Approximate methods of field calculation in induction logging

Approximate Methods of Field Calculation in Induction Logging 

In this section we will describe two methods of field calculation which have played an essential role in developing such aspects of induction logging as  

In 1949 Henry Doll developed an approximate theory of induction logging. The basis of this theory is the assumption that for a sufficiently resistive medium and at relatively low frequencies one can neglect interaction of induced currents. For this reason the phase of these currents is 90°, regardless of the distance from the transmitter coil, and the measured signal is a sum of elementary signals created by currents in various parts of the medium, which depend on the conductivity of the corresponding part of the medium only. 

As follows from the analysis of the field of a magnetic dipole in a uniform medium (Chapter 2), such behavior of the field and induced currents is closer to reality with decreasing frequency as well as conductivity. 

The range of frequencies and resistivities of a nonuniform medium and also geometric parameters, when this theory remains valid will be established by comparison with results of calculations, making use of the exact solution. 

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