relMT

Software to determine relative earthquake moment tensors

Installation

Installation of relMT is easy. The basic installation requires:

• The FFTW library (often provided via the system package manager)
• The Python packages NumPy, SciPy, PyYAML

Based on Conda and Pip

We recommend to create a conda environment or to install into an existing one. Choose any Python version greater or equal 3.10

# Create and activate the environment
conda create -n relmt python
conda activate relmt

# Install the Fastest Fourier Transform in the West
conda install -c conda-forge fftw

Now install relMT locally

git clone https://github.com/wasjabloch/relMT
cd relMT
pip install .

For plotting, we require:

• Matplotlib for all plotting
• networkx to visualize connections of equations in the linear system
• Pyrocko to plot moment tensors

Consider installing these packages using the plot optional dependency:

pip install .[plot]

Some additional functionality requires community packages:

• Import of waveforms and station inventories via ObsPy`
• Computation of spectra with Multitaper
• Conversion to and from Cartesian coordinates with UTM

Consider installing these packages using the extra optional dependency:

pip install .[extra]

If you are working in IPython, or Jupyter, install the package in the same Conda environment to avoid version conflicts

conda install ipython

or

conda install jupyter

If you consider contributing to relMT, please install the development version

pip install .[dev]

Documentation

The documentation is hosted at: https://relmt.readthedocs.io/en/latest/

Rationale

The algorithm consists of the following steps:

1. Choose a cluster of seismic events for which the Green's function can be assumed equal
2. Align P and S wave train observations to the sample
3. At each seismic station, decompose the wave trains into principal components
4. Measure relative P-wave and S-wave amplitudes
5. Set up a linear system that relates relative amplitudes to moment tensors
6. Solve the linear system using algebraic methods

References

The algorithms are based on the following research articles:

Dahm, T., J. Horalek, and J. Sileny (2000). Comparison of absolute and relative moment tensor solutions for the January 1997 West Bohemia Earthquake swarm. Studia Geophys. et Geod., https://doi.org/10.1023/A:1022166926987

Plourde, A. P., and M. G. Bostock (2019). Relative moment tensors and deep Yakutat seismicity, Geophys. J. Int., https://doi.org/10.1093/gji/ggz375

Bostock, M. G., A. P. Plourde, D. Drolet, and G. Littel (2021). Multichannel alignment of S waves, Bull. Seismol. Soc. Am., https://doi.org/10.1785/0120210076

Drolet, D., M. G. Bostock, A. P. Plourde, and C. G. Sammis (2022). Aftershock distributions, moment tensors and stress evolution of the 2016 Iniskin and 2018 Anchorage Mw 7.1 Alaskan intraslab earthquakes. Geophys. J. Int., https://doi.org/10.1093/gji/ggac165

Drolet, D., M.G. Bostock, and S. Peacock (2023). Relative Moment Tensor Inversion for Microseismicity: Application to Clustered Earthquakes in the Cascadia Forearc. Seismica. https://doi.org/10.26443/seismica.v2i4.1311

Acknowledgments

This software package is part of the relMT project that has received funding from the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101146483