Brian P. Bonner

Ultrasonic velocity-porosity relationships for sandstone analogs made from fused glass beads

Using fused glass beads, we have constructed a suite of clean sandstone analogs, with porosities ranging from about 1 to 43 percent, to test the applicability of various composite medium theories that model elastic properties. We measured P‐ and S‐wave velocities in dry and saturated cases for our synthetic sandstones and compared the observations to theoretical predictions of the Hashin‐Shtrikman bounds, a differential effective medium approach, and a self‐consistent theory known as the coherent potential approximation. The self‐consistent theory fits the observed velocities in these sandstone analogs because it allows both grains and pores to remain connected over a wide range of porosities. This behavior occurs because this theory treats grains and pores symmetrically without requiring a single background (host) material, and it also allows the composite medium to become disconnected at a finite porosity. In contrast, the differential effective medium theory and the Hashin‐Shtrikman upper bound overest...

Influence of microstructure on rock elastic properties

Depending on details of the composite microstructure, different theories may be needed to obtain good agreement with measured elastic properties. This observation is especially pertinent whenever the composite is porous, as is normally true for rocks. Predictions of three theories are compared to data for porous glass samples. The differential effective medium (DEM) theory and Hashins composite spheres assemblage (H) do a good job of predicting elastic behavior of a porous foam composed of glass. The self-consistent (SC) effective medium theory does equally well at predicting behavior of a sintered glass-bead sample. The realizable microstructure of each theoretical model is a good analog of the microstructure for one or the other of these two very different porous glasses. Velocities of granular rocks such as sandstones may be estimated accurately using the SC theory, whereas velocities of rocks such as basalts having isolated cracks and pores may be better estimated using either the DEM theory or Hashins model.

Estimating rock porosity and fluid saturation using only seismic velocities

Evaluation of the fluid content in deep earth reservoirs or fluid contaminants in shallow earth environments has required the use of geophysical imaging methods such as seismic reflection prospecting. Interpretation of seismic velocities and amplitudes is based on theories of fluid‐saturated and partially saturated rocks that have been available since the 1950s. Here we present a new synthesis of the same physical concepts that uses compressional‐wave velocities together with shear‐wave velocities in a scheme that is much simpler to understand and apply yet yields detailed information about porosity and fluid saturation magnitudes and spatial distribution. The key idea revolves around the fact that the density and the Lame elastic parameter λ are the only two parameters determining seismic velocities that also contain information about fluid saturation. At low enough frequencies, Gassmanns well‐known equations show that the shear modulus is independent of the fluid saturation level. We use these facts to...

Slow wave propagation in air‐filled porous materials and natural rocks

Slow compressional waves in fluid‐saturated porous solids offer a unique acoustical means to study certain material properties, such as tortuosity and permeability. We present a novel experimental technique based on the transmission of airborne ultrasound through air‐filled porous samples. The suggested method can be used to measure the velocity and attenuation of the slow compressional wave in a wide frequency range from 30 to 500 kHz. More important, the technique is so sensitive that it provides irrefutable evidence of slow wave propagation in air‐saturated natural rocks and lends itself quite easily to tortuosity measurements in such materials, too.

Ultrasonic Attenuation Measurement by Spectral Ratios Utilizing Signal Processing Techniques

A new approach using signal averaging and signal processing is described for measuring ultrasonic attenuation of compressional (P) and shear (S) waves in highly attenuative (low Q) materials. Broadband ultrasonic pulses in the frequency range of 0.7-1.1 MHz are transmitted through a specimen to be characterized for comparison to a reference with low dissipation. Attenuation is calculated from the ratio of spectral amplitudes which are corrected for diffraction effects. An experimental example is given based upon measurements made on dry polycrystalline sodium chloride (halite or rock salt) from Avery Island, LA. The measured QP of compressional waves is 46 ± 5.5 and QS of shear waves is 12 ± 0.3. This is a through transmission technique which gives results for materials so lossy that multiple echoes cannot be detected.

