Introduction

Magnetic methods are employed for direct and indirect mapping of hydrocarbon reservoirs, geological structures, and thermal state of the crust (Glenn and Badgery 1998). The method measures variations in the magnitude of the earth’s magnetic field resulting from the magnetic properties of the underlying rocks. Due to the inaccessibility and inability to cover a wide range of areas, airborne magnetic survey has been applied to acquire subsurface data in the past decades. Such data gives information about the Depth to Bottom of Magnetic Sources (DBMS), location, and extent of sedimentary basins that are required in understanding the thermal distribution in the area. Suitable information about the thermal structure of the lithosphere is necessary because of an extensive multiplicity of geodynamic examinations. These examinations include rock deformation, hydrocarbon maturation, mineral phase boundaries, rates of chemical reactions, electrical conductivity, magnetic susceptibility, seismic velocity, and mass density (Ross et al. 2006) and information about the thermal structure could only be obtained if the DBMS is known. The DBMS or Curie point depth (CPD) is the temperature at which magnetic minerals lose their ferromagnetism. Various ferromagnetic minerals have differing Curie temperatures, but the Curie temperature of titano-magnetite, the most common magnetic mineral in igneous rocks, is in the range of about 580 °C (Nwankwo et al. 2008). Magnetic minerals hotter than their Curie temperature are paramagnetic and, from the viewpoint of the earth’s surface, are essentially nonmagnetic. Thus, the Curie temperature isotherm corresponds to the basal surface of magnetic crust and can be obtained from the lowest wavenumbers of magnetic anomalies, after removing the appropriate International Geomagnetic Reference Field (IGRF) from the aeromagnetic data (Ross et al. 2006). DBMS is an important parameter in understanding the temperature distribution in the crust and the rheology of the earth’s lithosphere, which can be derived from aeromagnetic data and can be used as a representation for temperature at depth (Ravat et al. 2007; Bansal et al. 2011; Nwankwo 2015).

Many studies around the world have shown that DBMS could be estimated from the analysis of aeromagnetic data; these include Okubo et al. (1985), Tanaka et al. (1999), Ross et al. (2006), Ravat et al. (2007), Bansal et al. (2011, 2013), Gabriel et al. (2011), Nwankwo et al. (2011), Kasidi and Nur (2012, 2013), Guimaraes et al. (2013), Nwankwo (2015), Nwankwo and Shehu (2015), and Abraham et al. (2015). This research work therefore presents an evaluation of DBMS, geothermal gradients, and heat flow values in part of Chad Basin, northeast Nigeria from the recently acquired high resolution aeromagnetic (HRAM) data using spectral analysis method. There are minimal records of studies on geothermal structure in Chad Basin using low resolution aeromagnetic data but no record of previous research work done using HRAM exist within the basin, though a few of them were accounted for in the upper and lower Benue trough surrounding the basin. These include Osazuwa et al. (1981) who used two profiles of gravity data in the upper Benue trough to estimate a sedimentary thickness, which is equivalent to the Depth to the Top of Magnetic Source (DTMS) varying between 1.0 and 2.2 km. Nur et al. (1999) estimated the CPD of the upper Benue trough to be varying between 23.80 and 28.70 km. Nwankwo et al. (2009) interpreted 14 well log data from an oil well in the Nigeria sector of Chad Basin and estimated the heat flow trend in the basin to be between 63.6 and 105.6 mW/m2. Abubakar et al. (2010) also analyzed and interpreted nine aeromagnetic maps covering the upper Benue trough and obtain depth to causative body to be between 2.40 and 8.09 km. Kurowska and Schoeneich (2010) estimated the geothermal gradient values ranging from 11.37 to 58 °C/km using thermal data collected during pumping tests in water wells within the basin. Kasidi and Nur (2012) interpreted aeromagnetic data over Sarti in Northeastern Nigeria and computed CPD values varying between 26 and 28 km, geothermal gradient varying between 21 and 23 °C/km, and heat flow varying between 53 and 58 mW/m2. Lawal et al. (2015) also obtained the DTMS over Maiduguri, northeastern part of Chad Basin to be between 1.50 and 4.20 km. Abraham et al. (2015) estimated an average DBMS in Wikki Warm Spring (WWS) located in parts of Benue Basin, which links up the Chad Basin in the north to be 10.72 km with an average thermal gradient of 54.11 °C/km and average heat flow values of 135.28 mW/m2. An estimate of the DBMS obtained from this work would supplement the available geophysical information within the area and also contributes immensely in understanding the geothermal structures and geodynamic processes in the basin.

