Truncated minimal-norm Gauss-Newton method applied to the inversion of FDEM data

Electromagnetic induction techniques are among the most popular methods for non-invasive investigation of the soil. The collection of data is allowed by frequency domain electromagnetic devices. Starting from these data, the reconstruction of some soil properties is a challenging task, as the inverse problem is ill-posed, meaning that the problem is underdetermined, ill-conditioned, that is, the solution is sensitive to the presence of noise in the data, and nonlinear. Iterative procedures are commonly used to solve nonlinear inverse problems and the Gauss–Newton method is one of the most popular. When the problem is ill-conditioned, the Gauss–Newton method is coupled with regularization techniques, to transform the problem into a well-conditioned one. In this paper, we propose a minimal-norm regularized solution method based on the Gauss–Newton iteration to invert FDEM data. Some numerical examples on synthetic data, regarding the reconstruction of a vertical portion of the soil, show good performances.