From Seismic Interferometry to Resonant Ultrasound Spectroscopy in Rock Acoustics

The aim of this paper is to introduce an alternative laboratory technique for measuring the elastic constants of solid samples, including rock samples, simultaneously using the principles of Seismic Interferometry (SI) and Resonant Ultrasound Spectroscopy (RUS). The solid sample is randomly excited by a pneumatic air gun and hang to a minimal number of contact points in order to allow free vibrations. The sample is in point contact with two passive piezoelectric transducers which measure the sample response. According to the principle of SI, the cross-correlation between the two recorded noisy ultrasonic signals allows to retrieve Green’s function of the sample between these two contact points. The Fourier transform of the correlation function is closely related to the resonance spectrum of the solid sample, and can be analysed using the principles of RUS. Then the resonance peaks are identified and inverted in terms of the elastic constants of the solid samples. The method is checked on a standard aluminium cylinder. The inverted elastic constants are quite consistent with those independently measured on the same material with the conventional ultrasonic pulse transmission technique. Similar successful results on rock samples are shown to illustrate the relevance of the method to rock acoustics.