A Computational Channel Model for Magnetic Induction-Based Subsurface Applications

Abstract

There are many underground applications based on magnetic fields generated by an oscillating magnetic source. For them, a magnetic dipole in a three-layered region with upper semi-infinite air layer can be a convenient idealization used for their planning, development, and operation. Solutions are in the form of the well-known Sommerfeld integral expressions that can be evaluated by numerical methods. A set of field expressions to be numerically evaluated by an efficient algorithm are not collected comprehensively yet, or at least in a directly usable form. In this paper, the explicit magnetic field solutions for the vertical magnetic dipole and the horizontal magnetic dipole for a general source-observer location are derived from the Hertz vector. They can be properly combined to model the problem of a tilted magnetic dipole source for horizontally or inclined stratified media. As a result, a complete set of integral equations of the Sommerfeld type valid from the near zone to the far zone are formulated. A method for numerical evaluation of the field expressions for high accurate computations is described. The numerical results are validated using the finite element method for all the possible source-receiver configurations and three well-spanned frequencies of typical subsurface applications. Both numerical solutions agree according to the normalized root-mean-square error-based fit metric. Numerical results for two cases of study are presented to see its usefulness for subsurface applications. A MATLAB implementation of the mathematical description outlined in this paper and the proposed evaluation method is freely available for download