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Published February 2019 | Supplemental Material + Published
Journal Article Open

LoadDef: A Python‐Based Toolkit to Model Elastic Deformation Caused by Surface Mass Loading on Spherically Symmetric Bodies


Temporal variations of surface masses, such as the hydrosphere and atmosphere of the Earth, load the surfaces of planetary bodies causing temporal variations in deformation. Surface shear forces and gravitational fields also drive ongoing planetary deformation. Characterizing the spatiotemporal patterns of planetary deformation can constrain allowable models for the interior structure of a planetary body as well as for the distribution of surface and body forces. Pertinent applications include hydrology, glaciology, geodynamics, atmospheric science, and climatology. To address the diversity of emerging applications, we introduce a software suite called LoadDef that provides a collection of modular functions for modeling planetary deformation within a self‐consistent, Python‐based computational framework. Key features of LoadDef include computation of real‐valued potential, load, and shear Love numbers for self‐gravitating and spherically symmetric planetary models; computation of Love‐number partial derivatives with respect to planetary density and elastic structure; computation of displacement, gravity, tilt, and strain load Green's functions; and computation of three‐component surface displacements induced by surface mass loading. At a most basic level, only a planetary‐structure model and a mass‐load model must be supplied as input to LoadDef to utilize all the main features of the software. The end‐to‐end forward‐modeling capabilities for mass‐loading applications lay the foundation for sensitivity studies and geodetic tomography. LoadDef results have been validated with Global Navigation Satellite System observations and verified against independent software and published results. As a case study, we use LoadDef to predict the solid Earth's elastic response to ocean tidal loading across the western United States.

Additional Information

©2019. The Authors. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made. Received 8 OCT 2018. Accepted 18 JAN 2019. Accepted article online 25 JAN 2019. Published online 6 FEB 2019. The source code and user manual for LoadDef are distributed under the GNU General Public License v3.0, and are available from https://github.com/hrmartens/LoadDef. Data sets, detailed methods, and additional figures may be found in the supporting information. The model we used for Mars structure is from the collection of models of Khan et al. (2018; http://jupiter.ethz.ch/~akhan/amir/Models.html). We thank Bryan Riel for advice on the MPI implementation. We also thank early users of LoadDef for feedback on usability. We acknowledge support from the National Science Foundation Geophysics Program funding under grant EAR‐1417245. This manuscript is based upon work supported by the NASA Earth and Space Science Fellowship to HRM under grant NNX14AO04H as well as by the National Science Foundation Graduate Research Fellowship to HRM under grant DGE1144469. Additional support has been provided by NASA EPSCoR through the Montana Space Grant Consortium under grant NNX15AK40A. We are grateful for the efforts and insightful comments of two anonymous reviewers that significantly strengthened the manuscript and software.

Attached Files

Published - Martens_et_al-2019-Earth_and_Space_Science.pdf

Supplemental Material - downloadSupplement_doi=10.1029_2F2018EA000462_file=ess2262-sup-0001-Supplementary.pdf

Supplemental Material - downloadSupplement_doi=10.1029_2F2018EA000462_file=ess2262-sup-0002-Data_Set_SI-S01.txt

Supplemental Material - downloadSupplement_doi=10.1029_2F2018EA000462_file=ess2262-sup-0003-Data_Set_SI-S02.txt

Supplemental Material - downloadSupplement_doi=10.1029_2F2018EA000462_file=ess2262-sup-0004-Data_Set_SI-S03.txt

Supplemental Material - downloadSupplement_doi=10.1029_2F2018EA000462_file=ess2262-sup-0005-Data_Set_SI-S04.txt

Supplemental Material - downloadSupplement_doi=10.1029_2F2018EA000462_file=ess2262-sup-0006-Data_Set_SI-S05.txt

Supplemental Material - downloadSupplement_doi=10.1029_2F2018EA000462_file=ess2262-sup-0007-Data_Set_SI-S06.txt

Supplemental Material - downloadSupplement_doi=10.1029_2F2018EA000462_file=ess2262-sup-0008-Data_Set_SI-S07.txt

Supplemental Material - downloadSupplement_doi=10.1029_2F2018EA000462_file=ess2262-sup-0009-Data_Set_SI-S08.txt


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