Low-frequency Assumption Research Articles

Frequency-Dependent Seismic Anisotropy of Porous Rocks with Penny-Shaped Cracks

Porous reservoirs with aligned fractures exhibit frequency-dependent seismic anisotropy because of wave-induced fluid flow between pores and fractures. To relate the elastic properties of porous rocks with aligned fractures at low frequency, we use the linear slip model of fractures and anisotropic Gassmann fluid substitution. We combine this low-frequency anisotropic Gassmann model with a dispersion relationship, based on a penny-shaped crack model of fractures, to account for frequency-dependent anisotropy.The combined model is validated using experimental measurements of angle-dependent wave velocities of synthetic porous sandstone with aligned disc-shaped cracks. For the low-frequency anisotropic Gassmann model, the agreement between the measured and predicted velocities is reasonably good for both 5-wave velocities, but P-wave anisotropy is overestimated by approximately 25%. This quantitative difference can be explained by fluid diffusion effects occurring at the relatively high frequencies used in the experiment (100 kHz), which are not accounted for by the low-frequency assumption of anisotropic Gassmann theory. The predictions of the combined frequency-dependent model, which considers this effect, give very good agreement with measured velocities.

Experimental verification of the anisotropic Gassmann model for fluid substitution in fractured reservoirs

Porous reservoirs with aligned fractures exhibit frequency dependent seismic anisotropy due to wave induced fluid flow between pores and fractures. We model this frequency dependent anisotropy by combining the low-frequency anisotropic Gassmann model with the Hudson et al. model for frequency dependent properties of a porous material with penny-shaped cracks. The predictions of the anisotropic Gassmann model are compared with experimental measurements of elastic wave velocities as function of angle for a synthetic sample with aligned disc-like cracks. The properties of the host rock and fracture compliances are obtained from P, SV, and SH velocities measured on the dry sample. The dry fractured porous rock properties serve as input to anisotropic Gassmann fluid substitution model, which is used to compute the saturated rock properties. The stiffnesses of the saturated fractured porous rock are used to calculate the angular dependent compressional and shear wave velocities. The predicted velocities are then compared to the measured velocities. The agreement is reasonably good for both S-wave velocities, but P-wave anisotropy is overestimated by about 25%. This discrepancy can be explained by the fact that the low frequency assumption of the anisotropic Gassmann model does not account for the fluid diffusion effects occurring at relatively high frequencies used in the experiment (100 KHz). A combination of the low frequency anisotropic Gassmann model with the Hudson et al. frequency dependency accounts for fluid diffusion effects and results in an excellent agreement for P- as well as S- waves.

Reynolds number effects on flow/acoustic mechanisms in spherical windscreens.

There is a practical need to fully understand the mechanisms involved in the flow/pressure fluctuations around a screened microphone. A stream of uniform flow with low-frequency turbulence encountering a rigid, impermeable spherical windscreen is considered in this study. Pressure distributions on the surface of the sphere are determined by the flow structure. Pressure fluctuations at the center of the sphere are then calculated based on the integration of surface pressure distributions. Because of the low-frequency assumption, results from steady-state laminar flows can be used to investigate the Reynolds number effects on wind noise reduction. Three types of flow have been studied in this paper: an inviscid case, a low-Reynolds-number Stokes flow, and intermediate- and high-Reynolds-number flows. A Reynolds-number/wind-noise-reduction correlation shows that the wind noise reduction increases with decreasing Reynolds number.

A probabilistic model for the response of an electrically short two-conductor transmission line driven by a random plane wave field

A probabilistic approach for the characterization of wiring-harness susceptibility to external interference is presented. The problem of field-coupling onto a uniform, lossless, electrically-short two-conductor transmission line loaded by terminal resistances is considered. The external field is modeled as a plane wave with random parameters. By virtue of the low-frequency assumption, the statistical properties of the induced current magnitude in one of the line loads are derived, for different characterizations of the external wave. Investigated configurations include: waves with random amplitude, waves with random amplitude and polarization, waves with random amplitude and direction of incidence, and waves with random amplitude, polarization and direction of incidence. Analytical expressions for the probability density function of the current (voltage) induced in one of the line loads are derived. The proposed model allows the computation of statistical parameters of interest, such as expected values, variances, and confidence intervals of the currents (voltages) in the line loads.

On the existence of Alfvénic solitary waves

It is argued that dispersive Alfvén solitary waves of the nonoscillatory type do not exist in one dimension. Previous calculations that claim existence have neglected the nonlinear ion polarization drift in the low-frequency limit. If the nonlinear ion polarization term is retained or if no low-frequency assumption is made, solitary wave solutions are not found.

Superluminal velocity of photons in a gravitational background

The influence of radiative corrections on the photon propagation in a gravitational background is investigated without the low-frequency assumption ω ⪡ m. The conclusion is made in this way that the velocity of light can exceed unity.