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AB-Ares committed Jul 16, 2021
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These functions solve the [Banerdt (1986)](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB091iB01p00403) system of equations under different assumptions. Various improvements have been made to the model including the possibility to account for finite-amplitude correction and filtering [(Wieczorek & Phillips, 1998)](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/97JE03136), lateral density variations at any arbitrary depth and within the surface or moho-relief [(Wieczorek et al., 2013)](https://science.sciencemag.org/content/early/2012/12/04/science.1231530?versioned=true), and density difference between the surface topography and crust [(Broquet & Wieczorek, 2019)](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019JE005959).

## Comments
### Dependencies
We note that some of these functions rely heavily on the [pyshtools](https://shtools.github.io/SHTOOLS/) package of [Wieczorek & Meschede (2018)](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018GC007529) that is used to perform the spherical harmonic transforms, Legendre polynomial expansions, and finite-amplitude calculations.

### Contribute
This code is still under development and benchmarking. If you find any bugs or errors in the code, please report them in GitHub or to adrien.broquet at oca.eu.

For this code, we work on the develop branch and merge it to the main branch (with a new version number) everytime significant addtions/improvements are made. If you plan on making contributions, please base everything on the develop branch.

### Benchmarks
Moho-relief calculations have been benchmarked to the [ctplanet](https://github.com/MarkWieczorek/ctplanet) package of Mark Wieczorek.
Displacement calculations have been benchmarked to the analytical model of [Broquet & Wieczorek (2019)](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019JE005959).
Strain calculations reproduce results published in the literature (e.g., [Banerdt & Golombek 2000](https://www.lpi.usra.edu/meetings/lpsc2000/pdf/2038.pdf)).

## Methods
`Thin_shell_matrix` Solve the [Banerdt (1986)](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB091iB01p00403) system of 5 equations under the mass-sheet approximation and assuming that potential internal density variations are contained within a spherical shell. The system links 8 parameters expressed in spherical harmonics: the topography, geoid at the surface, geoid at the moho depth, net acting load on the lithosphere, tangential load potential, flexure of the lithosphere, isostatic crustal root variations, and internal density variations. Minor corrections have been made in the geoid equations.

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`Venus_crust_displacement` A script that demonstrates how to calculate the moho-relief and strains on Venus, as a function of the mean planetary crustal thickness and elastic thickness.

## Comments
### Dependencies
We note that some of these functions rely heavily on the [pyshtools](https://shtools.github.io/SHTOOLS/) package of [Wieczorek & Meschede (2018)](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018GC007529) that is used to perform the spherical harmonic transforms, Legendre polynomial expansions, and finite-amplitude calculations.

### Contribute
This code is still under development and benchmarking. If you find any bugs or errors in the code, please report them in GitHub or to adrien.broquet at oca.eu.

For this code, we work on the develop branch and merge it to the main branch (with a new version number) everytime significant addtions/improvements are made. If you plan on making contributions, please base everything on the develop branch.

### Benchmarks
Moho-relief calculations have been benchmarked to the [ctplanet](https://github.com/MarkWieczorek/ctplanet) package of Mark Wieczorek.
Displacement calculations have been benchmarked to the analytical model of [Broquet & Wieczorek (2019)](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019JE005959).
Strain calculations reproduce results published in the literature (e.g., [Banerdt & Golombek 2000](https://www.lpi.usra.edu/meetings/lpsc2000/pdf/2038.pdf)).

## How to install and run Displacement_strain_planet
If you would like to modify the source code, download the Displacement_strain_planet repository and install using pip (or pip3 depending on your installation).
```bash
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