Calculation of electrical potentials along a longitudinal section of a 2-D terrain

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 511-516 ◽  
Author(s):  
Shi-zhe Xu ◽  
Dahai Zhang ◽  
Baiyao Ruan ◽  
Shikun Dai ◽  
Yuguo Li
Keyword(s):  
Fourier Transform ◽  
Point Source ◽  
Apparent Resistivity ◽  
Inverse Fourier Transform ◽  
Vertical Plane ◽  
Longitudinal Section ◽  
Electric Resistivity ◽  
Electrical Potentials ◽  
Terrain Corrections ◽  
The Fourier Transform

The problem of 2-D terrain corrections for point-source electric resistivity data is considered. The total electric potential is divided into normal and anomalous terms. An integral equation is derived for the Fourier transform of the anomalous potential and is solved using a boundary element method. An inverse Fourier transform is applied to recover the anomalous potential along a “longitudinal” profile passing through the point source and oriented perpendicular to the vertical plane containing the 2-D terrain variations. The sum of the normal and anomalous potentials are then used to calculate an apparent resistivity. A sample calculation demonstrates that the longitudinal apparent resistivity calculated in this manner is less sensitive to terrain variations than the traditional “transverse” apparent resistivity that is computed from potential measurements made parallel to the vertical plane containing the 2-D terrain variations.

A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform

2011 ◽  
Vol 3 (5) ◽  
pp. 572-585 ◽  
Author(s):  
A. Tadeu ◽  
C. S. Chen ◽  
J. António ◽  
Nuno Simões
Keyword(s):  
Fourier Transform ◽  
Helmholtz Equation ◽  
Initial Conditions ◽  
Inverse Fourier Transform ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Static Response ◽  
Particular Solution ◽  
The Fourier Transform ◽  
Transfer Problems

AbstractFourier transform is applied to remove the time-dependent variable in the diffusion equation. Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation, which is solved by the method of fundamental solutions and the method of particular solutions. The particular solution of Helmholtz equation is available as shown in [4, 15]. The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm. Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.

scholarly journals Inversion of Fourier Transforms by Means of Scale-Frequency Series

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Nassar H. S. Haidar
Keyword(s):  
Fourier Transform ◽  
Nonlinear Programming ◽  
Fourier Transforms ◽  
Inverse Fourier Transform ◽  
Double Series ◽  
Nonlinear Programming Problem ◽  
Continuous Scale ◽  
Free Parameters ◽  
The Fourier Transform ◽  
Dual Scale

We report on inversion of the Fourier transform when the frequency variable can be scaled in a variety of different ways that improve the resolution of certain parts of the frequency domain. The corresponding inverse Fourier transform is shown to exist in the form of two dual scale-frequency series. Upon discretization of the continuous scale factor, this Fourier transform series inverse becomes a certain nonharmonic double series, a discretized scale-frequency (DSF) series. The DSF series is also demonstrated, theoretically and practically, to be rate-optimizable with respect to its two free parameters, when it satisfies, as an entropy maximizer, a pertaining recursive nonlinear programming problem incorporating the entropy-based uncertainty principle.

scholarly journals The effect of spatial coherence of sources on synthetic aperture mapping

1991 ◽  
Vol 131 ◽  
pp. 10-14
Author(s):  
Daniel F.V. James
Keyword(s):  
Fourier Transform ◽  
Inverse Fourier Transform ◽  
Spatial Coherence ◽  
Full Description ◽  
Coherent Light ◽  
Partially Coherent ◽  
Interference Fringes ◽  
Partially Coherent Light ◽  
The Fourier Transform ◽  
Coherence Area

The interferometric mapping of astronomical objects relies on the van-Cittert Zernike theorem, one of the major results of the theory of partially coherent light [see, Bom and Wolf (1980), chapter 10]. This theorem states that the degree of spatial coherence of the field from a distant spatially incoherent source is proportional to the Fourier transform of the intensity distribution across the source. Measurement of the degree of spatial coherence, by, for example, measuring the visibility of interference fringes, allows the object to be mapped by making an inverse Fourier transform. (For a full description of this technique see Thompson, Moran and Swenson, 1986.)In this paper I present a summary of the results an investigation into what happens when the distant source is not spatially coherent (James, 1990). Using a heuristic model of a spherically symmetric partially coherent source, an analytic expression for the error in the measurement of the effective radius, expressed as a function of coherence area, can be obtained.

scholarly journals The Evolution of Linearized Perturbations in a Magnetohydrodynamic Boundary Layer

2014 ◽  
Vol 19 (2) ◽  
pp. 397-406
Author(s):  
A.R. Vijayalakshmi ◽  
P.M. Balagondar
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Fourier Transform ◽  
Shear Flow ◽  
Point Source ◽  
Piecewise Linear ◽  
Transverse Velocity ◽  
Piecewise Linear Approximation ◽  
Initial Value ◽  
The Fourier Transform

Abstract The evolution of linearized perturbations in a magnetohydrodynamic shear flow is studied using the initial value problem approach. Here the resulting equation in time posed by using the Fourier transform is solved for the Fourier amplitudes for modeled boundary layer for different initial disturbances. The shear flow prototype here is a piecewise linear approximation of a magnetohydrodynamic boundary layer. The initial disturbances that are considered are a point source of the field of transverse velocity and magnetic field. Solutions are obtained for small values of Alfve’n velocity. The velocity plots are drawn for different values of Alfve’n velocity.

On-line electron-optical correlation computing in the CTEM

1978 ◽  
Vol 36 (1) ◽  
pp. 88-89 ◽  
Author(s):  
R. Guckenberger ◽  
W. Hoppe
Keyword(s):  
Fourier Transform ◽  
Correlation Function ◽  
Transfer Function ◽  
Inverse Fourier Transform ◽  
Main Peak ◽  
Optical Correlation ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
On Line ◽  
The Fourier Transform

Light diffractograms of electron micrographs are frequently used to study the transfer function of the microscope. In order to utilize diffractograms for control operations in the microscope, several attempts have been undertaken to obtain on-line diffractograms /1 - 3/. Alternatively correlation functions (CF) may be used /4-8/. In this paper we describe an electron-optical device for the computation of such CF and its on-line operation in a microscope.The auto-correlation function (ACF) is the inverse Fourier transform of the squared modulus of the Fourier transform (diffractogram) of an image. Therefore it also contains the transfer function. It is its zero peak (main peak) which is of particular interest. In noisy images the main ACF-peak of the noise contributes in an unwanted way to the main ACF-peak of the image. This can be avoided if the ACF will be computed of two images which are identical except for noise /9/ (noise-reduced ACF= NRACF).

scholarly journals Ruin Probabilities and Complex Analysis

2021 ◽  
Author(s):  
Andrew Leung
Keyword(s):  
Fourier Transform ◽  
Continuous Time ◽  
Complex Analysis ◽  
Inverse Fourier Transform ◽  
Ruin Probabilities ◽  
Heavy Tailed Distributions ◽  
Complex Functions ◽  
Heavy Tailed ◽  
The Fourier Transform ◽  
The Relationship

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity
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