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Mathematics of the Not-So-Solid Solid Earth

  • Scott D. KingEmail author
Chapter
Part of the Mathematics of Planet Earth book series (MPE, volume 5)

Abstract

As a result of climatic variations over the past 700,000 years, large ice sheets in high-latitude regions of the Earth formed and subsequently melted, loading and unloading the surface of the Earth. This chapter introduces the mathematical analysis of the vertical motion of the solid Earth in response to this time-varying surface loading. This chapter focuses on two conceptual models: the first, proposed by Haskell [Physics, 6, 265–269 (1935)], describes the return to equilibrium of a viscous half-space after the removal of an applied surface load; the second, proposed by Farrell and Clark [Geophys. J. Royal Astr. Soc., 46, 647–667 (1976)], illustrates the changes in sea level that occur when ice and water are rearranged on the surface of the Earth. The sea level equation proposed by Farrell and Clark accounts for the fact that sea level represents the interface between two dynamic surfaces: the sea surface and the solid Earth, both of which are changing with time.

Keywords

Gravitational potential Sea level Stokes equation Viscous relaxation 

Notes

Acknowledgements

The author acknowledges support from NSF Grant EAR-1250988.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of GeosciencesVirginia TechBlacksburgUSA

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