3D electrical resistivity inversion using prior spatial shape constraints  

基于空间形态先验约束的三维电阻率反演成像方法(英文)

作　　者：李术才[1] 聂利超[1] 刘斌[1] 宋杰[1] 刘征宇[1] 苏茂鑫[1] 徐磊[1] 

机构地区：[1]山东大学岩土与结构工程研究中心,济南250061

出　　处：《Applied Geophysics》2013年第4期361-372,510,共13页应用地球物理（英文版）

基　　金：supported by the National Program on Key Basic Research Project of China(973 Program)(No.2013CB036002,No.2014CB046901);the National Major Scientific Equipment Developed Special Project(No.51327802);National Natural Science Foundation of China(No.51139004,No.41102183);the Research Fund for the Doctoral Program of Higher Education of China(No.20110131120070);Natural Science Foundation of Shandong Province(No.ZR2011EEQ013);the Graduate Innovation Fund of Shandong University(No.YZC12083)

摘　　要：To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical data regarding the extent of a geological anomaly are important prior information. We propose the use of shape constraints in 3D electrical resistivity inversion, Three weighted orthogonal vectors （a normal and two tangent vectors） were used to control the resistivity differences at the boundaries of the anomaly. The spatial shape of the anomaly and the constraints on the boundaries of the anomaly are thus established. We incorporated the spatial shape constraints in the objective function of the 3D resistivity inversion and constructed the 3D resistivity inversion equation with spatial shape constraints. Subsequently, we used numerical modeling based on prior spatial shape data to constrain the direction vectors and weights of the 3D resistivity inversion. We established a reasonable range between the direction vectors and weights, and verified the feasibility and effectiveness of using spatial shape prior constraints in reducing excessive structures and the number of solutions. We applied the prior spatially shape-constrained inversion method to locate the aquifer at the Guangzhou subway. The spatial shape constraints were taken from ground penetrating radar data. The inversion results for the location and shape of the aquifer agree well with drilling data, and the number of inversion solutions is significantly reduced.三维电阻率探测反演存在着多解性的固有难题,增加已知数据和先验信息、施加先验约束是压制反演多解性的可行途径。针对该问题,将地质推断或其他地球物理勘探方法获得的确定性的异常体空间形态信息作为一种重要的已知先验信息,提出了一种基于异常体空间形态先验约束的三维电阻率反演成像方法,利用已知异常体边界的三个正交方向向量(法向量及两个切向量)及各向异性的权重系数来控制异常体边界区域的法方向及切方向电阻率差异程度,从而实现已知异常体边界空间形态的刻画及其先验约束的表征。将上述异常体空间形态先验约束施加到三维电阻率反演目标函数中,并建立了基于空间形态先验约束的三维电阻率反演成像方程。然后,开展了基于空间形态先验约束的数值反演算例,对三维电阻率反演方向向量及其权重进行了系统探讨,得到了方向向量权重合理的取值范围,验证了空间形态先验约束在降低多余构造,压制多解性方面的可行性和有效性。最后,将该方法用于广州地铁含水层探测中,将地质地雷得到的异常体空间形态施加到三维电阻率反演中,较准确的反演出地下含水层的位置和形态,通过与现场钻孔对比,可发现空间形态约束方法显著的压制了三维电阻率探测反演的多解性问题,具有良好的实用性。

关 键 词：electrical resistivity INVERSION prior spatial constraints direction vector GEOPHYSICS geotechnical engineering. 

分 类 号：P631.3[天文地球—地质矿产勘探]