地面矩形大定源电磁法频率域三维非线性共轭梯度反演

本文实现了地面矩形大定源三维频率域反演.矩形大定源三维模型响应计算采用交错网格有限差分技术.正演的微分方程为异常电场满足的非齐次Helmholtz方程,方程右手边源项中的大定源产生的背景格林函数由虚界面法结合虚框法计算.频率域三维反演采用非线性共轭梯度反演技术.反演的数据类型为垂直磁场的频率域响应Hz的实部和虚部分量.数值结果表明,(1)三维模型正演模拟数值结果与前人一致,为三维反演奠定基础;(2)针对两个三维导电模型,分别进行了三维反演数值试算.反演结果可以清晰恢复出异常体的电阻率和位置信息,表明地面矩形大定源三维频率域非线性共轭梯度反演具有可行性.本文研究的意义在于,在电磁响应时频转换技术的基础上,如果将野外实测的瞬变电磁数据变换为对应的频率响应,则结合本文提出的三维反演技术,可以为矩形大定源瞬变电磁数据的三维解释提供一个新的思路.

Three-dimensional inversion of frequency-domain EM data from a large rectangular loop using the non-linear conjugated gradient method

This work has developed a three-dimensional inversion of electromagnetic data in the frequency domain excited by a large rectangular loop. The inversion is performed using the non-linear conjugated gradient method (NLCG). During the inversion, frequency domain model responses of secondary electrical fields are estimated by a three-dimensional staggered grid finite difference scheme. On the right-hand side of Helmholtz equation, the primary field from a rectangular large loop on the ground is summed up by that from a number of virtual squares which span the loop. For each square, the corresponding Green's function is computed by a virtual interface method. The real and imaginary components of the frequency-domain vertical magnetic field in and out the loop are used as the input of the inversion. The accuracy of the forward modeling is consistent with previous work. Two models have been used to testify the inversion algorithm. The synthetic results show that (1) three-dimensional frequency-domain inversion can recover the position and relative resistivity of abnormal bodies, proving the feasibility of the inversion. (2) The application of the NLCG method to the frequency-domain large loop makes the interpretation of fixed loop TEM data possible.