DETERMINATION OF THE CURIE POINT DEPTH, THERMAL GRADIENT AND HEAT FLOW OF PARTS OF CENTRAL AND NORTH-EASTERN NIGERIA USING SPECTRAL ANALYSIS TECHNIQUE

Radially power spectrum was applied to the aeromagnetic data covering an area 36,300km 2 and bounded by latitudes 7.5 o N and 11.5 o N and longitudes 7.5 o E and 10.5 o E., divided into 35 square blocks (with 50% overlapping and approximately 64 by 64 data points) and each block analysed using the spectral centroid method to obtain depth to the top, centroid and bottom of magnetic sources. The result shows that the curie point depths, range from 17.711km to 34.34km, with a mean value of 26.21km, geothermal gradient, range from 16.89 0 C km -1 to 32.75 0 C km -1 , with a mean value of 22.83 0 C km -1 and heat flow, range from 42.22 mWm -2 to 81.87 mWm -2 , with a mean value of 57.07 mWm -2 . These results correlate with the existing geothermal and geo-tectonic signatures of the area. Hence, the possibility of the existence of geothermal resources in the study area and its possible exploration is not far fetch.


Introduction
The Curie point depth is the theoretical surface where ferromagnetic minerals are converting to paramagnetic minerals and it is assumed to have a temperature of approximately 580 0 C , above which the former loses its magnetism and can be considered an indicator of the bottom of a magnetic crust. Hinze et al., 2013, in the Laboratory experiments they carried out, showed that ferromagnetic materials lose their magnetism above the Curie temperature (580 °C) because the thermal energy is sufficient to maintain a random alignment of the magnetic moments of the iron minerals. Also, Manea and Manea, 2011 opined that, an estimate of the bottom of magnetized crust represents a direct indicator of the Curie isotherm, and variations in the thickness of the magnetized crust can be explained as variations in temperature.
Magnetic minerals warmer than their Curie point depth temperatures are paramagnetic and are essentially nonmagnetic. The present study attempts to determine the depths to the top and bottom of the magnetized crust and to characterize the heat flow within the study area using Curie point depth (CPD) estimates from spectral analysis of aeromagnetic data. In this study, the spectral analysis technique will be utilized in order to estimate the CPD from aeromagnetic data over the study area bounded by latitudes 7.50'N to 11.50'N and longitudes 7.50'E to 10.50'E located within the central and northeast Nigeria ( Fig.1. and Fig. 2). The study area covered 36,300 km 2 and it is made up of the cretaceous Benue trough, Precambrian basement Complex, Sedimentary Basins (Gongola and Yola Basins), Jurassic younger Granites, and tertiary -recent sediments of the central and north-eastern Nigeria (Carter et al., 1963;Ekwueme, 1987;Kogbe, 1989;Farnbauer and Tietz, 2000;Reyment, 1965;Adelana et al., 2008). Also, two prominent Hot Springs are located within the area, Wiki hot spring in Yankari, Bauchi state and Akiri hot spring in Awe, Nasarawa state ( Fig.1.).
These warm springs makes the study very significant as they are clear indication of surface manifestation of geothermal activities within the study area. The possibility of harnessing geothermal resources in the area for economic and other purposes are not far fetch. This cannot be over emphasised, as the current over dependence of Nigeria on fossil fuel (oil and natural gas) has constituted an obstacle to the development of geothermal energy resources in the country and technological advancement. Nur et al., 1999;Obaje, 2009;Eletta and Udensi 2012;Salako 2012;Abdulsalam et al., 2013;Ikumbur et al., 2013;Igwesi and Umego 2013;Bello et al., 2017;Mohammed et al., 2019;Abdullahi et al., 2019, have done several works in different parts of the world both on local and regional scale using the magnetic method to determine the Curie point depth. Results obtained from this study will be invaluable in the development and a better understanding of the thermal and crustal structure of the study for geothermal exploration and exploitation.

Study Area
Surface Geothermal manifestation -Hot springs.

MATERIALS AND METHODS
The idea of using the magnetic method to determine the Curie point depth was based on the theory proposed by Bhattacharrya (1966) and developed by (Spector and Grant,1970;Blakely, 1988;Blakely, 1995;Tanaka et al., 1999) were they stated that geomagnetic anomalies collected from aeromagnetic data can be utilise to compute the curie point depth of an area. Bhattacharyya and Leu, 1975;Byerly and Stolt, 1977;Blakely and Hassanzadeh, 1981;Blakely, 1988;Smith and Braile, 1994;Tanaka et al., 1999;Chiozzi et al., 2005;Eppelbaum and Pilchin, 2006;Trifonova et al., 2009;Aboud et al., 2011, all used geomagnetic anomalies, which are retrieved from magnetic survey (Aeromagnetic data) to estimate the Curie point depth. The high resolution aeromagnetic dataset, which consist of sheet 102 -107, 124 -129, 145 -150, 166 -171, 187 -192, 208 -213, 229 -234 and 249 -254 utilized for this study was obtained as controlled maps of total magnetic intensity on a scale of 1:100000 compiled by the Nigerian Geological Survey Agency as a part of the nation-wide aeromagnetic survey between 2005 and 2010. The survey was flown in drape mode using real time global positioning system at a sensor mean terrain clearance of 80-100m. Traverse and Tie line spacing were 500m and 2000m respectively in NW-SE and NE-SW directions and the data were recorded at a sampling interval of 100m (NGSA, 2010) and stored in grid form. The study area is covered by forty-eight aeromagnetic maps of total-field intensity in ½º by ½º sheets. The data were initially pre-processed by Fugro Airborne Survey and Consultant teams, pre-processing operation included micro levelling, removal of cultural effects as well as filtering for noise contents. Total magnetic field intensity maps of the area comprising of the sheets (Fig. 3) were plotted using Oasis Montaj software (version 8.4). The composite colour map (Fig. 3) effectively displayed both long wavelength and short wavelength features. Oasis Montaj software (version 8.4) grid maths was used to generate the residual magnetic field intensity map Fig.4. from the total magnetic field intensity grid.

