Gradient-boosted equivalent sources

Santiago R. Soler, Leonardo Uieda

This is a preprint which has not yet been peer-reviewed.


This paper describes how we used the gradient-boosting machine learning method to scale equivalent source processing to millions gravity and magnetic data. Equivalent sources allow us take into account the observation height and the physics of potential fields (mainly, they are harmonic functions) when processing and interpolation, which are often ignored by other methods. This leads to great results but it's involves large linear models, so processing datasets of this magnitude is tricky. By using gradient-boosting to fit the model in small chunks, we can process millions of data even on a modest laptop (and in a reasonable amount of time).

This research was done entirely with open-source software and open data! This means that anyone should be able to fully reproduce our results using the information in the paper and the material in the associated GitHub repository.

This is the final part of Santiago's PhD thesis.

Visual abstract for the paper: How can we interpolate over 1 million
gravity/magnetic data at variable heights? By adapting the gradient-boosting
method from machine learning to equivalent source processing. Includes a
diagram of the algorithm and an interpolation example showing that the method
is able to fit large amounts of data and still retain spectral content of the


The equivalent source technique is a powerful and widely used method for processing gravity and magnetic data. Nevertheless, its major drawback is the large computational cost in terms of processing time and computer memory. We present two techniques for reducing the computational cost of equivalent source processing: block-averaging source locations and the gradient-boosted equivalent source algorithm. Through block-averaging, we reduce the number of source coefficients that must be estimated while retaining the minimum desired resolution in the final processed data. With the gradient boosting method, we estimate the sources coefficients in small batches along overlapping windows, allowing us to reduce the computer memory requirements arbitrarily to conform to the constraints of the available hardware. We show that the combination of block-averaging and gradient-boosted equivalent sources is capable of producing accurate interpolations through tests against synthetic data. Moreover, we demonstrate the feasibility of our method by gridding a gravity dataset covering Australia with over 1.7 million observations using a modest personal computer.


Soler, S., & Uieda, L. (2021). Gradient-boosted equivalent sources. EarthArXiv. doi:10.31223/x58g7c