Calculation of Sommerfeld integrals for conductive media at low frequencies

Wei, Yingkang; Holter, B.; Simonsen, Ingve; Kuhnle, Jacob; Husby, Karsten; Norum, Lars

doi:10.1109/iwem.2011.6021473

Cited by 1 publication

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Notice that this routine is focused on the accuracy of the results for a general subsurface application and does not try to speed-up calculations. To this end, many works on the topic can be found in the literature (Hochman & Leviatan, 2010;Long et al, 2001;Wei et al, 2011).…”

Section: Proposed Integration Algorithmmentioning

confidence: 99%

A Computational Channel Model for Magnetic Induction‐Based Subsurface Applications

et al. 2019

View full text Add to dashboard Cite

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.

show abstract

Section: Proposed Integration Algorithmmentioning

confidence: 99%