Purpose of this document

This document explains how to reproduce the figures from [1] from the beginning to the end. It describes the following steps:

Each of these steps but the last is optional:

Get and compile the code

The procedure outlined in the following paragraphs yields an Lzip-compressed2 tarball named dune-tectonic.tar.lz. It contains a 2D executable one-body-problem-2D and a 3D executable one-body-problem-3D as well as configuration files, copies of the dynamically linked libraries, and even a dynamic linker. By downloading such a tarball directly from here one can choose to skip this section.

The numerical simulations whose results are presented in [1] are based on the 2016-PippingKornhuberRosenauOncken branch of the dune-tectonic C++ code.

It depends on version 2.5 of a few dune modules (see also the dune.module file) which are available from the DUNE project and the FU Berlin (some from the former, some from the latter).

The building procedure has been automated through docker. In the following, we will always assume that the variable tag has been set to 2016-PippingKornhuberRosenauOncken and that the git repository of Dockerfiles has been cloned in the following way.

git clone https://git.imp.fu-berlin.de/pipping/${tag}-docker.git

Building dune-tectonic is now as simple as:

cd ${tag}-docker

Docker makes it easy to automate and sandbox the process of obtaining ready-to-run executables on x86_64 Linux; the entire process could be completed without docker, though. Turning a Dockerfile into a regular shell-script is entirely straightforward. The idea of using docker for reproducible research was put forward in [2]

Run the simulations

The purpose of this section is to obtain the following list of directories, each containing a file named output.h5:


These files3 can be downloaded through a script from the aforementioned git repository of Dockerfiles by executing the following commands:

cd ${tag}-docker

after which this entire section can be skipped.

To be able to reproduce all the figures from [1], one needs to run twenty-one 2D computations and a single 3D computation.

Each of the programs below can be passed the option -io.printProgress true in order to enable a progress indicator. Without this option, which is off by default, completing a time step will cause no output to be written to the console so that it may seem as if the program was stuck.

The 3D simulation can be run like this (after unpacking the tarball we obtained earlier to the current directory):

## In the directory 3d-lab/rtol=1e-5_diam=1e-2
./ld-linux-x86-64.so.2 --library-path . ./one-body-problem-3D \
    -v.fpi.tolerance ${rtol} \
    -timeSteps.refinementTolerance ${rtol} \
    -boundary.friction.smallestDiameter ${diam}

while a 2D simulation can be run like this (again, after unpacking the tarball to the current directory):

## In the directory 2d-lab-fpi-tolerance/rfpitol=1e-7
./ld-linux-x86-64.so.2 --library-path . ./one-body-problem-2D \
    -v.fpi.tolerance ${rfpitol}

where rfpitol should take the values 1e-7, 2e-7, 3e-7, 5e-7, 10e-7, 20e-7, 30e-7, 50e-7, 100e-7, 200e-7, 300e-7, 500e-7, 1000e-7, 2000e-7, 3000e-7, 5000e-7, 10000e-7, 20000e-7, 30000e-7, 50000e-7, 100000e-7.

Dependening on the resources available to you, you might want to run all of the 2D simulations in parallel on a cluster (e.g. through slurm), in parallel on one or more multi-core machines (e.g. via GNU Parallel), but probably not in sequence (it would take weeks!). The number of available CPUs is the limiting factor here since none of the 2D simulations needs more than 100M of RAM.

All but one of the 2D simulation plots (Figure 7) only put the data set 2d-lab-fpi-tolerance/rfpitol=100e-7 to use. If the reproduction of Figure 7 or the 3D simulation plots is not a priority, a lot of computing time can be saved by running just this one simulation.

Extracting relevant quantities

To be able to talk about seismic events or earthquakes and quantities related to them, we need to decide on criteria that allow a machine to determine the spatial and temporal extect of such an occurrence, and then apply these criteria. This task is carried out by a collection of R scripts which live alongside the LaTeX sources we will talk about in the next section. Once they are run, they populate a directory called generated with various CSV and contour files. By downloading the expected contents of this directory as a tarball from here one can choose to skip this section.

The aforementioned R tools reside in the tools directory of the 2016-PippingKornhuberRosenauOncken-plots git repository.

Before running them, the file config.ini needs to be edited such that simulation is set to the directory which contains 2d-lab-fpi-tolerance and 3d-lab from the previous section as immediate subdirectories. The boxplot from Figure 5 also requires a local copy of the file B_Scale-model-earthquake-data.zip from [3], whose location should be recorded in config.ini as the experiment directory.

Finally, we install the necessary R packages (namely Rcpp and h5) and run the scripts via


This entire process, too, is automated through a Dockerfile, so that one only needs to take the following steps to obtain the file generated.tar.lz.

cd ${tag}-docker

Generating the plots

The LaTeX/pgfplots code that is used to produce the final figures is available from the 2016-PippingKornhuberRosenauOncken-plots git repository that also hosts the R tools from the previous section which we used to populate the directory called generated. We will now need the contents of this directory.

To recreate the plot from Figure 6, which is contained in 2d-dip-contours-performance.tikz, we can use the standalone LaTeX document standalone/2d-dip-contours-performance.tex which contains nothing but this figure and process it with a LaTeX processor, e.g. via

latexmk -pdf standalone/2d-dip-contours-performance.tex

The process of doing this for all figures can also be automated via

make -f standalone/Makefile pdf

In either case, the resulting PDF files can be found in the current working directory. The Makefile also makes it easy to turn these PDF files into PNG files via

make -f standalone/Makefile png

assuming that ImageMagick is installed.

Naturally, also these steps are automated through a Dockerfile, so that one only needs to run the following commands to obtain the file figures.tar.lz (filled with PNG images), which is also available from here):

cd ${tag}-docker


The above steps should generate a series of PNG images which are shown here.


  1. E. Pipping, R. Kornhuber, M. Rosenau, and O. Oncken: On the efficient and reliable numerical solution of rate-and-state friction problems, Geophys. J. Int. 204.3 (2016) 1858–1866. DOI

  2. C. Boettiger: An introduction to Docker for reproducible research, with examples from the R environment, ACM SIGOPS OSR 49.1. (2015) 71–79. DOI arXiv

  3. M. Rosenau, F. Corbi, S. Dominguez, M. Rudolf, M. Ritter, E. Pipping: Supplement to "Analogue earthquakes and seismic cycles: Experimental modelling across timescales", GFZ Data Services (2016). DOI

  1. Creating a macOS executable works just as well, prebuilt binaries are not provided, however. The same goes for Linux on architectures other than x86_64.

  2. Lzip was used here because it led to considerably higher rates of compression than the more widely available gzip, is less susceptible to corruption and does not contain the modification time of the input so that identical input will lead to identical output. It is hoped that Lzip will see more widespread use in the future so that this choice will lead to less and less discomfort for the user.

  3. The files you can download here are different from the ones that one-body-problem-2D generates in that they've been post-processed as follows:

    h5repack -l CONTI output.h5 repacked.h5
    h5repack -f GZIP=9 repacked.h5 compressed.h5

    The purpose is quicker random access and a smaller file size.