Error Analysis in Measured Conductivity under Low Induction Number Approximation for Electromagnetic Methods

George Caminha-Maciel,Irineu Figueiredo

doi:10.1155/2013/720839

Abstract

We present an analysis of the error involved in the so-called low induction number approximation in the electromagnetic methods. In particular, we focus on the EM34 equipment settings and field configurations, widely used for geophysical prospecting of laterally electrical conductivity anomalies and shallow targets. We show the theoretical error for the conductivity in both vertical and horizontal dipole coil configurations within the low induction number regime and up to the maximum measuring limit of the equipment. A linear relationship may be adjusted until slightly beyond the point where the conductivity limit for low induction number (B=1) is reached. The equations for the linear fit of the relative error in the low induction number regime are also given.

Highlights

The induction method consists basically in determining subsurface rock conductivities with the help of electromagnetic fields generated by a coil at the Earth’s surface and by catching the response to this field from the conducting media under surface by using a reception coil [1–3].From the Maxwell equations, in particular the Faraday induction law applied to an infinite homogenous half-plane, the subsurface rock conductivity can be estimated through the ratio between the magnetic field measured in the receiving coil and the magnetic field produced at the transmission coil with both at surface
The time variation of the magnetic field Hp, called primary magnetic field, produced by the electric current in the transmission coil generates a small alternate current in the soil. This electric current, on its turn, produces a magnetic field Hs, called secondary field, which can be measured at the receiving coil together with the primary field
The same linear behaviour is seen in the apparent conductivity (Figure 3) for vertical and horizontal dipole configurations, as seen by the fitted straight line to the logarithmic scaled error curves on the low induction number regime (10−2 mS/m–40 mS/m) given by log (ε)

Summary

Introduction

The induction method consists basically in determining subsurface rock conductivities with the help of electromagnetic fields generated by a coil at the Earth’s surface and by catching the response to this field from the conducting media under surface by using a reception coil [1–3]. This result can be used when coils are in the vertical or horizontal dipole orientations These two situations are described by different sets of equations for the secondary field; these equations give the same result for the component in quadrature of the ratio between the primary and secondary fields under low induction number conditions. We calculate the relative difference between this conductivity value and that obtained through the low induction number approximation

Methods

Conclusions