Volume 61, pp. 173-195, 2024.

Linear FDEM subsoil data inversion in Banach spaces

P. Díaz de Alba, C. Estatico, M. Lazzaretti, and G. Rodriguez

Abstract

The applicative motivation of this paper is the reconstruction of some electromagnetic features of the earth superficial layer by measurements taken above the ground. We resort to frequency domain electromagnetic data inversion through a well-known linear integral model by considering three different collocation methods to approximate the solution of the continuous problem as a linear combination of linearly independent functions. The discretization leads to a strongly ill-conditioned linear system. To overcome this difficulty, an iterative regularization method based on Landweber iterations in Banach spaces is applied to reconstruct solutions which present discontinuities or have a low degree of smoothness. This kind of solutions are common in many imaging applications. Several numerical experiments show the good performance of the algorithm in comparison to other regularization techniques.

Full Text (PDF) [577 KB], BibTeX , DOI: 10.1553/etna_vol61s173

Key words

first-kind Fredholm integral equations, electromagnetic induction, inverse problems in geophysics, collocation methods, iterative regularization, Landweber method, Banach spaces

AMS subject classifications

45B05, 65F22, 65R20, 86A22

Links to the cited ETNA articles

[18]	Vol. 47 (2017), pp. 1-17 Gian Piero Deidda, Patricia Díaz de Alba, and Giuseppe Rodriguez: Identifying the magnetic permeability in multi-frequency EM data inversion
[25]	Vol. 37 (2010), pp. 321-336 Tommy Elfving, Touraj Nikazad, and Per Christian Hansen: Semi-convergence and relaxation parameters for a class of SIRT algorithms
[38]	Vol. 53 (2020), pp. 459-480 Federica Pes and Giuseppe Rodriguez: The minimal-norm Gauss-Newton method and some of its regularized variants