Location and geology of the study area

The area of study, which is a part of the sedimentary Chad Basin, Nigeria, is bounded by northings 1,200,000 and 1,500,000 mN and eastings 769,000 and 1,049,900 mE (Fig. 1). It covers states such as Bornu, Yobe, and Jigawa. It is situated at the northwest of Northeastern Nigeria. Olugbemiro et al. (1997) reported that the Nigerian sector of Chad Basin is bounded to the east by the Mandara Mountains and in the south by the Benue trough and Biu Plateau. It encompasses the southeastern portion of the basin, which is situated in a tectonically energetic area with features, which spreads northwest to the Air Plateau and Southwest towards the Benue trough, the third and unsuccessful arm of a three-layered rift joint developed as a result of the separation of African and South American plates in early Cretaceous times (Carter et al. 1963).

Fig. 1
figure 1

Map of Nigeria showing the study area, areas of basement complex, and sediments

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Geologically, the basin, which houses the study area, has been described by many authors (Idowu and Ekweozor 1993; Nur 2001; Obaje 2009; Odebode 2010, etc.). This basin is believed to be a broad sediment-filled depression stranding Northeastern Nigeria and adjourning parts of Chad Republic. The sedimentary rocks have a cumulative thickness of over 3.6 km and consist of thick basal continental sequence and transitional calcareous deposit. It combines with the Sokoto Basin in the west of the Damergou gap between the Air and Zinder massifs (Wright et al. 1985). The generalized stratigraphic column of the Basin has been described by Odebode (2010) to be sedimentary sequence made up of Chad Formation, Kerri-Kerri Formation, Gombe Formation, Fika Shale, Gongila Formation, and Bima Sandstone. Sedimentation began in Chad (Bornu) Basin during Upper Cretaceous (probably Uppermost Albian) when over 1000 m of continental, sparsely fossil-ferrous, unwell-organized intermediate to rough-grained, feld-spathic sandstone which can be regarded to as the Bima Formation was deposited uncomfortably overlain the Precambrian basement rocks. Other sedimentary stratigraphy sequences were formed as a result of oceanic intrusion into Chad drainage and extensional deformation that occurred in the basin.

The area is marked by two distinct climatic conditions. The rainy season lasts usually from May to September with an average temperature of 30–46 °C depending on the rainfall pattern for the particular year. The dry season heralded annually by the dry, dusty Harmattan winds which blows off the Sahara Desert occurs between October and April with an average temperature of 30–37 °C. The mean annual rainfall is 7.8 mm and a relative humidity of an about 50–80%. The vegetation, which is predominantly of the Savannah-type, is divided in to two zones: Sahel Savannah towards the north and Sudan Savannah to the south.

