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

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 ( ) is reached. The equations for the linear fit of the relative error in the low induction number regime are also given. 1. 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]. 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. Then we can take laterally distributed measurements along a transect for identifying conductivity-related anomalies. We can also get information on the vertical conductivity structure by varying the coil’s dipole configurations (vertical dipole or horizontal dipole) as well as by increasing the instrument height. This information is very useful in several geophysical problems as, for example, water prospecting or mapping pollution plumes. The basic model for both configurations is described in Figure 1 where a transmission coil Tx with a given alternate electric current at a given frequency is located on the terrain (assumed to be an uniform semiplane) and a receiving coil Rx is located at a short distance from Tx. The time variation of the magnetic field , 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 , called secondary field, which can be measured at the receiving coil together with the primary field. Figure 1: Representation of the transmission (Tx) and reception (Rx) coils for both the vertical and the horizontal dipole configurations.