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empymod 1.4.4

Open-source full 3D electromagnetic modeller for 1D VTI media

The electromagnetic modeller empymod can model electric or magnetic responses due to a three-dimensional electric or magnetic source in a layered-earth model with vertical transverse isotropic (VTI) resistivity, VTI electric permittivity, and VTI magnetic permeability, from very low frequencies (DC) to very high frequencies (GPR). The calculation is carried out in the wavenumber-frequency domain, and various Hankel- and Fourier-transform methods are included to transform the responses into the space-frequency and space-time domains.

More information

For information regarding installation, requirements, documentation, examples, contributing and so on:

Installation from source

You can clone or download the latest version from GitHub and either add the path to empymod to your python-path variable, or install it in your python distribution via:

python install


The modeller comes with a test suite using pytest. If you want to run the tests, just install pytest and run it within the empymod-top-directory.


Pytest will find the tests, which are located in the tests-folder. It should run all tests successfully. Please let me know if not!

Note that installations of empymod via conda or pip do not have the test-suite included. To run the test-suite you must download empymod from GitHub.


A collection of ideas of what could be added or improved in empymod. Please get in touch if you would like to tackle one of these problems!

  • Additional modelling routines
    • tdem (TEM) Issues that have to be adressed: ramp waveform, windowing, loop integration, zero-offset (coincident loop).
      • in-loop
      • coincident loop
    • Ramp waveform
    • Arbitrary waveform
    • Improve the GPR-routine
    • Load and save functions to easily store and load model information (resistivity model, acquisition parameters, and modelling parameters) together with the modelling data (using pickle or shelve).
  • Inversion: Inversion routines, preferably a selection of different ones.
  • Improve documentation
    • Move main part from empymod/ to docs/*.rst
    • Add actual equations, instead of only references to them
    • Add general EM introduction and derivation
    • Add a few simple example of its usage including figures
    • Add more explanations regarding the different transforms
  • Additional (semi-)analytical functions (where possible)
    • Complete full-space (electric and magnetic source and receiver); space-time domain
    • Extend diffusive half-space solution to magnetic sources and receivers; space-frequency and space-time domains
    • Complete half-space
  • Fourier transform
    • Change fft to use discrete sine/cosine transforms instead, as all other Fourier transforms
    • If previous step is successful, clean up the internal decisions (utils.check_time) when to use sine/cosine transform (not consistent at the moment, some choice only exists with ffht impulse responses, fqwe and fftlog use sine for impulse, and all three use sine for step-on responses and cosine for step-off responses)
  • Hankel transform
    • Add the fht-module from FFTLog for the Hankel transform.
  • Module to design digital filters
    • Hankel transform (almost ready)
    • Extend to Fourier transform
  • Extend examples (example-notebooks)
    • Add different methods (e.g. DC)
    • Reproduce published results
  • A cython, numba, or pure C/C++ implementation of the kernel and the transform modules. Maybe not worth it, as it may improve speed, but decrease accessibility. Both at the same time would be nice. A fast C/C++-version for calculations (inversions), and a Python-version to tinker with for interested folks. (Probably combined with default parallelisation, removing the numexpr variant.)
  • Abstraction of the code.
  • GUI.
  • Add a benchmark suite, e.g., in addition to the testing suite.
  • Add some clever checks, e.g. as in Key (2012): abort loops if the field is strongly attenuated (more relevant if once an inversion is implemented).
  • Move empymod from channel ‘prisae’ to ‘conda-forge’ (pros/cons?).


If you publish results for which you used empymod, please give credit by citing this article:

Werthmüller, D., 2017, An open-source full 3D electromagnetic modeler for 1D VTI media in Python: empymod: Geophysics, 82, WB9-WB19; DOI: 10.1190/geo2016-0626.1.

Also consider citing Hunziker et al. (2015) and Key (2012), without which empymod would not exist:

Hunziker, J., J. Thorbecke, and E. Slob, 2015, The electromagnetic response in a layered vertical transverse isotropic medium: A new look at an old problem: Geophysics, 80, F1-F18; DOI: 10.1190/geo2013-0411.1.

Key, K., 2012, Is the fast Hankel transform faster than quadrature?: Geophysics, 77, F21-F30; DOI: 10.1190/geo2011-0237.1.

All releases have a Zenodo-DOI, provided on the release-page.


This product includes software that was initially (till 01/2017) developed at The Mexican Institute of Petroleum IMP (Instituto Mexicano del Petróleo). The project was funded through The Mexican National Council of Science and Technology (Consejo Nacional de Ciencia y Tecnología). Since 02/2017 it is a personal effort, and new contributors are welcome!


Copyright 2016-2017 Dieter Werthmüller

Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

See the LICENSE-file in the root directory for a full reprint of the Apache License.

File Type Py Version Uploaded on Size
empymod-1.4.4-py3-none-any.whl (md5) Python Wheel py3 2017-09-19 179KB
empymod-1.4.4.tar.gz (md5) Source 2017-09-19 182KB