scholarly journals Simulations of ionospheric refraction on radio interferometric data

2021 ◽  
Vol 38 ◽  
Author(s):  
J. Kariuki Chege ◽  
C. H. Jordan ◽  
C. Lynch ◽  
J. L. B. Line ◽  
C. M. Trott
Keyword(s):  
Power Spectra ◽  
Low Frequency ◽  
Neutral Hydrogen ◽  
Simulated Data ◽  
Software Tool ◽  
Calibration Procedure ◽  
Murchison Widefield Array ◽  
The Impact ◽  
Thin Screen ◽  
Data Calibration

Abstract The Epoch of Reionisation (EoR) is the period within which the neutral universe transitioned to an ionised one. This period remains unobserved using low-frequency radio interferometers, which target the 21 cm signal of neutral hydrogen emitted in this era. The Murchison Widefield Array (MWA) radio telescope was built with the detection of this signal as one of its major science goals. One of the most significant challenges towards a successful detection is that of calibration, especially in the presence of the Earth’s ionosphere. By introducing refractive source shifts, distorting source shapes, and scintillating flux densities, the ionosphere is a major nuisance in low-frequency radio astronomy. We introduce sivio, a software tool developed for simulating observations of the MWA through different ionospheric conditions, which is estimated using thin screen approximation models and propagated into the visibilities. This enables us to directly assess the impact of the ionosphere on observed EoR data and the resulting power spectra. We show that the simulated data captures the dispersive behaviour of ionospheric effects. We show that the spatial structure of the simulated ionospheric media is accurately reconstructed either from the resultant source positional offsets or from parameters evaluated during the data calibration procedure. In turn, this will inform on the best strategies of identifying and efficiently eliminating ionospheric contamination in EoR data moving into the Square Kilometre Array era.

scholarly journals Comparison of Observing Modes for Statistical Estimation of the 21 cm Signal from the Epoch of Reionisation

2014 ◽  
Vol 31 ◽  
Author(s):  
Cathryn M. Trott
Keyword(s):  
Power Spectrum ◽  
Signal To Noise Ratio ◽  
High Redshift ◽  
Power Spectra ◽  
Low Frequency ◽  
Neutral Hydrogen ◽  
Beam Shape ◽  
Drift Scan ◽  
Murchison Widefield Array ◽  
Aperture Arrays

AbstractNoise considerations for experiments that aim to statistically estimate the 21 cm signal from high redshift neutral hydrogen during the Epoch of Reionisation (EoR) using interferometric data are typically computed assuming a tracked observation, where the telescope pointing centre and instrument phase centre are the same over the observation. Current low frequency interferometers use aperture arrays of fixed dipoles, which are steered electronically on the sky, and have different properties to mechanically-steered single apertures, such as reduced sensitivity away from zenith, and discrete pointing positions on the sky. These properties encourage the use of two additional observing modes: (1) zenith drift, where the pointing centre remains fixed at the zenith, and the phase centre tracks the sky, and (2) drift + shift, a hybrid mode where the telescope uses discrete pointing centres, and the sky drifts during each fixed pointing. These three observing modes view the sky differently, and therefore yield different uncertainties in the power spectrum according to the balance of radiometric noise and cosmic variance. The coherence of measurements made by the instrument in these modes dictates the optimal reduction in thermal noise by combination of coherent modes, and the reduction in cosmic variance by combination of incoherent modes (views of different patches of the sky). Along with calibration and instrument stability considerations, the balance between these noise components provides one measure for the utility of these three modes for measuring a statistical signature of the EoR signal. We provide a general framework for estimating the uncertainty in the power spectrum for a given observing mode, telescope beam shape, and interferometer antenna distribution. We then apply this framework to the Murchison Widefield Array (MWA) using an analysis of the two-dimensional (2D) and one-dimensional (1D) power spectra for 900 hours of observing. We demonstrate that zenith drift scans can yield marginally lower uncertainty in the signal power compared with tracked scans for the MWA EoR experiment, and that moderately higher signal-to-noise ratio (S/N) estimates of the amplitude (3%) and slope (1%) of the 1D power spectrum are accessible, translating directly into a reduction in the required observing time to reach the same estimation precision. We find that the additional sensitivity of pointing at zenith, and the reduction in cosmic variance available with a zenith drift scan, makes this an attractive observing mode for current and future arrays.

