Zone of main contribution to the measured signal for a circular current loop source and receiver on the surface of a conductive half‐space

Abstract

A B S T R A C TThe electric and magnetic fields generated by an individual horizontal current ring induced inside a homogeneous conductive half-space, originating from an external large circular loop source of current in the presence of a flat half-space, are deduced. A check of self-consistency for these expressions led to the known general functions for these fields due to the same external source in the presence of that medium. The current rings' mutual coupling related to the magnetic field's radial component is thoroughly analysed and its specific members are presented. The existence of a relatively small zone inside the half-space responsible for the main contribution for the signal measured at the observation point, with the source and receiver on the ground surface, is made evident. For increasing values of frequency, at a given transmitterreceiver (T-R) configuration, this zone shrinks and its central point moves away from a maximum depth of about 30% and horizontal distance of nearly 85%, of the T-R separation, to a point very close to the receiver position. The coordinates of the central point of this zone of main contribution are provided as approximated functions in terms of the induction number [(μ 0 ωσ/2) 1/2 r ].

Multi‐frequency electromagnetic method for inductive measurement of ground induced polarization and resistivity

“…For each field measurement using a (T, R) configuration, there is a main contribution zone in the interior of an equivalent homogeneous isotropic half‐space that is responsible for most of the signal measured at the receiver on the actual half‐space surface. This fact was analytically demonstrated by Machado and Dias (), which is briefly reproduced in the following.…”

“…2D isovalue zones for the (dimensionless) normalized time‐average magnetic energy density associated with the magnetic field radial component, which is observed in the receiver position, generated by the current rings of coordinates () and parameterized by the induction number for 0.1 (a), 0.5 (b), 1 (c), 3 (d), 5 (e) and 10 (f) (after Machado and Dias ).…”

“…It provides the physical basis for plotting the equivalent homogeneous half‐space values of (or its inverse, the apparent resistivity ) and the apparent relative polarization parameter as well, which are associated with a measured pair ( X , Y ), at the central point of the referred plateau zone. Thus, the normalized coordinates of the central point in the main value plateau are given as follows (Machado and Dias ): where …”

“…The full and empty circles are for the complete functions. The solid lines are used for the reduced functions () and () with and 1.0 (after Machado and Dias ).…”

“…3 prototype in 2008 (funded by the Brazilian Oil Company, PETROBRAS). This group has performed equipment design (in collaboration with the manufacturers), theoretical and field work, specific software development for data processing and interpretation procedures (Sato 1979;Dias, Sato and Lima 2005;Dias et al 2006;Machado 2009;Dias, Lima and Sato 2012;Machado and Dias 2012;Sifontes 2015;Sifontes, Sato and Moumoni 2016). Without a reliable algorithm for inverting the field data, this paper presents an alternative procedure taking the EM coupling variation as the parameter of interest.…”