ELECTROMAGNETIC TRANSIENT RESPONSE OF A CONDUCTING SPHERE EMBEDDED IN A CONDUCTIVE MEDIUM

Geophysics ◽  
1973 ◽  
Vol 38 (5) ◽  
pp. 864-893 ◽  
Author(s):  
Shri Krishna Singh
Keyword(s):  
Transient Response ◽  
Time Domain ◽  
Massive Sulfide ◽  
Displacement Current ◽  
Static Approximation ◽  
Electromagnetic Transient ◽  
Conducting Sphere ◽  
Quasi Static Approximation ◽  
Displacement Currents ◽  
The Time Domain

This paper is concerned with the time‐domain electromagnetic prospecting of massive sulfide ore bodies which are surrounded by conductive host rocks. The electromagnetic transient response of a permeable and conducting sphere embedded in a finitely conducting infinite space is derived. The source is a magnetic dipole of arbitrary orientation which is located outside the sphere. The contributions from the displacement currents have been neglected. The solution thus obtained is compared with the known solution under “quasi‐static” approximation in which the displacement current in the sphere and both the conduction and the displacement currents in the outer medium are neglected. From the numerical results presented, it is clear that the validity of the quasi‐static approximation in the time domain, if the outer host rock is conductive, must be carefully investigated. If the finite outer conductivity is taken into account, magnetic modes are modified and electric modes become important. Five response functions, each a function of five parameters, are required to describe the secondary magnetic field.

scholarly journals Effect of Displacement Current on the Finite-Difference Modeling of Natural Source Electromagnetic Diffusion

2020 ◽  
Vol 10 (8) ◽  
pp. 2744
Author(s):  
Yahui Xue ◽  
Jianxin Liu ◽  
Rong Liu ◽  
Zhuo Liu ◽  
Rongwen Guo ◽  
...  
Keyword(s):  
Finite Difference ◽  
Displacement Current ◽  
Low Frequencies ◽  
Static Approximation ◽  
Conduction Current ◽  
Quasi Static Approximation ◽  
Modeling Accuracy ◽  
Em Field ◽  
Displacement Currents ◽  
Earth Conductivity

For electromagnetic (EM) modeling based on the electric-field formulation at low frequencies, the quasi-static approximation (i.e., only the conduction current is considered and the displacement current is ignored) is commonly applied, and a small conductivity value for the air layer is chosen subjectively. Actually, in the air layer, due to the use of the small conductivity value, the quasi-static approximation is ubiquitously violated. However, the effect of the violation of the quasi-static approximation in the air on EM modeling is not well examined in the literature. In this paper, we investigate this issue by comparing the finite-difference modeling results from the calculation with the quasi-static approximation and those considering both the conduction and displacement currents. For the quasi-static approximation, the conductivity in the air is set to be different small values, and zero air conductivity is used for the modeling with both the conduction and displacement currents considered. Several simple models are designed to verify the numerical solution and study how the assigned conductivity for the air affects the modeling accuracy. One flat model and two models with topography are designed to examine the effect of the quasi-static approximation on the EM modeling results. For frequencies used in typical geophysical applications of EM diffusion, using the quasi-static approximation is able to produce accurate modeling results for models with typical earth conductivity. However, if the rough surface topography is considered, the use of the quasi-static approximation can reduce the EM modeling accuracy substantially at much lower frequencies (as low as several hundred Hz), which is probably due to the inaccurate description of EM waves in the air, and poses problems for applications based on direct EM field interpretation.

Generalized Modes in Time-Domain Seakeeping Calculations

2012 ◽  
Vol 56 (04) ◽  
pp. 215-233
Author(s):  
Johan T. Tuitman ◽  
Šime Malenica ◽  
Riaan van't Veer
Keyword(s):  
Rigid Body ◽  
Transient Response ◽  
Time Domain ◽  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Nonlinear Load ◽  
Large Amplitude Motions ◽  
Rigid Body Modes ◽  
The Time Domain

The concept of "generalized modes" is to describe all degrees of freedom by mode shapes and not using any predefined shape, like rigid body modes. Generalized modes in seakeeping computations allow one to calculate the response of a single ship, springing, whipping, multibody interaction, etc., using a uniform approach. The generalized modes have already been used for frequency-domain seakeeping calculations by various authors. This article extents the generalized modes methodology to be used for time-domain seakeeping computations, which accounts for large-amplitude motions of the rigid-body modes. The time domain can be desirable for seakeeping computations because it is easy to include nonlinear load components and to compute transient response, like slamming and whipping. Results of multibody interaction, two barges connected by a hinge, whipping response of a ferry resulting from slamming loads, and the response of a flexible barge are presented to illustrate the theory.

