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 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.

The Sub‐Ice Structure of Mt. Melbourne Volcanic Field (Northern Victoria Land, Antarctica) Uncovered by High‐Resolution Aeromagnetic Data

“…A schematic view of the internal structure of the MVF is given by a 2D forward model (Ghirotto et al., 2021; Talwani & Heirtzler, 1962) performed along a E‐W profile shown in Figure 4b, shown and discussed in Figure 7.…”

Hamiltonian Monte Carlo Probabilistic Joint Inversion of 2D (2.75D) Gravity and Magnetic Data

“…Algorithms to compute gravity and magnetic anomalies for 2D polygonal bodies based on line integrals (Hubbert, 1948) date back to Talwani et al (1959) and Talwani and Heirtzler (1964). Since then, such formulations have been the basis for the majority of the computer programs performing such calculations (a review can be found in Ghirotto et al (2021)).…”

Magnetic Anomalies Caused by 3D Polyhedral Structures With Arbitrary Polynomial Magnetization

“…But they are all limited to magnetic bodies with simple shapes and magnetization. For instance, several authors derived analytical solutions of the magnetic anomaly for two-dimensional magnetic structures with homogeneous magnetization (Ghirotto et al, 2021;Jia & Meng, 2009;Jia & Wu, 2011;Kravchinsky et al, 2019;Nabighian, 1972;Talwani & Heirtzler, 1964). Analytical solutions of the magnetic anomaly were available for 3D homogeneous targets with specific geometries, such as a homogeneous prism (Bhaskara Rao & Ramesh Babu, 1991;Bhattacharyya, 1964;Blakely, 1995;Cady, 1980;Holstein et al, 2013;Plouff, 1976;Rasmussen & Pedersen, 1979;Shuey & Pasquale, 1973), a homogeneous cylinder (K. S. Singh & Sabina, 1978).…”