Curie point depth estimation
The technique for computing the depth extent of magnetic sources, which deals with the examination of the patterns of the anomalies, and provide the relationship between the spectrum of the magnetic anomalies and the depth to magnetic sources, by transforming the spatial data into frequency domain proposed by Spector and Grant (1970), was adopted in this study and has been proven to be reliable in the calculation of average depth to magnetic crust. It stipulates that, from graphs of the logarithms of the spectral energies for the various blocks, one can estimate the depth to Centroid (Z o ) of the magnetic source from the slope of the longest wavelength part of the spectrum Where {[ɸ ∆ (| |) 1/2 ]/| |} is the radially averaged power spectrum of the anomaly, /k/ is the wave number, and D is a constant and estimate the depth to the top boundary (Z t ) of that distribution from the slope of the second longest wavelength spectral segment (Okubo et al, 1985), Where [ɸ ∆ (| |) 1/2 ] is the radially averaged power spectrum of the anomaly, /k/ is the wave number, and B is the sum of constants independent of /k/. According to (Okubo et al., 1985;Tanaka et al., 1999), the basal depth (Z b ) of the magnetic source can be calculated from the equation, The obtained basal depth ( Z b ) of magnetic sources in the study area is assumed to be the Curie point depth (Bhattacharyya andLeu 1975 andOkubo et al., 1985).

Estimation of Heat flow and thermal gradient
The expression for the calculation of heat flow and thermal gradient values as derived from Fourier's law (Fourier 1955) is given by; Where q is the heat flow and λ is the coefficient of thermal conductivity. In this equation, it is assumed that the direction of the temperature variation is vertical and the temperature gradient is constant. According to Tanaka, et al, (1999), the Curie temperature (θ) can be obtained from the Curie point depth (Z b ) and the thermal gradient using the following equation; Provided that there are no heat sources or heat sinks between the earth surface and the Curie point depth, the surface temperature is 0°C and is constant. The Curie temperature depends on magnetic mineralogy. The commonest magnetic substance in the earth is magnetite (Fe 2 O 4 ), with Curie temperature approximately 580°C (Nwankwo et al., 2011). From equation (4) and equation (5), the heat flow (q) can be express as; In this equation, the Curie point depth is inversely proportional to the heat flow (Tanaka et al. 1999;Stampolidis, et al., 2005). In this research, the Curie point temperature of 580 °C and thermal conductivity of 2.5Wm -1 °C -1 as average for igneous rocks was used as standard (Nwankwo et al., 2011) in the study area. In order to compute the thermal gradient and heat flow, Equation (6) was utilised. See Table 1 below.
Radially power spectrum was applied to the residual magnetic field intensity grid map of the study area divided into 35 square blocks (each block covers a square area of 110 by 110km, which approximately represent a square grid of 64 by 64 data points, c1 -c2, (Fig.5)   110km each) from c1 to c35 at 50% overlapping.

Results and Discussion
Radially power spectrum was applied to the aeromagnetic data of the study area divided into 35 square blocks (with 50% overlapping). Fig.6 shows the sample graphs of the logarithms of  Ln(P(k) 1/2 /(/k/)) Wavenumber/k/(rad/km)

Conclusion
In this research, high resolution aeromagnetic data has been used to investigate the present of anomalies and the curie point depth of the study area. The quantitative (Spectral analysis) interpretation technique was chosen to achieve the outlined objectives of this research. From (Fig.7.) the curie point depths are deeper in the south, southwest, northwest, and northeast of the study area and shallower in the extreme northeast, southeast and part of the west. From Fig.8., the thermal gradient tends to be higher mainly in the north, central and extreme southeast of the study area and lower in most of the south, extreme southwest and extreme northwest. From Fig.9, the heat flow tends to be higher mainly in the north, central and extreme southeast of the study area and lower in most of the south, extreme southwest and extreme northwest. The above characteristics of these areas according to Stein and Stein (1994) and Tanaka et al., (1999), reveals that, they might probably be good sources for geothermal and thereby recommended for both geothermal exploration and exploitation.

Availability of data and materials
Not applicable