Stratigraphic filter theory: Combined effects of parallel bedding and random inhomogeneities

Geophysics ◽  
1986 ◽  
Vol 51 (8) ◽  
pp. 1531-1537 ◽  
Author(s):  
I. Lerche
Keyword(s):  
Time Delay ◽  
Power Spectrum ◽  
Layered Medium ◽  
Mean Field ◽  
Power Spectra ◽  
Low Frequencies ◽  
High Frequencies ◽  
Bedding Planes ◽  
Scattering Centers ◽  
The Mean

Mean field renormalization techniques determine the phase distortion (time delay) and effective attenuation as functions of frequency for a plane acoustic wave, normally incident on a layered medium, when the medium also contains a distribution of scattering centers at random sites. The power spectra of impedance fluctuations of both the bedding layers and the random centers contribute to the time delay and mean field effective attenuation. At low frequencies (long wavelengths), the power spectrum of the bedding planes dominates the mean wave response, producing most of the time delay and the effective attenuation. At high frequencies (short wavelengths), the random scattering centers dominate the mean wave behavior. The wave no longer propagates exactly perpendicularly to bedding planes since the random scattering centers cast energy into directions transverse to the normal to the bedding planes. The precise frequency dependence of both the time delay and the effective attenuation of the mean wave are sensitive to the power spectrum of impedance fluctuations of the bedding planes relative to the power spectrum of the random scattering centers.

scholarly journals Demonstrating the Tapered Gridded Estimator (TGE) for the Cosmological HI 21-cm Power Spectrum using 150 MHz GMRT observations

2020 ◽  
Author(s):  
Srijita Pal ◽  
Somnath Bharadwaj ◽  
Abhik Ghosh ◽  
Samir Choudhuri
Keyword(s):  
Power Spectrum ◽  
Unbiased Estimate ◽  
Power Spectra ◽  
Neutral Hydrogen ◽  
Statistical Error ◽  
Temperature Fluctuations ◽  
Radio Frequency Interference ◽  
Rectangular Region ◽  
Angular Power Spectrum ◽  
The Mean

Abstract We apply the Tapered Gridded Estimator (TGE) for estimating the cosmological 21-cm power spectrum from 150 MHz GMRT observations which corresponds to the neutral hydrogen (HI) at redshift z = 8.28. Here TGE is used to measure the Multi-frequency Angular Power Spectrum (MAPS) Cℓ(Δν) first, from which we estimate the 21-cm power spectrum P(k⊥, k∥). The data here are much too small for a detection, and the aim is to demonstrate the capabilities of the estimator. We find that the estimated power spectrum is consistent with the expected foreground and noise behaviour. This demonstrates that this estimator correctly estimates the noise bias and subtracts this out to yield an unbiased estimate of the power spectrum. More than $47\%$ of the frequency channels had to be discarded from the data owing to radio-frequency interference, however the estimated power spectrum does not show any artifacts due to missing channels. Finally, we show that it is possible to suppress the foreground contribution by tapering the sky response at large angular separations from the phase center. We combine the k modes within a rectangular region in the ‘EoR window’ to obtain the spherically binned averaged dimensionless power spectra Δ2(k) along with the statistical error σ associated with the measured Δ2(k). The lowest k-bin yields Δ2(k) = (61.47)2 K2 at k = 1.59 Mpc−1, with σ = (27.40)2 K2. We obtain a 2 σ upper limit of (72.66)2 K2 on the mean squared HI 21-cm brightness temperature fluctuations at k = 1.59 Mpc−1.

scholarly journals Kinetic field theory: Non-linear cosmic power spectra in the mean-field approximation

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Matthias Bartelmann ◽  
Johannes Dombrowski ◽  
Sara Konrad ◽  
Elena Kozlikin ◽  
Robert Lilow ◽  
...  
Keyword(s):  
Field Theory ◽  
Power Spectrum ◽  
Mean Field ◽  
Power Spectra ◽  
Field Approximation ◽  
Density Fluctuations ◽  
Mean Field Approximation ◽  
Non Linear ◽  
Two Parameters ◽  
Kinetic Field

We use the recently developed Kinetic Field Theory (KFT) for cosmic structure formation to show how non-linear power spectra for cosmic density fluctuations can be calculated in a mean-field approximation to the particle interactions. Our main result is a simple, closed and analytic, approximate expression for this power spectrum. This expression has two parameters characterising non-linear structure growth which can be calibrated within KFT itself. Using this self-calibration, the non-linear power spectrum agrees with results obtained from numerical simulations to within typically \lesssim10\,\%≲10% up to wave numbers k\lesssim10\,h\,\mathrm{Mpc}^{-1}k≲10hMpc−1 at redshift z = 0z=0. Adjusting the two parameters to optimise agreement with numerical simulations, the relative difference to numerical results shrinks to typically \lesssim 5\,\%≲5%. As part of the derivation of our mean-field approximation, we show that the effective interaction potential between dark-matter particles relative to Zel’dovich trajectories is sourced by non-linear cosmic density fluctuations only, and is approximately of Yukawa rather than Newtonian shape.

