Electromagnetic induction techniques are often used to ascertain the presence of conductive substances in the subsoil. The device we are interested in generates an electromagnetic field and measures the secondary field produced by eddy currents induced by the primary field. We analyze a linear model which reproduces the device readings, consisting of a system of two Fredholm linear integral equations of the first kind. After studying the continuous problem in various function spaces, we describe three collocation methods to transform the integral equations into a system of linear equations, which is solved by a regularization technique. Numerical experiments show the performance of the different discretizations, and of a particular approach to deal with the integral truncation error. We also verify the influence on the solution of regularization matrices based on the discretization of the first and second derivative.

Recovering the electrical conductivity of the soil via a linear integral model

P. Díaz de Alba
;
L. Fermo;C. van der Mee;G. Rodriguez
2019

Abstract

Electromagnetic induction techniques are often used to ascertain the presence of conductive substances in the subsoil. The device we are interested in generates an electromagnetic field and measures the secondary field produced by eddy currents induced by the primary field. We analyze a linear model which reproduces the device readings, consisting of a system of two Fredholm linear integral equations of the first kind. After studying the continuous problem in various function spaces, we describe three collocation methods to transform the integral equations into a system of linear equations, which is solved by a regularization technique. Numerical experiments show the performance of the different discretizations, and of a particular approach to deal with the integral truncation error. We also verify the influence on the solution of regularization matrices based on the discretization of the first and second derivative.
Fredholm integral equations of the first kind, Electromagnetic induction, Inverse problems in geophysics, Collocation methods, TSVD regularization
File in questo prodotto:
File Dimensione Formato  
linear18.pdf

Solo gestori archivio

Tipologia: versione editoriale
Dimensione 447.43 kB
Formato Adobe PDF
447.43 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/257791
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 3
social impact