### Radiogenic Heat Production  
Rocks contain variable amounts of primordial radionuclides that generate heat to a certain extent, due to the conversion of the radioactive decay mass to energy. These include \({}^{40}\)K and the radioisotopes of the decay series of \({}^{238}\)U, \({}^{235}\)U, and \({}^{232}\)Th.  
The heat generated by the natural radioactive decay in the Earth's crust constitutes a substantial portion of the terrestrial heat flow. Some authors [21; 22] have proposed that the radiogenic heat production of granite rocks (RHP in \(\mu\)W\(\cdot\)m\({}^{-3}\)) can be calculated by taking into account the heat generation constant (i.e., the amount of heat released per unit time and per gram of U, Th, and K) and the uranium, thorium, and potassium concentrations (\(C_{U}\), \(C_{Th}\), and \(C_{K}\), respectively) in a rock by using the following expression:  
\[\mathrm{RHP}=10-5\,\rho\,\left(9.52\ C_{U}+2.56\ C_{Th}+3.48\ C_{K}\right) \tag{1}\]  
where \(\rho\) is the density of the rock (kg m\({}^{-3}\)) and \(C_{U}\), \(C_{Th}\), and \(C_{K}\) are the concentrations of uranium (weight ppm), thorium (weight ppm), and potassium (weight %), respectively.  
The heat production unit (\(\mu\)Wm\({}^{-3}\)) may be converted into heat generation units (1 HGU = 10\({}^{-13}\) cal cm\({}^{-3}\) s\({}^{-1}\)) by the equivalence 1 HGU = \(\mu\)W m\({}^{-3}\) estimated for the Gansboden granite gneiss at the Guspsibach heat flow site in the Central Alps of Switzerland [23]. The radioelement concentration (Ur) is calculated by Ur equivalents: 1 ppm of U in equilibrium (1 ppm eU) = 1 Ur; 1 ppm of Th equilibrium (1 ppm eTh) = 0.5 Ur; 1 wt % of K = 2 Ur [24; 25].  
The RHP is a scalar petrophysical property independent of in situ temperature and pressure. Both \({}^{232}\)Th and \({}^{238}\)U are the most important radionuclides that contribute to heat production (about 85%), while \({}^{40}\)K contributes to a lesser extent [17]. They also give rise to daughter radionuclides present in the Earth's crust rocks, with the U and Th decay chains being the most geologically significant in such heat production.  
There are several methods that allow determination of the radioisotope concentrations in rocks for assessing the rate of heat production. Some laboratory analytical techniques indirectly assess the activity concentrations in rock samples, namely, inductively coupled plasma atomic emission spectrometry and mass spectrometry, instrumental neutron activation analyses, and X-ray fluorescence spectrometry. Low background gamma-ray spectrometry directly estimates the activity concentrations of such radionuclides [22; 26]. The latter technique is the only one that gives direct indication of any possible disequilibrium in the U and Th decay chains. However, disequilibrium is infrequent in rocks [27].  
It is also possible to assess the concentrations of radioisotopes by handheld, carborne, and airborne gamma-ray spectrometry. These techniques are used for estimating the concentrations of radioelements in the surface rocks, and borehole gamma-ray spectrometry is used to acquire a continuous spectrum of the U, Th, and K concentrations of subsurface rocks [28]. This kind of field method allows a quick, albeit imprecise, assessment of the radioisotope contents of rocks, making it possible to assess the heat production from these data [29]. Laboratory analyses require fieldwork, sampling, and analyses that are costly and time-consuming. However, portable gamma-ray spectrometry (GRS) can be a quick and cheap procedure. When GRS measurements are carried on rock outcrops, a 2\(\pi\)r geometry (plain area) is needed to avoid over- or underestimation of the radioisotopes of K, U, and Th [29].