Geometric 3-D inversion of airborne time-domain electromagnetic data with applications to kimberlite pipes prospecting in a complex medium

Abstract

We consider an approach to solving 3-D inverse problems of airborne time-domain electromagnetic (TD-EM) survey in complex geoelectrical conditions, when the responses of target objects in the measured signal are relatively small and mixed with responses of rugged topography, 3-D inhomogeneities in overburden layers, and other interfering 3-D objects. For parameterization of the geoelectrical model of the geological medium, global and local structures are used. A block structure is a grid with large cells whose boundaries can move during the inversion process. Block structures are characterized by two types of parameters: geometric and physical. Geometric parameters include the coordinates of the boundaries of blocks in block structures, which are used for recovering local bodies or 3-D inhomogeneities within the layers, and physical parameters are the conductivities inside the blocks. In addition, the geometric parameters include displacements of control points, which are used for describing curved surfaces. The functional employed for inversion includes regularizing terms that allow controlling the self-crossing of geometric boundaries and extension of physical parameters beyond the boundaries of the allowed values range. Regularization coefficients are calculated adaptively at each iteration of the nonlinear 3-D inversion. In order to separate the responses of 3-D inhomogeneities located under the overburdens from those of 3-D inhomogeneities inside the overburdens, we propose to carry out 3-D inversion in two stages. At the first stage, over a shortened time range, we recover the conductivity distribution using global block structures and the shape of the boundaries of the overburden layers using control points. At the second stage, the entire time range is used. In those places where the significant residuals remained at late times, local block structures are employed to recover local objects (including target ones) under the overburden layers. This enables us to define quite accurately the position in plan, top border depth, and type of 3-D inhomogeneities, which are located under the overburdens, at the second stage of geometric inversion. To calculate 3-D time-domain electromagnetic fields, we use the vector finite element method implemented on optimized non-conforming hexahedral meshes with the possibility of adjoining the faces of several finite elements to the face of one finite element. The workability of the proposed approaches is demonstrated on synthetic airborne TD-EM data as well as on experimental airborne data, which are obtained as a result of methodical work over the kimberlite pipe deposit. The proposed geoelectrical model parameterization and the approach to 3-D inversion allow the discovery of relatively small 3-D target objects, when many non-target objects, including 3-D inhomogeneities in the overburdens, give several times greater responses in the measured signals.