Some methods for solving of 3D inverse problem of magnetometry

D. V. Lukyanenko, A. G. Yagola

Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia

Abstract: Recovery of magnetic target parameters from magnetic sensor measurements has attracted wide interests and found many practical applications. However, difficulties present in identifying the magnetization due to the complications of magnetization distributions over investigated object, errors and noises of measurement data, degrade the accuracy and quality of the restored parameters. In this paper we consider a modern model for the mentioned problem (magnetic inversion based on both total magnetic intensity data and full tensor gradient magnetic data) and some method of its solving. This method involves taking into account the round-off errors, accumulation of which could significantly influences the restored solution in the case of using model with full tensor gradient magnetic data. Tikhonov reg- ularization has been applied in solving the inversion problem with the modified generalized
discrepancy principle (that include information about accumulated round-off errors) for the choosing regularization parameter.

Keywords: magnetometry, full tensor magnetic gradient, inverse problem, Tikhonov regularization, generalized discrepancy principle, round-off errors.

MSC: 45B05, 45Q05, 65R32, 65F22

Received: 22.08.2016

Language: English