地-井瞬变电磁三维交错网格有限差分正演及响应特性

Three-Dimension Forward Modeling and Characteristics for Surface-Borehole Transient Electromagnetic by Using Staggered-Grid Finite Difference Method

为了研究地-井瞬变电磁响应特征,获得不同井位低阻薄板异常体的响应规律:首先采用交错网格有限差分技术离散二次场满足的频率域赫姆霍兹方程;然后结合虚框叠加等效和虚拟界面法将发射源和接收位置扩展到任意层位,解决了全空间背景格林函数的计算问题;之后利用MUMPS求解器求解频率域二次场,再经过余弦变换,获得井中任意位置的瞬变电磁响应;最后采用三维模型对本文算法的正确性进行验证,设计了均匀半空间和嵌入低阻薄板的三维模型,获得垂直磁场的三维分布,分析均匀导电半空间中低阻薄板对地-井瞬变电磁三维响应的影响特点。结果表明:本文三维地-井瞬变电磁计算方案的计算精度与前人基本相同;水平导电薄板的存在主要影响板体附近及穿过薄板的井中瞬变响应,最大的特点是在异常体位置附近的中期时间道响应出现变号现象。本文的研究为定性解释地-井瞬变电磁法异常提供一个技术手段,也为地-井瞬变电磁三维反演奠定基础。

In this study, we developed three-dimension forward modeling for surface-borehole transient electromagnetic （TEM） by using staggered-grid finite difference method, and obtained transient electromagnetic response characteristics from different borehole positions for a conductive thin plate. The Helmholtz function is disereted by staggered-grid finite difference method in frequency domain, then the abnormal-field is quickly processed using MUMPS package. Background Green function can be efficiently computed by equivalent fictitious square overlay method and virtual interface method, which extending the transmitter and receiver to anywhere in full space. The cosine- transformation was performed for borehole transient electromagnetic response in any position, then the mentioned algorithm was validated by three-dimension model. We designed two three-dimension conductive models, one is the homogeneous half-space, the other is an embedded conductive plate, to get the three-dimension distribution of vertical magnetic field in the time domain, and then we analyzed the influence of ＇the conductive body on transient electromagnetic response. It is shown that the solution of three-dimension transient electromagnetic in this study is comparable to those of the predecessors~. The existence of a conductive plate influences mainly on borehole TEM near the plate body and through the conductive thin plate; and TEM symbol change occurs in the middle time channels near the abnormal body. The proposed research provides a technical method for qualitative interpretation of surface- borehole transient electromagnetic data, and lays the foundation for threE-dimension inversion of surface-borehole transient electromagnetic