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.

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.

Fast finite-difference time-domain modeling for marine-subsurface electromagnetic problems

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. A19-A23 ◽  
Author(s):  
Frank A. Maaø
Keyword(s):  
Low Frequency ◽  
Computational Time ◽  
Small Displacement ◽  
Displacement Current ◽  
Domain Modeling ◽  
Low Frequencies ◽  
Electromagnetic Problems ◽  
Time Domain Modeling ◽  
Displacement Currents ◽  
Propagation Velocities

In the low-frequency limit, the displacement currents in the Maxwell equations can be neglected. However, for numerical simulations, a small displacement current should be present to achieve numerical stability. This requirement leads to a large range of propagation velocities with high velocities for the high frequencies and low velocities for the low frequencies. As a consequence, the number of time steps may become large. I show that it is possible to transform mathematically the original physical problem to one that has propagation velocities with less frequency dependence. Hence, the number of time steps necessary for a signal to travel a certain distance with the lowest velocity is significantly reduced. A typical example shows a reduction in computational time by a factor of 40. A comparison of the solutions from plane-layered modeling in the frequency and wavenumber domain and the proposed method shows good agreement between the two. The proposed method can also be used for other systems of diffusive equations.

Electromagnetic Response for Horizontal Electric Dipole Source Considering Conduct & Displacement Current

2014 ◽  
Vol 513-517 ◽  
pp. 3340-3344
Author(s):  
Jia Bin Yan ◽  
Xiang Yu Huang ◽  
Peng Yu Wu
Keyword(s):  
Electric Dipole ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
Displacement Current ◽  
Geophysical Application ◽  
Horizontal Electric Dipole ◽  
Em Field ◽  
Transform Zone ◽  
Displacement Currents ◽  
And Diffusion

Electromagnetic (EM) field is often referred to diffusion (quasi-static assumption) that displacement currents are neglected during data processing in geophysical application, while the ratio of conduct currents to displacement currents is higher than 10, that is ,we think EM field is diffusion dominated and wave dominate for the ratio less than 0.1. Our simulating with Horizontal Electric Dipole Field indicated that frequency range of wave dominated is that the ratio is less than 0.007, the magnitude curves of EM component and impedance referring to diffusion and wave are different from those of diffusion. And in transform zone () the curves are different from those of wave and diffusion.

Pseudoacoustic tilted transversely isotropic modeling with optimal k-space operator-based implicit finite-difference schemes

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. T139-T157 ◽  
Author(s):  
Shigang Xu ◽  
Yang Liu
Keyword(s):  
Finite Difference ◽  
Spatial Modeling ◽  
Wave Equations ◽  
Transversely Isotropic ◽  
Dispersion Relations ◽  
High Order ◽  
Space Operator ◽  
Modeling Accuracy ◽  
Tti Media ◽  
Temporal And Spatial

Current temporal high-order finite-difference (FD) stencils are mainly designed for isotropic wave equations, which cannot be directly extended to pseudoacoustic wave equations (PWEs) in tilted transversely isotropic (TTI) media. Moreover, it is difficult to obtain the time-space domain FD coefficients for anisotropic PWEs based on nonlinear dispersion relations in which anisotropy parameters are coupled with FD coefficients. Therefore, a second-order FD for temporal derivatives and a high-order FD for spatial derivatives are commonly used to discretize PWEs in TTI media. To improve the temporal and spatial modeling accuracy further, we have developed several effective FD schemes for modeling PWEs in TTI media. Through combining the [Formula: see text] (wavenumber)-space operators with the conventional implicit FD stencils (i.e., regular-grid [RG], staggered-grid [SG], and rotated SG [RSG]), we establish novel dispersion relations and determine FD coefficients using least-squares (LS). Based on [Formula: see text]-space operator compensation, we adopt the modified LS-based implicit RG-FD, implicit SG-FD, and implicit RSG-FD methods to respectively solve the second- and first-order PWEs in TTI media. Dispersion analyses indicate that the modified implicit FD schemes based on [Formula: see text]-space operator compensation can greatly increase the numerical accuracy at large wavenumbers. Modeling examples in TTI media demonstrate that the proposed FD schemes can adopt a short FD operator to simultaneously achieve high temporal and spatial modeling accuracy, thus significantly improve the computational efficiency compared with the conventional methods.

A high order finite-difference scheme for time-domain modelling of time-varying seismoelectric waves

Geophysics ◽  
2021 ◽  
pp. 1-49
Author(s):  
Yanju Ji ◽  
Li Han ◽  
Xingguo Huang ◽  
Xuejiao Zhao ◽  
Kristian Jensen ◽  
...  
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Time Domain ◽  
Calculation Method ◽  
High Order ◽  
Difference Approximation ◽  
Time Varying ◽  
Time Step ◽  
Static Approximation ◽  
High Order Finite Difference

Simulation of the seismoelectric effect serves as a useful tool to capture the observed seismoelectric conversion phenomenon in porous media, thus offering promising potential in underground exploration activities to detect pore fluids such as water, oil and gas. The static electromagnetic (EM) approximation is among the most widely used methods for numerical simulation of the seismoelectric responses. However, the static approximation ignores the accompanying electric field generated by the shear wave, resulting in considerable errors when compared to analytical results, particularly under high salinity conditions. To mitigate this problem, we propose a spatial high-order finite-difference time-domain (FDTD) method based on Maxwell's full equations of time-varying EM fields to simulate the seismoelectric response in 2D mode. To improve the computational efficiency influenced by the velocity differences between seismic and electromagnetic waves, different time steps are set according to the stability conditions, and the seismic feedback values of EM time nodes are obtained by linear approximation within the seismic unit time step. To improve the simulation accuracy of the seismoelectric response with the time-varying EM calculation method, finite-difference coefficients are obtained by solving the spatial high-order difference approximation based on Taylor expansion. The proposed method yields consistent simulation results compared to those obtained from the analytical method under different salinity conditions, thus indicating its validity for simulating seismoelectric responses in porous media. We further apply our method to both layered and anomalous body models and extend our algorithm to 3D. Results show that the time-varying EM calculation method could effectively capture the reflection and transmission phenomena of the seismic and EM wavefields at the interfaces of contrasting media. This may allow for the identification of abnormal locations, thus highlighting the capability of seismoelectric response simulation to detect subsurface properties.

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