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The aim of the study was to develop a methodology for calculating and optimizing devices for the magnetic exploration of fossils containing materials with a high magnetic permeability. The proposed technique is based on the calculation of electrostatic fields perturbed by conducting bodies and of magnetic fields perturbed by ferromagnets with a high magnetic permeability. It uses an integral equation of the first kind. This technique is preferable to the technique consisting in the use of an integral equation of the second kind, since in the situation under consideration, the latter does not have a unique solution and requires transformation. Prospects for the development of this area allow one to bring geophysical services to the service market on a new scientific and technical production level; reduce the environmental burden on nature by replacing magnetometric measurements with energy-saving, environmentally safe technology; and ensure the export potential of magnetometric equipment.