STATISTICAL MODELS FOR INTERPRETING AEROMAGNETIC DATA

A mathematical basis for the application of power spectrum analysis to aeromagnetic map interpretation is developed. An ensemble of blocks of varying depth, width, thickness, and magnetization is considered as a statistical model. With the use of the fundamental postulate of statistical mechanics, a formula which can be used to analyze the power spectrum of an aeromagnetic map is developed. The influences of horizontal size, depth, thickness, and depth extent of the blocks on the shape of the power spectrum are assessed. Examples which include power spectra of maps from Canada and Central America demonstrate the application of the approach. In the cases studied a double ensemble of blocks appears to best explain the observed power spectrum characteristics.

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Log-log scale roughness spectroscopy of surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100146965 ◽

1993 ◽

Vol 51 ◽

pp. 224-225

Author(s):

P. Fraundorf ◽

B. Armbruster

Keyword(s):

Power Spectrum ◽

Autocorrelation Function ◽

Power Spectra ◽

Scanning Force Microscopy ◽

Scanning Tunneling ◽

Tunneling Microscopy ◽

Force Microscopy ◽

Scanning Force ◽

Lateral Structure ◽

Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

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Heart rate variability (HRV) power spectrum analysis (PSA) as a quantitative measurement of stress and relaxation--Methodological considerations

PsycEXTRA Dataset ◽

10.1037/e538922013-062 ◽

2005 ◽

Author(s):

O. Hoos ◽

K. Hottenrott

Keyword(s):

Heart Rate ◽

Heart Rate Variability ◽

Power Spectrum ◽

Spectrum Analysis ◽

Quantitative Measurement ◽

Power Spectrum Analysis ◽

Methodological Considerations

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The anisotropy of the power spectrum in periodic cosmological simulations

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab874 ◽

2021 ◽

Vol 503 (4) ◽

pp. 5638-5645

Author(s):

Gábor Rácz ◽

István Szapudi ◽

István Csabai ◽

László Dobos

Keyword(s):

Dark Matter ◽

Power Spectrum ◽

Large Scale ◽

Cold Dark Matter ◽

Initial Conditions ◽

Power Spectra ◽

Cosmological Simulations ◽

Spherical Collapse ◽

Lower Amplitude ◽

Hydrodynamical Simulations

ABSTRACT The classical gravitational force on a torus is anisotropic and always lower than Newton’s 1/r2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard Lambda cold dark matter (ΛCDM) initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations is a consequence of the missing large-scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

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

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3831 ◽

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.

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Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab522 ◽

2021 ◽

Author(s):

Robin E Upham ◽

Michael L Brown ◽

Lee Whittaker

Keyword(s):

Power Spectrum ◽

Random Noise ◽

Power Spectra ◽

Stage Iv ◽

Wishart Distribution ◽

Weak Lensing ◽

Dependence Structure ◽

Gaussian Fields ◽

Non Gaussian ◽

Parameter Constraints

Abstract We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

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