Electromagnetic modeling of 3-D sources over 2-D inhomogeneities in the time domain

Geophysics ◽  
1992 ◽  
Vol 57 (8) ◽  
pp. 994-1003 ◽  
Author(s):  
Michael Leppin
Keyword(s):  
Differential Equations ◽  
Diffusion Equation ◽  
Time Domain ◽  
Magnetic Induction ◽  
Host Rock ◽  
Vertical Component ◽  
Wavenumber Domain ◽  
Transient Electromagnetic ◽  
Wide Range ◽  
The Time Domain

A numerical method is presented by which the transient electromagnetic response of a two‐dimensional (2-D) conductor, embedded in a conductive host rock and excited by a rectangular current loop, can be modeled. This 2.5-D modeling problem has been formulated in the time domain in terms of a vector diffusion equation for the scattered magnetic induction, which is Fourier transformed into the spatial wavenumber domain in the strike direction of the conductor. To confine the region of solution of the diffusion equation to the conductive earth, boundary values for the components of the magnetic induction on the ground surface have been calculated by means of an integral transform of the vertical component of the magnetic induction at the air‐earth interface. The system of parabolic differential equations for the three magnetic components has been integrated for 9 to 15 discrete spatial wavenumbers ranging from [Formula: see text] to [Formula: see text] using an implicit homogeneous finite‐difference scheme. The discretization of the differential equations on a grid representing a cross‐section of the conductive earth results in a large, sparse system of linear equations, which is solved by the successive overrelaxation method. The three‐dimensional (3-D) response has been computed by an inverse Fourier transformation of the cubic spline interpolated scattered magnetic induction in the wavenumber domain using a digital filtering technique. To test the algorithm, responses have been computed for a two‐layered half‐space and a vertical prism embedded in a conductive host rock. These examples were then compared with results obtained analytically or numerically using frequency‐domain finite‐element and time‐domain integral equation methods. The new numerical procedure gives satisfactory results for a wide range of 2-D conductivity distributions with conductivity ratios exceeding 1:100, provided the grid is sufficiently refined at the corners of the conductivity anomalies.

Analytical approximate solutions of the time-domain diffusion equation in layered slabs

2002 ◽  
Vol 19 (1) ◽  
pp. 71 ◽  
Author(s):  
Fabrizio Martelli ◽  
Angelo Sassaroli ◽  
Yukio Yamada ◽  
Giovanni Zaccanti
Keyword(s):  
Diffusion Equation ◽  
Time Domain ◽  
Approximate Solutions ◽  
The Time Domain

Three-dimensional numerical modeling of gravity and magnetic anomaly in a mixed space-wavenumber domain

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. G41-G54 ◽  
Author(s):  
Shikun Dai ◽  
Dongdong Zhao ◽  
Shunguo Wang ◽  
Bin Xiong ◽  
Qianjiang Zhang ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Fourier Transform ◽  
Differential Equations ◽  
Numerical Solution ◽  
Magnetic Anomaly ◽  
Large Scale ◽  
Vertical Component ◽  
Wavenumber Domain ◽  
Gravity And Magnetic ◽  
Gravity And Magnetic Anomaly

Fast and accurate numerical modeling of gravity and magnetic anomalies is the basis of field-data inversion and quantitative interpretation. In gravity and magnetic prospecting, the computation and memory requirements of practical modeling is still a significant issue, which leads to the difficulty of using efficient and detailed inversions for large-scale complex models. A new 3D numerical modeling method for gravity and magnetic anomaly in a mixed space-wavenumber domain is proposed to mitigate the difficulties. By performing a 2D Fourier transform along two horizontal directions, 3D partial differential equations governing gravity and magnetic potentials in the spatial domain are transformed into a group of independent 1D differential equations wrapped with different wavenumbers. Importantly, the computation and memory requirements of modeling are greatly reduced by this method. A modeling example with 4,040,100 observations can be finished in approximately 28 s on a desktop using a single core, and the independent differential equations are highly parallel among different wavenumbers. The method preserves the vertical component in the space domain, and thus a mesh for modeling can be finer at a shallower depth and coarser at a deeper depth. In general, the new method takes into account the calculation accuracy and the efficiency. The finite-element algorithm combined with a chasing method is used to solve the transformed differential equations with different wavenumbers. In a synthetic test, a model with prism-shaped anomalies is used to verify the accuracy and efficiency of the proposed algorithm by comparing the analytical solution, our numerical solution, and a well-known numerical solution. Furthermore, we have studied the balance between computational accuracy and efficiency using a standard fast Fourier transform (FFT) method with grid expansion and the Gauss-FFT method. A model with topography is also used to explore the ability of modeling topography with our method. The results indicate that the proposed method using the Gauss-FFT method has characteristics of fast calculation speed and high accuracy.