Application of the variable projection scheme for frequency-domain full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. R249-R257 ◽  
Author(s):  
Maokun Li ◽  
James Rickett ◽  
Aria Abubakar
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Simulated Data ◽  
Calibration Procedure ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Unknown Parameters ◽  
Variable Projection ◽  
Full Waveform ◽  
Data Calibration

We found a data calibration scheme for frequency-domain full-waveform inversion (FWI). The scheme is based on the variable projection technique. With this scheme, the FWI algorithm can incorporate the data calibration procedure into the inversion process without introducing additional unknown parameters. The calibration variable for each frequency is computed using a minimum norm solution between the measured and simulated data. This process is directly included in the data misfit cost function. Therefore, the inversion algorithm becomes source independent. Moreover, because all the data points are considered in the calibration process, this scheme increases the robustness of the algorithm. Numerical tests determined that the FWI algorithm can reconstruct velocity distributions accurately without the source waveform information.

scholarly journals Making maps of cosmic microwave background polarization for B-mode studies: the POLARBEAR example

2017 ◽  
Vol 600 ◽  
pp. A60 ◽  
Author(s):  
Davide Poletti ◽  
Giulio Fabbian ◽  
Maude Le Jeune ◽  
Julien Peloton ◽  
Kam Arnold ◽  
...  
Keyword(s):  
Cosmic Microwave Background ◽  
Time Domain ◽  
Power Spectra ◽  
Low Frequency ◽  
Frequency Noise ◽  
Spectrum Estimation ◽  
Microwave Background ◽  
Polarization Studies ◽  
Ordered Data ◽  
The Impact

Analysis of cosmic microwave background (CMB) datasets typically requires some filtering of the raw time-ordered data. For instance, in the context of ground-based observations, filtering is frequently used to minimize the impact of low frequency noise, atmospheric contributions and/or scan synchronous signals on the resulting maps. In this work we have explicitly constructed a general filtering operator, which can unambiguously remove any set of unwanted modes in the data, and then amend the map-making procedure in order to incorporate and correct for it. We show that such an approach is mathematically equivalent to the solution of a problem in which the sky signal and unwanted modes are estimated simultaneously and the latter are marginalized over. We investigated the conditions under which this amended map-making procedure can render an unbiased estimate of the sky signal in realistic circumstances. We then discuss the potential implications of these observations on the choice of map-making and power spectrum estimation approaches in the context of B-mode polarization studies. Specifically, we have studied the effects of time-domain filtering on the noise correlation structure in the map domain, as well as impact it may haveon the performance of the popular pseudo-spectrum estimators. We conclude that although maps produced by the proposed estimators arguably provide the most faithful representation of the sky possible given the data, they may not straightforwardly lead to the best constraints on the power spectra of the underlying sky signal and special care may need to be taken to ensure this is the case. By contrast, simplified map-makers which do not explicitly correct for time-domain filtering, but leave it to subsequent steps in the data analysis, may perform equally well and be easier and faster to implement. We focused on polarization-sensitive measurements targeting the B-mode component of the CMB signal and apply the proposed methods to realistic simulations based on characteristics of an actual CMB polarization experiment, POLARBEAR. Our analysis and conclusions are however more generally applicable.

scholarly journals ACAT1 Benchmark of RANS-Informed Analytical Methods for Fan Broadband Noise Prediction: Part II—Influence of the Acoustic Models

Acoustics ◽  
2020 ◽  
Vol 2 (3) ◽  
pp. 617-649
Author(s):  
Sébastien Guérin ◽  
Carolin Kissner ◽  
Pascal Seeler ◽  
Ricardo Blázquez ◽  
Pedro Carrasco Laraña ◽  
...  
Keyword(s):  
Analytical Methods ◽  
Acoustic Waves ◽  
Power Spectra ◽  
Low Frequency ◽  
Broadband Noise ◽  
Experimental Results ◽  
Acoustic Analogy ◽  
Noise Sources ◽  
Acoustic Models ◽  
The Impact

A benchmark dedicated to RANS-informed analytical methods for the prediction of turbofan rotor–stator interaction broadband noise was organised within the framework of the European project TurboNoiseBB. The second part of this benchmark focuses on the impact of the acoustic models. Twelve different approaches implemented in seven different acoustic solvers are compared. Some of the methods resort to the acoustic analogy, while some use a direct approach bypassing the calculation of a source term. Due to differing application objectives, the studied methods vary in terms of complexity to represent the turbulence, to calculate the acoustic response of the stator and to model the boundary and flow conditions for the generation and propagation of the acoustic waves. This diversity of approaches constitutes the unique quality of this work. The overall agreement of the predicted sound power spectra is satisfactory. While the comparison between the models show significant deviations at low frequency, the power levels vary within an interval of ±3 dB at mid and high frequencies. The trends predicted by increasing the rotor speed are similar for almost all models. However, most predicted levels are some decibels lower than the experimental results. This comparison is not completely fair—particularly at low frequency—because of the presence of noise sources in the experimental results, which were not considered in the simulations.

