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Theoretical approach for the depth of penetration of in situ magnetic susceptibility measurements
Author(s) -
Esparza Francisco J.,
MéndezDelgado Sóstenes,
GómezTreviño Enrique
Publication year - 2014
Publication title -
near surface geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.639
H-Index - 39
eISSN - 1873-0604
pISSN - 1569-4445
DOI - 10.3997/1873-0604.2014020
Subject(s) - magnetic susceptibility , weighting , geology , penetration depth , penetration (warfare) , in situ , mineralogy , mathematics , optics , physics , acoustics , operations research , meteorology , quantum mechanics
We present a mathematical approach for analysing in‐situ magnetic susceptibility measurements in terms of elementary contributions from different depths within the soil. Our analysis leads to a compact integral formula that relates the actual measurements to the depth profile of magnetic susceptibility within the soil, in such a way that the former is simply a weighted spatial average of the latter. The degree of penetration of a given measurement is then readily quantified by the weighting function of the corresponding instrument. Our results match and complement the experimental determinations of other workers to currently used susceptibility meters. We provide theoretical curves for the depth of penetration of four instruments that have been studied in the literature, and also refine previous estimations of the characteristic depths intrinsic to each instrument.