Magnetic radial inversion for 3-D source geometry estimation

by Leonardo B. Vital¹, Vanderlei C. Oliveira Jr.¹, and Valéria C. F. Barbosa¹

¹Observatório Nacional

This repository contains the manuscript and supplementary code and data for the article "Magnetic radial inversion for 3-D source geometry estimation" submitted for publication in Geophysical Journal International.

This method estimates the geometry of a 3D magnetic source from total field anomaly data.

Figure 1: Result for complex model simulation. The blue prisms represent the true model and the red prisms represent the estimated model.

Abstract

We present a method for inverting total-field anomaly data to estimate the geometry of a uniformly magnetized 3-D geological source in the subsurface. The method assumes the total-magnetization direction is known. We approximate the source by an ensemble of vertically juxtaposed right prisms, all of them with the same total-magnetization vector and depth extent. The horizontal cross-section of each prism is a polygon defined by a given number of equi-angularly spaced vertices from 0º to 360º, whose polygon vertices are described by polar coordinates with an origin defined by a horizontal location over the top of each prism. Because our method estimates the radii of each polygon vertex we refer to it as \textit{radial inversion}. The position of these vertices, the horizontal location of each prism, and the depth extent of all prisms are the parameters to be estimated by solving a constrained nonlinear inverse problem of minimizing a goal function. We run successive inversions for a range of tentative total-magnetization intensities and depths to the top of the shallowest prism. The estimated models producing the lowest values of the goal function form the set of candidate solutions. To obtain stabilized solutions, we impose the zeroth- and first-order Tikhonov regularizations on the shape of the prisms. The method allows estimating the geometry of both vertical and inclined sources, with a constant direction of magnetization, by using the Tikhonov regularization. Tests with synthetic data show that the method can be of utility in estimating the shape of the magnetic source even in the presence of a strong regional field. Results obtained by inverting airborne total-field anomaly data over the Anit{'a}polis alkaline-carbonatitic complex, in southern Brazil, suggest that the emplacement of the magnetic sources was controlled by NW-SE-trending faults at depth, in accordance with known structural features at the study area.

Software implementation

This code runs a non-linear inversion algorithm and its suplementary functions.

All source code used to generate the results and figures in the paper are in the code folder. The foldercode contains the folders anitapolis, complex, dipping, dipping-regional, and simple, which correspond to the paper applications. The calculations and figure generation are all run inside Jupyter notebooks. The data used in this study is provided in data and the sources for the manuscript text and figures are in manuscript. Results generated by the code are saved in results inside each application folder. See the README.md files in each directory for a full description.

Getting the code

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

git clone https://github.com/pinga-lab/magnetic-radial-inversion.git

or download a zip archive.

A copy of the repository is also archived at .

Dependencies

You'll need a working Python environment to run the code. The recommended way to set up your environment is through the Anaconda Python distribution which provides the conda package manager. Anaconda can be installed in your user directory and does not interfere with the system Python installation. The required dependencies are specified in the file environment.yml.

We use conda virtual environments to manage the project dependencies in isolation. Thus, you can install our dependencies without causing conflicts with your setup (even with different Python versions).

Run the following command in the repository folder (where environment.yml is located) to create a separate environment and install all required dependencies in it:

conda env create

Reproducing the results

Before running any code you must activate the conda environment:

source activate radial-mag

or, if you're on Windows:

activate radial-mag

This will enable the environment for your current terminal session. Any subsequent commands will use software that is installed in the environment.

To build and test the software, produce all results and figures, and compile the manuscript PDF, run this in the top level of the repository:

make all

If all goes well, the manuscript PDF will be placed in manuscript.

The way to explore the code results is to execute the Jupyter notebooks individually. To do this, you must first start the notebook server by going into the repository top level and running:

jupyter notebook

This will start the server and open your default web browser to the Jupyter interface. In the page, go into the code folder, select the desired application folder, and select the notebook that you wish to view/run.

The notebook is divided into cells (some have text while other have code). Each cell can be executed using Shift + Enter. Executing text cells does nothing and executing code cells runs the code and produces it's output. To execute the whole notebook, run all cells in order.

License

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 LICENSE.md for the full license text.

The manuscript text is not open source. The authors reserve the rights to the article content, which is currently submitted for publication in the Geophysical Journal Internationa.