Time- and Frequency- Domain Analysis of Transient Electroosmotic Flow Induced by Sinusoidal AC Electric Field in a Curved Microtube

2005 ◽  
Author(s):  
Win-Jet Luo ◽  
Jia-Kun Chen ◽  
Ruey-Jen Yang
Keyword(s):  
Phase Shift ◽  
Electric Field ◽  
Transient Response ◽  
Time Domain ◽  
Electroosmotic Flow ◽  
Sustained Oscillation ◽  
Sustained Oscillations ◽  
Ac Electric Field ◽  
Velocity Response ◽  
The Time Domain

A backwards-Euler time-stepping numerical method is applied to simulate the transient response of electroosmotic flow in a curved microtube. The velocity responses of the flow fields induced by applied sinusoidal AC electric fields of different frequencies are investigated. The transient response of the system is fundamentally important since both the amplitude and the time duration of the transient response must be maintained within tolerable or prescribed limits. When a sinusoidal AC electric field is applied, the transient response of the output velocity oscillates in the time-domain. However, after a certain settling time, the output velocity attains a sustained oscillation with the same amplitude as the driving field. In this study, the transient response of the electroosmotic flow is characterized by the time taken by the velocity response to reach the first peak, the peak of the sustained oscillation, the maximum overshoot, the settling time, and the bandwidth of the sustained oscillations in the time-domain. Meanwhile, the performance of the system is identified by plotting the output velocity response and the output velocity phase-shift against the frequency of the applied signal. A finite time is required for the momentum to diffuse fully from the walls to the center of the curved microtube cross-section. As the applied frequency is increased, the maximum overshoot and the bandwidth and peak of the sustained oscillations gradually decrease since insufficient time exists for the momentum to diffuse fully to the center of the microtube. Additionally, the phase-shift between the applied electric field and the output velocity response gradually increases as the frequency of the applied signal is increased.

SELECTION OF A SUITABLE MODEL FOR QUANTITATIVE INTERPRETATION OF TOWED‐BIRD AEM MEASUREMENTS

Geophysics ◽  
1978 ◽  
Vol 43 (3) ◽  
pp. 576-587 ◽  
Author(s):  
G. J. Palacky
Keyword(s):  
Half Plane ◽  
Time Domain ◽  
Massive Sulfide ◽  
Suitable Model ◽  
Dual Frequency ◽  
Plane Model ◽  
Short Delay ◽  
Ore Bodies ◽  
Delay Times ◽  
The Time Domain

Many steeply dipping massive sulfide ore bodies have a dike‐like shape, and this has led to wide acceptance of the vertical half‐plane model in the interpretation of electromagnetic data. This model assumes that the conductor is thin, but the restriction has not been considered critical and in practice has frequently been disregarded. Conductance and conductor depth estimates based on the results of towed‐bird AEM surveys have been observed to be lower and less accurate than those obtained from helicopter EM and ground EM measurements. In order to explain the low reliability of the towed‐bird estimates, AEM responses over 17 Canadian ore bodies were analyzed. In the study, field results obtained by the time‐domain Input system and two dual‐frequency quadrature systems were interpreted. Error in conductance and depth estimates results from the frequency‐dependent, diffusive behavior of thick geologic conductors. This dependence makes invalid the basic assumption made in the interpretation of dual‐frequency quadrature EM data, that of the equivalence of response parameters at two frequencies. The estimated conductance and depth are too small when applying the current interpretation procedure based on amplitude ratios at two high and widely separated frequencies. The error is smaller in the case of Input time‐domain measurements, because the delay times are relatively long and the channels narrowly spaced. The vertical half‐plane model has been found to hold for ore bodies less than 10 m wide. In the case of wide mineralized zones, which are more important economically, the vertical half‐plane model could be successfully applied only at long delay times. Applying the vertical half‐plane nomogram at short delay times, the conductance and depth were underestimated, and better values could only be achieved by fitting the field data to a horizontal ribbon model. The consistently low conductance values interpreted from towed‐bird measurements for wide conductive zones have probably resulted in not selecting many potential massive sulfide targets for ground followup.

