Rational Function Fitting of Electromagnetic Transfer Functions from Frequency-Domain and Time-Domain Data

2018 ◽

Vol 12 (7-8) ◽

pp. 76-83

Author(s):

E. V. KARSHAKOV ◽

J. MOILANEN

Keyword(s):

Fourier Transform ◽

Frequency Domain ◽

Time Domain ◽

Frequency Interval ◽

Single Spectrum ◽

Simultaneous Inversion ◽

Homogeneous Half Space ◽

Time Domain Data ◽

The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

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Effects of Noise, Time-Domain Damping, Zero-Filling and the FFT Algorithm on the “Exact” Interpolation of Fast Fourier Transform Spectra

Applied Spectroscopy ◽

10.1366/0003702884429094 ◽

1988 ◽

Vol 42 (5) ◽

pp. 715-721 ◽

Cited By ~ 38

Author(s):

Francis R. Verdun ◽

Carlo Giancaspro ◽

Alan G. Marshall

Keyword(s):

Fourier Transform ◽

Frequency Domain ◽

Time Domain ◽

Word Length ◽

Peak Position ◽

Double Precision ◽

Time Domain Data ◽

Roundoff Errors ◽

Data Points ◽

Lorentzian Spectrum

A frequency-domain Lorentzian spectrum can be derived from the Fourier transform of a time-domain exponentially damped sinusoid of infinite duration. Remarkably, it has been shown that even when such a noiseless time-domain signal is truncated to zero amplitude after a finite observation period, one can determine the correct frequency of its corresponding magnitude-mode spectral peak maximum by fitting as few as three spectral data points to a magnitude-mode Lorentzian spectrum. In this paper, we show how the accuracy of such a procedure depends upon the ratio of time-domain acquisition period to exponential damping time constant, number of time-domain data points, computer word length, and number of time-domain zero-fillings. In particular, we show that extended zero-filling (e.g., a “zoom” transform) actually reduces the accuracy with which the spectral peak position can be determined. We also examine the effects of frequency-domain random noise and roundoff errors in the fast Fourier transformation (FFT) of time-domain data of limited discrete data word length (e.g., 20 bit/word at single and double precision). Our main conclusions are: (1) even in the presence of noise, a three-point fit of a magnitude-mode spectrum to a magnitude-mode Lorentzian line shape can offer an accurate estimate of peak position in Fourier transform spectroscopy; (2) the results can be more accurate (by a factor of up to 10) when the FFT processor operates with floating-point (preferably double-precision) rather than fixed-point arithmetic; and (3) FFT roundoff errors can be made negligible by use of sufficiently large (> 16 K) data sets.

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Inversion of airborne geophysics over the DO-27/DO-18 kimberlites — Part 2: Electromagnetics

Interpretation ◽

10.1190/int-2016-0140.1 ◽

2017 ◽

Vol 5 (3) ◽

pp. T313-T325 ◽

Cited By ~ 17

Author(s):

Dominique Fournier ◽

Seogi Kang ◽

Michael S. McMillan ◽

Douglas W. Oldenburg

Keyword(s):

Frequency Domain ◽

Time Domain ◽

Three Dimensions ◽

Data Sets ◽

Conductivity Model ◽

Time Domain Data ◽

Conductivity Structure ◽

Lake Bottom ◽

Geologic Interpretation ◽

Lateral Extent

We focus on the task of finding a 3D conductivity structure for the DO-18 and DO-27 kimberlites, historically known as the Tli Kwi Cho (TKC) kimberlite complex in the Northwest Territories, Canada. Two airborne electromagnetic (EM) surveys are analyzed: a frequency-domain DIGHEM and a time-domain VTEM survey. Airborne time-domain data at TKC are particularly challenging because of the negative values that exist even at the earliest time channels. Heretofore, such data have not been inverted in three dimensions. In our analysis, we start by inverting frequency-domain data and positive VTEM data with a laterally constrained 1D inversion. This is important for assessing the noise levels associated with the data and for estimating the general conductivity structure. The analysis is then extended to a 3D inversion with our most recent optimized and parallelized inversion codes. We first address the issue about whether the conductivity anomaly is due to a shallow flat-lying conductor (associated with the lake bottom) or a vertical conductive pipe; we conclude that it is the latter. Both data sets are then cooperatively inverted to obtain a consistent 3D conductivity model for TKC that can be used for geologic interpretation. The conductivity model is then jointly interpreted with the density and magnetic susceptibility models from a previous paper. The addition of conductivity enriches the interpretation made with the potential fields in characterizing several distinct petrophysical kimberlite units. The final conductivity model also helps better define the lateral extent and upper boundary of the kimberlite pipes. This conductivity model is a crucial component of the follow-up paper in which our colleagues invert the airborne EM data to recover the time-dependent chargeability that further advances our geologic interpretation.

