Resonance inversion for elastic moduli of anisotropic rocks

Abstract

In this research, acoustic resonance spectroscopy was applied to determine the dynamic elastic constants of isotropic glass and transversely isotropic rock cubes. This technique consists of resonating the specimen over a broad range of frequencies, measuring the resonance frequencies, and computing the elastic constants by nonlinear inversion of the measured resonance frequencies. Specimens were tested under unconfined, traction free conditions. Resulting surface vibrations were measured using a miniature accelerometer and their spectral characteristics were analyzed. The inversion was performed using a numerical algorithm based on the Rayleigh–Ritz method that minimized the difference between measured and computed resonance frequencies iteratively. Mode shapes of the anisotropic specimens were also measured using a laser Doppler vibrometer and compared with the prediction of the numerical model. Comparison between the elastic moduli of rock specimens determined by static loading tests, resonance inversion, and ultrasonic transmission tests showed good agreement between the ultrasonic and resonance results but the moduli determined from ultrasonic measurements were consistently higher than the resonance inversion. Such results may be due to the frequency-dependence of the wave velocity in microscopically heterogeneous rock and nonelastic (frictional) deformation of the rock specimen during the static loading tests.