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.

Joint Channel and Antenna Modeling for Magnetic Induction Communication in Inhomogeneous Media

“…It is worth noting that existing works [22], [23] aiming to obtain accurate electric and magnetic fields in layered media using computational electromagnetic approaches are different from this paper. Here, we leverage the electromagnetic field model and solutions in [23] and develop a channel and antenna model for MIC.…”

“…In this paper, we consider M as a complex number and existing MC models neglect this issue. By using Kirchhoff's Voltage Law in (22) and (23), we can obtain the transmission power, which is…”

“…As we will show in Section IV, only considering the near field underestimates MIC's performance. Third, although fullwave magnetic field analyses can be found in [22], [23] and many other related works, the considered geometry is more complicated than the problem that is studied in this paper, e.g., the inhomogeneous media have multiple layers, and the transmitter's location is always in medium 1. Since both the sensor and the reader can transmit and receive signals, it requires a more comprehensive model that can capture the scenarios where the transmitter and the receiver located in any medium.…”

A new radiolocation method for precise depth estimation and its application to the analysis of changes in groundwater levels in Colonia Clunia Sulpicia

“…The correct estimation of the depth d using Equation (1) depends on how well the actual shape of the magnetic field fits the model and on the inaccuracies in the measurements of ρ and α null (see Figure 7b). In the following, all these sources of error are analysed by simulation (Ayuso et al, 2019).…”