任意形状水平接地导线源瞬变电磁法一维正反演研究

1D forward modeling and inversion algorithm for grounded galvanic source TEM sounding with an arbitrary horizontal wire

本文发展了一种适应于任意形状水平接地导线源瞬变电磁法的一维正反演方法,可用于长偏移距、短偏移距、多通道测量接地导线源瞬变电磁数据.正演误差通常在1%以内.弧形导线源与直导线源的正演对比表明:导线源赤道方向电磁场容易受到导线源形态的影响,而轴向方向电场所受影响较小.采用修改的矩阵传播法求取水平电场和垂直磁感应场的敏感度.结果表明:相比扰动法,在层数越多时,矩阵传播法优势越明显,当层数达到64层时,效率提高近30倍.反演方法采用正则化Gauss-Newton迭代法实现.反演结果表明:单纯使用磁感应场时间导数进行反演对高导异常层恢复良好,而对低导异常层重构并不理想,且用反演模型生成的电场预测数据与原始电场数据差距较大.使用单一接收点电场进行反演结果也并不理想,而当使用多个接收点处电场值进行共同反演时,高导异常层与低导异常层均能得到较好的体现,相应电场及磁感应场的预测数据与原始数据均吻合的比较好.对有磁导率异常的模型进行反演表明,电场与磁感应场共同反演能够较好地体现地层电导率与磁导率的变化规律.

We present a 1 D forward and inversion method for grounded galvanic source Transient Electromagnetic（ TEM）sounding with an arbitrary horizontal grounded wire. In the forward modeling,the Hankel and SIN/COS integrals are calculated using filter methods,with the adaptive approach applied to choose an appropriate abscissa range of the filters,and the lagged approach to reduce the calculation of Hankel or SIN/COS transforms with a same kernel. The relative errors are less than 1% in most cases. A comparison of a straight and an arc-shaped grounded source shows obvious influence of the source shape on the electromagnetic field at the receivers on the perpendicular direction,while little influence is detected at the receivers on the axial direction. A modified Matrix Propagation（ MP） algorithm is developed to calculate the sensitivities of the horizontal electric field and vertical induced magnetic field. Compared to the perturbation method,with more layeres,the advantage of the modified MP algorithm is more apparent. For a 64 layered model,the time cost of perturbation is35. 4 s,while it takes only 1. 3 s using the modified MP algorithm,which improves nearly 30 times.The Gauss-Newton iteration method combined with the Tikhonov regularization is adopted for inversion. The inversion result using only the derivative of the vertical induced magntic field over time shows a good reconstruction of the conductive layer,but an unsatisfactory recovery of the resistive layers, especially the resistive layer shielded by the upper conductive layer. The inversion result is also not ideal when using the electric data of only one receiving station. When the electric data of multi-stations are taking into inversion, the conductive layer and resistive layers are all presented well in the reconstructed model. Meanwile,the predicted electric data and magnetic data fit the raw data very well,even though the magnetic data are not brought into inversion. As to the model with magnetic permeable layers,the joint inversion of electric data and induced magnetic data presents a good recovery of the variation trend of both the conductivity and the permeability.