Differential Acoustic Resonance Spectroscopy: Improved Theory and Application in the Low Frequency Range

ziff davis;

Differential acoustic resonance spectroscopy (DARS) was developed to examine changes in the resonant frequencies of a cavity perturbed by the introduction of a centimetre-sized sample. Resonant frequency shifts, measured at different resonance modes and between empty and
sample-loaded cavities, were used to infer the acoustic properties of the loaded samples in the low frequency range (0.5–2 kHz). To some extent, this laboratory-based measurement technique fills an experimental gap between the low-frequency stress–strain method (quasistatic to several kHz) and the ultrasonic transmission technique (hundreds of kHz to MHz). By means of an effective perturbation model against the DARS system, this study presents a Green’s function-based theoretical derivation of an amended DARS perturbation formula under a general impedance boundary condition. Numerical and experimental results show that the amended DARS perturbation is able to reflect the DARS operation mechanism more accurately and more precisely than past efforts. In addition, inversion was performed by fitting the resonance frequencies, measured at various locations inside the DARS resonance cavity, in a least-square sense to estimate the acoustic properties of a test sample. Inversion implementation at different resonance modes makes it possible to perform direct dispersion analysis on reservoir rocks at different low-frequency bands. The results of this study show that the DARS laboratory device, in conjunction with the amended perturbation formula and the proposed inversion strategy, are useful tools for estimating the acoustic properties of centimetre-sized rock samples in the low frequency range.