Determination of the Direction of Magnetization and Orientation of a Tilted Sheet From Downhole Magnetic Gradient Tensor Data

A tilted sheet model can usefully represent a dipping vein, dyke, sedimentary layer, or metasedimentary unit. Downhole magnetometer measurements provide proximal remote sensing of magnetic properties of magnetized sheets from a different perspective than ground or aeromagnetic surveys. However, a priori geometric information about a sheet is still required to constrain its magnetization, unless the measurements include data acquired in a borehole that penetrates the sheet. In particular, if only external measurements are available, knowledge of the dip of the sheet is required to constrain the direction of magnetization and an estimate of the thickness of the sheet is required to constrain the intensity of magnetization. This article describes a program for determination of both the direction of magnetization and geometry of a sheet from downhole magnetic gradient tensor data. We give expressions for the magnetic gradient tensor on the axis of a vertical borehole within a tilted sheet. We use an invariant of the tensor to determine the location and thickness of the sheet and tensor components to obtain the direction of magnetization and orientation of the sheet. An iterative procedure can improve the accuracy of the estimated parameters. We also discuss the robustness of the proposed program in the presence of variations in the diameter of the borehole, measurement offset from the center of the borehole, and nonuniform dip of the sheet. Experiments verify the proposed program and demonstrate the advantages of downhole magnetic gradient tensor measurements. The method can be extended to inclined boreholes by a straightforward rotation of coordinate axes.