Radiogenic Heat Production

The abundances of naturally radioactive elements in the Earth crust constitute a large heat source to the surface heat flow, which is the density of outflow of heat from the Earth interior. Because radioactive heat sources are of first-order control to geotherms of the lithosphere, their quantification laterally and vertically is an essential goal of heat-flow analyses. Especially for the continental lithosphere, which is of extreme complexity in composition compared to oceanic lithosphere, knowledge of the distribution of radiogenic elements is essential when calculating geotherms. This lithosphere includes significant radiogenic heat production and comprises, in the upper crust, on average about 40% of total surface heat flow. An extreme example from the Variscan Erzgbirge (Germany) shows elevated surface heat flows (90-110 mW/m²) in Variscan granites, which are on average between 5 and 8 km thick. This uppermost, thin part of this crust alone produces almost half (40-50%) of the surface heat flow in Erzgebirge granite areas. Where granites occur, the entire crust contributes, on average, 70-90 mW/m² to the surface heat flow, which is some 2-4 times higher than would be expected from the estimates of the average composition of the continental bulk crust [Förster & Förster, 2000, JGR, 105, B12, 27,917-27,938]. Variability of radiogenic heat production in granitic rocks depends on a number of factors of which the following are most important: (a) type of granite, (b) degree of fractionation, and (c) intensity of alteration. In the study of Variscan Erzgebirge granites, observations were made that can be generalized for crustal studies.
All natural radioactive isotopes generate heat to a certain extent, but only the contributions of the decay series of ²³⁸U, ²³⁵U, ²³²Th, and of the isotope ⁴⁰K are geologically significant. The radiogenic heat production rate (A) used in geothermal studies is a scalar and isotropic petrophysical property independent of in situ temperature and pressure. It is calculated using the concentrations (c) of U, Th (in ppm), and K (in weight percent) in a given sample, the heat production constants for U, Th, and K (9.52 W/kg, 2.56 W/kg, and 3.48 W/kg, respectively), and the density ρ [kg/m³] of the rock [Rybach, 1988]:

A [µW/m³] = 10^-5 ρ (9.52 c_U + 2.56c_Th + 3.48c_K)

The analytical methods of determining U, Th, and K at the GFZ Potsdam comprise:
 

• High-precision analytical techniques using homogenized rock powders (PB 4.2). Potassium can be determined conventionally by wavelength-dispersion X-ray fluorescence spectrometry using fused lithium tetraborate discs. Th and U can be analyzed by inductively coupled plasma-mass spectrometry (ICP-MS; Perkin-Elmer/Sciex Elan Model 500) according to the method and with the precision and accuracy outlined by Dulski [1994]. Th and U in metamorphic rocks also can be measured by ICP-MS (Fisons/VG Plasma Quad PQ 2+) as described in Govindaraju et al. [1994]. The analytical precision for both ICP-MS methods generally is better than 5 %.
• The radiogenic heat production rate of subsurface rocks also can be determined indirectly from well logs either from a spectral gamma-ray log (GRS) or from an integrated gamma-ray spectrum (GR). For this purpose, the empirical relationship between heat production and GR readings (in API units) by Bücker & Rybach [1996] can be used:

A [µW/m³] = 0.0158 (GR [API] - 0.8)

The equation is based on 160 data comparisons made in granite, gneiss, amphibolite, basalt, and carbonate. Data cover the range from 0 to 350 API and 0.03 - 7.0 µW/m³. The equation gives estimates of A within about ± 0.1 µW/m³.