Power spectral analysis of the diaphragm electromyogram

1983 ◽  
Vol 54 (6) ◽  
pp. 1579-1584 ◽  
Author(s):  
T. K. Aldrich ◽  
J. M. Adams ◽  
N. S. Arora ◽  
D. F. Rochester
Keyword(s):  
Power Spectrum ◽  
Signal To Noise Ratio ◽  
Normal Subjects ◽  
Chronic Obstructive ◽  
Signal To Noise ◽  
Low Frequencies ◽  
Mean Values ◽  
The Mean ◽  
Noise Ratio ◽  
Diaphragm Fatigue

We studied the power spectrum of the diaphragm electromyogram (EMG) at frequencies between 31 and 246 Hz in four young normal subjects and five patients with chronic obstructive lung disease (COPD). Diaphragm EMGs were analyzed during spontaneous breathing and maximum inspiratory efforts to determine the effect of signal-to-noise ratio on the power spectrum and if treadmill exercise to dyspnea was associated with diaphragm fatigue. We found that the centroid frequencies of the power spectra (fc) were strongly correlated (r = 0.93) with ratios of power at high frequencies to power at low frequencies (H/L) for all subjects. Of the two indices, H/L had the largest standard deviation expressed as a percentage of the mean. The mean values of both of these decreased significantly after exercise, fc from 100.2 to 97.3 and H/L from 1.07 to 0.97. Signal-to-noise ratios were higher in maximal inspiratory efforts and after exercise in normal subjects and higher in COPD patients. The signal-to-noise ratio was correlated negatively with fc and H/L, indicating that these indices of the shape of the power spectrum are influenced by signal strength and noise levels as well as muscle function. We conclude that the fc and H/L index similar qualities of the power spectrum, that they are partially determined by the signal-to-noise ratio, and that, in some cases, exercise to dyspnea is associated with apparently mild diaphragm fatigue.

scholarly journals 2012 Dahlberg Award Winner Dental morphological variation among six Pre-Hispanic South American populations with implications for the peopling of the New World

2018 ◽  
Vol 26 (1-2) ◽  
pp. 20-32 ◽  
Author(s):  
Alejandra Ortiz
Keyword(s):  
New World ◽  
South American ◽  
Northern Coast ◽  
State University ◽  
Arizona State University ◽  
Dental Anthropology ◽  
Low Frequencies ◽  
High Frequencies ◽  
Statistical Program ◽  
The Mean

The analysis of the human dentition pro-vides important information on the origins and dispersals of the first American inhabitants. However, most of this work has focused on North America, whereas less research has been devoted to variation within Central and South America. This study examines the permanent dentitions of 340 individuals from six pre-Hispanic South American populations and places them in the broader context of the peopling of the New World. Non-metric dental data were collected using the Arizona State University Dental Anthropology System (ASUDAS). Intra- and inter-regional comparisons were assessed using the Mean Measure of Divergence statistical program. All samples are characterized by relatively high frequencies of UM1 enamel extension and LM1 deflecting wrinkle and low frequencies of UM1 cusp 5 and LM2 Y-groove pattern. Although preliminary, results indicate that populations from Chile, Venezuela and Peru-Northern Coast are dentally similar and follow the Sinodont dental pattern. The Peru-Southern Highlands sample is the most divergent of the South American groups examined, showing the closest affinities with Sundadonts. Finally, no clear pattern was found for Bolivia and Peru-Amazonian Andes, as most of their trait frequencies fall within the range of overlap between Sinodont and Sundadont populations.

scholarly journals Acoustic streaming and the induced forces between two spheres

2016 ◽  
Vol 810 ◽  
pp. 378-391 ◽  
Author(s):  
D. Fabre ◽  
J. Jalal ◽  
J. S. Leontini ◽  
R. Manasseh
Keyword(s):  
Acoustic Streaming ◽  
Lateral Force ◽  
Oscillating Flow ◽  
Low Frequencies ◽  
High Frequencies ◽  
Steady Streaming ◽  
The Mean ◽  
Linear Problems ◽  
Parameter Measuring ◽  
Dimensional Domain

The ability of acoustic microstreaming to cause a pair of particles to attract or repel is investigated. Expanding the flow around two spheres in terms of a small-amplitude parameter measuring the amplitude of the forcing, the leading order is an oscillating flow field with zero mean representing the effect of the applied acoustic field, while the second-order correction contains a steady streaming component. A modal decomposition in the azimuthal direction reduces the problem to a few linear problems in a two-dimensional domain corresponding to the meridional ($r,z$) plane. The analysis computes both the intricate flow fields and the mean forces felt by both spheres. If the spheres are aligned obliquely with respect to the oscillating flow, they experience a lateral force which realigns them into a transverse configuration. In this transverse configuration, they experience an axial force which can be either attractive or repulsive. At high frequencies the force is always attractive. At low frequencies, it is repulsive. At intermediate frequencies, the force is attractive at large distances and repulsive at small distances, leading to the existence of a stable equilibrium configuration.

