Inversion of electrical conductivity data with Tikhonov regularization approach: some considerations

G. P. Deidda, E. Bonomi, C. Manzi


Electromagnetic induction measurements, which are generally used to determine lateral variations of apparent
electrical conductivity, can provide quantitative estimates of the subsurface conductivity at different depths.
Quantitative inference about the Earth's interior from experimental data is, however, an ill-posed problem. Using
the generalised McNeill's theory for the EM38 ground conductivity meter, we generated synthetic apparent
conductivity curves (input data vector) simulating measurements at different heights above the soil surface. The
electrical conductivity profile (the Earth model) was then estimated solving a least squares problem with Tikhonov
regularization optimised with a projected conjugate gradient algorithm. Although the Tikhonov approach improves
the conditioning of the resulting linear system, profile reconstruction can be surprisingly far from the desired true
one. On the contrary, the projected conjugate gradient provided the best solution without any explicit regularization
( a= 0) of the objective function of the least squares problem. Also, if the initial guess belongs to the image of the
system matrix, Im(A), we found that it provides a unique solution in the same subspace Im(A).


inverse problems;Tikhonov regularization;projected conjugate gradient;high-frequency electromagnetics

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Published by INGV, Istituto Nazionale di Geofisica e Vulcanologia - ISSN: 2037-416X