Distribution of Radioactive Elements and Their Relation to the Radiogenic Heat Production at Jabal Kharazah Area, North Eastern Desert, Egypt

A map of radiogenic heat production RHP was constructed from airborne spectral gamma-ray data of Jabal Kharazah area, North Eastern Desert, Egypt. The study area possesses a range of RHP varying from 0.2 to 5.7 μW/m-3 with an average value 1.38 μW/m-3, while the standard deviation value is 0.7 μW/m-3. The maximum values are associated with the acidic rocks in the northeast, southeast and a small portion in the northwest zones. About 68% of the readings are higher than the average RHP value in the area, thus Jabal Kharazah area can be considered as heat production area due to the relatively high radioactive mineral concentrations. There are excellent relationships between the derived RHP and the three radioactive elements, Uranium (eU), Thorium (eTh) and Potassium (K).


Introduction
Jabal Kharazah area is located in the North Eastern Desert of Egypt. The study area is mainly covered by the Precambrian basement rocks as well as Cretaceous and Quaternary sediments as shown in Figure 1. This area enclosed Wadi Dara area which was characterized earlier as radiogenic heat producing area (Aziz, 2014). Radiogenic heat production RHP rate is a physical property defining the amount of heat liberated in a unit time per unit volume of rock by the decay of unstable radioactive isotopes; in unit of μW/m −3 (Clauser, 2011). During radioactive decay, Figure 1. Location and geologic map of Jabal Kharazah area, North Eastern Desert, Egypt after (Conoco, 1987(Conoco, , 1988. mass is converted into energy, except for the tiny amount associated with the antineutrinos and neutrinos generated in β−− β+− decay or electron capture. Respectively, all of this energy is converted into heat (Clauser, 2011).
RHP in crustal rocks is dominated by contributions from three radioactive elements, namely uranium, thorium, and potassium. These have long half-life times, comparable to the age of Earth, sufficient abundances in rocks and significant proportions of their emission are fully converted to heat within the rocks. (Pollack & Chapman, 1977) showed that RHP contributes about 45% of the surface heat flow observed over the continents, while (Lachenbruch, 1970), (Swanberg, 1972) and (Lowrie, 1997) showed that its magnitude exponentially decreases with depth. RHP is high in the upper crust and can be estimated as a function of crustal age at any depth within the crust. In contrast, RHP is always low at the mantle reaching 1 -2 μW/m −3 mostly due to the total heat flow. The main purpose of this paper is to provide new insights on the geothermal setting of the Jabal Kharazah area based on the existing airborne gamma-ray data. We attempt to map surface RHP from the airborne gamma-ray data. RHP can be used for several purposes (Bücker & Rybach, 1996). It can be used for explanation of temperature variations with depth and interpretation of existing heat flow variations. Also it can be used in selecting suitable new sits for making heat flow and/or heat production measurements.

Geologic Setting
The study area is composed of different exposures rock units which extend from Precambrian to Quaternary sediments. The exposed Precambrian rocks of the study area are sorted from old to recent as follow: metagabbro, intrusive metagabbro, metavolcanics, metasediments, Hammamat sediments, older granite, older granite (calc-alkaline), younger granite and Dokhan volcanics, while the Cretaceous rocks are sorted in the same manner as Malha Formation, Wadi Qena Formation, Galala Formation, Umm Omeiyid Formation and Hawashiya Formation, also the western Gulf of Suez Formation is exposed and represents the Tertiary exposed rocks. Finally, the Quaternary sediments are composed of wadi sediments and Quaternary conglomerates. Complexity of the structure of the study area is tightly related to the regional structures in the North Eastern Desert affecting faults and fractures trending NNW-SSE, NNE and ENE-WSW according to (Conoco, 1987(Conoco, , 1988.

