Global Rates of Geologic Cycling: Tectonic Diffusion of Upper Crustal Lithosomes

• Published in: The Journal of geology Vol. 120; no. 2; pp. 121 - 133
• Main Authors: Gombosi, David J., Wilkinson, Bruce H.
• Format: Journal Article
• Language: English
• Published: Chicago University of Chicago Press 01-03-2012; University of Chicago, acting through its Press
• Subjects: Boundary conditions; Continental crust; Diffusion coefficient; Earth; Erosion; Frequency distribution; Geology; Granite; Isotopes; Plate tectonics; Rocks; Subsidence; Tectonic uplift; Tectonics; United States > US
• ISSN: 0022-1376; 1537-5269
• DOI: 10.1086/663974

Age frequency distributions of various rock types now exposed at Earth's surface primarily reflect characteristic crustal depths at which they originate and the cumulative influence of vertical tectonic movements that displace them. Abundances of mid- to upper-crustal lithosomes increase rapidly to some modal age and then gradually decrease with increasing age. Paucity of exposures younger than the modal age reflects an intrinsic interval of geologic time needed for tectonic movements to exhume rock units, while increasing rarity of exposures older than the modal age reflects the overall dispersion (uplift and erosion, subsidence and burial) from initial lithosome positions relative to Earth's surface. We develop a random-walk model that describes the geologic cycling of crustal rock as a tectonically driven diffusive system because, at a globally averaged spatial and temporal scale, tectonic subsidence/burial and uplift/erosion are essentially random processes. From this, we produce solutions to the diffusion equation with an appropriate source term and boundary conditions that predict the crustal distribution of lithosomes in time and depth. We next use diffusion of implanted isotopes and trace elements as a computational analogue for the diffusion of crustal lithosomes on a tectonic scale. Both comprise random dispersion within systems with an absorbing boundary, and either is represented by one-dimensional diffusion. We use analytical solutions from atomic diffusion studies to derive a “tectonic diffusion” coefficient that describes the movement of lithosomes in time-crustal depth space. Tectonic diffusion coefficients from best-fit approximations to age frequency distributions of porphyry copper deposits, globally exposed granite plutons, North American granite plutons, and dated samples of U.S. granitic rock, expressed asD(m2/s), are 10−8.68, 10−8.22, 10−8.60, and 10−8.18, respectively. As context for these values, diffusion coefficients in dilute aqueous Earth surface temperatures are on the order of 10−8to 10−9m2/s, while gaseous diffusion coefficients at Earth surface temperatures are on the order of 10−5m2/s. Tectonic dispersion of crustal rock bodies relative to Earth's surface occurs at rates that are approximately the same as those in fluids over comparable ranges of temperature and pressure.