Materials and methods

HRAM data acquisition

Thirty-two HRAM maps (sheet numbers 20, 21, 22, 23, 24, 25, 25A, 41, 42, 43, 44, 45, 46, 47, 63, 64, 65, 66, 67, 68, 69, 70, 86, 87, 88, 89, 90, 91, 92, 112, 113, and 114) and contours of Total Magnetic Intensity (TMI) published by the Nigerian Geological Survey Agency (NGSA) airborne geophysical series flown between 2004 and 2010 on a scale of 1:1000, 000 were acquired and analyzed in this study. The acquisition, processing, and compilation of the these data, which was partly financed by the Federal Government of Nigeria and the World Bank as part of major project known as the Sustainable Management for Mineral Resources Project, were carried out by Fugro Airborne Surveys Ltd. Johannesburg. The survey was acquired from an aircraft flown at a height of 80 m with 500-m line spacing, 80-m mean terrain clearance, and the tie line spacing of 500 m oriented in the NW–SE direction. Regional correction based on the IGRF (2005) was removed from the data. Reduction to the pole (RTP) correction was performed on the data. This is because total magnetic data contains both short and long wavelength anomalies, and by applying this correction, it will correct the spatial shift in DBMS (Li et al. 2013), the shape, and the peak of the magnetic anomalies over their causative sources (Saada, 2016). Therefore, RTP correction applied 0.7° declination and 1.6° inclination for this basin using an Oasis Montaj software, version 6. Also since DBMS is related to deep magnetic sources only and RTP magnetic anomalies comprise of effects of shallow and deep sources (Thebault et al. 2010), then effects of topography and shallow magnetic sources have to be removed from the data so that DBMS can be accurately estimated (Saada, 2016). In view of this, a low-pass filtering technique was adopted in this work (Abraham et al. 2015) and an interactive filtering in the Magmap program of Oasis Montaj software was used to remove and boost the effects of shallow- and deep-seated magnetic sources.

Calculating the DBMS

The application of centroid method to the aeromagnetic data is based on the derivation of an expression by Bhattacharyya and Leu (1977) for the power spectrum applied on the data over a single rectangular block generalized by Spector and Grant (1970) by assuming that the magnetic anomalies are due to an ensemble of vertical prisms. Nwankwo (2015) and Spector and Grant (1970) showed that the contributions from the depth, width, and thickness of magnetic source ensembles affect the shape of power spectrum. Therefore, Tanaka et al. (1999) described that two methods exist in obtaining the DBMS: the first method studied the shape of isolated magnetic anomalies (Bhattacharyya and Leu 1977) while the second examined the statistical properties of patterns of magnetic anomalies (Spector and Grant 1970). Both methods provide relationship between spectrum of magnetic anomalies and depth of a magnetic source by transforming the spatial data into frequency domain. Shuey et al. (1977) revealed that the second method is more appropriate for regional compilations of magnetic anomalies. Maus et al. (1997) specified that the area required to estimate the DBMS should not be less than few hundred kilometers.

The method used in this work for estimating DBMS is based on the spectral analysis of magnetic anomaly data which was described by Spector and Grant (1970). They obtained DTMS (Z t ) and centroid depth (Z 0) from the gradient of log power spectrum. Okubo et al. (1985) established a method in obtaining DBMS (Z b ) based on spectral analysis of Spector and Grant (1970). Following the technique offered by Tanaka et al. (1999), it was assumed that the layer extends indefinitely far in all horizontal directions. Depth to top bound of a magnetic source is small compared with the horizontal scale of a magnetic source and that magnetization M(x, y) is a random function of x and y. Blakely (1995) introduced the power–density spectra of the total field anomaly P ΔT :

$$ {P}_{\varDelta T}\left({k}_x,{k}_y\right)={\varPhi}_M\left({k}_x,{k}_y\right)\times F\left({k}_x,{k}_y\right) $$
(1)

Where:

$$ F\left({k}_x,{k}_y\right)=4\pi {C}_m^2{\left|{\varTheta}_m\right|}^2{\left|{\varTheta}_f\right|}^2{e}^{-2\left|k\right|{Z}_t}\Big(1-{e}^{-\left|k\right|{\left({Z}_b-{Z}_t\right)}^2} $$
(2)

and P M is power–density spectra of the magnetization, C m is proportionality constant, Z b and Z t are basal and top depths of the magnetic source. Θ m  and Θ f are factors for magnetization direction and geomagnetic field direction, respectively. This equation can simplified by noting that all terms are radially symmetric except |Θ m |2 and |Θ f |2. Also, Θ m and Θ f are constant. If M(x, y) is totally random and uncorrelated and P M (k x , k y ) is constant, then the radial average of P ΔT can be given as:

