# Geospeedometry

**Geospeedometry** is the science of measuring the timescales and/or temperatures of thermal events in the history of a metamorphic or igneous rock using diffusion profiles of elements within individual minerals. "*Geospeedometry"* refers to the *speed*, or timescale, of thermal events in geologic materials. The term first appeared in the literature in 1983;^{[1]} prior thermochronometric studies focused on diffusion of iron and magnesium in olivine provided the foundation for the field.^{[2]}^{[3]}^{[4]} Geospeedometry has since developed rapidly as further studies have experimentally calibrated the diffusivity of elements in various minerals.

## Diffusion Theory

Geospeedometry makes use of the temperature dependence of the chemical diffusion of elements between zones of a mineral grain. According to Fick's second law, the concentration of an element in one dimension across a diffusive interface is given by the partial differential equation

where

is the diffusion coefficient, or**D***diffusivity*(m^{2}s^{−1}) of the element in the mediumis the position (length)**x**is time**t**is the concentration of the element;**C***C(x,t)*is a function dependent on both length and time.

For a one-dimensional interface at *x =* 0 with a fixed concentration **C _{0}**,

where *erfc* is the complementary error function.

The diffusivity of an element in a medium is given by the temperature-dependent Arrhenius equation

where

is the maximum diffusivity at infinite temperature; also known as the pre-exponential factor (m**D**_{0}^{2}s^{−1})is the activation energy for diffusivity (J mol**E**_{A}^{−1})is the gas constant (J mol**R**^{−1}K^{−1})is absolute temperature (K)**T**

Given an experimentally determined * D_{0}* for a given element in a given substance, an empirical diffusion profile can be used to calculate the peak temperature or duration of a thermal pulse experienced by the substance.

## Methodology

Geologists apply diffusion theory to natural minerals in order to understand the thermal histories of igneous and metamorphic systems. Diffusion profiles of a given element are measured between growth zones of a single mineral, or at the interface between two different minerals. In order to measure a diffusion profile in a single crystal, geologists measure one-dimesional transects using high spatial resolution instruments such as the scanning electron microscope, electron microprobe, secondary ion mass spectrometry or nanoscale secondary ion mass spectrometry.

## Limitations

Because the solution to the diffusion equation requires a knowledge of both temperature and time duration of a thermal event, one must be independently constrained in order to measure the other. In geologic systems, neither the temperature nor time duration of thermal events is known a priori. An independent geothermometer must be used to constrain peak temperature in order to use geospeedometry to calculate the duration of a thermal pulse. Conversely, the duration of heating must be constrained independently using geochronology to estimate maximum temperatures.^{[5]} There is ongoing debate in the literature as to geospeedometry's utility to understand large scale magma storage and remobilization.^{[6]}

## References

**^**Lasaga, Antonio C. (1983-01-01). "Geospeedometry: An Extension of Geothermometry". In Saxena, Surendra K. (ed.).*Kinetics and Equilibrium in Mineral Reactions*. Advances in Physical Geochemistry.**3**. Springer New York. pp. 81–114. doi:10.1007/978-1-4612-5587-1_3. ISBN 9781461255895.**^**Buening, D. K.; Buseck, Peter R. (1973-10-10). "Fe-Mg lattice diffusion in olivine".*Journal of Geophysical Research*.**78**(29): 6852–6862. doi:10.1029/JB078i029p06852. ISSN 2156-2202.**^**Taylor, L. A.; Onorato, P. I. K.; Uhlmann, D. R. (1977-01-01). "Cooling rate estimations based on kinetic modelling of Fe-Mg diffusion in olivine".*Lunar and Planetary Science Conference Proceedings*.**8**: 1581–1592. Bibcode:1977LPSC....8.1581T.**^**Lehmann, J. (1983). "Diffusion between Olivine and Spinel: application to geothermometry".*Earth and Planetary Science Letters*.**64**: 123–138. doi:10.1016/0012-821x(83)90057-2 – via Elsevier Science Direct.**^**Barboni, Mélanie; Boehnke, Patrick; Schmitt, Axel K.; Harrison, T. Mark; Shane, Phil; Bouvier, Anne-Sophie; Baumgartner, Lukas (2016-12-06). "Warm storage for arc magmas".*Proceedings of the National Academy of Sciences*.**113**(49): 13959–13964. doi:10.1073/pnas.1616129113. ISSN 0027-8424. PMC 5150383. PMID 27799558.**^**Miller, Calvin F. (2016-12-06). "Eruptible magma".*Proceedings of the National Academy of Sciences*.**113**(49): 13941–13943. doi:10.1073/pnas.1617105113. PMC 5150370.