Spreading of Epidemics on Scale-Free Networks with Time Delay

2012 ◽  
Vol 562-564 ◽  
pp. 1386-1389
Author(s):  
Yuan Mei Wang ◽  
Tao Li
Keyword(s):  
Field Theory ◽  
Time Delay ◽  
Mean Field Theory ◽  
Mean Field ◽  
Sir Model ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
Theoretical Results

In the SIR model once a node is cured after infection it becomes permanently immune,but we assume this immunity to be temporary. So we obtain an epidemic model with time delay on scale-free networks. Using the mean field theory the spreading threshold and the spreading dynamics is analyzed. Theoretical results indicate that the threshold is significantly dependent on the topology of scale-free networks and time delay. Numerical simulations confirmed the theoretical results.

scholarly journals Control of Collective Dynamics in a Network of Bistable Time-Delay Systems Coupled via the Mean Field

2019 ◽  
Vol 19 (4) ◽  
pp. 258-269
Author(s):  
Vladimir I. Ponomarenko ◽  
◽  
Danil D. Kulminskiy ◽  
Ekaterina I. Borovkova ◽  
Mikhail D. Prokhorov ◽  
...  
Keyword(s):  
Time Delay ◽  
Mean Field ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Collective Dynamics ◽  
The Mean

Stratigraphic filtering, Part II: Model spectra

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2775-2783 ◽  
Author(s):  
N. C. Banik ◽  
I. Lerche ◽  
J. R. Resnick ◽  
R. T. Shuey
Keyword(s):  
Time Delay ◽  
Corner Frequency ◽  
Stratigraphic Sequence ◽  
Long Tail ◽  
Low Frequencies ◽  
High Frequencies ◽  
Seismic Wavelet ◽  
Scattered Energy ◽  
Short Period ◽  
Time Domains

We describe filtering by short‐period multiples in one dimension using a combination of the O’Doherty‐Anstey (1971) formula with a stochastic model in which the autocorrelation of acoustic impedance decreases exponentially with lag [Formula: see text] while the spectrum of reflection coefficients rises with frequency up to a corner, then is approximately constant, [Formula: see text] An impedance log with these statistics is a generalization of the classic random telegraph wave. The parameter [Formula: see text], the mean‐square fractional fluctuation of impedance, is typically less than 1 percent, although we show an example where it is as high as 13 percent. The corner frequency [Formula: see text] is inversely related to average bed thickness. Typical values are 50–100 Hz, at the upper end of the normal seismic band. The cyclic stratification discussed by O’Doherty and Anstey (1971) and others corresponds to [Formula: see text] above the seismic band. Some logs have more reflection power at low frequencies than predicted from high frequencies by this model. We describe in both frequency and time domains the filtering of a seismic wavelet by multiples in such a stratigraphic sequence. The impulse response has a direct arrival, followed by a long tail of multiply scattered energy. The greater the impedance fluctuations or the longer the traveltime, the more amplitude is transferred from the primary to the multiples. We discuss in less detail several other models, including periodic and nearly periodic bedding. We also include two numerical applications of the O’Doherty‐Anstey formula; we show on a specific logged interval the formula’s remarkable accuracy for both attenuation and time delay; and we describe the reduction in computed time delay due to coarser sampling of the log.

scholarly journals Long Term X-ray Variability of NGC 4151

1994 ◽  
Vol 159 ◽  
pp. 402-402
Author(s):  
I. E. Papadakis ◽  
I. M. McHardy
Keyword(s):  
Power Spectrum ◽  
Light Curve ◽  
Power Spectra ◽  
Low Frequency ◽  
Short Time Scale ◽  
Low Frequencies ◽  
X Ray ◽  
Ngc 4151 ◽  
Short Time

Short time scale X-ray power spectra of AGN are in general well fitted by a power law with slopes between −1 and −2 but we expect these slopes to flatten at low frequencies (indication of such a flattening has already been seen in NGC 5506). We have searched for such a low-frequency break in the power spectrum of NGC 4151 by investigating its long term X-ray light curve (2–10 keV). To construct this light curve we used Ariel V SSI, OSO-8, HEAO-1, Ariel VI, EXOSAT ME and GINGA LAC data.

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