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Time-resolving the COVID-19 outbreak using frequency domain analysis

10.1101/2020.05.07.20094078 ◽

2020 ◽

Author(s):

Keno L. Krewer ◽

Mischa Bonn

Keyword(s):

Steady State ◽

Severe Acute Respiratory Syndrome ◽

Spectral Density ◽

Frequency Domain ◽

Time Domain ◽

Case Fatality ◽

Frequency Domain Analysis ◽

Time Domain Data ◽

Current Outbreak ◽

The Time Domain

AbstractDifficulties assessing and predicting the current outbreak of the severe acute respiratory syndrome coronavirus 2 can be traced, in part, to the limitations of a static description of a dynamic system. Fourier transforming the time-domain data of infections and fatalities into the frequency domain makes the dynamics easily accessible. Defining a quantity like the “case fatality” as a spectral density allows a more sensible comparison between different countries and demographics during an ongoing outbreak. Such a case fatality informs not only how many of the confirmed cases end up as fatalities, but also when. For COVID-19, knowing this time and using the entire case fatality spectrum allows determining that an outbreak had entered a steady-state (most likely its end) about 14 days before this is obvious from time-domain data. The lag between confirmations and deaths also helps to estimate the effectiveness of contact management: The larger the lag, the less time the average confirmed person had to infect people before quarantine.

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Frequency domain subspace identification of fractional order systems using time domain data with outliers

Asian Journal of Control ◽

10.1002/asjc.2370 ◽

2020 ◽

Author(s):

Zongyang Li ◽

Yiheng Wei ◽

Jiachang Wang ◽

Yongting Deng ◽

Jianli Wang ◽

...

Keyword(s):

Frequency Domain ◽

Fractional Order ◽

Time Domain ◽

Subspace Identification ◽

Fractional Order Systems ◽

Time Domain Data

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Optimization of Frequency Domain Fatigue Analysis for Unbonded Flexible Risers

10.1115/omae2021-62886 ◽

2021 ◽

Author(s):

Jiabei Yuan ◽

Yucheng Hou ◽

Zhimin Tan

Keyword(s):

Frequency Domain ◽

Time Domain ◽

Transfer Functions ◽

Hybrid Approach ◽

Fatigue Analysis ◽

System Response ◽

Similar Response ◽

Potential Cost ◽

Spectrum Prediction ◽

Flexible Risers

Abstract Fatigue analysis of flexible risers is a demanding task in terms of time and computational resources. The traditional time domain approach may take weeks of time in global simulation, local modelling and post-processing of riser responses to get fatigue results. Baker Hughes developed a fast hybrid approach, which is based on a frequency domain technique. The new approach was first implemented at the end fitting region and then to all other regions of the riser. Studies showed that the hybrid approach achieved convenient and conservative results in a significant shorter period of time. To improve the accuracy and reduce conservatism of the method, Baker Hughes has further optimized the analysis procedure to seek better results approaching true solutions. Several methods were proposed and studied. The duration of representative cases and noncritical cases have been extended. The steps to predict stress spectrum based on transfer functions have also been updated. From previous studies, only one transfer function was built for fatigue load cases with similar response spectra. This assumption linearizes the system response and produces certain level of discrepancy against true time domain solution. In this study, multiple ways of spectrum prediction are evaluated and compared. The paper summarizes several techniques to further optimize the hybrid frequency domain approach. The updated fatigue results are found to be more accurate. The optimized approach therefore gives more flexibility to engineers to approach the true solutions, which were originally acquired from full 3-hr time domain simulations. The approach requires less analysis time and reduces iterations in pipe structure and riser configuration design, which leads to faster project execution and potential cost reduction.

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