$$ {P}_{\varDelta T}\left(\left|k\right|\right)={A}_1{e}^{-2\left|k\right|{Z}_t}{\left(1-{e}^{-\left|k\right|\left({Z}_b-{Z}_t\right)}\right)}^2 $$
(3)

where A 1 is constant and k is the wavenumber. For wavelengths less than about twice the thickness of the layer, Eq. (3) can be written as:

$$ \ln \left[{P}_{\varDelta T}{\left(\left|k\right|\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right]=\ln {A}_2-\left|k\right|{Z}_t $$
(4)

where A 2 is a constant, and depth to the top bound of magnetic source can be obtained by fitting a straight line through the high wavenumber region of a radially average power spectrum of the magnetic anomaly.

Also, Eq. (3) can be rewritten as:

$$ {P}_{\varDelta T}{\left(\left|k\right|\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}={A}_3{e}^{-\left|k\right|{Z}_0}\left({e}^{-\left|k\right|\left({Z}_t-{Z}_0\right)}-{e}^{-\left|k\right|\left({Z}_b-{Z}_t\right)}\right) $$
(5)

where A 3 is a constant. At long wavelength, Eq. 5 is:

$$ {P}_{\varDelta T}{\left(\left|k\right|\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}={A}_3{e}^{-\left|k\right|{Z}_0}\left({e}^{-\left|k\right|\left(-d\right)}-{e}^{-\left|k\right|(d)}\right)\approx {A}_3{e}^{-\left|k\right|{Z}_0}2\left|k\right|d $$
(6)

where 2d is the thickness of the magnetic source. From Eq. 6, we can have:

$$ \ln \left\{\left[{P}_{\varDelta T}{\left(\left|k\right|\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right]/\left|k\right|\right\}=\ln {A}_4-\left|k\right|{Z}_0 $$
(7)

where A 4 is a constant, k is the wavenumber, and Z 0 which is the centroid of the magnetic source can be estimated by fitting a straight line through the low wavenumber region of the radially averaged frequency-scaled power spectrum. The DBMS can therefore be obtained using the relation (Okubo et al. 1985; Tanaka et al. 1999) as:

$$ {Z}_b=2{Z}_o-{Z}_t $$
(8)

Fractal-based methods of calculating the DBMS

The application of Eqs. (4) and (7) to aeromagnetic data set results in overestimation of centroid depth values due to the assumption of random and uncorrelated distribution of sources (Bansal et al. 2011; Abraham et al. 2015; Nwankwo 2015). Modifying these equations would result in scaling distribution of sources, which is equivalent to fractal distribution of magnetic sources and these modified methods are called fractal-based method of depth estimation (Bansal et al. 2011). For the fractal-based method, the radial average power spectrum of the magnetization ϕ m (k) follows the relation:

$$ {\phi}_m(k)\ \alpha\ {k}^{-\beta } $$
(9)

where β is the scaling exponent due to source distribution and its value depends on the lithology and heterogeneity of the subsurface (Bansal et al. 2011; Abraham et al. 2015). In this work, we choose 1.5 as the scaling component because the study area is a sedimentary terrain and this value is found to be appropriate (Bansal et al. 2011; Abraham et al. 2015; Nwankwo 2015). Therefore, in order to calculate the DBMS using fractal method, the power spectrum of Eqs. (4) and (9) can be combined so that the equation to be used in computing depth to the top of magnetic sources can be rewritten as:

$$ \ln \left({k}^{\beta }P(k)\right)={A}_2-2{kZ}_t $$
(10)

Also, combining Eqs. (7) and (9) gives the power spectrum for computing the centroid depth and this can be rewritten as:

$$ \ln \left({k}^{\beta}\frac{P(k)}{k^2}\right)={A}_3-2{kZ}_0 $$
(11)

From Eq. (8), the geothermal gradient is related to the DBMS as:

$$ \frac{dT}{dZ}=\raisebox{1ex}{${\theta}_c$}\!\left/ \!\raisebox{-1ex}{${Z}_b$}\right. $$
(12)

where θ c is the Curie temperature approximated to be 580 °C and \( \frac{dT}{dZ} \) is the geothermal gradient which could only be obtained if certain assumptions are true:

  1. 1.

