Mathematical modeling of electric field in induction logging

We estimated the instrumental error introduced by logging tools into the measured plane and axisymmetrical electric fields. The problem can be solved either through investigation of analytical solutions or using integral equations. The difference between the true and the measured fields increases with frequency of electromagnetic waves and tool thickness and conductivity. The difference is lower in the case when the axisymmetrical electric field is measured by a closed loop than in the case of logging with a straight tool for the plane field. The greater the radius of the closed loop for the axisymmetrical field logging, the larger instrumental errors, the frequency being the same.