## A vector finite element solver of three-dimensional modelling for a long grounded wire source based on total electric field

**LI Jian-Hui;Colin G.Farquharson;HU Xiang-Yun;ZENG Si-Hong;Hubei Subsurface Multi-scale Imaging Key Laboratory,Institute of Geophysics and Geomatics, China University of Geosciences;Department of Earth Sciences,Memorial University of Newfoundland;State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining & Technology;**

Due to the easiness of removing source singularity,the primary/secondary field algorithm is one of popular algorithms for three-dimensional modelling in geophysical electromagnetic methods.However,it is cumbersome to implement this algorithm if a transmitting source is laid on a rugged surface of the Earth or background models are complex.The total field algorithm is analternative scheme to numerically simulate the electromagnetics,and its difficulty is how to enforce the source item in the Helmholtz equation of electric field or its magnetic vector potential,especially observation points are located near the transmitting source.In controlled-source electromagnetic methods,transmitting sources including a long grounded wire can be viewed as a combination of many horizontal electric dipoles(HEDs).In our three-dimensional scheme,the source item in the Helmholtz equation of total electric field,the governing equation for vector finite element(FE)method,could be dealt with in the form of HED.The numerical accuracy of FE method depends on meshing quality to some extent,which is evaluated by the maximum allowable radius-edge ratio and the minimum allowable dihedral angle for the unstructured tetrahedral elements generated by the TetGen software.Taking the electric field excited by a HED within a 0.01S·m-1 whole-space as examples,the results show that as the maximum allowable radius-edge ratio decreases or the minimum allowable dihedral angle increases,the numerical accuracy will be improved.By this model,we also validated the algorithm presented here.For a conductive prism buried in a homogeneous half-space with a 100m-long grounded wire,the electric field calculated by our algorithm was compared with those calculated by the integral equation method based on secondary electric field,the finite volume method based on total electric field and the FE method based on magnetic vector potential.The results show that these four numerical solutions coincide well with each other,and the behavior of the electric field well indicates the conductive prism.Then,we applied the algorithm presented here to compute the amplitude and phase of the electric field for the model of disc-shape hydrocarbon buried in seabed.Through this model,the validity and ability of modelling the electromagnetic field for irregular bodies were tested simultaneously.Finally,an inclined fault,contact zone and metalliferous vein are always approximated by an inclined plate in three-dimensional modelling.For the inclined plate model with different conductivities,the electric field excited by a 1000m-long grounded wire source was calculated.The electric field for the inclined plate of 0.0333S·m-1 has stronger anomaly responses than those for the inclined plate of 0.0167S·m-1.In the following study,this algorithm will be applied to three-dimensional modelling for a long grounded wire source laid on a rugged surface.

【Fund】：
国家自然科学基金项目(41274077;41474055;41504088);;
中国矿业大学深部岩土力学与地下工程国家重点实验室开放基金(SKLGDUEK1312);;
同济大学海洋地质国家重点实验室开放基金(MGK1405)联合资助

【CateGory Index】： P631.325

【CateGory Index】： P631.325

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