by Felipe F. Melo and Valéria C.F. Barbosa
This paper was published in the journal Geophysics. Melo, F.F., Barbosa, V.C.F., 2018. Correct structural index in Euler deconvolution via base-level estimates. Geophysics 83 (6), J87–J98. https://doi.org/10.1190/geo2017-0774.1.
This repository contains the source code to perform an additional synthetic test with four sources and a constant base level. The codes euler_python.py, the synthetic data synthetic_data.dat presented in the paper and the codes synthetic_test.py, estimates_statistics.py and plot_functions.py to generate the results of the synthetic test.
The euler_python program is compatible with both Python 2.7 and Python 3.7 programming language.
In most applications, the Euler deconvolution aims to define the nature (type) of the geologic source (i.e., the structural index [SI]) and its depth position. However, Euler deconvolution also estimates the horizontal positions of the sources and the base level of the magnetic anomaly. To determine the correct SI, most authors take advantage of the clustering of depth estimates. We have analyzed Euler’s equation to indicate that random variables contaminating the magnetic observations and its gradients affect the base-level estimates if, and only if, the SI is not assumed correctly. Grounded on this theoretical analysis and assuming a set of tentative SIs, we have developed a new criterion for determining the correct SI by means of the minimum standard deviation of base-level estimates. We performed synthetic tests simulating multiple magnetic sources with different SIs. To produce mid and strongly interfering synthetic magnetic anomalies, we added constant and nonlinear backgrounds to the anomalies and approximated the simulated sources laterally. If the magnetic anomalies are weakly interfering, the minima standard deviations either of the depth or base-level estimates can be used to determine the correct SI. However, if the magnetic anomalies are strongly interfering, only the minimum standard deviation of the base-level estimates can determine the SI correctly. These tests also show that Euler deconvolution does not require that the magnetic data be corrected for the regional fields (e.g., International Geomagnetic Reference Field [IGRF]). Tests on real data from part of the Goiás Alkaline Province, Brazil, confirm the potential of the minimum standard deviation of base-level estimates in determining the SIs of the sources by applying Euler deconvolution either to total-field measurements or to total-field anomaly (corrected for IGRF). Our result suggests three plug intrusions giving rise to the Diorama anomaly and dipole-like sources yielding Arenópolis and Montes Claros de Goiás anomalies.
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euler_python.py: General Python module containing the functions to compute de derivatives and Euler deconvolution.
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synthetic_test.py: Python script to generate the synthetic results. The script loads the total-field anomaly of a synthetic model from the file "synthetic_data.dat" and computes the Euler deconvolution using the functions in "euler_python.py". The results are generated using the functions "plot_functions.py" for the plots and "estimates_statistics.py" to compute the statistics of the data.
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plot_functions.py: Python script to generate the figures in the synthetic tests results.
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estimates_statistics.py: Python script to compute the mean of the northing, easting and depth estimates.
Test data:
- synthetic_data.dat: Synthetic total-field anomaly data generated using the Python packaged "Fatiando a Terra": http://fatiando.org/. This data is an example used in the current publication.
You can download a copy of all the files in this repository by cloning the git repository:
git clone https://github.com/ffigura/Euler-deconvolution-plateau.git
The Python program Euler deconvolution - "euler_python.py" requires the Python library "numpy", the scripts "synthetic_test.py" and "plot_functions.py" require the Python packages "numpy" and "matplotlib", and the script "estimates_statistics.py" requires the Python package "numpy". The easier way to get Python and all libraries installed is through the Anaconda Python distribution (https://www.anaconda.com/distribution/). After installed Anaconda, install the libraries by running the following command in your terminal:
conda install numpy matplotlib
The program for Euler deconvolution "euler_python.py" and the additional codes "synthetic_test.py", "plot_functions.py" and "estimates_statistics.py" are compatible with both Python 2.7 and 3.7.
The results and figures for the synthetic test are reproducible from the folder /test_4_sources.
Running the code synthetic_test.py will allow the reprodution of the results. For more information
read the file README.MD or README.txt in the folder /code.
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 Geophysics.