    There are no heat sources or heat sinks between the earth’s surface and the DBMS.

  2. 2.

    The surface temperature is 0 °C.

  3. 3.

    The geothermal gradient \( \frac{dT}{dZ} \) is constant (Bansal et al. 2011; Nwankwo and Shehu 2015).

The heat flow q z can also be estimated using the Fourier’s equation (1955):

$$ {q}_z=k\frac{dT}{dz} $$
(13)

where k is the thermal conductivity and it is assumed to be 2.5 W/m °C for igneous rocks (Bansal et al. 2011; Nwankwo 2015).

Application to HRAM data set

For the purpose of this analysis, the TMI sheets listed previously were merged in to a composite map (Fig. 2) with magnetic anomaly values ranging from −138 to 220 nT. In order to evaluate the DBMS of the study area, the composite anomaly map must be divided into blocks or lengths of various dimensions in other to obtain the basal depth. Generally, many authors have divided magnetic anomaly map into overlapping blocks ranging from 40 × 40 to 320 × 320 km and publishable results have been obtained. However, the spectrum of the map contains depth information to a length of ((L)/2π) (Shuey et al. 1997). Although if the source bodies have bases deeper than length, the spectral peak occurs at a frequency lower than the fundamental frequency for the map and cannot be resolved using spectral analysis (Abraham et al. 2015; Saada 2016). In view of the above, we first apply the spectral analysis to the RTP map with removed short wavelengths of the study area with the dimension 277 × 385 km and give depth information about the bottom of magnetic source to be 44.10 km (Fig. 3). This depth has provided us the response of the deepest magnetic layer and has also reflected maximum spectral where the source bottom is detectable (Fig. 4). Secondly, the RTP map with short wavelengths removed was carefully overlapped (about 50% overlap) into 25 blocks covering 110 km by 110 km. The choice of the window size became necessary because of the complexity of the geology of the area and the need to sample more data point and preserve the spectral peaks (Okubo et la., 1985). In addition, Okubo et al. (1985) suggested that centroid depth estimation could be derived from data window as small as 40 × 40 km, but Ravat et al. (2007) said the window dimension of 40 × 40 km could only lead to estimates on shallow or intermediate layers and not the deepest layers. This window size was found to be appropriate for the purpose of obtaining satisfactory information about depth to the centre of magnetic source (Ravat et al. 2007; Nwankwo and Shehu 2015). The coordinates at the center of block which represent the sampled point were used for plotting the evaluated DBMS. The 2-D Fast Fourier Transform (FFT) was applied to each block (Eqs. 10 and 11) in order to convert the space domain grid data to the frequency domain. The DBMS (Z b ) are calculated by estimating the DTMS (Z t ) and centroid (Z 0) using (Eq. 8). The depth to the top (Z t ) and centroid (Z 0) of the magnetic source for each block were made by fitting a straight line through the high wavenumber and low wavenumber parts of the power spectrum and the scale wavenumber power spectrum, respectively. In view of the uncertainties from the slope of the straight line segment, we evaluated the standard errors from the Z t and Z 0 using the error definition of (Ian, 2014).

Fig. 2
figure 2

Composite map of total magnetic intensity (TMI) of the study area

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Fig. 3
figure 3

Reduced to pole (RTP) aeromagnetic map of the study area

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Fig. 4
figure 4

Radially average power spectrum for estimation of DBMS from the main grid of the RTP TMI (277 × 385 km)

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However, geothermal gradient and heat flow parameters were estimated using Eqs. (12) and (13).

