SBTides: A Modular Toolkit for Modeling Viscoelastic Solid Body Tides in Python

William Joseph Durkin, Clayton Davis

Abstract: Tidal forcings drive the vertical and horizontal deformation of a planet’s crust and perturb its gravitational field, i.e., solid body tides. The ability to accurately model these deformations is critical for realizing precise satellite orbits and understanding the displacement of geodetic markers that are used in developing stable planetary reference systems. Solid body tidal deformations are sensitive to both the elastic and viscous properties of a planet’s deep interior and provide valuable constraints on the mechanical, chemical, and thermal planetary structure. Modeling the Earth’s viscoelastic solid body tides can be performed using open-source codes. Similar toolsets for modeling viscoelastic solid body tides on other celestial bodies are not yet available. To fill this gap and support the emerging geodetic infrastructure on the Moon, MITRE and the National Geospatial-Intelligence Agency (NGA) are developing SBTides: a modular, open-source python toolkit for modeling viscoelastic solid body tides. Following the approach of Williams and Boggs (2015), we express the tidal potential as the summation of sets of time-varying Stokes’ coefficients for each of the dominant tidal frequencies. This approach allows for viscoelastic deformation to be modeled using frequency-dependent, complex tidal Love numbers. The deformational response to varying rheologic properties of the Moon’s interior can be modeled with SBTides using functions that interface with external toolkits such as ALMA3 (Melini et al., 2022) that compute complex viscoelastic tidal Love numbers. While SBTides is developed with the immediate focus of modeling solid body tides on the Moon, the approach is designed to apply generically to other moons and planets where spherical, radially symmetric rheologic structure approximations are appropriate.
Published in: Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023)
September 11 - 15, 2023
Hyatt Regency Denver
Denver, Colorado
Pages: 790 - 799
Cite this article: Durkin, William Joseph, Davis, Clayton, "SBTides: A Modular Toolkit for Modeling Viscoelastic Solid Body Tides in Python," Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023), Denver, Colorado, September 2023, pp. 790-799. https://doi.org/10.33012/2023.19355
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