Supplementary material for "Dual-Layer Gradient-Boosted Equivalent Sources for Magnetic Data"

This repository contains the data and source code used to produce the results presented in:

Uppal, I., Uieda, L., Oliveira Jr., V. C., Holme, R. (2025). Dual-Layer Gradient-Boosted Equivalent Sources for Magnetic Data. Geophysical Journal International. DOI: 10.1093/gji/ggaf359

Abstract

Magnetic data often require interpolation onto a regular grid at constant height before further analysis. A widely used approach for this is the equivalent sources technique, which has been adapted over time to improve its computational efficiency and accuracy of the predictions. However, many of these adaptations still face challenges, including border effects in the predictions or reliance on a stabilising parameter. To address these limitations, we introduce dual-layer gradient-boosted equivalent sources to: (1) use a dual-layer approach to improve the predictions of both short- and long-wavelength signals, as well as, reduce border effect; (2) use block-averaging and the gradient-boosted equivalent sources method to reduce the computational load; (3) apply block K-fold cross-validation to guide optimal parameter selection for the model. The proposed method was tested on both synthetic datasets and the ICEGRAV aeromagnetic dataset to evaluate the methods ability to interpolate and upward continue onto a regular grid, as well as predict the amplitude of the anomalous field from total-field anomaly data. The dual-layer approach proved better compared to the single-layer approach when predicting both short- and long-wavelength signals, particularly in the presence of truncated long-wavelength anomalies. The use of block-averaging and the gradient-boosting method enhances the computational efficiency, being able to grid over 400,000 data points in under 2 minutes on a moderate workstation computer.

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.