Determination of Curie Point Depth, Heat Flow and Geothermal Gradient from High Resolution Aeromagnetic Data around Lamurde Area, Adamawa State, North-Eastern Nigeria

Analysis of high resolution of aeromagnetic data was carried out over Lamurde, Adamawa state north-eastern Nigeria to determine the Curie point depth (CPD), heat flow and geothermal gradient. The aeromagnetic data used for this work was obtained at Nigerian geological survey agency, the total magnetic intensity was processed to produce the residual magnetic map which was divided into 4 overlapping blocks, each block was subjected to spectral analyses to obtain depths to the top boundary and centroid, while depth to bottom of the magnetic sources was calculated using empirical formula. The depths values obtained were then used to assess the CPD, heat flow and geothermal gradient in the area. The result shows that the CPD varies between 9.62 and 10.92 km with an average of 10.45 k, the heat flow varies between 150.73 and 132.78 mWm∙ ̊C with an average of 139.12 mWm∙ ̊C and the geothermal gradient in the study area varies between 12.16 and 15.67  ̊C/km with an average of 13.39  ̊C/km. In view of the above results, the high heat flow may be responsible for maturation of hydrocarbon in Benue Trough as well as responsible for the lead Zinc Mineralization. Again by implication, Lamurde area can be a good area for geothermal reservoir exploration for an alternative source for power generation.

Several studies have shown that magnetic data can be used to determine the thermal structure of the earth's crust in various geologic environments [1] [2] [3], for example, dominant magnetic minerals in the earth crust change from being ferromagnetic to paramagnetic at a temperature known as Curie Point Temperature (CPT). Magnetite (FeZO 4 ) is the most common magnetic materials in igneous rocks and has an approximate CPT of 580˚C [4]. At temperature above CPT, the thermal agitation of the ferromagnetic rock material leads to the spontaneous alignment of the different domains in the minerals and becomes randomized to the point that ferromagnetic minerals become totally paramagnetic [5].
The surface lineaments around the study area and their influence on the hot springs manifestations have not been previously investigated. The depth to the Figure 1. Location/topographic map of the study area [10].

Geology of the Study Area
The geology of the area is made up of Precambrian basement complex rocks which are believed to be mainly of gneiss-migmatites complex remnants of meta-sediments and older granite. Deformation described as Augen gneisses due to their eye shaped structure.
The older granites of Nigeria are calc-alkaline in chemical composition. These are also granite rock seen to have intrude the basement complex. Analysis have shown that, older granite are muscovite, granite, biotite granite aplite, quartz diorite etc. they show weak alignment of constituent platy minerals which a times result to their weak foliation.
The Cretaceous sedimentary rocks, which include rocks of Dukul, Yolde and Bima sandstone formation [11], describe the Benue Trough was in details and suggests that the Cretaceous sediment belongs to the oldest sedimentary Bima Sandstone whose lower beds are more feldspathic than the higher beds. The Bima Sandstone which overlies the basement complex at the base of sedimentary succession was derived from granitic rocks [12]. The lower beds of the formation are invariably series of calcareous sandstone and shale which marks the transition from continental to marine shale with a number of limestone beds towards the base of the formation, known as Yolde Formation.
The Tertiary-Recent volcanic rocks in the study area consist of the basalts, trachyte, rhyolite, and newer basalts of eastern arm of Cameroon volcanic line.
[13] discussed the events of volcanisms in the Benue Valley, and the Adamawa basement, which was compared with that of the Cameroon volcanic line. In this area the volcanic rocks are dominantly basalts. Open Journal of Geology Stratigraphically, the basement complex rocks are the oldest and the Quaternary alluvium deposit being the youngest which formed mainly from the weathered rocks dominating the study area ( Figure 2).

Materials and Methods
The data for this study is a high resolution aeromagnetic data obtained from Nigeria geological survey Agency [15]. The total magnetic intensity data was processed to produce residual magnetic map. This data was divided into overlapping blocks to carry out spectral analysis, which was then used to obtain the depths to top boundary and Centroid. Steps for determining depth to top bound and centroid has been discussed extensively by several authors [16] [17] [18] [19].
The analysis was done using computer software (Oasis Montaj) and Mat lab designed for analysis of potential field data. In this research, the spectral analysis To carry out the analysis, the initial step according to [6] was followed to estimate the depth to the centroid (Z 0 ) of the magnetic sources from the slope of Figure 2. Geologic map of the study area (after [14]).
where P(K) is the radially averaged power spectrum of the anomaly / / K is the spatial wave number and A is a constant.
The second step was to estimation of the depth to the top boundary (Z t ) of the magnetic source from the slope of the line with the second wave length.
( ) ( ) where, B is a sum of constants independent of / / K . The basal depth (Z b ) of the magnetic source is then computed from the equation: The obtained basal depth (Z b ) of a magnetic source is assumed to be equal to the CPD.
Analysis of CPD is one of the methods used to estimate the temperature gradient and the heat flow in the crust. Heat flow is defined by Fourier's Law as: where Q is the heat flow and d 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 dT/dZ is constant. Accordingly, the Curie temperature; can be obtained from the Curie Point depth (Z b ) and the thermal gradient dT/dZ using the following equation: Equations (4) and (5) give a relationship between the CPD (Z b ) and the heat flow (Q) as: In Equation (6), the Curie point depth is inversely proportional to the heat flow. In this research, the Curie Point Temperature of 580˚C and thermal conductivity of 2.5 mWm −1 •˚C −1 as average for igneous rocks was used as Standard.
In order to calculate the thermal gradient and heat flow in the study area, Equations (5) and (6) were used.

Discussion of Results
Having examined both the TMI and the residual map of the study area ( Figure 3 and Figure 4), it is observed that, the study area is made up of magnetic high and magnetic low signatures. The magnetic high observed on the TMI (Figure 3)   ley. However, low magnetic area is in the south eastern part of Figure 4 while the high magnetic areas spread across the study area. This can be related to the differences in depth to top boundary and centroid in the study area as obtained.
The average power and wave number spectra for each of the four overlapping blocks were calculated and used to estimate the CDPs ( Figure 5). The right-hand side of high-wave-number portion of the spectra which was used to estimate the depth to top boundary of the magnetic sources (Z t ), while the left-hand side indicated the slope of the lower-wave-number-scaled spectra, which was also used to estimate the depth to centroid (Z 0 ) of the magnetic sources.
The results from the analysis and the one obtain from empirical formula are shown on  [20], when the CPD results is  and in addition to that the shallow CPD and high heat flow is responsible for some hot springs in Lamurde and environs.

Conclusions
The high resolution aeromagnetic anomaly data over Lamurde and Environs, It is known that geodynamics processes are mainly controlled by the thermal structure of the earth crust; therefore, this study is anticipated to contribute significantly to the quantitative appraisal of the CPD, heat flow and geothermal gradient in Lamurde and Environs.