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Gradient-boosted equivalent sources

by Santiago Soler and Leonardo Uieda

The data and Python code used to produce all results and figures in the paper:

Soler, S. R. and Uieda, L. (2021). Gradient-boosted equivalent sources, Geophysical Journal International. doi:10.1093/gji/ggab297

Version of record
PDF on EarthArXiv (pre-copyedited)
Archive of this repository


We present the gradient-boosted equivalent sources: a new methodology for interpolating very large datasets of gravity and magnetic observations even on modest personal computers, without the high computer memory needs of the classical equivalent sources technique. This new method is inspired by the gradient-boosting technique, mainly used in machine learning.


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.

Reproducing the results

You can download a copy of all the files in this repository by cloning the git repository:

git clone

or click here to download a zip archive.

All source code used to generate the results and figures in the paper are in the notebooks folder. There you can find the Jupyter notebooks that performs all the calculations to generate all figures and results presented in the paper. Inside the notebooks/boost_and_layouts folder you can find the Python files that define functions and classes that implement the new methodologies introduced in the paper.

The sources for the manuscript text and figures are in manuscript.

See the files in each directory for a full description.

Setting up your environment

You'll need a working Python 3 environment with all the standard scientific packages installed (numpy, pandas, scipy, matplotlib, etc). The easiest (and recommended) way to get this is to download and install the Anaconda Python distribution.

Besides the standard scientific packages that come pre-installed with Anaconda, you'll also need to install some extra libraries like: Numba for just-in-time compilation; Harmonica, Verde, Boule and Pooch from the Fatiando a Terra project; Cartopy and PyGMT for generating maps and more.

Instead of manually install all the dependencies, they can all be automatically installed using a conda environment.

  1. Change directory to the cloned git repository:
    cd eql-gradient-boosted
  2. Create a new conda environment from the environment.yml file:
    conda env create -f environment.yml
  3. Activate the new environment:
    conda activate eql-gradient-boosted

For more information about managing conda environments visit this User Guide

Alternative way

In case the previous method doesn't work by the time you are trying to create the environment, you could use one of the conda-lock files.

  1. Install conda-lock on the base environment or on any environment you want:
    conda install -c conda-forge conda-lock
  2. Create the eql-gradient-boosted environment out of the conda-*.lock file. If you are using a GNU/Linux distribution, run the following:
    conda-lock install -n eql-gradient-boosted --file conda-linux-64.lock
    If you are a MacOS user, run the following instead:
    conda-lock install -n eql-gradient-boosted --file conda-osx-64.lock
  3. Activate the new environment:
    conda activate eql-gradient-boosted

This alternative method works only for x86 (64 bits) processors under GNU/Linux or MacOS.

Reproducing the results

We have a Makefile that provides commands that automatically run the notebooks, run the tests, check code style, etc.

In order to be able to use it, you would need to install GNU Make. It comes pre-installed with most of the GNU/Linux distributions, or it can be installed through the package manager of your OS. If you're running Windows or Mac OS, you can install make through conda:

conda install --channel conda-forge make

Then you can automatically rerun all the notebooks with:

make run

Some notebooks might take several minutes to run, depending on the resources of your system The notebook that grids the Australia gravity data would need around 12GB of RAM in order to estimate the coefficients through the gradient-boosted equivalent sources.

Testing the code and check style

You can also use the Makefile to run the unit tests for our gradient-boosting implementation, the construction of source layouts and more:

make test

You also check if the code follows the styles from PEP8:

make check

Or automatically reformat it through Black:

make format

For more commands defined in the Makefile, please run:

make help


All source code is made available under a BSD 3-clause license. You can freely use and modify the code, without warranty, so long as you provide attribution to the authors. See for the full license text.

Manuscript text, figures, data and the results of numerical tests are available under the Creative Commons Attribution 4.0 License (CC-BY).