Simulation of induction logging by the finite-element method

The response of an electromagnetic induction logging tool passing through many invaded thin beds is simulated by the finite-element method. This simulation has achieved high accuracy by using a difference potential which enables the transmitter-receiver mutual coupling to be treated analytically. Consequently the removal of the mutual coupling from the induction tool response has no numerical ill effects. The finite-element model is truncated at a very large distance with a zero field outside the model. In order to achieve both accuracy and computational efficiency, the grid is projected to the truncation surface by gradually increasing its size according to an estimated error analysis of the finite-element method. The numerical results were verified against analytical solutions for limiting cases and excellent agreement was obtained. In the presence of skin effect, which is beyond Doll’s analysis by geometrical factor theory, the finite-element solution conveniently provides a way to check and improve the interpretation of induction logs. It also lends itself to future applications in tool design, signal processing, and resistivity inversion schemes.