Magnetic anomalies caused by 2D polygonal structures with uniform
arbitrary polarization: new insights from analytical/numerical
comparison among available algorithm formulations
Abstract
Since the ’60s of the last century, the calculation of the magnetic
anomaly caused by 2D uniformly-polarized bodies with polygonal
cross-section was mainly performed using the popular algorithm of
Talwani & Heirtzler (1962, 1964). Recently, Kravchinsky et al. (2019)
claimed errors in the above algorithm formulation, proposing new
corrective formulas and questioning the effectiveness of almost sixty
years of magnetic calculations. Here we showed, demonstrating analytical
equivalence of the two approaches, that Kravchinsky et al.’s formulas
simply represent an algebraic variant of those of Talwani & Heirtzler.
Moreover, we performed intensive numerical analysis generating a large
amount of random magnetic scenarios, involving both changing-shape
polygons and a realistic geological model, showing a complete agreement
among the magnetic responses of the two discussed algorithms and the one
proposed by Won & Bevis (1987). Additionally, we released the source
code of the algorithms in Julia and Python languages.