Results and discussion

Result of DBMS obtained from the main grid 277 × 385 window shows a value of 44.10 km where an appearance of significant spectral maximum reflects that the bottom of magnetic source is noticeable (Fig. 4) with estimated geothermal gradient of 13.15 °C/km and the evaluated heat flow of the area is 31.56 mW/m2. With this result, it will be observed that the computed geothermal gradient and the heat flow values are closer to the lower bound range values obtained from the window size of 110 × 110 km. Also, the graphical plots of natural logarithm of the power spectrum and the scaled wavenumber power spectral against wavenumber were made for each of the overlapping 12 blocks in the study area. Figure 5a shows the plot of natural logarithm of the power spectrum against wavenumber and the gradient of the high wavenumber portion leads to the estimation of the depth to the top of magnetic sources (Z t ), while Fig. 5b shows the plot of natural logarithm of the scaled wavenumber power spectral against wavenumber and the gradient of the low wavenumber portion of the plot leads to the estimation of centroid method. Subsequently, the DBMS (Z b ) which is regarded as a proxy for temperature at depth was calculated using Eq. (8), while geothermal gradient and heat flow parameters were obtained using Eqs. 12 and 13. The results of the estimated depths for the 25 blocks are shown in Table 1. The DTMS ranges between 1.61 and 4.93 km with an average value of 2.93 km, the centroid depth ranges between 10.13 and 23.72 km with an average value of 15.82 km, and the DBMS values vary between 18.18 and 43.64 km with an average value of 28.70 km. In addition, the geothermal gradient was found to be varying between 13.29 and 31.90 °C/km with an average value of 21.98 °C/km and heat flow parameters vary between 33.23 and 79.76 mW/m2 with an average value of 54.93 mW/m2, respectively.

Fig. 5
figure 5figure 5figure 5

Examples of radially averaged spectral plots for estimation of DTMS (a) and centroid depth (b)

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Table 1 Estimated heat parameters
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The variation in the depth to the top of a magnetic source obtained from the study area has revealed a spatial relationship between the elevation and depression in the Precambrian basement complex and the overlying sediments. In exploring sedimentary basins, it is a general assumption that intrusive rocks within the crystalline basement complex are truncated by erosion at their surface. With this, the depth to the top of this basement is equal to the thickness of the sediments found in the area. But Wright et al. (1985) maintain that the minimum sedimentary thickness required to attaining a threshold temperature for the beginning of hydrocarbon maturation is 2.3 km. However, results of the sedimentary thickness obtained from this study are in agreement with previous research work carried out within the basin (Nur 2001; Afolabi 2011; Lawal et al. 2015) and has a value higher than 2.3 km. Hence, hydrocarbon exploration is said to be feasible in this part of the basin. Consequently, the present research reveals that DBMS/CPD is indeed reliant on the geological situation. Salk et al. (2005) and Nwankwo and Shehu (2015) reported that DBMS are shallower than 10 km for volcanic and geothermal fields, which are commonly associated with plate boundaries and geodynamics. However, DBMS ranging between 15 and 25 km are consequence of island arcs and ridges and deeper than 20 km in plateaus and trenches. Generally, units that comprise of high heat flow values correspond to volcanic and metamorphic regions because of high heat thermal conductivities. In addition, tectonically active regions affect the Curie depth and heat flow.

Figure 6 shows that DBMS values trend NE–SW with the shallowest (18 km) found in the northwestern portion of the basin, while deepest (> 40 km) is noticeable at the southern part of the basin. This deeper portion of the basin extends in to the Republic of Chad and Upper Benue trough where similar results have been obtained (Nur et al. 1999). They obtained a DBMS value ranging between 18 and 28 km in the Benue trough of north-central Nigeria. Also, Kasidi and Nur (2012, 2013) obtain a DBMS value ranging between 24 and 28 km in the basement complex terrain of Northeastern Nigeria. It will also be observed from the map that shallow DBMS are derivation of negative magnetization, which is found to be consistent with the low magnetic values of HRAM map (Fig. 2) and this is known fact that shallow CPD create negative magnetization (Salk et al. 2005). Generally, shallow DBMS values obtained from the study area, which corresponds to high heat flow values emphasizes the effects of large-scale tectonic event as a major influence on thermal history. Bansal et al. (2011) reported that potential regions for geothermal exploration are characterized by high heat flow, high temperature gradient, and shallow DBMS.

