Magnetic Anomalies Caused by 2D Polygonal Structures With Uniform Arbitrary Polarization: New Insights From Analytical/Numerical Comparison Among Available Algorithm Formulations

• Published in: Geophysical research letters Vol. 48; no. 7
• Main Authors: Ghirotto, Alessandro, Zunino, Andrea, Armadillo, Egidio, Mosegaard, Klaus
• Format: Journal Article
• Language: English
• Published: 16.04.2021
• Subjects: 2D forward modeling; Computational geophysics; Exploration geophysics; Induced magnetization; Magnetic anomaly; Remnant magnetization
• ISSN: 0094-8276; 1944-8007; 1944-8007
• DOI: 10.1029/2020GL091732

Since the '60s of the last century, the calculation of the magnetic anomalies caused by 2D uniformly polarized bodies with polygonal cross‐section has been mainly performed using the popular algorithm of Talwani and Heirtzler (1962, 1964). Recently, Kravchinsky et al. (2019, https://doi.org/10.1029/2019GL082767) claimed errors in the above algorithm formulation, proposing new corrective formulas and questioning the effectiveness of almost 60 years of magnetic calculations. Here we show that the two approaches are equivalent and Kravchinsky et al.'s formulas simply represent an algebraic variant of those of Talwani and Heirtzler. Moreover, we analyze 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 and Bevis (1987, https://doi.org/10.1190/1.1442298). We release the source code of the algorithms in Julia and Python languages. Plain Language Summary Forward magnetic calculation plays a major role in geophysics to model magnetization, location, and shape of magnetic sources. One of the most popular approaches to calculate magnetic anomalies due to two‐dimensional bodies is based on the formulas of Talwani and Heirtzler (1962, 1964), that have been widely used both for scientific and industrial applications from the sixties. Recently, these formulas have been questioned by Kravchinsky et al. (2019, https://doi.org/10.1029/2019GL082767) casting doubts on the truthfulness of all the magnetic models and interpretations obtained to date. We examined and compared the two calculation approaches, both from an analytical and numerical point of view. In detail, we corrected some inaccuracies in Kravchinsky et al.'s formulas and we found complete equivalence between the two discussed formulations, showing that they simply represent two algebraic variants of the same mathematical approach. We also performed intensive numerical tests comparing the results of the two algorithms with a third one proposed by Won and Bevis (1987, https://doi.org/10.1190/1.1442298). The three mathematical approaches gave the same magnetic responses for all the tested models, demonstrating total agreement between the three formulations. Key Points Kravchinsky et al. (2019) claimed errors and omissions in the formulas of Talwani and Heirtzler (1962) for 2D forward magnetic calculation Our analysis reveals that Kravchinsky et al.'s formulas are algebraically equivalent to those of Talwani and Heirtzler Numerical tests show a complete agreement among the two above formulations and the one by Won and Bevis (1987)