Generalized positivity constraint on magnetic equivalent layers

by Andre L. A. Reis, Vanderlei C. Oliveira Jr., Valeria C. F. Barbosa

This paper has been published in Geophysics. The version of record

Reis, A.L.A, Oliveira Jr., V. C., & Barbosa, V. C. F., 2020. Generalized positivity constraint on magnetic equivalent layers, Geophysics, doi: 10.1190/geo2019-0706.1.

is available online at: 10.1190/geo2019-0706.1

This repository contains the data and code used to produce all results and figures shown in the paper. This version of this repository is available at pinga-lab/eqlayer-magnetization-direction

We present a novel methodology for estimating the magnetization direction of geological sources using equivalent-layer technique. Moreover, we prove the existence of an equivalent layer having an all-positive magnetic-moment distribution for the case in which the magnetization direction of this layer is the same as that of the true sources.

Application of the methodology to the Montes Claros complex of Goias Alkaline Province, center of Brazil. (a) Predicted data of Montes Claros complex with estimated magnetization direction. (b) The positive magnetic-moment distribution. (c) The figure of an equivalent layer representation.

Abstract

It is known from potential theory that a continuous and planar layer of dipoles can exactly reproduce the total-field anomaly produced by arbitrary 3D sources. We prove the existence of an equivalent layer having an all-positive magnetic-moment distribution for the case in which the magnetization direction of this layer is the same as that of the true sources, regardless of whether the magnetization of the true sources is purely induced or not. By using this generalized positivity constraint, we present a new iterative method for estimating the total magnetization direction of 3D magnetic sources based on the equivalent-layer technique. Our method does not impose a priori information either about the shape or depth of the sources, does not require regularly spaced data, and presumes that the sources have a uniform magnetization direction. At each iteration, our method performs two steps. The first one solves a constrained linear inverse problem to estimate a positive magnetic-moment distribution over a discrete equivalent layer of dipoles. We consider that the equivalent sources are located on a plane and have an uniform and fixed magnetization direction. In the second step we use the estimated magnetic-moment distribution and solve a nonlinear inverse problem for estimating a new magnetization direction for the dipoles. The algorithm stops when the equivalent layer yields a total-field anomaly that fits the observed data. Tests with synthetic data simulating different geological scenarios show that the final estimated magnetization direction is close to the true one. We apply our method to a field data from the Goiás Alkaline Province (GAP), over the Montes Claros complex, center of Brazil. The results suggest the presence of intrusions with remarkable remanent magnetization, in agreement with the current literature for this region.

Reproducing the results

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

git clone https://github.com/pinga-lab/eqlayer-magnetization-direction.git

or click here to download a zip archive.

All source code used to generate the results and figures in the paper are in the code folder. There you can find the Python codes that performs the synthetic data calculations and scripts to generate all figures and results presented in the paper.

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

See the README.md files in each directory for a full description.

Setting up your environment and dependencies

You'll need a working Python 2.7 environment with all the standard scientific packages installed (numpy, scipy, matplotlib, etc). The easiest (and recommended) way to get this is to download and install the Anaconda Python distribution. Make sure you get the Python 2.7 version.

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

You'll also need to install version 0.5 of the Fatiando a Terra library. See the install instructions on the website.

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.

Data and the results of numerical tests are available under the Creative Commons Attribution 4.0 License (CC-BY).

The manuscript text and figures are not open source. The authors reserve the rights to the article content, which has been accepted for publication in Geophysics.