ONE-DIMENSIONAL MODELLING FOR PROTON MAGNETIC RESONANCE SOUNDING MEASUREMENTS OVER AN ELECTRICALLY CONDUCTIVE MEDIUM

Abstract

The theory of the proton magnetic resonance sounding (a.k.a. surface nuclear magnetic resonance) was first developed in free space. In this case, the alternative excitation field has no phase variation. Hence there is no major difficulty in determining the effect of its active component, that is the one perpendicular to the static field. But over a conductive medium, the excitation field induces eddy currents, resulting in a secondary field that also has to be considered. The computation made up to now in this case did not consider the detailed physical behaviour of an excitation field which is elliptically polarised: only an extrapolation of the linearly polarised case was made which turns out to be only an approximation.This paper presents the proper formalism that permits to take rigorously into account the effect of the elliptically polarised field on the rotation of the magnetic moment of the protons, so as to obtain the correct derivation of the magnetic resonance signal produced. When compared with the approximate algorithm previously used for 1D modelling, computation results show that no significant differences arise for resistivities as low as 1 Ω m. It is only for a 2D water distribution in a medium with a 1D geoelectrical structure that differences can be observed.