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README.md

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# PlateFlex: Software for mapping the effective elastic thickness of the lithosphere
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![](./plateflex/examples/picture/logo_plateflex.png)
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## Software for mapping the effective elastic thickness of the lithosphere
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The flexure of elastic plates is a central concept in the theory of plate tectonics,
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where the Earth's lithosphere (crust and uppermost mantle) reacts to applied loads
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by bending, a process referred to as flexural isostasy. The plate elasticity is
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parameterized by the *flexural rigidity*, which is proportional to the product of
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Young's modulus with the cube of the elastic plate thickness. Estimating the *effective*
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by bending, a process referred to as flexural isostasy. Estimating the *effective*
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elastic thickness (<i>T<sub>e</sub></i>) of the lithosphere (thickness
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of an equivalent ideal elastic plate) gives important clues on the rheology of the
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lithosphere and its thermal state.
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Estimating <i>T<sub>e</sub></i> can be done by modeling the cross-spectral properties
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(admittance and coherence) between topography and gravity anomaly data,
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which are proxies for the distribution of flexurally compensated surface and subsurface
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loads. These spectral properties can be calculated using different spectral
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estimation techniques - however, to map <i>T<sub>e</sub></i> variations it is
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important to use analysis windows small enough for good spatial resolution, but
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large enough to capture the effect of flexure at long wavelengths. The wavelet
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transform is particularly well suited for this analysis because it avoids splitting
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the grids into small windows and can therefore produce cross-spectral functions
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at each point of the input grid.
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lithosphere and its thermal state. Estimating <i>T<sub>e</sub></i> can be done by
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modeling the cross-spectral properties (admittance and coherence) between topography
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and gravity anomaly data, which are proxies for the distribution of flexurally
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compensated surface and subsurface loads.
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This package contains `python` and `fortran` modules to calculate the wavelet spectral
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and cross-spectral quantities of 2D gridded data of topography and gravity anomalies.
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Once obtained, the wavelet cross-spectral quantities (admittance and coherence) are
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used to determine the parameters of the effectively elastic plate, such as the
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effective elastic thickness (<i>T<sub>e</sub></i>), the initial subsurface-to-surface
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load ratio (<i>F</i>) and optionally the initial phase difference between
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surface and subsurface loads (<i>alpha</i>). The software uses the analytical
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functions with *uniform F and alpha* to fit the admittance and/or coherence functions.
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The estimation can be done using non-linear least-squares or probabilistic (i.e., bayesian)
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inference methods.
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The analysis can be done using either the Bouguer or Free air gravity anomalies, and
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surface and subsurface loads (<i>alpha</i>). The estimation can be done using non-linear
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least-squares or probabilistic (i.e., bayesian) inference methods. The analysis can
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be done using either the Bouguer or Free air gravity anomalies, and
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over land or ocean areas. Computational workflows are covered in the Jupyter
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notebooks bundled with this package. The software contains methods to make beautiful and
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insightful plots using the `seaborn` package.
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> **_NOTE:_** The cross-spectral quantities calculated here are the real-valued admittance and squared-real coherency, as discussed in the [references](#references)
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notebooks bundled with this package. The software contains methods to make
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publication-quality plots using the `seaborn` package.
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[![Build Status](https://travis-ci.com/paudetseis/PlateFlex.svg?branch=master)](https://travis-ci.com/paudetseis/PlateFlex)
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## Usage
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Installation, Usage, API documentation and Jupyter Notebooks are described at
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https://paudetseis.github.io/PlateFlex/
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### Documentation
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<!-- #### Citing
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Installation, Usage and API documentation are described at https://paudetseis.github.io/PlateFlex/
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If you use `PlateFlex` in your work, please cite the Zenodo DOI (https://zenodo.org/badge/latestdoi/204565459)
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and the following paper:
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### How to make new gridded data sets
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- Audet, P., Thomson, C.J., Bostock, M.G., and Eulenfeld, T. (2019). Telewavesim:
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Python software for teleseismic body wave modeling. Journal of Open Source Software,
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4(44), 1818, https://doi.org/10.21105/joss.01818
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-->
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#### Contributing
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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.
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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.
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Examples of straightforward contributions include notebooks that describe published examples of elastic thickness
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results. Suggestions for improvements (speed, accuracy, etc.) are also welcome.
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## References
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#### References
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- Audet, P. (2014). Toward mapping the effective elastic thickness of planetary lithospheres
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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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