Kenneth W. Winkler

Seismic attenuation: Effects of pore fluids and frictional‐sliding

Seismic wave attenuation in rocks was studied experimentally, with particular attention focused on frictional sliding and fluid flow mechanisms. Sandstone bars were resonated at frequencies from 500 to 9000 Hz, and the effects of confining pressure, pore pressure, degree of saturation, strain amplitude, and frequency were studied. Observed changes in attenuation and velocity with strain amplitude are interpreted as evidence for frictional sliding at grain contacts. Since this amplitude dependence disappears at strains and confining pressures typical of seismic wave propagation in the earth, we infer that frictional sliding is not a significant source of seismic attenuation in situ. Partial water saturation significantly increases the attenuation of both compressional (P) and shear (S) waves relative to that in dry rock, resulting in greater P‐wave than S‐wave attenuation. Complete saturation maximizes S‐wave attenuation but causes a reduction in P‐wave attenuation. These effects can be interpreted in term...

Friction and seismic attenuation in rocks

Precise experimental results, combined with theoretical predictions, indicate that seismic energy loss caused by grain boundary friction is important only at low confining pressure and at strains greater than about 10−6. Since these conditions are generally not encountered in seismology, frictional attenuation is not important in situ. Other mechanisms such as fluid flow must dominate seismic attenuation in the upper crust.

Permeability and borehole Stoneley waves: Comparison between experiment and theory

We performed laboratory experiments to evaluate theoretical models of borehole Stoneley wave propagation in permeable materials. A Berea sandstone and synthetic samples made of cemented glass beads were saturated with silicone oils. We measured both velocity and attenuation over a frequency band from 10 kHz to 90 kHz. Our theoretical modeling incorporated Biot theory and Deresiewicz-Skalak boundary conditions into a cylindrical geometry and included frequency-dependent permeability. By varying the viscosity of the saturating pore fluid, we were able to study both low-frequency and high-frequency regions of Biot theory, as well as the intermediate transition zone. In both low-frequency and high-frequency regions of the theory, we obtained excellent agreement between experimental observations and theoretical predictions. Velocity and attenuation (1/Q) are frequency-dependent, especially at low frequencies. Also at low frequencies, velocity decreases and attenuation increases with increasing fluid mobility (permeability/viscosity). More complicated behavior is observed at high frequencies. These results support recent observations from the oil field suggesting that Stoneley wave velocity and attenuation may be indicative of formation permeability.

Fracture evaluation using reflected Stoneley-wave arrivals

We use the low‐frequency reflected Stoneley‐wave mode to locate permeable fractures intersecting a borehole and to estimate their effective apertures. Assuming a model in which the average aperture of the fracture is roughly constant, theoretical work relates the magnitude of the Stoneley‐wave reflectivity to an effective fracture width, We treat both the case of a horizontal fracture and the case of a fracture crossing the borehole at an angle. Laboratory experiments verify the analytic solution for the case of a horizontal fracture. Full‐waveform array sonic data were also acquired in a wellbore with a long recording time (25.5 ms) in order to capture the late Stoneley‐wave arrivals. The data processing involves computation of the Stoneley‐wave reflectivity response using the measured direct and reflected Stoneley‐wave arrivals. A least‐squares fit to the arrival time of the reflected‐wave arrivals is used to estimate the locations of permeable fractures, and the effective width of the fractures is esti...

Effects of borehole stress concentrations on dipole anisotropy measurements

We show both experimentally and theoretically how stress concentrations affect the velocity field around a borehole, and how the velocity field influences dipole anisotropy measurements. At low frequencies the dipole mode is sensitive to the far-field stresses primarily, so standard sonic log interpretation correctly yields the direction of maximum stress. At higher frequencies, the dipole mode is sensitive to near-field stress concentrations such that the fast polarization direction is aligned with the direction of minimum tectonic stress. These effects combine to produce a crossover in the dipole dispersion curves measured in the fast and slow directions. With broad-band dipole data, the dispersion crossover can be used as an indicator of stress-induced anisotropy dominating over weak intrinsic anisotropy.

