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

• Main Authors: C. Manzi, E. Bonomi, G. P. Deidda
• Format: Article
• Language: English
• Published: Istituto Nazionale di Geofisica e Vulcanologia (INGV) 2003-06-01
• Series: Annals of Geophysics
• Subjects: inverse problems; Tikhonov regularization; projected conjugate gradient; high-frequency electromagnetics
• Online Access: http://www.annalsofgeophysics.eu/index.php/annals/article/view/3427
• ISSN: 1593-5213; 2037-416X

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).