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.

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Unpublished Studies ◽  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.

Vertical propagation of low-frequency waves in finely layered media

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. T87-T94 ◽  
Author(s):  
Alexey Stovas ◽  
Børge Arntsen
Keyword(s):  
Reflection Coefficient ◽  
Low Frequency ◽  
Effective Medium ◽  
Frequency Limit ◽  
Data Matching ◽  
Anisotropy Effect ◽  
Vertical Propagation ◽  
The Matrix ◽  
Backus Averaging ◽  
Time Average

Multiple scattering in finely layered sediments is important for interpreting stratigraphic data, matching well-log data with seismic data, and seismic modeling. Two methods have been used to treat this problem in seismic applications: the O’Doherty-Anstey approximation and Backus averaging. The O’Doherty-Anstey approximation describes the stratigraphic-filtering effects, while Backus averaging defines the elastic properties for an effective medium from the stack of the layers. It is very important to know when the layered medium can be considered as an effective medium. In this paper, we only investigate vertical propagation. Therefore, no anisotropy effect is taken into consideration. Using the matrix-propagator method, we derive equations for transmission and reflection responses from the stack of horizontal layers. From the transmission response, we compute the phase velocity and compare the zero-frequency limit with the effective-medium velocity from Backus averaging. We also investigate how the transition from time-average medium to effective medium depends on contrast; i.e., strength of the reflection-coefficient series. Using numerical examples, we show that a transition zone exists between the effective medium (low-frequency limit) and the time-average medium (high-frequency limit), and that the width of this zone depends on the strength of the reflection-coefficient series.

Ray velocity and ray attenuation in homogeneous anisotropic viscoelastic media

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. D119-D127 ◽  
Author(s):  
Václav Vavryčuk
Keyword(s):  
High Frequency ◽  
Sedimentary Rocks ◽  
Strong Anisotropy ◽  
Frequency Signal ◽  
High Frequency Signal ◽  
Velocity Anisotropy ◽  
Viscoelastic Media ◽  
Slowness Vector ◽  
Complex Valued ◽  
Unit Vectors

Asymptotic wave quantities such as ray velocity and ray attenuation are calculated in anisotropic viscoelastic media by using a stationary slowness vector. This vector generally is complex valued and inhomogeneous, and it predicts the complex energy velocity parallel to a ray. To compute the stationary slowness vector, one must find two independent, real-valued unit vectors that specify the directions of its real and imaginary parts. The slowness-vector inhomogeneity affects asymptotic wave quantities and complicates their computation. The critical quantities are attenuation and quality factor ([Formula: see text]-factor); these can vary significantly with the slowness-vector inhomogeneity. If the inhomogeneity is neglected, the attenuation and the [Formula: see text]-factor can be distorted distinctly by errors commensurate to the strength of the velocity anisotropy — as much as tens of percent for sedimentary rocks. The distortion applies to strongly as well as to weakly attenuative media. On the contrary, the ray velocity, which defines the wavefronts and physically corresponds to the energy velocity of a high-frequency signal propagating along a ray, is almost insensitive to the slowness-vector inhomogeneity. Hence, wavefronts can be calculated in a simplified way except for media with extremely strong anisotropy and attenuation.

scholarly journals Wave Propagation in Rocks – Investigating the Effect of Rheology

2020 ◽  
Author(s):  
Tamás Fülöp
Keyword(s):  
Wave Propagation ◽  
High Frequency ◽  
Space Dimension ◽  
Low Frequency ◽  
Elastic Behaviour ◽  
Frequency Limit ◽  
Dispersion Error ◽  
Rock Types ◽  
Velocity Prediction ◽  
Symplectic Schemes

