by Florian Wagner, Coline Mollaret, Thomas Günther, Andreas Kemna, and Christian Hauck

This repository contains the data and code to reproduce all results and figures published in the following paper:

Wagner, F. M., Mollaret, C., Günther, T., Kemna, A., & Hauck, C. (2019). Quantitative imaging of water, ice, and air in permafrost systems through petrophysical joint inversion of seismic refraction and electrical resistivity data. Geophysical Journal International, 219, 1866-1875, doi:10.1093/gji/ggz402.

The code realizes both conventional and petrophysical joint inversion of seismic refraction and electrical resistivity data as schematically shown above.

Quantitative estimation of pore fractions filled with liquid water, ice, and air is crucial for a process-based understanding of permafrost and its hazard potential upon climate-induced degradation. Geophysical methods offer opportunities to image distributions of permafrost constituents in a non-invasive manner. We present a method to jointly estimate the volumetric fractions of liquid water, ice, air, and the rock matrix from seismic refraction and electrical resistivity data. Existing approaches rely on conventional inversions of both data sets and a suitable a-priori estimate of the porosity distribution to transform velocity and resistivity models into estimates for the four-phase system, often leading to non-physical results. Based on two synthetic experiments and a field data set from an Alpine permafrost site (Schilthorn, Bernese Alps, Switzerland), it is demonstrated that the developed petrophysical joint inversion provides physically plausible solutions, even in the absence of prior porosity estimates. An assessment of the model covariance matrix for the coupled inverse problem reveals remaining petrophysical ambiguities, in particular between ice and rock matrix. Incorporation of petrophysical a-priori information is demonstrated by penalizing ice occurrence within the first two meters of the subsurface where the measured borehole temperatures are positive. Joint inversion of the field data set reveals a shallow air-rich layer with high porosity on top of a lower-porosity subsurface with laterally varying ice and liquid water contents. Non-physical values (e.g., negative saturations) do not occur and estimated ice saturations of 0-50% as well as liquid water saturations of 15-75% are in agreement with the relatively warm borehole temperatures between -0.5 °C and 3 °C. The presented method helps to improve quantification of water, ice, and air from geophysical observations.

All source code used to generate the results and figures in the paper are in the code folder. A Python library holds the important bits and pieces, which are resued for calculations and figure generation run in Python scripts. The field data used in this study are provided in the data folder and the sources for the manuscript text and figures (LaTeX) are in manuscript. See the README.md files in each directory for a full description.

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

git clone https://github.com/florian-wagner/four-phase-inversion.git

or download a zip archive.

You'll need a working Python environment on a Linux machine to run the code. Other operating systems are generally possible, but have not been tested. 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

Before running any code you must activate the conda environment:

conda activate four-phase-inversion

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

To build 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/output.

You can also run individual steps in the process using the Makefiles from the code and manuscript folders. See the respective README.md files for instructions.

unset PYTHONPATH # to avoid conflicts with packages outside the conda env
git clone https://github.com/florian-wagner/four-phase-inversion.git
cd four-phase-inversion
conda env create
conda activate four-phase-inversion
cd code
make build
make all

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 itself is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

The software implementation is based on pyGIMLi (and its dependencies), which would not exist without the dedication of Carsten Rücker. This repository is heavily inspired by a template for reproducible research papers by Leonardo Uieda.