Estimates of velocity dispersion between seismic and ultrasonic frequencies

It is generally accepted that acoustic velocities in fluid‐saturated rocks vary with frequency. Evidence comes from experimental measurements and from theoretical causality arguments. We have developed a simple analysis technique that gives estimates of total velocity dispersion between zero frequency and any measurement frequency. The technique requires compressional (P) and shear (S) wave velocity measurements on dry and fully saturated rock. Assuming that the dry velocities are independent of frequency, the Biot‐Gassmann equations are used to calculate the zero‐frequency velocities in the fully saturated rock. Any difference between the measured velocities and the calculated zero‐frequency velocities is interpreted as evidence of dispersion. Application of this analysis technique to a variety c ultrasonic data sets gives consistent results. In many rocks, dispersion between zero frequency and ultrasonic frequencies is on the order of 10 percent at low effective stress, and it decreases to only a few pe...

The interaction of tube waves with borehole fractures; Part II, Analytical models

We solve, numerically, the equations of elastodynamics that govern the propagation of waves in a fluid‐filled borehole intersected by one or more fluid‐filled fractures, thus extending earlier work on formations presumed to be rigid. The model is axis symmetric, and it allows for arbitrary radial and vertical variations in the elastic properties of the formation. We have developed a novel gridding scheme that takes advantage of the assumed thinness of the fracture compared to any relevant wavelength; this technique obviates the necessity for a mesh within the fracture itself and thereby saves computational time and memory. We illustrate our technique by means of examples with single and double fractures with or without washouts, as well as examples with variable width fractures. We compute the frequency‐dependent reflection and transmission coefficients of tube waves by fractures from the time waveforms generated by the present method. Major conclusions of this work are (1) reflections of tube waves by fr...

Contact microphysics and viscous relaxation in sandstones

We present a microphysical model for acoustic attenuation and dispersion in sedimentary materials. The theory governs the response of two grains in contact to small sinusoidal loadings. Surface energy and fluid saturation are included explicitly. Grain surfaces are microscopically rough and irregular. We postulate that contact between grains forms numerous small solid‐solid contacts and that narrow interconnected gaps remain between the surfaces. The stress relaxation is hydrodynamic. As the grains oscillate, liquid must be squeezed out of and sucked back into the gaps. The theory offers a unified explanation of several heretofore apparently unrelated observations. The resulting equations predict the stiffness and loss as a function of frequency, effective pressure, fluid adsorption, saturation, viscosity, and temperature. Insofar as the micromechanical predictions relate to continuum acoustic properties, the agreement with observation is excellent.

Acoustic evidence of mechanical damage surrounding stressed boreholes

Laboratory experiments demonstrate that acoustic waveforms recorded in a borehole provide evidence of stress-induced mechanical damage in surrounding rock. In the experiments, external uniaxial stress was applied perpendicular to the borehole. Stress concentrations near the borehole wall caused velocities of refracted compressional-wave to vary with azimuth. Low velocities occurred in zones of tensile stress, and high velocities occurred in zones of compressive stress. Velocity variations are on the order of 10%. At high values of externally applied uniaxial stress, rock exceeded its yield strength and permanent damage developed. This damage decreased the measured velocities by approximately 10%, especially in the zones of compressive stress concentration. The heterogeneous nature of the velocities surrounding the borehole resulted in low-velocity channels parallel to the borehole wall, caused either by tensile stress concentrations or by mechanical damage. These low-velocity channels may be responsible for high-amplitude bright-spots that appear on variable density plots of azimuthal waveform scans. The amplitude increases can be on the order of 500% and are associated with low-velocity zones, not with decreased attenuation. The hypothesized mechanism is acoustic focusing, whereby velocity gradients refract acoustic waves back towards the borehole.

Formation nonlinear constants from sonic measurements at two borehole pressures

Granular structure and microcracks in rocks cause large nonlinearities in the constitutive relations that result in the stress dependence of acoustic‐wave velocities. The nonlinear constitutive relations of isotropic materials are described in terms of two linear and three nonlinear elastic constants. For nonhyperelastic materials such as rocks, these constants are defined in terms of strain derivatives of stresses for either the load or unload cycle. Acoustic waveforms at an array of receivers recorded at two different borehole pressures can be used to estimate two of the three formation nonlinear constants. Processing of these time waveforms produced by a monopole or dipole source yields the Stoneley or flexural dispersions, respectively. The differences in the Stoneley and flexural dispersions caused by a known change in the borehole pressure are then utilized in a multifrequency inversion model that yields two of the three independent nonlinear constants of the formation. These two nonlinear constants...