Rocks exhibit beyond-Hookean, delayed and damped elastic, behaviour (creep, relaxation etc.). In many cases, the Poynting–Thomson–Zener (PTZ) rheological model proves to describe these phenomena successfully. A forecast of the PTZ model is that the dynamic elasticity coefficients are larger than the static (slow-limit) counterparts. This prediction has recently been confirmed on a large variety of rock types. Correspondingly, according to the model, the speed of wave propagation depends on frequency, the high-frequency limit being larger than the low-frequency limit. This frequency dependence can have a considerable influence on the evaluation of various wave-based measurement methods of rock mechanics. As experience shows, commercial finite element softwares are not able to properly describe wave propagation, even for the Hooke model and simple specimen geometries, the seminal numerical artefacts being instability, dissipation error and dispersion error, respectively. This has motivated research on developing reliable numerical methods, which amalgamate beneficial properties of symplectic schemes, their thermodynamically consistent generalization (including contact geometry), and spacetime aspects. The present work reports on new results obtained by such a numerical scheme, on wave propagation according to the PTZ model, in one space dimension. The simulation outcomes coincide nicely with the theoretically obtained phase velocity prediction.

Analysis of seismic anisotropy parameters for sedimentary strata

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D495-D502 ◽  
Author(s):  
Fuyong Yan ◽  
De-Hua Han ◽  
Samik Sil ◽  
Xue-Lian Chen
Keyword(s):  
Seismic Anisotropy ◽  
Sedimentary Rocks ◽  
Measurement Data ◽  
Transversely Isotropic ◽  
Theoretical Expression ◽  
Strong Correlations ◽  
Backus Averaging ◽  
Anisotropy Parameters ◽  
Intrinsic Anisotropy ◽  
Gas Bearing

Based on a large quantity of laboratory ultrasonic measurement data of sedimentary rocks and using Monte Carlo simulation and Backus averaging, we have analyzed the layering effects on seismic anisotropy more realistically than in previous studies. The layering effects are studied for different types of rocks under different saturation conditions. If the sedimentary strata consist of only isotropic sedimentary layers and are brine-saturated, the [Formula: see text] value for the effective transversely isotropic (TI) medium is usually negative. The [Formula: see text] value will increase noticeably and can be mostly positive if the sedimentary strata are gas bearing. Based on simulation results, [Formula: see text] can be determined by other TI elastic constants for a layered medium consisting of isotropic layers. Therefore, [Formula: see text] can be predicted from the other Thomsen parameters with confidence. The theoretical expression of [Formula: see text] for an effective TI medium consisting of isotropic sedimentary rocks can be simplified with excellent accuracy into a neat form. The anisotropic properties of the interbedding system of shales and isotropic sedimentary rocks are primarily influenced by the intrinsic anisotropy of shales. There are moderate to strong correlations among the Thomson anisotropy parameters.

Correspondence between the low- and high-frequency limits for anisotropic parameters in a layered medium

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA25-WA33 ◽  
Author(s):  
Mercia Betania Costa e Silva ◽  
Alexey Stovas
Keyword(s):  
Wave Propagation ◽  
Layer Thickness ◽  
High Frequency ◽  
Layered Medium ◽  
Homogeneous Medium ◽  
Low Frequency ◽  
Single Layer ◽  
Vertical Axis ◽  
Frequency Limit ◽  
High Frequency Limit

Wave propagation in a layered medium when the wavelength is much greater than each layer thickness (low frequency) produces a response equivalent to that of wave propagation in an equivalent single-layer medium. This equivalent medium is transversely isotropic with symmetry about a vertical axis (VTI), and the elastic parameters are computed with the Backus averaging technique. Conversely, when the wavelength is comparable to each layer thickness (high frequency), the directional dependence of the phase velocity in the transmission response also can be simulated by replacing the layered medium with a single homogeneous medium with properties derived from a time average. It then can be treated approximately as a VTI medium. To compute the medium parameters, a method based on fitting the traveltime parameters is used. We investigated the relationship between Thomsen’s anisotropic parameters [Formula: see text] and [Formula: see text] computed for the equivalent medium in the low-frequency limit and for the homogenized medium in the high-frequency limit. In our experiments, we used a medium in which layers of only two isotropic materials alternate repeatedly. For the high-frequency limit, we obtained solutions for PP- and SS-wave propagation.