Geophysical Data
The study area was surveyed by measuring the spectrometric data using NaI crystals, producing maps of TC in (Ur), eU in (ppm), eTh in (ppm) and K in (

Radiogenic Heat Production
The main interior sources of heat in Earth are the heat content of the primitive Earth directly after formation due to gravitational shrinkage and the decay of unstable radioactive isotopes. The radiogenic decay of the unstable isotopes of uranium (238U, 235U), thorium (232Th) and potassium (40K) delivers the largest internal source of heat; these radionuclides are enriched in the Earth's crust and mantle (McDonough & Sun, 1995;Jaupart et al., 2007;Stacey & Davis, 2008). In this study, an attempt is presented to produce surface radioactive heat production map using the airborne spectral gamma-ray data.
Calculating RHP Rate RHP has been calculated from concentrations of radio-elements measured in the laboratory (Fernàndez et al., 1998) and directly from gamma-ray logs (Bücker & Rybach, 1996). Also, radioactive heat production has been estimated from airborne gamma-ray data (Thompson et al., 1996;Salem et al., 2005). Heat production of a rock is the total heat produced by the radioactive isotopes of U, Th, and K. It is defined as the quantity of heat produced by radioactivity in unit volume of the rock per unit time, and is expressed in μW/m −3 . It can be estimated using the following relation after (Rybach, 1986): RHP (μW/m −3 ) = ρ(0.0952 CU + 0.0256 CTh + 0.0348 CK) where ρ is the dry density of rock (g/cm 3 ) and CU, CTh and CK are the concentrations of U and Th in ppm and K in % respectively. Average density for each rock unit is presented in (Table 1) after (Shaaban, 1973). Besides, the measurements of radioelements with each rock unit eU, eTh and K which are used to cal-culate the radioactive heat production. The resulted data then interpolated using Kriging method and contoured producing a map which represents the spatial distribution of RHP within the studied area and facilitates its comparison with other maps. In order to get the best results for delineating the surface radioactive heat production in the study area, the geologic map is prepared and re-projected by outlining different rock units and subsequently estimating the radioactive heat production of each rock unit. The surface radioactive heat production ( Figure 6) represents the final product, which displays the anomalous radioactive heat production zones in the study area. (Hasterok et al., 2018) studied the plutonic-metaplutonic rocks, volcanic-metavolcanic rocks and sedimentary rocks using the same equation to calculate RHP. They found that the lowest calculated RHP value of the plutonic and metaplutonic rocks is (0.095 μW/m −3 ) related to the predotgabbro while the highest RHP value is (3.4 μW/m −3 ) related to the foid syenite. The lowest RHP value of volcanic and metavolcanic rocks is (0.54 μW/m −3 ) related to the komatiiet while the highest RHP value is (3.4 μW/m −3 ) related to the phonolite. The lowest RHP value of the sedimentary rocks is (0.31 μW/m −3 ) related to the quartz arenite while the highest RHP value is (11 μW/m −3 ) related to the oxide rock unit. Figure 6 illustrates the distribution of RHP values in the study area, where more

Data Interpretation
The RHP values distributed in the study area were calculated and shown in Fig By superimposing the heat production map ( Figure 6) over the geologic map ( Figure 1) it was possible to allocate and define characteristic RHP values pertaining each geologic rock unit. The data from TC, eU, eTh and K maps were taken into account. In this way the geologic boundaries between rock units were redefined.

Binary Relationships
Regression analysis or binary relation diagram is a form of predictive modelling technique which investigates the relationship between a dependent (target) and independent variable (s) (predictor). This technique is used for forecasting, time series modelling and finding the causal effect relationship between the variables. It might also considered as a set of statistical processes for estimating the relationships between a dependent variable (often called the "outcome variable") and one or more independent variables (often called "predictors", "covariates", or "features"). The most common form of regression analysis is linear regression, in which a researcher finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion. It can define the relation as strong from the correlation coefficient value (r) and the resulted equation can be used to derive a property from other. All RHP values were treated statistically to define the RHP values of different rock units to describe the different relationships. Simple straight line relationships were supposed, supported by the elongated relationships. Consequently straight line relations were calculated as shown in Figure 7. The straight line relationships represent a guide to the expected RHP values in other similar rock types in the surrounding areas.

Conclusion
The calculated RHP of Jabal Kharazah area are dependent on the radioactive minerals concentrations and the average rock densities. The RHP in the study area range from 0.2 to 5.7 μW/m −3 and the average value was calculated as 1.38 μW/m −3 . The highest values were recorded associated with younger granites, older granites and wadi sediments. More than 95% from the RHP values are more than the average of RHP in the crust (1 μW/m −3 ), while, about 68% from readings are more than the average RHP value in the study area (1.38 μW/m −3 ). The results of binary relationships between the RHP and the radioactive elements illustrate that these relations are strongly positive with eU, eTh and K for the studied rock units of Jabal Kharazah area.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.