Fig. 6
figure 6

DBMS map of the study area (CI = 1.0 km)

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Figure 7 shows the heat flow map of the study area with high heat flow observed at the northwestern portion of the area (> 72 mW/m2) which correspond to high geothermal gradient (31.90 °C/km) and shallow DBMS (18.83 km) while low heat flow is observed at the central portion of the study area, which also correspond to low geothermal gradient and high DBMS. Nwankwo and Shehu (2015) reported that the minimum heat flow required for considerable generation of geothermal energy is close to 60 mW/m2, while values ranging from 80 to 100 mW/m2 and above indicate anomalous geothermal condition but these anomalous geothermal conditions were not observed in the study area. Areas observed with high flow values correspond to active volcanic and metamorphic rocks and can also be governed by deep magnetic mass that is yet to complete its cooling in association with young volcanism and faulted structures (Wright 1976). Jones (1975) also reported that regions of high geothermal gradient could lead to the generation of hydrocarbon at shallow depth, while regions of low geothermal gradient may not be viable for hydrocarbon exploration except at a greater depth. This is because geothermal gradient plays a major role in hydrocarbon generation; along with several other factors (e.g., rapid burial of organic debris in an oxygen-depleted environment), the right temperature needed to convert organic matters into hydrocarbon is necessary. The thermal regime in a sedimentary basin is one of the main factors affecting the formation and accumulation of hydrocarbons. The generation of hydrocarbon and the types produced are dependent on the temperature reached by the organic-rich source rocks during the burial history (Bachu and Burwash 1989). Also, since heat flow depends on the upwelling heat flow from the upper mantle where the oceanic crust is formed and more than 80% of the heat flowing to the earth’s surface is from the decay of radioactive elements (K, U, and Th) in the crust and mantle but the abundance of this heat is largely hosted in the continental crust. Therefore, low values of heat flow evaluated from the southern and eastern region of the area are due to the decreasing the thickness of the continental crust to the south along the transition zone towards the oceanic portion of the African plate.

Fig. 7
figure 7

Heat flow map of the study area (CI = 1.0 mW/m2)

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Conclusion

Evaluation of DBMS and heat flow parameters from the spectral analysis of the recently acquired TMI data of part of Nigerian sector of Chad Basin has been made. The study has therefore offered numerical information about the thermal structure, distribution, and rheology of Chad Basin, Nigeria, which can serve as a thermal index for the area. RTP and low-pass filtering technique were performed on the TMI data. The RTP is to enable the effect of true shape and position of magnetic anomalies over causative bodied to be well reflected, while low-pass filtering technique is to suppress effects from shallow magnetic sources and enhance effects from the basal ones, which are related to the Curie point depth. In view of the above, the filtered TMI data were analyzed and radially power spectrum was applied to the main grid (277 × 385 km) which gave rise to DBMS value of 44.10 km and this corresponds to the geothermal gradient of 13.15 °C/km and heat flow value of 31.56 mW/m2. These values are very close to lower bound range obtained from the 110 × 110-km grid block size. Therefore, the DBMS values obtained from the radially average power spectrum of the 110 × 110 km grid increase from the northwestern part of the study area to southern and eastern part of the area. The DBMS are consistent with the observed geothermal gradient and heat flow parameters. High heat flow values (> 70 mW/m2) were observed in the northwestern part where the DBMS values are low, whereas low heat flow values (< 40 mW/m2) were observed where DBMS values are deep. These evaluated values, which are resultant of magnetic data, show similar results with those based on well log and thermal data within the study area (Nwankwo et al. 2009; Kurowska and Schoeneich (2010). Therefore, this area is characterized by both low and high heat flow.

It would be recommended to carry out a more detailed temperature measurement located at various depths within the study area.