To: “Biot‐consistent elastic moduli of porous rocks: Low‐frequency limit,” by Leon Thomsen which appeared on p. 2797–2807 in December 1985 GEOPHYSICS:

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 1033-1033
Keyword(s):  
Elastic Moduli ◽  
Low Frequency ◽  
Porous Rocks ◽  
Frequency Limit ◽  
Text Page

The following typesetting errors have been noted in the article: Page 2802: equation (8) should read equation (9); ϕ should read [Formula: see text] in equation (13). Budiansky and O’Connell (1977) should read O’Connell and Budiansky (1977). 1˜6v* should read [Formula: see text]*, 1˜6v should read [Formula: see text]. Page 2803: 1˜6τ should read [Formula: see text], 1¯6θ should read [Formula: see text], [ + should read [1 + in equation (16b), 1¯6γ should read [Formula: see text]. Page 2804: [Formula: see text] should read [Formula: see text] in equations (17b), (17d). 1¯6τ should read [Formula: see text], 1¯6γ should read [Formula: see text], ϕ should read [Formula: see text] in equation (19), [Formula: see text] should read [Formula: see text] in step (9), [Formula: see text] should read [Formula: see text]

scholarly journals Biot‐consistent elastic moduli of porous rocks: Low‐frequency limit

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2797-2807 ◽  
Author(s):  
Leon Thomsen
Keyword(s):  
Bulk Modulus ◽  
Model Theory ◽  
Elastic Moduli ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Porous Rocks ◽  
Seismic Frequencies ◽  
New Formulation ◽  
Special Case ◽  
Finite Concentrations

The semiphenomenological Biot‐Gassmann (B-G) formulation of the low‐frequency elastic moduli of porous rocks does contain two well‐known predictions: (1) the shear modulus of an unsaturated rock (which is permeated by a compressible fluid, e.g., gas) is identical to that of the same rock saturated with liquid, and (2) the unsaturated bulk modulus differs from the saturated bulk modulus by a defined amount. These predictions are tested by ultrasonic data on a large number of sedimentary rocks and are approximately verified, despite the evident frequency discrepancy. The B-G theory makes only minimal assumptions about the microscopic geometry of the rock; therefore, any model theory which does make such assumptions (e.g., spherical pores) should be a special case of B-G theory. In particular, such model theories should also predict the two relations described above. Standard models for dilute concentrations of spherical pores and/or ellipsoidal cracks do predict these relationships. However, in general, the “Self‐Consistent” (S-C) model (developed to deal with finite concentrations of heterogeneities) violates these predictions and hence is not consistent with the underlying Biot‐Gassmann theory. [The special case of S-C theory, corresponding to pores only (no cracks), is consistent with the B-G model.] A new formulation of the model theory, for finite concentrations of heterogeneities of ideal shape, is developed so as to be explicitly consistent with B-G. This “Biot‐consistent” (B-C) formalism is the first theory truly suitable for modeling most sedimentary rocks at seismic frequencies, in terms of porosity and pore shape.

Evaluation of Special Hearing Aids for Deaf Children

1971 ◽  
Vol 36 (4) ◽  
pp. 527-537 ◽  
Author(s):  
Norman P. Erber
Keyword(s):  
Hearing Aids ◽  
High Frequency ◽  
Hearing Aid ◽  
Low Frequency ◽  
Acoustic Stimulation ◽  
Deaf Children ◽  
Frequency Range ◽  
Frequency Limit ◽  
Unpublished Studies ◽  
Published Research

Two types of special hearing aid have been developed recently to improve the reception of speech by profoundly deaf children. In a different way, each special system provides greater low-frequency acoustic stimulation to deaf ears than does a conventional hearing aid. One of the devices extends the low-frequency limit of amplification; the other shifts high-frequency energy to a lower frequency range. In general, previous evaluations of these special hearing aids have obtained inconsistent or inconclusive results. This paper reviews most of the published research on the use of special hearing aids by deaf children, summarizes several unpublished studies, and suggests a set of guidelines for future evaluations of special and conventional amplification systems.

Onset of size effects in lattice thermal conductivity and lifetime of low-frequency thermal phonons

2012 ◽  
Vol 1404 ◽  
Author(s):  
A.A. Maznev
Keyword(s):  
Thin Film ◽  
Thermal Conductivity ◽  
Size Effects ◽  
Lattice Thermal Conductivity ◽  
Low Frequency ◽  
Square Root ◽  
Relaxation Rates ◽  
Frequency Limit ◽  
Conductivity Of Thin Films ◽  
Closed Form Formula

ABSTRACTThe onset of size effects in phonon-mediated thermal transport along a thin film at temperatures comparable or greater than the Debye temperature is analyzed theoretically. Assuming a quadratic frequency dependence of phonon relaxation rates in the low-frequency limit, a simple closed-form formula for the reduction of the in-plane thermal conductivity of thin films is derived. The effect scales as the square root of the film thickness, which leads to the prediction of measurable size-effects even at “macroscopic” distances ~100 μm. However, this prediction needs to be corrected to account for the deviation from the ω−2 dependence of phonon lifetimes at sub-THz frequencies due to the transition from Landau-Rumer to Akhiezer mechanism of phonon dissipation.

scholarly journals Nonlinear interaction between acoustic gravity waves

1996 ◽  
Vol 14 (3) ◽  
pp. 304-308 ◽  
Author(s):  
P. Axelsson ◽  
J. Larsson ◽  
L. Stenflo
Keyword(s):  
Gravity Waves ◽  
Nonlinear Interaction ◽  
Low Frequency ◽  
Resonant Interaction ◽  
Coupling Coefficients ◽  
Symmetric Form ◽  
Frequency Limit ◽  
Acoustic Gravity Waves

Abstract. The resonant interaction between three acoustic gravity waves is considered. We improve on the results of previous authors and write the new coupling coefficients in a symmetric form. Particular attention is paid to the low-frequency limit.

