MMT Numerical Libraries: Multipole Inversion

Library for the numerical inversion of a scan grid detecting the magnetic signal from magnetic sources using a multipole expansion of the magnetic potential of the sources. The mathematical background of this method and its application to experimental data of a synthetic sample is developed in

D. Cortés-Ortuño, K. Fabian, L. V. de Groot Single Particle Multipole Expansions From Micromagnetic Tomography Geochemistry, Geophysics, Geosystems 22(4), e2021GC009663 (2021) DOI: https://doi.org/10.1029/2021GC009663

This library is developed as part of the Mimatom / MMT project.

Library

This library has two main modules

• multipole_inversion/magnetic_sample.py : contains the MagneticSample class to create a magnetic system with magnetic point sources (dipole or higher order multipole sources) and generate the scan signal. This class also has methods to save the scan signal data in npz format and the scan grid specifications in json format.

• multipole_inversion/multipole_inversion.py : contains the MultipoleInversion class to perform a numerical inversion from a scan signal data. This class requires scan surface specifications, particle (point source) locations and the scan signal data. These can be passed from the MagneticSample output or be specified manually (useful for combining with other workflows such as micromagnetic simulations).

An additional module to plot results from the inversions is provided in multipole_inversion/plot_tools.py. Magnetic susceptibility and magnetic field functions can be found in the main library as well, although not all of them are documented in the tutorial yet.

Installation

Via PyPI or from this repository using pip . or poetry install or poetry build (which can be used with pip). Poetry is recommended for development.

CUDA

This library contains an optional Nvidia CUDA library to populate the forward matrix in the multipole_inversion code. To build this library you need to set the CUDAHOME or CUDA_PATH environment variables to the location of CUDA in your system. Alternatively, the nvcc compiler path can be set in the PATH variable. The it is only necessary to install or build the library using poetry install or poetry build.

Tutorial

For now you can visualize the Jupyter notebooks from the jupytext scripts in the doc/tutorial/ folder. These notebooks can also be generated from their associated jupytext script, for example,

jupytext --to notebook multipoles_inversion_test.py 

The documentation of the classes can be generated using sphinx and the scripts to do this are located in the doc folder. Future releases of this library will include an online documentation of this code.

Cite

If you find this library useful please cite us (you might need LaTeX's url package)

@Misc{Cortes2022,
  author       = {Cortés-Ortuño, David and Fabian, Karl and de Groot, Lennart V.},
  title        = {{MMT Numerical Libraries: Multipole Inversion}},
  publisher    = {Zenodo},
  note         = {Github: \url{https://github.com/Micromagnetic-Tomography/multipole_inversion}},
  year         = {2022},
  doi          = {10.5281/zenodo.6473257},
  url          = {https://doi.org/10.5281/zenodo.6473257},
}

If you have a new version of biblatex you can also use @Software instead of @Misc, and add a version={} entry. You can also cite the paper with the theoretical framework of this library:

@article{Cortes2021,
author = {Cortés-Ortuño, David and Fabian, Karl and de Groot, Lennart V.},
title = {Single Particle Multipole Expansions From Micromagnetic Tomography},
journal = {Geochemistry, Geophysics, Geosystems},
volume = {22},
number = {4},
pages = {e2021GC009663},
keywords = {magnetism, micromagnetic tomography, multipole, paleomagnetism, rock magnetism},
doi = {https://doi.org/10.1029/2021GC009663},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021GC009663},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2021GC009663},
note = {e2021GC009663 2021GC009663},
year = {2021}
}