Resonant Ultrasound Spectroscopy: theory and application

Resonant Ultrasound Spectroscopy (RUS) uses normal modes of elastic bodies to infer material properties such as elastic moduli and Q. In principle, the complete elastic tensor can be inferred from a single measurement. For centimeter- sized samples RUS fills an experimental gap between low- frequency stress- strain methods (quasi- static up to a few kHz) and ultrasonic time- delay methods (hundreds of kHz to GHz). We use synchronous detection methods to measure the resonance spectra of homogeneous rock samples. These spectra are then fit interactively with a model to extract the normal- mode frequencies and Q factors. Inversion is performed by fitting the normal- mode frequencies. We have successfully applied this technique to a variety of isotropic and anisotropic samples, both man- made and natural. In this paper we will show in detail the procedure applied to a cylindrical core of Elberton granite. By means of a statistical fit of the measured normal modes and an independent laser ultrasonic measurement, the granite core was inferred to have orthorhombic symmetry. A 10 per cent P- wave anisotropy was measured in the plane perpendicular to the core axis.