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

Hilary R. Martens, Luis Rivera, Mark Simons

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


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.

Original languageEnglish
Pages (from-to)311-323
Number of pages13
JournalEarth and Space Science
Issue number2
StatePublished - Feb 1 2019


  • Earth deformation
  • Earth structure
  • Love numbers
  • load Green's functions
  • ocean tidal loading
  • surface mass loading


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