Magnetic anomalies caused by 2D polygonal structures with uniform arbitrary polarization: new insights from analytical/numerical comparison among available algorithm formulations

Abstract

Modeling of magnetic anomalies is a fundamental tool in exploration geophysics. Since the appearance of early electronic computers, calculation of the magnetic field from models of the subsurface and the related inverse problem have played a major role in the geological interpretation of magnetic anomalies.An early mathematical formulation for anomalies due to 2D polygonal structures of uniform polarization is found in Talwani and Heirtzler (1962, 1964). Their algorithm remains the most used and cited to date. Thanks to its wide applicability, Talwani and Heirtzler's approach has become popular, both for expeditious interpretation of magnetic data and as a forward engine for inverse methods. Moreover, the aforementioned 2D formulation can be extended to 3D bodies (Plouff 1975(Plouff , 1976Talwani, 1965). More recently, Won and Bevis (1987) proposed an evolution of the original formulation by Talwani and Heirtzler which avoids the use of trigonometric functions, achieving a speed up of the calculation of magnetic anomaly.

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

“…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)).…”

“…For 2D models, there are essentially two main ways to parameterize the subsurface (Blakely, 1996): a cell‐based approach, where the subsurface is subdivided into a finite number of homogeneous cells (e.g., Bhattacharyya, 1964; Banerjee & Das Gupta, 1977; Y. Li & Oldenburg, 1998, 2000; Y. Li et al., 2010; Nagy, 1966) and a polygon‐based parameterization where contrasts in density or magnetization are represented by polygons (geological bodies) inside which density and magnetization are constant (e.g., Ghirotto et al., 2021; Talwani et al., 1959; Talwani & Heirtzler, 1964). If the structures present in the subsurface can be approximated by such polygonal bodies, then this approach becomes advantageous with respect to cell‐based parameterizations in that the number of model parameters is strongly reduced and the body is treated as a single entity.…”

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).…”