Experimental studies on perturbed acoustic resonant spectroscopy by a small rock sample in a cylindrical cavity

Abstract

A measurement system for acoustic resonant spectroscopy (ARS) is established, and the effects of resonant cavity geometry, inner perturbation samples and environmental temperature on the ARS are investigated. The ARSs of the small samples with various sizes and acoustic properties are measured. The results show that at the normal pressure, the resonant frequency decreases gradually with the increase of liquid temperature in the cylindrical cavity, while the resonant amplitude increases. At certain pressure and temperature, both the resonant frequency and the amplitude decrease greatly when there exist air bubbles inside the cavity fluid. The ARS is apparently affected by the sample porosity and the sample location in the resonant cavity. At the middle of the cavity, the resonant frequencies reach their maximum values for all of the measurement samples. The resonant frequencies of the porous rock samples are smaller than those of the compacted samples if other acoustic parameters are the same. As the sample is moved from the top to the middle of the cavity along its axis, the resonant amplitude increases gradually for the compacted rocks while decreases for the unconsolidated rocks. Furthermore, the resonant amplitude increases firstly and then decreases if the porosity of the rock sample is relatively small. In addition, through the comparisons between the experimental and theoretical results, it is found that the effects of the acoustic parameters and sizes of the samples and the size of the cylindrical cavity on the laboratory results agree well with the theoretical ones qualitatively. These results may provide basic reference for the experiment study of rock acoustic properties in a low frequency using ARS.Keywords: acoustic resonant spectroscopy, acoustic velocity and attenuation, experiment measurement, rock acoustic property.

Some theoretical aspects of elastic wave modeling with a recently developed spectral element method

“…Although isotropic and elastic media are considered, this method can be extended to anisotropic and porous elastic ones, for example, poroelastic wave modelling and numerical modelling for acoustic resonance spectroscopy of a rock sample [38] . Note that, since p q r s t + + + + is an even number, it is easy to show that m L is also even number.…”

An accurately fast algorithm of calculating reflection/transmission coefficients

“…(8) and (9), for a harmonic particle vibration with a given angular frequency ω , the relation between the particle displacement vector and the polarization coefficients for the incident wave can be written as (11) and the relation between the particle displacement vector and the polarization coefficients for the mode conversion waves can be written as…”

“…Based on their different assumptions, Richards and Frasier [2] , Aki and Richards [3] , Shuey [4] and Thomsen [5] gave several approximate expressions for isotropic models. Fa et al [6] and Che et al [7] researched the directivity of acoustic waves radiated by a linear-array source in borehole, Chen et al [8] performed the experimental study on the physical property of a small rock sample, and their purposes are for the studies of reflection/transmission of acoustic waves radiated by the a linear array source or a general source in borehole. One important application of reflection coefficient studies is the analysis of amplitude variations with offset (AVO).…”

Resonant frequency shifts induced by a large spherical object in an air-filled acoustic cavity

“…[3][4][5][6][7][8][9] Most of these studies are theoretical, dealing with more or less elaborate techniques to predict the frequency resonance shifts for various object shapes and sizes, as well for different boundary conditions. Experimental results are scant, exceptions being the rather complete studies performed by Barmatz et al 5 and Chen et al 9 In this letter, we present an experimental study of longitudinal mode resonant frequency shifts induced by a solid spherical object in a quasi-one-dimensional air-filled acoustic cavity. We compare our results with Leung's theory, which does not account quantitatively for the observations.…”