scholarly journals Calculations of near-field emissions in frequency-domain into time-dependent data with arbitrary wave form transient perturbations

2012 ◽  
Vol 1 (2) ◽  
pp. 26
Author(s):  
Y. Liu ◽  
B. Ravelo ◽  
J. Ben Hadj Slama
Keyword(s):  
Time Domain ◽  
Near Field ◽  
Wave Spectrum ◽  
Computational Method ◽  
Time Dependent ◽  
Dependent Data ◽  
Wave Form ◽  
Frequency Dependent ◽  
Transient Electromagnetic ◽  
The Time Domain

This paper is devoted on the application of the computational method for calculating the transient electromagnetic (EM) near-field (NF) radiated by electronic structures from the frequency-dependent data for the arbitrary wave form perturbations i(t). The method proposed is based on the fast Fourier transform (FFT). The different steps illustrating the principle of the method is described. It is composed of three successive steps: the synchronization of the input excitation spectrum I(f) and the given frequency data H0(f), the convolution of the two inputs data and then, the determination of the time-domain emissions H(t). The feasibility of the method is verified with standard EM 3D simulations. In addition to this method, an extraction technique of the time-dependent z-transversal EM NF component Xz(t) from the frequency-dependent x- and y- longitudinal components Hx(f) and Hy(f) is also presented. This technique is based on the conjugation of the plane wave spectrum (PWS) transform and FFT. The feasibility of the method is verified with a set of dipole radiations. The method introduced in this paper is particularly useful for the investigation of time-domain emissions for EMC applications by considering transient EM interferences (EMIs).

scholarly journals A Formal Time-domain Approach to Cold Magnetised Plasmas

1988 ◽  
Vol 41 (1) ◽  
pp. 55 ◽  
Author(s):  
Werner Weiglhofer
Keyword(s):  
Differential Equations ◽  
Time Domain ◽  
Scalar Potential ◽  
Coupled System ◽  
Dielectric Tensor ◽  
Tensor Operator ◽  
Transient Wave ◽  
The Time Domain ◽  
Limiting Case ◽  
Wave Phenomena

Representations of the electromagnetic and the average velocity field for a cold magnetised plasma are derived in terms of scalar potential functions. These Hertz potentials are solutions of a coupled system of integro-differential equations of second Qrder. Different from other approaches, the analysis is carried out in the time domain and is therefore especially suited for the investigation of transient wave phenomena. Furthermore, the dielectric tensor operator of the plasma is derived. Mter solving the system of integro-differential equations for a special limiting case, the applicability of the method presented is demonstrated and generalisations are discussed.

scholarly journals Innovative Multi-Site Photoplethysmography Analysis for Quantifying Pulse Amplitude and Timing Variability Characteristics in Peripheral Arterial Disease

2018 ◽  
Author(s):  
Michael Bentham ◽  
Gerard Stansby ◽  
John Allen
Keyword(s):  
Peripheral Arterial Disease ◽  
Frequency Domain ◽  
Time Domain ◽  
Domain Analysis ◽  
Arterial Disease ◽  
Timing Variability ◽  
Wide Range ◽  
Healthy Control ◽  
The Time Domain ◽  
Peripheral Arterial

