Supplementary material for "Multipole Modeling for Magnetic Microscopy Constrained by Euler Deconvolution"

This repository contains the data and source code used to produce the results presented in: Souza-Junior et al. (2026). Multipole Modeling for Magnetic Microscopy Constrained by Euler Deconvolution. EarthArXiv. doi:10.31223/X5K20C Abstract Magnetic microscopy provides high spatial resolution and can operate at small sensor-to-sample distances, with emerging technologies offering further improvements in both capabilities. Under these conditions, dipolar approaches become increasingly limited because higher-order magnetic contributions can no longer be neglected when retrieving reliable full-vector information for paleomagnetic and rock magnetic applications. However, multipolar representations often require prior knowledge of source geometry and expansion center location, which can involve costly auxiliary measurements and additional processing complexity. This challenge becomes particularly relevant for planar magnetic microscopy observations, where the incomplete sampling geometry violates the ideal assumptions of spherical harmonic (SH) expansions. Here, we present an Euler-based approach that provides initial estimates of the expansion center for SH inversions, with optional nonlinear refinement through simplex optimization. The proposed methodology was evaluated using both synthetic micromagnetic models and real magnetic microscopy data, and its performance was compared with conventional dipolar approaches. Synthetic experiments with known ground-truth models demonstrated improved accuracy of SH-based inversions, particularly for near-surface measurements where higher-order magnetic signals become significant, while maintaining comparable performance at larger sensor heights. Application to real data showed broadly similar results for both approaches in most cases, although the SH framework produced more coherent solutions for anomalies affected by magnetic interference from neighboring sources. Using spherical harmonics up to degree 10, the method provides a practical framework for rapidly inverting sources with appreciable non-dipolar contributions and recovering their magnetic structure directly from planar magnetic anomaly measurements. License All Python source code (including .py and .ipynb files) is made available under the MIT license. You can freely use and modify the code, without warranty, so long as you provide attribution to the authors. See LICENSE-MIT.txt for the full license text. The manuscript text (including all LaTeX files), figures, and data/models produced as part of this research are available under the Creative Commons Attribution 4.0 License (CC-BY). See LICENSE-CC-BY.txt for the full license text.