scholarly journals Fundamental uncertainty levels of 21 cm power spectra from a delay analysis

2019 ◽  
Vol 487 (4) ◽  
pp. 5840-5853 ◽  
Author(s):  
Adam E Lanman ◽  
Jonathan C Pober
Keyword(s):  
Power Spectrum ◽  
Power Spectra ◽  
Low Frequency ◽  
Sample Variance ◽  
Model Parameters ◽  
Delay Analysis ◽  
Analysis Strategies ◽  
Murchison Widefield Array ◽  
Fundamental Uncertainty ◽  
Combining Estimates

Abstract Several experimental efforts are underway to measure the power spectrum of 21 cm fluctuations from the epoch of reionization (EoR) using low-frequency radio interferometers. Experiments like the Hydrogen Epoch of Reionization Array (HERA) and Murchison Widefield Array Phase II (MWA) feature highly redundant antenna layouts, building sensitivity through redundant measurements of the same angular Fourier modes, at the expense of diminished UV coverage. This strategy limits the numbers of independent samples of each power spectrum mode, thereby increasing the effect of sample variance on the final power spectrum uncertainty. To better quantify this effect, we measure the sample variance of a delay-transform based power spectrum estimator, using both analytic calculations and simulations of flat-spectrum EoR-like signals. We find that for the shortest baselines in HERA, the sample variance can reach as high as 20 per cent, and up to 30 per cent for the wider fields of view of the MWA. Combining estimates from all the baselines in a HERA- or MWA-like 37 element redundant hexagonal array can lower the variance to 1−3 per cent for some Fourier modes. These results have important implications for observing and analysis strategies, and suggest that sample variance can be non-negligible when constraining EoR model parameters from upcoming 21 cm data.

scholarly journals Calibration and 21-cm power spectrum estimation in the presence of antenna beam variations

2019 ◽  
Vol 492 (2) ◽  
pp. 2017-2028 ◽  
Author(s):  
Ronniy C Joseph ◽  
C M Trott ◽  
R B Wayth ◽  
A Nasirudin
Keyword(s):  
Data Analysis ◽  
Power Spectrum ◽  
Low Frequency ◽  
Analytic Description ◽  
Spectral Features ◽  
Spectrum Estimation ◽  
Power Spectrum Estimation ◽  
Murchison Widefield Array ◽  
The Impact ◽  
Expected Signal

ABSTRACT Detecting a signal from the Epoch of Reionization (EoR) requires an exquisite understanding of Galactic and extragalactic foregrounds, low-frequency radio instruments, instrumental calibration, and data analysis pipelines. In this work, we build upon existing work that aims to understand the impact of calibration errors on 21-cm power spectrum (PS) measurements. It is well established that calibration errors have the potential to inhibit EoR detections by introducing additional spectral features that mimic the structure of EoR signals. We present a straightforward way to estimate the impact of a wide variety of modelling residuals in EoR PS estimation. We apply this framework to the specific case of broken dipoles in Murchison Widefield Array (MWA) to understand its effect and estimate its impact on PS estimation. Combining an estimate of the percentage of MWA tiles that have at least one broken dipole (15–40 per cent) with an analytic description of beam errors induced by such dipoles, we compute the residuals of the foregrounds after calibration and source subtraction. We find that that incorrect beam modelling introduces bias in the 2D-PS on the order of $\sim 10^3\, \mathrm{mK}^2 \, h^{-3}\, \mathrm{Mpc}^{3}$. Although this is three orders of magnitude lower than current lowest limits, it is two orders of magnitude higher than the expected signal. Determining the accuracy of both current beam models and direction-dependent calibration pipelines is therefore crucial in our search for an EoR signal.

USING FIELD DATA FOR THE EVALUATION OF THE IMPACT OF ULTRA-LOW FREQUENCY MOTIONS ON THE FATIGUE OF MOORING LINES

2019 ◽  
Author(s):  
Guilherme Borzacchiello ◽  
Carl Albrecht ◽  
Fabricio N Correa ◽  
Breno Jacob ◽  
Guilherme da Silva Leal
Keyword(s):  
Field Data ◽  
Low Frequency ◽  
Mooring Lines ◽  
The Impact

Analyzing the Impact of Healthy Behavior on Weight Change with a Provable Mathematical Model (Preprint)

