Three-Dimensional FDTD Modeling of TEM Excited by a Loop Source Considering Ramp Time
详细信息
- 责任者：Sun Huaifeng (Geotechnical and Structural Engineering Research Center ; Shandong University ; Jinan 250061 ; China) ; Li Xiu
- 刊名：Chinese Journal of Geophysics
- 出版年：2013
- 卷期：56(3)
- 关键词：瞬变电磁法 ; transient electromagnetic methods
- 页码：p.1049-1064
- 图表：illus., 1 table, 46 refs.
- 分类号：1600
- issnNo：ISSN0001-5733
- isbnNo：CN11-2074/P
摘要
Transient electromagnetic(TEM) diffusion equations can be directly derived from the Maxwell equations.However,the diffusion equations do not contain the first derivative of the electric field to time,thus the explicit finite difference equations in the time domain cannot be derived.In this work,the du Fort-Frankel method solving finite difference equations is referenced and an additional fictitious displacement current is introduced into the diffusion equations to form explicit difference equations.Two modifications are made based on the famous finite difference TEM modeling method in the time domain by Wang and Hohmann.Firstly,the loop current is introduced into Maxwell equations by means of current density according to Ampere circuital theorem.A loop source is added in modeling.Secondly,the ramp time is considered in modeling.By the first modification,primary fields of TEM are included in modeling and the excitation source is no longer dependent on a homogeneous half-space model as the initial condition.The algorithm can be applied to very complex models with non-uniform surface resistivity distributions.In real TEM data acquisition,the ramp current is not a step and the ramp time is not zero.The ramp time can be considered in modeling by the second modification.The modified TEM 3D FDTD modeling method is checked by several numerical examples,the analytical solution of a homogeneous half-space model,digital filter solutions of four types of three-layer earth,integral-equation solution and Wang′s FDTD solution for a low resistivity 3D body in a homogeneous half-space.The central loop induced electromotive force of an H model with different ramp times are simulated by the 3D FDTD modeling method to show the influences of ramp times.Finally,a complex 3D model with two mined out water bodies are built simplified from real geological data and fixed loop TEM responses are simulated using a 1 μs ramp time.The apparent resistivity curves and contours are also drawn.
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