Photoplethysmography (PPG) is a simple-to-perform vascular optics measurement technique that can detect changes in blood volume in the microvascular tissue bed. Beat-to-beat analysis of the PPG waveform enables the study of the variability of pulse features such as amplitude and pulse arrival time (PAT), and when quantified in the time and frequency domains, has considerable potential to shed light on perfusion changes associated with peripheral arterial disease (PAD). In this pilot study innovative multi-site bilateral finger and toe PPG recordings from 43 healthy control subjects and 31 PAD subjects were compared (recordings each at least 5 minutes, collected in a warm temperature-controlled room). Beat-to-beat normalized amplitude and PAT variability was then quantified in the time-domain using SD and IQR measures and in the frequency-domain bilaterally using Magnitude Squared Coherence (MSC). Significantly reduced normalized amplitude variability (healthy control 0.0384 (IQR 0.0217-0.0744) vs PAD 0.0160 (0.0080-0.0338) (p<0.001) and significantly increased PAT variability (healthy control 0.0063 (0.0052-0.0086) vs PAD 0.0093 (0.0078-0.0144) (p<0.001) was demonstrated in PAD using the time-domain analysis. Frequency-domain analysis demonstrated significantly lower MSC values across a range of frequency bands for PAD patients. These changes suggest a loss of right-to-left body side coherence and cardiovascular control in PAD. This study has also demonstrated the feasibility of using these measurement and analysis methods in studies investigating multi-site PPG variability for a wide range of cardiac and vascular patient groups.

scholarly journals Application of L1 Trend Filtering Technology on the Current Time Domain Spectroscopy of Dielectrics

Electronics ◽  
2019 ◽  
Vol 8 (9) ◽  
pp. 1046
Author(s):  
Changyou Suo ◽  
Zhonghua Li ◽  
Yunlong Sun ◽  
Yongsen Han
Keyword(s):  
Time Series ◽  
Time Domain ◽  
Time Complexity ◽  
Time Range ◽  
Test Results ◽  
Current Time ◽  
Time Domain Spectroscopy ◽  
Filtering Algorithms ◽  
Wide Range ◽  
The Time Domain

The current time domain spectroscopy of dielectrics provides important information for the analysis of dielectric properties and mechanisms. However, there is always interference during the testing process, which seriously affects the analysis of the test results. Therefore, the effective filtering of current time domain spectroscopy is particularly necessary. L1 trend filtering can estimate the trend items exactly in a set of time series. It has been widely used in the fields of economics and sociology. Therefore, this paper attempts to apply L1 trend filtering to the current time domain spectroscopy. Firstly, polarization and depolarization currents are measured in the laboratory. Then the test results are filtered by L1 trend filtering and the filtering effects are compared with several common filtering algorithms, such as a sliding mean filter and Savitzky–Golay smoothing filter. Finally, the robustness and time complexity of L1 trend filtering are analyzed. The filtering results show that because the polarization currents vary in a wide range of the time domain (about 2–3 orders of magnitude), smooth and undistorted curves in the whole test time range can hardly be obtained through common filtering algorithms, while they can be obtained by L1 trend filtering. The results of robustness analysis and time complexity analysis show that L1 trend filtering can extract the trend items accurately in the time series under given different noise levels, and the execution time is also lower than 176.67 s when the number of tested points is no more than 20,000. Those results show that L1 trend filtering can be applied to the time domain current spectroscopy of dielectrics.

Time-Domain Poroelastic Green's Functions

2003 ◽  
Vol 11 (03) ◽  
pp. 491-501 ◽  
Author(s):  
Andrzej Hanyga
Keyword(s):  
Differential Equations ◽  
Asymptotic Solution ◽  
Time Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Isotropic Case ◽  
The Time Domain ◽  
Singular Memory ◽  
Asymptotic Time

A method previously developed for asymptotic solution of systems of integro-differential equations with singular memory is applied to the determination of the time-domain asymptotic Green's function of Biot's poroelasticity. Asymptotic time-domain Green's functions are constructed in a neighborhood of the wavefronts. The general anisotropic medium as well as the isotropic case are considered.

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