An algorithm for the automatic resolution of the position, orientation and dipole moment of a magnetic dipole antenna buried in rock

摘要

AbstractudIn this paper, an algorithm for accurately finding the position, orientation and dipole moment ofuda transmitting dipole antenna buried in rock is presented. The algorithm is based on simplifiedudradiation equations that are shown to be valid within a region of space in the extreme near fieldudsurrounding the antenna called termed quasi-static region. Within this region, medium dependentudpropagation effects are negligible, allowing accurate, medium independent resolution of position,udorientation and dipole moment.udThe magnetic field magnitude and direction values observed at a number of arbitrarily located pointsudin space are used by the algorithm to generate a system of nonlinear equations. This system ofudequations is solved using a simultaneous multi-variable Newton-Raphson solver with line searchesudand backtracking providing a measure of global convergence. An additional method, based on anuditerated random search, further improves the global convergence capability of the algorithm.udIf the dipole moment of the transmitting antenna is known, measurements from two observer pointsudare sufficient to resolve the position and orientation of the dipole. If the dipole moment is unknown,udthree observer points are required to solve for the unknown position, orientation and dipole moment.udThe algorithm is able to find an exact solution using exact theoretical measurements, and a minimisedudleast squares solution where measurements are subject to noise.udThe theory relating to the algorithm is discussed including distance-frequency relations for the quasistaticudregion of a number of common rock types. Probabilistic modelling, simulation and test resultsudof the algorithm are also included.