Abstract
A general mathematical model of balanced global isostasy is presented that describes the geometrical relationships among atmospheric, oceanic, lithospheric, and asthenospheric components relative to a fixed, external frame of reference in terms of 19 parameters of mass, density, area, and thickness in five basic equations and various corollaries. The model is applicable and necessary for evaluating lithospheric processes that operate on a global scale or that affect globally oriented parameters such as sea level, freeboard, and ocean basin depth. It also provides a means of testing the internal consistency of a given set of mass, density, volume, and area parameters relative to present crustal geometry by showing how well they combine to predict present continental free-board. With modification, the basic model can be used to examine more complex questions involving glacially induced sea level fluctuations and long-term crustal evolution resulting from differential energy flux to Earth, short-term modulation of heat flux from the asthenosphere, and long-term monotonic cooling.
Similar content being viewed by others
References
Airy, G. B., 1855, An Hypothesis of Crustal Balance: Philos. Trans. R. Soc. Lon., v. 145, p. 101–104.
Bond, G., 1978, Speculations on Real Sea-Level Changes and Vertical Motions of Continents at Selected Times in the Cretaceous and Tertiary Periods: Geology, v. 6, p. 247–250.
Cogley, J. G., 1984, Continental Margins and the Extent and Number of Continents: Rev. Geophys. Space Phys., v. 22, p. 101–122.
Condie, K. C., 1982, Plate Tectonics & Crustal Evolution: Pergamon Press, New York, 310 p.
Haq, B. U.; Hardenbol, J.; and Vail, P. R., 1987, Chronology of Fluctuating Sea Levels since the Triassic: Science, v. 235, p. 1156–1167.
Harrison, C. G. A.; Brass, G. W.; Saltzman, E.; Sloan II, J.; Southam, J.; and Whitman, J. M., 1981, Sea Level Variations, Global Sedimentation Rates and the Hypsographic Curve: Earth Planet. Sci. Lett., v. 54, p. 1–16.
Hays, J. D. and Pitman III, W. C., 1973, Lithospheric Plate Motion, Sea Level Changes and Climatic and Ecological Consequences: Nature. v. 246, p. 18–22.
Hidore, J. J., 1969, A Geography of the Atmosphere: Wm. C. Brown Company Publishers, Dubuque, Iowa, 106 p.
Jordan, T. H., 1975, The Continental Tectosphere: Rev. Geophys. Space Phys., v. 13, n. 3, p. 1–12.
Jordan, T. H., 1978, Composition and Development of the Continental Tectosphere: Nature, v. 272, p. 544–548.
Jordan, T. H., 1979, The Deep Structure of Continents: Sci. Amer., v. 240, n. 1, p. 92–107.
Kominz, M. A., 1984, Oceanic Ridge Volumes and Sea-Level Changes: An Error Analysis: p. 109–127in J. S. Schlee (Ed.), Interregional Unconformities and Hydrocarbon Accumulation: Amer. Assoc. Pet. Geol., Mem. 36.
Kossinna, E., 1933, Die Erodoberflache: p. 869–954in B. Gutenberg (Ed.), Handbuch der Geophysik, v. 2, Borntraeger, Berlin.
Officer, C. B., 1974, Introduction to Theoretical Geophysics: Springer-Verlag, New York, 385 p.
Parsons, B. and Sclater, J. G., 1977, An Analysis of the Variation of Ocean Floor Bathymetry and Heat Flow with Age: J. Geophys. Res., v. 83, p. 803–827.
Pitman III, W. C., 1978, Relationship Between Eustasy and Stratigraphic Sequences of Passive Margins: Geol. Soc. Amer. Bull., v. 89, p. 1389–1403.
Pratt, J. H., 1858, The Deflection of the Plumb-Line in India and the Compensatory Effect of a Deficiency of Matter Below the Himalaya Mountains: Philos. Trans. R. Soc. Lond., v. 149, p. 745–778.
Reymer, A. and Schubert, G., 1984, Phanerozoic Addition Rates to the Continental Crust and Crustal Growth: Tectonics, v. 3, n. 1, p. 63–77.
Sahagian, D., 1987, Epeirogeny and Eustatic Sea Level Changes as Inferred from Cretaceous Shoreline Deposits: Applications to the Central and Western United States: J. Geophys. Res., v. 92, p. 4895–4904.
Schubert, G. and Reymer, A., 1985, Continental Volume and Freeboard Through Geologic Time: Nature, v. 316, p. 336–339.
Suppe, J., 1985, Principles of Structural Geology: Prentice-Hall, Englewood Cliffs, New Jersey, 537 p.
Turcotte, D. L. and Burke, K., 1978, Global Sea-Level Changes and the Thermal Structure of the Earth: Earth and Planet. Sci. Lett., v. 41, p. 341–346.
Turcotte, D. L. and Schubert, G., 1982, Geodynamics Applications of Continuum Physics to Geological Problems: John Wiley & Sons, New York, 450 p.
Wise, D. U., 1972, Freeboard of Continents Through Time: p. 87–100in R. Shagam et al., (Eds.), Studies in Earth and Space Sciences, Geological Society of America Memoir 132.
Wise, D. U., 1974, Continental Margins, Freeboard and the Volumes of Continents and Oceans Through Time: p. 45–58in C. A. Burk and C. L. Drake (Eds.), The Geology of Continental Margins: Springer-Verlag, New York.
Worsley, T. R.; Nance, D.; and Moody, J. B., 1984, Global Tectonics and Eustasy for the Past 2 Billion Years: Mar. Geol., v. 58, p. 373–400.
Worzel, J. L., 1974, Standard Oceanic and Continental Structure: p. 59–66in C. A. Burk and C. L. Drake (Eds.), The Geology of Continental Margins: Springer-Verlag, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dockal, J.A., Laws, R.A. & Worsley, T.R. A general mathematical model for balanced global isostasy. Math Geol 21, 147–170 (1989). https://doi.org/10.1007/BF00893212
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00893212