基于电场总场矢量有限元法的接地长导线源三维正演

电磁场数值模拟的背景场/异常场算法是三维正演的有效策略之一,优点为采用解析法计算电磁场背景场代替场源项、克服了场源奇异性,缺点为不适用于发射源布置于起伏地表或背景模型复杂的情形.总场算法是直接对电磁场总场开展数值模拟,其难点是有效加载场源、保证近区与过渡区数值解精度.本文以水平电偶源形式分段加载接地长导线源,并以电场总场Helmholtz方程为矢量有限元法控制方程,实现了基于非结构化四面体网格剖分的接地长导线源频率域电磁法三维正演.通过与均匀全空间中水平电偶源产生的电场解析解对比,验证了本文算法的正确性,并分析了四面体外接圆半径与其最短棱边的最大比值和四面体二面角最小值对数值解精度的影响规律.通过与块状高导体地电模型的积分方程法、有限体积法和基于磁矢量势Helmholtz方程的有限元法数值解对比,进一步验证了本文算法正确性,同时说明了非结构化四面体网格能够更加精细地剖分电性异常体,利于获得精确数值解.

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

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 an alternative 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.#br#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 0.01 S·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.#br#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 0.0333 S·m^-1 has stronger anomaly responses than those for the inclined plate of 0.0167 S·m^-1.#br#In the following study, this algorithm will be applied to three-dimensional modelling for a long grounded wire source laid on a rugged surface.