A generalized O’Doherty‐Anstey formula for waves in finely layered media

Geophysics ◽  
1994 ◽  
Vol 59 (11) ◽  
pp. 1750-1762 ◽  
Author(s):  
Serge A. Shapiro ◽  
Holger Zien ◽  
Peter Hubral
Keyword(s):  
Layered Medium ◽  
Perturbation Technique ◽  
Finite Thickness ◽  
Low Frequency ◽  
Variable Density ◽  
Analytic Description ◽  
Mean Values ◽  
Time Harmonic ◽  
Backus Averaging ◽  
Theory Result

We investigate the angle‐dependent plane wave transmissivity of a pressure wave in a random, multilayered, acoustic, variable velocity and variable density medium. The main result of our consideration is a simple, explicit analytic description of the influence of such a medium on the transmissivity kinematics and dynamics for the whole frequency range. We assume that the velocity and density dependencies on depth are typical realizations of random stationary processes. Moreover, the fluctuations in both values must be relatively small compared to their constant mean values (of the order of 30 percent or smaller). In our derivation, we combine the small perturbation technique with the localization and self‐averaging theory. We obtain the attenuation and the phase of the time‐harmonic transmissivity, as well as the pulse form of the transient transmissivity from an angle‐dependent combination of the auto‐ and crosscorrelation functions of both the sonic and density logs. Our results for the kinematics of the transmissivity yield the wellknown “Backus averaging” in the low‐frequency limit. Likewise, they provide the ray theory result as the high‐frequency asymptotic value. The analytic expression for the transmissivity can be viewed as a generalization of the O’Doherty‐Anstey formula. Numerical computations of the actual transmissivity show fluctuations around the theoretical prediction given by our formula, which is strictly valid only in the case of infinitely thick media. The larger the layered medium, the smaller are these fluctuations. They can be well estimated with a formula which we derive to describe the deviations between the analytic and the exact transmissivity obtained for a layered medium of finite thickness.

Effect of Incisions in the Brainstem Commissural Network on the Short-Term Vestibulo-Ocular Adaptation of the CAT

1991 ◽  
Vol 1 (3) ◽  
pp. 223-239
Author(s):  
G. Cheron
Keyword(s):  
Low Frequency ◽  
Adaptive Plasticity ◽  
Training Procedure ◽  
Optokinetic Response ◽  
Mean Values ◽  
Ocular Reflex ◽  
Optokinetic Reflex ◽  
Before And After ◽  
Vestibulo Ocular Reflex ◽  
Vor Adaptation

This study was intended to test the adaptive plasticity of the vestibulo-ocular reflex before and after either a midsagittal or parasagittal incision in the brainstem. Eye movements were measured with the electromagnetic search coil technique during the vestibulo-ocular reflex (VORD) in the dark, the optokinetic reflex (OKN), and the visuo-vestibular adaptive training procedure. Two types of visual-vestibular combined stimulation were applied by means of low frequency stimuli (0.05 to 0.10 Hz). In order to increase or decrease the VORD gain, the optokinetic drum was oscillated either 180∘ out-of-phase or in-phase with the vestibular stimulus turntable. This “training” procedure was applied for 4 hours. Initial measurements of the VORD were normal with a mean gain value of 0.92 ± 0.08. After 4 hours of “training” with the out-of-phase condition (180∘), VORD gain reached mean values of 1.33 ± 0.11 (n = 6 cats). In the in-phase combination, the mean VORD gain decreased from 1.0 to 0.63 ± 0.02 (n = 2 cats). No significant change of VORD phase was found in any of the cats. Midsagittal or parasagittal pontomedullary brainstem incisions were performed in 4 cats. Recovery of the VOR was tested on the 2nd, 7th, and 30th day after operation. After the 30th day, recovery of the VORD gain stabilized at about 66% of the initial preoperative value. At this stage of the recovery, the optokinetic response (OKN) of the midsagittal-Iesioned cats was practically normal: in the parasagittal-Jesioned cats, the postoperative OKN responses were asymmetric. After stabilization of recovery, lesioned cats were trained with the same adaptation procedure. Although the direct effect of the visuo-vestibular combined stimulation during the training was still operative in all lesioned cats, the adaptive plasticity was completely abolished by the lesions. These results suggest that the commissural brainstem network may play a crucial role in the acquisition of the forced VOR adaptation.

scholarly journals ENVIRONMENT DENSITY OF A GIANT RADIO STRUCTURE FOR GALAXIES AND QUASARS WITH STEEP RADIO SPECTRA

2021 ◽  
Vol 26 (2) ◽  
pp. 165-172
Author(s):  
A. P. Miroshnichenko ◽  
Keyword(s):  
Low Frequency ◽  
Radio Spectrum ◽  
Power Relation ◽  
Cosmological Evolution ◽  
Inverse Power ◽  
Radio Sources ◽  
Frequency Spectra ◽  
Radio Structure ◽  
Mean Values ◽  
Index Value