2020 ◽  
Author(s):  
Ayan Chatterjee ◽  
Ram Bajpai ◽  
Pankaj Khatiwada
Keyword(s):  
Physical Activity ◽  
Mathematical Model ◽  
Health Behavior ◽  
Weight Change ◽  
Simulated Data ◽  
Negative Behavior ◽  
Healthy Behavior ◽  
Healthy Habits ◽  
Lifestyle Diseases ◽  
The Impact

BACKGROUND Lifestyle diseases are the primary cause of death worldwide. The gradual growth of negative behavior in humans due to physical inactivity, unhealthy habit, and improper nutrition expedites lifestyle diseases. In this study, we develop a mathematical model to analyze the impact of regular physical activity, healthy habits, and a proper diet on weight change, targeting obesity as a case study. Followed by, we design an algorithm for the verification of the proposed mathematical model with simulated data of artificial participants. OBJECTIVE This study intends to analyze the effect of healthy behavior (physical activity, healthy habits, and proper dietary pattern) on weight change with a proposed mathematical model and its verification with an algorithm where personalized habits are designed to change dynamically based on the rule. METHODS We developed a weight-change mathematical model as a function of activity, habit, and nutrition with the first law of thermodynamics, basal metabolic rate (BMR), total daily energy expenditure (TDEE), and body-mass-index (BMI) to establish a relationship between health behavior and weight change. Followed by, we verified the model with simulated data. RESULTS The proposed provable mathematical model showed a strong relationship between health behavior and weight change. We verified the mathematical model with the proposed algorithm using simulated data following the necessary constraints. The adoption of BMR and TDEE calculation following Harris-Benedict’s equation has increased the model's accuracy under defined settings. CONCLUSIONS This study helped us understand the impact of healthy behavior on obesity and overweight with numeric implications and the importance of adopting a healthy lifestyle abstaining from negative behavior change.

scholarly journals Bayesian modeling and significant features exploration in wavelet power spectra

2007 ◽  
Vol 14 (1) ◽  
pp. 79-88 ◽  
Author(s):  
D. V. Divine ◽  
F. Godtliebsen
Keyword(s):  
Data Analysis ◽  
Traditional Approach ◽  
Statistical Significance ◽  
Power Spectra ◽  
Simulated Data ◽  
Scale Space ◽  
Independent Random Variables ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Testing Procedures

Abstract. This study proposes and justifies a Bayesian approach to modeling wavelet coefficients and finding statistically significant features in wavelet power spectra. The approach utilizes ideas elaborated in scale-space smoothing methods and wavelet data analysis. We treat each scale of the discrete wavelet decomposition as a sequence of independent random variables and then apply Bayes' rule for constructing the posterior distribution of the smoothed wavelet coefficients. Samples drawn from the posterior are subsequently used for finding the estimate of the true wavelet spectrum at each scale. The method offers two different significance testing procedures for wavelet spectra. A traditional approach assesses the statistical significance against a red noise background. The second procedure tests for homoscedasticity of the wavelet power assessing whether the spectrum derivative significantly differs from zero at each particular point of the spectrum. Case studies with simulated data and climatic time-series prove the method to be a potentially useful tool in data analysis.

scholarly journals The halo model as a versatile tool to predict intrinsic alignments

2020 ◽  
Author(s):  
Maria Cristina Fortuna ◽  
Henk Hoekstra ◽  
Benjamin Joachimi ◽  
Harry Johnston ◽  
Nora Elisa Chisari ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Power Spectra ◽  
Stage Iv ◽  
Stage Iii ◽  
Radial Dependence ◽  
Additional Parameter ◽  
Small Scales ◽  
Cosmic Shear ◽  
Galaxy Populations ◽  
The Impact

Abstract Intrinsic alignments (IAs) of galaxies are an important contaminant for cosmic shear studies, but the modelling is complicated by the dependence of the signal on the source galaxy sample. In this paper, we use the halo model formalism to capture this diversity and examine its implications for Stage-III and Stage-IV cosmic shear surveys. We account for the different IA signatures at large and small scales, as well for the different contributions from central/satellite and red/blue galaxies, and we use realistic mocks to account for the characteristics of the galaxy populations as a function of redshift. We inform our model using the most recent observational findings: we include a luminosity dependence at both large and small scales and a radial dependence of the signal within the halo. We predict the impact of the total IA signal on the lensing angular power spectra, including the current uncertainties from the IA best-fits to illustrate the range of possible impact on the lensing signal: the lack of constraints for fainter galaxies is the main source of uncertainty for our predictions of the IA signal. We investigate how well effective models with limited degrees of freedom can account for the complexity of the IA signal. Although these lead to negligible biases for Stage-III surveys, we find that, for Stage-IV surveys, it is essential to at least include an additional parameter to capture the redshift dependence.

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