Numerical experiment and analysis of the differential acoustic resonance spectroscopy for elastic property measurements

Differential acoustic resonance spectroscopy (DARS) was recently developed to estimate the elastic parameters of rock samples with a resonant frequency perturbation caused by a test sample at kilohertz frequency. In the derivation of the DARS theory, the wave inside the cavity is assumed to be a harmonic acoustic plane wave, which may be a source of measurement errors. A simulation program may help researchers to understand the mechanism of this device and to find out whether the assumption in the theory derivation is correct. In this paper, we develop a simulation program based on the elastic wave equation in cylindrical coordinates, and model the DARS system. The modeled power spectrum agrees well with that obtained by the laboratory measurement. An analysis of the wave field snapshots and the pressure distribution curves shows that the standing wave inside the cavity along its long axis is asymmetrical. This study also investigates the relationships between the resonant frequencies and the density, the compressibility and the P-wave and S-wave velocities of the samples. By numerical experiments, this paper finds that only the compressibility can be estimated with the resonant frequency, when the sample is located at the velocity node. But when the sample is located at other positions, the P-wave and S-wave velocities can alter the shape of the vibration curve, though they have no impact on the resonant power spectrum. This implies that it may be possible to estimate the P-wave and S-wave velocities by using the full waveform of the vibration curve. (paper)