Purpose: Estimate of the environment density of giant (with the linear size of about megaparsec) radio structures for galaxies and quasars with steep low-frequency spectra taken from the UTR-2 catalogue. Study of the cosmological evolution of environment density of giant radio sources. Determination of dependence of contribution of radio lobes into the emission of giant sources with respect to their environment density. Design/methodology/approach: We use the sample of sources from the UTR-2 catalogue of extragalactic sources to estimate the environment density for giant sources with steep low-frequency spectra. The selection criteria for the examined objects are the following: 1) the spectral index value is equal or larger than 1; 2) the fl ux density of emission at the frequency of 25 MHz is larger than 10 Jy; 3) the sample sources are optically identifi ed. The value of environment density of examined sources is obtained with the assumption of equality of source jet luminosity (at the synchrotron mechanism of radio emission) and its corresponding kinetic luminosity. The analysis of the estimates of environment densities is made for different classes of the sample objects (for galaxies and quasars with linear steep spectra and with break steep spectra). Findings: The estimates of environment density have been derived for giant radio structures formed by the jets of sources with steep spectrum from the UTR-2 catalogue. On the average, the environment density for the quasar structure (~ 10-28 g/sm3) is lesser than the one for the galaxies (~ 10-27 g/sm3 to ~ 10-26 g/sm3). The larger jet environment density is typical for the galaxies and quasars with the break steep spectra than for those with the linear steep spectra. The inverse power relation of the jet environment density and the source redshift (the cosmological evolution of the jet environment density) has been derived. The contribution of jet-related radio lobes into the emission of sources displays the inverse power relation for the environment density of the corresponding radio structures. Conclusions: The mean values of obtained estimates of environment density of giant jets of radio sources with steep low-frequency spectra indicate the lesser environment density of quasar jets than that for the galaxy jets. Giant radio sources with steep low-frequency spectrum (especially, with break steep spectrum) reveal considerable evolution of environment density of jets. The larger contribution of radio lobes (jets) into the emission of sources corresponds to the lesser environment density of sources taken from the UTR-2 catalogue. It can be due to propagation of jets (surrounded by radio lobes) from powerful radio sources to distances of about megaparsec, until the balance of source’s environment density and extragalactic environment density is reached. Key words: steep low-frequency radio spectrum; giant radio structure; jets; radio lobes; galaxies; quasars; environment density

Nano-structured GeySi1-y:H Films Deposited by Low Frequency Plasma for Photovoltaic Application

2008 ◽  
Vol 1127 ◽  
Author(s):  
Andrey Kosarev ◽  
Alfonso Torres ◽  
Carlos Zuniga ◽  
Marco Adamo ◽  
Liborio Sanchez
Keyword(s):  
Electronic Properties ◽  
Urbach Energy ◽  
Low Frequency ◽  
Localized States ◽  
Statistical Parameters ◽  
Nano Structure ◽  
Mean Values ◽  
Temperature Dependence Of Conductivity ◽  
Wide Range ◽  
Grain Distribution

ABSTRACTIn this work we present the study of fabrication, Ge incorporation, structure and electronic properties of nano-structured GeySi1-y:H films with y>0.5 prepared by low frequency (LF) PECVD. GeySi1-y:H films were deposited by LF PECVD at a frequency f= 110 kHz from SiH4+GeH4+H2 gas mixture. SiH4 and GeH4 flows were varied to fabricate the films in wide range of 0<y<l. Hydrogen dilution was varied in the range of RH =20 to 80. Structure of the films was studied by AFM and SEM with consequent image processing to extract statistical parameters such as grain distribution and mean values. Composition of the films was characterized by SIMS and EDX. Electronic properties were characterized by temperature dependence of conductivity, spectral dependence of optical absorption. Sub-gap absorption was characterized by Urbach energy, EU; and defect absorption, αD. We observed grain like nano-structure with Gauss distribution of grain diameters by both AFM and SEM measurements. The most interesting films had mean grain diameter<D> = 24.0±0.7 nm, dispersion D=11.0±0.2 nm and fill factor FF=0.313, Ge content y=0.96-0.97(by SIMS and EDS). These films showed also the lowest values of Urbach energy EU = 0.030 eV and low defect absorption αD = 5×102 cm −1 (at photon energy hv = 1.04 eV) indicating on low density of localized states in mobility gap. Doped films have been also fabricated and studied. Finally we shall discuss application of the above films in photovoltaic devices.

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.

Short-wave low-frequency equilibrium spectra in a current-carrying plasma

1993 ◽  
Vol 50 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Maxim O. Vakoulenko
Keyword(s):  
Low Frequency ◽  
Short Wave ◽  
Integrals Of Motion ◽  
Mean Values ◽  
The Mean ◽  
A Current

Short-wave (wavelengths smaller than the ion gyroradius) low-frequency (frequencies not exceeding the ion gyrofrequency) electromagnetic equilibrium spectra are found in a current-carrying plasma. Owing to cross-field correlations, the mean values of the integrals of motion increase, whereas their cascade rates are inhibited.

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