Fractal behavior in continental crustal heat production

Abstract. The distribution of crustal heat production, which is the most important component in the elucidation of continental thermal structure, still remains a theoretical assumption. In general the heat production values must decrease with depth, but the form of decrease of heat production in the crust is not well understood. The commonly used heat production models are: "block model", in which heat production is constant from the surface to a given depth and the "exponential model", in which heat production diminishes as an exponential function of depth. The exponential model is more widely used wherein sources of the errors are heterogeneity of rock and long wavelength changes due to changes in lithology and tectonic elements, and as such exponential distribution does not work satisfactorily for the entire crust. In the present study, we analyze for the first time, deep crustal heat production data of six global areas namely Dharwar craton (India), Kaapvaal craton (South Africa), Baltic shield (Kola, Russia), Hidaka metamorphic belt (Japan), Nissho pluton (Japan) and Continental Deep Drilling site (KTB, Germany). The power spectrum of all the studied data sets exhibits power law behaviour. This would mean slower decay of heat production with depth, which conforms to the known geologic composition of the crust. Minimum value of the scaling exponent has been found for the KTB borehole, which is apparently related to higher heat production of gneisses, however for other study areas, scaling exponent is almost similar. We also found that the lower values of scaling exponents are related to higher heat production in the crust as is the case in KTB. Present finding has a direct relevance in computation of temperature-depth profiles in continental regions.