates the high accuracy of this method.