Transient response of an open resonator in the time domain

1997 ◽  
Vol 18 (2) ◽  
pp. 405-429 ◽  
Author(s):  
A. A. Vertiy ◽  
S. P. Gavrilov ◽  
D. S. Armağan ◽  
I. Ölçer
Keyword(s):  
Transient Response ◽  
Time Domain ◽  
Open Resonator ◽  
The Time Domain

Time-domain study of transient fields for a thin circular loop antenna

2002 ◽  
Vol 80 (9) ◽  
pp. 995-1003 ◽  
Author(s):  
S T Bishay ◽  
G M Sami
Keyword(s):  
Time Domain ◽  
Analytical Form ◽  
Loop Antenna ◽  
Inverse Laplace Transform ◽  
Wave Number ◽  
Earth Model ◽  
Circular Loop ◽  
Wave Forms ◽  
Displacement Currents ◽  
The Time Domain

The transient fields in the time-domain of a thin circular loop antenna on a two-layer conducting earth model are expressed in analytical form. In these expressions, the displacement currents both in the two-layer ground and in the air region are taken into consideration. The closed-form expressions of the time-domain are obtained as the inverse Laplace transform of the derived full-wave time-harmonic solution. These time-domain solutions are obtained as a summation of wave-guide modes plus contributions from branch cuts in the complex plane of the longitudinal wave number. Numerical examples are given to indicate the important features in the wave forms of the surface fields due to step and pulsed current excitation. These features provide the means of detecting the earth's stratification, measuring the overburden height, and determining the ratio of the conductivities of the layers. PACS Nos.: 41.20Jb, 42.25Bs, 42.25Gy, 44.05+e

scholarly journals Transient Response Estimation of an Offshore Wind Turbine Support System

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 891 ◽  
Author(s):  
Fushun Liu ◽  
Xingguo Li ◽  
Zhe Tian ◽  
Jianhua Zhang ◽  
Bin Wang
Keyword(s):  
Wind Turbine ◽  
Frequency Domain ◽  
Transient Response ◽  
Time Domain ◽  
Initial Conditions ◽  
Offshore Wind ◽  
Offshore Wind Turbines ◽  
Domain Method ◽  
The Time Domain ◽  
External Loads

To obtain reliable estimations of the dynamic responses of high-rising marine structures such as offshore wind turbines with obvious nonzero initial conditions, traditional frequency-domain methods cannot be employed because they provide only steady-state results. A novel frequency-domain transient response estimation method for offshore wind turbines is presented in this paper. This method builds upon a recent, significant theoretical development, which found that expressions of external loads in the frequency domain can be obtained by discretizing their eigenvalues and corresponding complex coefficients rather than directly by discrete Fourier transform (DFT) analysis, which makes it possible to deal with nonzero conditions in the frequency domain. One engineering advantage of this approach is its computational efficiency, as the motion equations of the system can be solved in the frequency domain. In order to demonstrate this approach, a case of a monopile-supported wind turbine with nonzero initial conditions was investigated. The numerical results indicate that the approach matches well with the time-domain method, except for a small, earlier portion of the estimated responses. A second case study of a sophisticated, jacket support wind turbine, involving practical issues such as complex external loads and computation efficiency, is also discussed, and comparisons of the results with the time-domain method and traditional frequency-domain method using the commercial software ANSYS are included here.

Transient Response of Irregular Surface by Periodically Distributed Semi-Sine Shaped Valleys: Incident SH Waves

2019 ◽  
Vol 14 (01) ◽  
pp. 2050005 ◽  
Author(s):  
Mehdi Panji ◽  
Saeed Mojtabazadeh-Hasanlouei
Keyword(s):  
Transient Response ◽  
Time Domain ◽  
Seismic Waves ◽  
Domain Boundary ◽  
Irregular Surface ◽  
Engineering Structures ◽  
Sh Waves ◽  
Corrugated Surfaces ◽  
Incident Plane ◽  
The Time Domain

An advanced direct half-plane time-domain boundary element method (BEM) was applied to obtain the seismic response of a linear elastic irregular surface including periodically distributed semi-sine shaped valleys subjected to propagating obliquely incident plane SH waves. After developing the method for complex multiple surface topographies, some verification examples were solved and compared with those of the published works. Then, the transient response of a rough surface with 2–16 semi-sine shaped valleys was determined as synthetic seismograms. In this regard, the depth ratio of the valleys was sensitized. Finally, amplification patterns of the surface were presented in some cases. The results showed that the method was able to analyze the multipart models in the time-domain. Moreover, the response of the sinusoidal corrugated surfaces was very effective against seismic waves in forming different patterns. The method was recommended to researchers for transient analysis of complex engineering structures and composite materials in nanoscale.

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