Transformation of Seismic Velocity Data to Extract Porosity and Saturation Values for Rocks

For wave propagation at low frequencies in a porous medium, the Gassmann-Domenico relations are well-established for homogeneous partial saturation by a liquid. They provide the correct relations for seismic velocities in terms of constituent bulk and shear moduli, solid and fluid densities, porosity and saturation. It has not been possible, however, to invert these relations easily to determine porosity and saturation when the seismic velocities are known. Also, the state (or distribution) of saturation, i.e., whether or not liquid and gas are homogeneously mixed in the pore space, is another important variable for reservoir evaluation. A reliable ability to determine the state of saturation from velocity data continues to be problematic. It is shown how transforming compressional and shear wave velocity data to the (rho/lambda, mu/lambda)-plane (where lambda and mu are the Lame parameters and rho is the total density) results in a set of quasi-orthogonal coordinates for porosity and liquid saturation that greatly aids in the interpretation of seismic data for the physical parameters of most interest. A second transformation of the same data then permits isolation of the liquid saturation value, and also provides some direct information about the state of saturation. By thus replotting the data in the (lambda/mu, rho/mu)-plane, inferences can be made concerning the degree of patchy (inhomogeneous) versus homogeneous saturation that is present in the region of the medium sampled by the data. Our examples include igneous and sedimentary rocks, as well as man-made porous materials. These results have potential applications in various areas of interest, including petroleum exploration and reservoir characterization, geothermal resource evaluation, environmental restoration monitoring, and geotechnical site characterization.

Excitation of surface waves of different modes at fluid–porous solid interface

The presence of ultrasonic surface waves of various modes on a fluid–porous solid interface is demonstrated and their velocities measured. The experimental technique (developed earlier by one of the authors for a fluid–isotropic solid interface) utilizes reflected broadband spectra from periodic surfaces. Three sharp minima corresponding to three mode‐converted waves coupled to the porous solid are observed. The velocities of these ‘‘surface’’ waves are in qualitative agreement with theoretical predictions [S. Feng and D. L. Johnson, J. Acoust. Soc. Am. 74, 906 (1983) and 74, 915 (1983)] and are identified as pseudo Rayleigh, pseudo Stoneley, and true Stoneley waves.

Automatic, digital system for profiling rough surfaces

Four pneumatically actuated reciprocating probes and a translating table are computer controlled to map surfaces with asperity heights of up to 25 mm. The height of a calibration surface can be determined to 0.002 mm. Individual traces may be sampled as often as every 0.025 mm with a neighboring trace as near as 0.031 mm. Surfaces with dimensions of up to 355×150 mm can be scanned with the system.

Slow wave imaging of permeable rocks

A high-resolution slow wave imaging system based on attenuation measurement of transmitted airborne ultrasonic waves was developed to study the inhomogeneous pore structure in permeable formations. Currently, the threshold sensitivity of our system is approximately 100 mD, making possible the characterization of typical petroleum reservoir rocks with spatial resolution of between 0.5 and 5 mm in the 50 kHz to 500 kHz frequency range. The degree of disorder in permeable solids is of crucial importance especially when the relative permeability is considered. It is expected that this new technique can complement such methods as hydrodynamic dispersion measurements and petrography for characterizing flow in porous rocks.

Nonlinear acoustic effects in rocks and soils

When natural materials are loaded by a stress field, dramatic changes in modulus occur as the microstructure deforms, even if there is no permanent macroscopic damage. The effect is primarily due to pervasive, thin microfractures which easily close under load. The pressure derivative of a generalized elastic modulus, M=dC/dP, for most intact solids equals ~5, but can be two orders of magnitude higher for rocks and soils [1]. Nonlinear terms in the stress strain relation that governs material response can therefore be very important. Measurements of longitudinal and shear velocity under hydrostatic and uniaxial loading for various rocks are reported to illustrate these phenomena. Observations of amplitude dependent attenuation are presented to show direct evidence of nonlinear behavior. New results presented here for partially saturated rocks show the strongest nonlinear response yet reported.