Effects of director rotation relaxation on viscoelastic wave dispersion in nematic elastomer beams

2018 ◽  
Vol 24 (4) ◽  
pp. 1103-1115 ◽  
Author(s):  
Dong Zhao ◽  
Ying Liu
Keyword(s):  
Wave Motion ◽  
Relaxation Times ◽  
Low Frequency ◽  
Wave Dispersion ◽  
Frequency Limit ◽  
Anisotropic Parameter ◽  
Acoustic Design ◽  
Phase Velocities ◽  
Nematic Elastomer ◽  
Viscoelastic Wave

In this paper, the transverse wave dispersion in a nematic elastomer (NE) Timoshenko beam is studied by considering anisotropy and viscoelasticity of NEs in the low frequency limit. Firstly, the characteristic equations of wave motion in an NE beam are derived, and then numerically solved to obtain the corresponding phase velocities and attenuation factors. The influences of anisotropic parameter, director rotation and rubber relaxation times on the wave dispersion in an NE beam are discussed. Results show that unlike the situation in general isotropic viscoelastic beam, non-classical viscoelastic wave dispersion is found in NE beams. Geometric dispersion is restrained with the vanishing of cut-off frequencies for shear waves due to director rotation relaxation of NEs. This unique property promises prospective applications of NE beams in optic or acoustic design.

A new procedure for processing strong-motion earthquake signals

1982 ◽  
Vol 72 (2) ◽  
pp. 643-661
Author(s):  
S. Shyam Sunder ◽  
Jerome J. Connor
Keyword(s):  
United States ◽  
Filter Design ◽  
Response Spectrum ◽  
Low Frequency ◽  
Strong Motion ◽  
Sampling Period ◽  
Frequency Limit ◽  
Processing Scheme ◽  
Proposed Model ◽  
Band Pass

Abstract A new procedure for routinely processing strong-motion earthquake signals using state-of-the-art filter design and implementation techniques is presented. The model, shown to be both accuratet and efficient, is sufficiently flexible so that the signal sampling period and filter parameters can be easily varied. A comparison of results from the existing United States model (Trifunac and Lee, 1973) and the proposed model show significant differences in the ground motion and response spectrum characteristics for the same set of filter limits. Drifts in integrated velocity and displacement characteristics and theoretically incorrect asymptotic behavior of response spectrum curves arising out of the existing United States processing scheme have been eliminated. In addition to the importance of appropriately selecting a low-frequency limit for band-pass filtering the signals, this work demonstrates the sensitivity of the acceleration trace to the particular choice of a high-frequency limit.

Helicity waves propagating in a plasma

1991 ◽  
Vol 45 (3) ◽  
pp. 481-488 ◽  
Author(s):  
Z. Yoshida
Keyword(s):  
Magnetic Field ◽  
Faraday Effect ◽  
Low Frequency ◽  
Plasma Waves ◽  
Frequency Limit ◽  
High Frequencies ◽  
Transverse Modes ◽  
Longitudinal Part ◽  
The Waves ◽  
Perturbed Magnetic Field

There exist plasma waves that transport helicity although they do not propagate electromagnetic energy. The dispersion relations of such helicity waves are studied. The electric field of the waves is parallel to the perturbed magnetic field, and both are perpendicular to the perturbed current. In cross-field propagation, a helicity wave is decomposed into two transverse modes with different polarizations and a longitudinal part. The helicity waves are principally Alfvénic in the low-frequency limit. At high frequencies, the Faraday effect comes into the polarization.

Comparison of seismic anisotropy of sedimentary strata at low- and high-frequency limits

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. MR1-MR10 ◽  
Author(s):  
Fuyong Yan ◽  
De-Hua Han ◽  
Tongcheng Han ◽  
Xue-Lian Chen
Keyword(s):  
High Frequency ◽  
Seismic Anisotropy ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Layered Media ◽  
Ray Theory ◽  
Frequency Limit ◽  
Anisotropic Properties ◽  
Velocity Anisotropy ◽  
Backus Averaging

The layer-induced seismic anisotropy of sedimentary strata is frequency-dependent. At the low-frequency limit, the effective anisotropic properties of the layered media can be estimated by the Backus averaging model. At the high-frequency limit, the apparent anisotropic properties of the layered media can be estimated by ray theory. First, we build a database of laboratory ultrasonic measurement on sedimentary rocks from the literature. The database includes ultrasonic velocity measurements on sandstones and carbonate rocks, and velocity-anisotropy measurements on shales. Then, we simulate the sedimentary strata by randomly selecting a certain number of rock samples and using their laboratory measurement results to parameterize each layer. For each realization of the sedimentary strata, we estimate the effective and apparent seismic anisotropy parameters using the Backus average and ray theory, respectively. We find that, relative to Backus averaging, ray theory usually underestimates the Thomsen parameters [Formula: see text] and [Formula: see text], and overestimates [Formula: see text]. For an effective layered medium consisting of isotropic sedimentary rocks, the differences are significant. These differences decrease when shales with intrinsic seismic anisotropy are included. For the same sedimentary strata, the seismic wave should perceive stronger seismic anisotropy than the ultrasonic wave.

Sign in / Sign up

Export Citation Format

Share Document