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Mathematics of the Not-So-Solid Solid Earth

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Mathematics of Planet Earth

Part of the book series: Mathematics of Planet Earth ((MPE,volume 5))

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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.

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Acknowledgements

The author acknowledges support from NSF Grant EAR-1250988.

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Authors and Affiliations

  1. Department of Geosciences, Virginia Tech, Blacksburg, VA, USA

    Scott D. King

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  1. Scott D. King
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Correspondence to Scott D. King .

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Editors and Affiliations

  1. Mathematics and Statistics, Georgetown University, Washington, DC, USA

    Hans G. Kaper

  2. DIMACS Center, Rutgers University, Piscataway, NJ, USA

    Fred S. Roberts

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King, S.D. (2019). Mathematics of the Not-So-Solid Solid Earth. In: Kaper, H., Roberts, F. (eds) Mathematics of Planet Earth. Mathematics of Planet Earth, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-22044-0_2

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