scholarly journals Primate communication in the pure ultrasound

2012 ◽  
Vol 8 (4) ◽  
pp. 508-511 ◽  
Author(s):  
Marissa A. Ramsier ◽  
Andrew J. Cunningham ◽  
Gillian L. Moritz ◽  
James J. Finneran ◽  
Cathy V. Williams ◽  
...  
Keyword(s):  
High Frequency ◽  
Background Noise ◽  
Low Frequency ◽  
Auditory Brainstem ◽  
Dominant Frequency ◽  
Ultrasonic Vocalizations ◽  
Energetic Efficiency ◽  
Frequency Limit ◽  
Vocal Signals ◽  
Brainstem Response

Few mammals—cetaceans, domestic cats and select bats and rodents—can send and receive vocal signals contained within the ultrasonic domain, or pure ultrasound (greater than 20 kHz). Here, we use the auditory brainstem response (ABR) method to demonstrate that a species of nocturnal primate, the Philippine tarsier ( Tarsius syrichta ), has a high-frequency limit of auditory sensitivity of ca 91 kHz. We also recorded a vocalization with a dominant frequency of 70 kHz. Such values are among the highest recorded for any terrestrial mammal, and a relatively extreme example of ultrasonic communication. For Philippine tarsiers, ultrasonic vocalizations might represent a private channel of communication that subverts detection by predators, prey and competitors, enhances energetic efficiency, or improves detection against low-frequency background noise.

On: “Dispersion of body waves in layered media” by I. N. Gupta (GEOPHYSICS, August, 1966, pp. 821–823)

Geophysics ◽  
1967 ◽  
Vol 32 (1) ◽  
pp. 124-125 ◽  
Author(s):  
Yosio Nakamura
Keyword(s):  
Time Delay ◽  
High Frequency ◽  
Layered Medium ◽  
Short Note ◽  
Low Frequency ◽  
Body Waves ◽  
Frequency Limit ◽  
Dispersive Effect ◽  
The Subject ◽  
Low Frequency Waves

In his short note, Gupta has shown that the dispersive effect of a finely layered medium may be responsible for some of the anomalous observations in explosive and earthquake investigations. In his note, the phase velocity of waves propagating perpendicular to a horizontally stratified structure at its low-frequency limit is compared with that at the high-frequency limit, and consequently a time delay for low-frequency waves has been denoted. The following discussion shows by a further calculation that a still greater time delay can be expected in other frequencies. The result will be of further help for the interpretations given in the subject note.

Simulations of high-resolution images of amorphous silicon films

1986 ◽  
Vol 44 ◽  
pp. 544-545
Author(s):  
G. Y. Fan ◽  
J. M. Cowley
Keyword(s):  
Electron Microscope ◽  
High Frequency ◽  
Fourier Transformation ◽  
Amorphous Materials ◽  
Low Frequency ◽  
Chromatic Aberration ◽  
Structure Information ◽  
Frequency Components ◽  
High Resolution Images ◽  
Spatial Frequency Spectrum

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.

SEM image sharpness analysis

1996 ◽  
Vol 54 ◽  
pp. 142-143
Author(s):  
M. T. Postek ◽  
A. E. Vladar
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Quantitative Information ◽  
Primary Electron ◽  
Image Sharpness ◽  
Critical Dimensions ◽  
Sem Image ◽  
Frequency Changes ◽  
Electron Microscopes ◽  
Scanning Electron

Fully automated or semi-automated scanning electron microscopes (SEM) are now commonly used in semiconductor production and other forms of manufacturing. The industry requires that an automated instrument must be routinely capable of 5 nm resolution (or better) at 1.0 kV accelerating voltage for the measurement of nominal 0.25-0.35 micrometer semiconductor critical dimensions. Testing and proving that the instrument is performing at this level on a day-by-day basis is an industry need and concern which has been the object of a study at NIST and the fundamentals and results are discussed in this paper.In scanning electron microscopy, two of the most important instrument parameters are the size and shape of the primary electron beam and any image taken in a scanning electron microscope is the result of the sample and electron probe interaction. The low frequency changes in the video signal, collected from the sample, contains information about the larger features and the high frequency changes carry information of finer details. The sharper the image, the larger the number of high frequency components making up that image. Fast Fourier Transform (FFT) analysis of an SEM image can be employed to provide qualitiative and ultimately quantitative information regarding the SEM image quality.

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