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https://github.com/santisoler/lapis2019

Poster presentation given at LAPIS 2019
https://github.com/santisoler/lapis2019

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Poster presentation given at LAPIS 2019

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# Gravitational fields of tesseroids with variable density



[![figshare](https://img.shields.io/badge/doi-10.6084%2Fm9.figshare.8242439-blue.svg?style=flat-square)](https://doi.org/10.6084/m9.figshare.8242439)



[Santiago R. Soler](https://www.github.com/santisoler)1,2,

[Agustina Pesce](https://www.github.com/aguspesce)1,2,

Mario E. Gimenez1,2

and

[Leonardo Uieda](https://www.leouieda.com)3



> 1CONICET, Argentina.


> 2Instituto Geofísico Sismológico Volponi, Universidad Nacional de San Juan, Argentina.


> 3Department of Earth Sciences, SOEST, University of Hawai'i at Mānoa, USA



Abstract submitted to

[LAPIS 2019: Inverse methods in Geophysics](http://lapis2019.fcaglp.unlp.edu.ar/).



[![Poster](poster.jpg)](poster.pdf)



## Abstract



We present a new methodology to compute the gravitational fields generated by

tesseroids (spherical prisms) whose density varies with depth according to

an arbitrary continuous function.

It approximates the gravitational fields through the Gauss-Legendre Quadrature along

with two discretization algorithms that automatically control its accuracy by adaptively

dividing the tesseroid into smaller ones.

The first one is a preexisting two dimensional adaptive discretization algorithm that

reduces the errors due to the distance between the tesseroid and the computation point.

The second is a new density-based discretization algorithm that

decreases the errors introduced by the variation of the density function with depth.

The amount of divisions made by each algorithm is indirectly controlled

by two parameters: the distance-size ratio and the delta ratio.

We have obtained analytical solutions for a spherical shell with radially variable

density and compared them to the results of the numerical model for linear,

exponential, and sinusoidal density functions.

The heavily oscillating density functions are intended only to test the algorithm to its

limits and not to emulate a real world case.

These comparisons allowed us to obtain optimal values for the distance-size and

delta ratios that yield an accuracy of 0.1% of the analytical solutions.

The resulting optimal values of distance-size ratio for the gravitational potential and

its gradient are 1 and 2.5, respectively.

The density-based discretization algorithm produces no discretizations in the linear

density case, but a delta ratio of 0.1 is needed for the exponential and most sinusoidal

density functions.

These values can be extrapolated to cover most common use cases, which are simpler than

oscillating density profiles.

However, the distance-size and delta ratios can be configured by the user to increase

the accuracy of the results at the expense of computational speed.

Lastly, we apply this new methodology to model the Neuquén Basin, a foreland basin in

Argentina with a maximum depth of over 5000m, using an exponential density function.



## Notes



The poster was entirely made with Inkscape using the Glacial Indifference and Linguistics

Por fonts, which are available under the SIL Open Font License.



If the fonts are not installed on your system, the `poster.svg` file won't look as

expected. Please install the needed fonts.



On `poster.pdf` the fonts have been converted to paths, so there's no need to install

the fonts to see `poster.pdf` correctly.



## License



This work is licensed under a

[Creative Commons Attribution 4.0 International License][cc-by].



[![CC BY 4.0][cc-by-image]][cc-by]



[cc-by]: http://creativecommons.org/licenses/by/4.0/

[cc-by-image]: https://i.creativecommons.org/l/by/4.0/88x31.png