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# PlateFlex: Software for mapping the effective elastic thickness of the lithosphere

![](./plateflex/examples/picture/logo_plateflex.png)

## Software for mapping the effective elastic thickness of the lithosphere

The flexure of elastic plates is a central concept in the theory of plate tectonics,
where the Earth's lithosphere (crust and uppermost mantle) reacts to applied loads
by bending, a process referred to as flexural isostasy. The plate elasticity is
parameterized by the *flexural rigidity*, which is proportional to the product of
Young's modulus with the cube of the elastic plate thickness. Estimating the *effective*
by bending, a process referred to as flexural isostasy. Estimating the *effective*
elastic thickness (<i>T<sub>e</sub></i>) of the lithosphere (thickness
of an equivalent ideal elastic plate) gives important clues on the rheology of the
lithosphere and its thermal state.

Estimating <i>T<sub>e</sub></i> can be done by modeling the cross-spectral properties
(admittance and coherence) between topography and gravity anomaly data,
which are proxies for the distribution of flexurally compensated surface and subsurface
loads. These spectral properties can be calculated using different spectral
estimation techniques - however, to map <i>T<sub>e</sub></i> variations it is
important to use analysis windows small enough for good spatial resolution, but
large enough to capture the effect of flexure at long wavelengths. The wavelet
transform is particularly well suited for this analysis because it avoids splitting
the grids into small windows and can therefore produce cross-spectral functions
at each point of the input grid.
lithosphere and its thermal state. Estimating <i>T<sub>e</sub></i> can be done by
modeling the cross-spectral properties (admittance and coherence) between topography
and gravity anomaly data, which are proxies for the distribution of flexurally
compensated surface and subsurface loads.

This package contains `python` and `fortran` modules to calculate the wavelet spectral
and cross-spectral quantities of 2D gridded data of topography and gravity anomalies.
Once obtained, the wavelet cross-spectral quantities (admittance and coherence) are
used to determine the parameters of the effectively elastic plate, such as the
effective elastic thickness (<i>T<sub>e</sub></i>), the initial subsurface-to-surface
load ratio (<i>F</i>) and optionally the initial phase difference between
surface and subsurface loads (<i>alpha</i>). The software uses the analytical
functions with *uniform F and alpha* to fit the admittance and/or coherence functions.
The estimation can be done using non-linear least-squares or probabilistic (i.e., bayesian)
inference methods.

The analysis can be done using either the Bouguer or Free air gravity anomalies, and
surface and subsurface loads (<i>alpha</i>). The estimation can be done using non-linear
least-squares or probabilistic (i.e., bayesian) inference methods. The analysis can
be done using either the Bouguer or Free air gravity anomalies, and
over land or ocean areas. Computational workflows are covered in the Jupyter
notebooks bundled with this package. The software contains methods to make beautiful and
insightful plots using the `seaborn` package.

> **_NOTE:_** The cross-spectral quantities calculated here are the real-valued admittance and squared-real coherency, as discussed in the [references](#references)
notebooks bundled with this package. The software contains methods to make
publication-quality plots using the `seaborn` package.

[![Build Status](https://travis-ci.com/paudetseis/PlateFlex.svg?branch=master)](https://travis-ci.com/paudetseis/PlateFlex)

## Usage
Installation, Usage, API documentation and Jupyter Notebooks are described at
https://paudetseis.github.io/PlateFlex/

### Documentation
<!-- #### Citing
Installation, Usage and API documentation are described at https://paudetseis.github.io/PlateFlex/
If you use `PlateFlex` in your work, please cite the Zenodo DOI (https://zenodo.org/badge/latestdoi/204565459)
and the following paper:
### How to make new gridded data sets
- Audet, P., Thomson, C.J., Bostock, M.G., and Eulenfeld, T. (2019). Telewavesim:
Python software for teleseismic body wave modeling. Journal of Open Source Software,
4(44), 1818, https://doi.org/10.21105/joss.01818
-->
#### Contributing

Although the examples above work as advertised, making new grids for your own project can be a daunting task. In the [wiki](https://github.com/paudetseis/PlateFlex/wiki/How-to-make-gridded-data-sets-to-use-with-PlateFlex) page we provide examples of how to reproduce the data sets used in the Jupyter notebooks from publicly available topography and gravity models.
All constructive contributions are welcome, e.g. bug reports, discussions or suggestions for new features. You can either [open an issue on GitHub](https://github.com/paudetseis/PlateFlex/issues) or make a pull request with your proposed changes. Before making a pull request, check if there is a corresponding issue opened and reference it in the pull request. If there isn't one, it is recommended to open one with your rationale for the change. New functionality or significant changes to the code that alter its behavior should come with corresponding tests and documentation. If you are new to contributing, you can open a work-in-progress pull request and have it iteratively reviewed.

Examples of straightforward contributions include notebooks that describe published examples of elastic thickness
results. Suggestions for improvements (speed, accuracy, etc.) are also welcome.

## References
#### References

- Audet, P. (2014). Toward mapping the effective elastic thickness of planetary lithospheres
from a spherical wavelet analysis of gravity and topography. Physics of the Earth and Planetary Interiors, 226, 48-82. https://doi.org/10.1016/j.pepi.2013.09.011
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