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Viscosity of the Earth's Mantle

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Lawrence M. Cathles
1362, Princeton Legacy Library
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Approximately 12,000 years ago, at the end of the last ice age, the three kilometers of ice that covered Canada, the large European glaciers in Fennoscandia and Siberia, and many other minor glaciers melted quickly. The resulting meltwaters increased the depth of the world's oceans by about 110 meters. The earth's response to this redistribution of loads was one of fluid flow. By studying the way in which that flow occurred, much can be learned about the viscosity structure of the earth's mantle: that is, how the fluid properties of the earth vary with depth. In this volume Lawrence M. Cathles III sets out to lay the theoretical foundations necessary to model the isostatic (fluid) adjustment of a self-gravitating viscoelastic sphere, such as the earth, and to use these foundations, together with geological evidence of the way the earth responded to the pleistocene land redistributions, to study the viscosity of the mantle.The author argues that the viscosity of the entire mantle is very close to 1022 poise, except for a low-viscosity channel, about 75 kilometers thick, in the uppermost mantle. This conclusion differs sharply from the common view that the earth's mantle becomes very viscous (1027 poise) below a depth of about 1000 kilometers.Originally published in 1975.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Frontmatter, pg. iACKNOWLEDGMENTS, pg. viiCONTENTS, pg. ixILLUSTRATIONS, pg. xiiiTABLES, pg. xixONE. Introduction, pg. 1A. Equations of Motion of Self-gravitating Elastic and Self-gravitating Viscous Spheres, pg. 9B. Constitutive Equations to Model the Earth, pg. 23C. Matrix Methods of Solution, pg. 30A. Flat Earth, Constant Gravitation, pg. 35B. Spherical Earth, pg. 72A. The Duration and Magnitude of the Ice Load: Meltwater Curves and Eustatic Sea Level, pg. 113B. The Lithosphere, pg. 144C. The Viscosity of the Uppermost Mantle, pg. 155D. The Upper Mantle, pg. 173E. The Viscosity of the Lower Mantle, pg. 196F. Summary of Conclusions: Recommendations for Further Work, pg. 267APPENDIX I. Sketch Derivation of the Navier-Stokes Equation after Eringen, pg. 277APPENDIX II. Flat Space Runge-Kutta Equations, pg. 285APPENDIX III .Reduction of Equation of Motion in Spherical Coordinates to Scaler Form after Backus (1967), pg. 291APPENDIX IV. Boundary Conditions at the Fluid Core, pg. 299APPENDIX V. Spherical Harmonics, pg. 307APPENDIX VI .The Isostatic Adjustment of a Layered Viscous Half-Space, pg. 319APPENDIX VII. Glacial Uplift in Canada, pg. 338BIBLIOGRAPHY, pg. 359INDEX, pg. 373

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