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High definition impedance imaging for mines and tunnels

The high definition impedance imaging (HDII) Electroscan algorithm casts the error norm problem into the interior of the region and iteratively minimizes the difference norm calculated between solutions achieved for applied currents (i.e. the Neumann problem) and the solution achieved for the measured voltages (i.e. the Dirichlet problem) - in the electrical-excitation case. This results in very sparse matrices instead of densely-packed Jacobian matrices. Minimization of the error yields a three-dimensional image of the conductivity distribution. The paper presents a rapid, sparse-matrix methodology for high definition admittivity imaging involving a very large number of voxels. It is a least-square algorithm, simultaneously involving all excitations, and it is error resilient and well-conditioned. The solution iterative procedure is accelerated by a variety of means such as: solution of mutually-constrained, three-dimensional field equations; successive point-iterative overrelaxation; multi-acceleration factors; measurements at a multiplicity of electrodes; and excitation modification for image enhancement. Laboratory, field, and simulation case studies are presented. Spatially restricted-region and open-region solutions are compared. Signal-source modeling is not required. Conductivity and, generally, admittivity values are able to be determined. And so, the imaging process has diagnostic capability. It is applicable to non-contact standoff excitations, e.g. magnetic fields, microwave/radar, sonic and elasticity wave excitations.