Spectral analysis of aeromagnetic data for geothermal energy investigation of Ikogosi Warm Spring - Ekiti State, southwestern Nigeria

Geological setting

About two thirds of Nigeria’s landmass is underlain by the Precambrian basement complex (Figure 1). The crystalline rocks in Nigeria are made up of the Precambrian basement complex and the Phanerozoic rocks. These crystalline basement rocks have been subjected to deformation of different intensities throughout the geological period. Consequently, NS, NE-SW, NW-SE, NNE-SSW, NNW-SSE and to a less extent, E-W fractures have developed (Olujide and Udoh [1989]; Eze et al. [2011]). The Precambrian basement rocks consist of the migmatite-gneissic-quartzite complex dated Archean to early Proterozoic (2,700 to 2,000 Ma). Other units include the NE-SW trending schist belts mostly developed in the western half of the country and the granitoid plutons of the Older Granite suite dated Late Proterozoic to early Phanerozoic (750 to 450 Ma). The main lithologies of the southwestern (SW) Nigeria basement complex includes the amphibolites, migmatite gneisses, granites and pegmatites. Others are the schist made up of biotite, quartzite, talk-tremolite and the muscovite. Crystalline rocks intruded into these schistose rocks (Oyinloye [2011]). The basement complex is in places intruded and interspersed also by the older granites which originated in the Pan-African orogeny. Basement complex rocks in Nigeria have been subjected to deformation of different intensities throughout the geological period. Consequently, fractures have developed.

The warm spring issues with a temperature of 38°C near the foot of the eastern slope of the north-south trending ridge from a thin quartzite unit within a belt of quartzite which includes quartz-mica schist and granulitic migmatite east of Ilesha (Figure 2). The Okemesi quartzite member is characterized by a North-South trending ridge called the Effon ridge (Elueze [1988]; Oyinloye [1992]). The quartzitic rocks are composed of dominant quartz with muscovite, chlorite and sericite occurring in minor proportions (Adegbuyi and Abimbola [1997]). Rogers et al. ([1969]) suggested that the source of springs in the Effon Psammite formation is associated with a faulted and fractured quartzite band sandwiched between schists. Chemical data show that quartzite is largely metamorphosed sandstones containing minor arkosic intercalations (Olade and Elueze [1979]; Elueze [1988]). On the basis of petrology, a medium pressure Barrovian and low medium pressure types of metamorphism had been suggested for the Precambrian basement rocks in southwestern Nigeria (Oyinloye [2011]). Chuku-Ike and Norman ([1977]) and Mbonu ([1990]) believe that the intersections of the NNE-SSW epeirogenic belts with the NW-SE fracture trends in Nigeria coincide with the centres of warm springs like the Wikki (Bauchi State) and Ikogosi (Ekiti State) springs. The issue of the springs is controlled by permeability developed within the quartzite as a result of intergranular pore spaces coupled with fracturing of the relatively competent quartzite (Rogers et al. [1969]).

Nigeria is not situated on any known seismic belt, yet between 1933 and 2000, Nigeria experienced fifteen seismic events, three of which occurred in 1 year (Figure 1). The intensities of these events ranged from III to VI based on the modified Mercalli Intensity Scale. Three of the events, the 1984 seismicity at Ijebu Ode, the 1990 at Ibadan and 2000 at Jushi-Kwari were instrumentally recorded. They had body wave magnitudes ranging from 4.3 to 4.5, local magnitudes between 3.7 and 4.2, and surface wave magnitudes of 3.7 to 3.9 (Ajakaiye et al. [1987]; Akpan and Yakubu [2010]; Eze et al. [2011]). Two of them (Ibadan and Ijebu Ode measurements) are located close to our study area (the Ikogosi Warm Spring area). Some of the important fault systems in Nigeria are the Ifewara, Zungeru, Anka and Kalangai fault systems. They are interpreted to have resulted from transcurrent movements (Garba [2003]; Eze et al. [2011]). Of these, only the Ifewara fault is located in the region of this study. Adepelumia et al. ([2008]) confirmed the existence of Ifewara shear zone formed by sharing activities during Late Precambrian times using multi-spectral scanner (MSS) and side-looking airborne radar (SLAR) images. They identified a NNE-SSW trending Ifewara fault system in the area and showed that the 250 km-long NE-SW trending Ifewara fault zone could be linked with Atlantic fracture system. Burke et al. ([1977]) and Hubbard ([1975]) believed that the pronounced age difference on both sides of the fault zone suggests that the zone may indeed be a suture of Kibaran age. Burke ([1969]) suggested possible relationship between the epicentres of some of the West African earthquakes and continentward extensions of oceanic fractures into the landmass. Stresses built up around plate boundaries could travel toward the centre of the plate triggering intraplate seismicity especially in pre-existing faults. The coastal area of Nigeria lies in close proximity to the boundary between the African plate and South American plate. Some of the seismic activities that occurred in the coastal areas of Nigeria have been possibly initiated by this process (Eze et al. [2011]).

Regional magnetic feature and geology

A high-resolution aeromagnetic survey over the Ikogosi Warm Spring and its surroundings was conducted between 2004 and 2008 and published by the Geological Survey of Nigeria (GSN) on a map scale of 1:100,000 series. The various map sheets obtained were processed and merged together to a common dataset. They were transformed to a total field anomaly dataset and gridded at 0.5 km. The analysis of magnetic field used reduced to the pole data (RTP). The RTP correction applied assumed a declination of −3° and an inclination of −10° for this region utilizing the method of Silva ([1986]). Figure 3 shows the geomagnetic anomaly field map of the study area. The map had the regional geomagnetic field and the effects of diurnal magnetic variations removed.

The magnetic map and geologic map shows a good correlation between exposed geologic units and magnetic signatures. The strong variations in magnetic intensity suggest a wide variety of different magnetic properties. Notable (positive) anomalies are observed at the Oshogbo, Okemesi and Ilesha locations (Figure 3) reaching values of 60 to 112 nT. This tends to correspond with the exposed undifferentiated metasediments noted in these locations (Figure 2). Positive anomalies of 50 to 70 nT are also observed at the Ijero-Ekiti location whose probable source could be traced to the undifferentiated metasediments in this region. Within the towns of Ado-Ekiti and Ikere, positive magnetic anomalies of 80 to 110 nT were obtained. We traced this observation to the Older Granites domiciled in this region. In other regions of the map encompassing the towns of Erinmo, Ifewara, Oriade, Ikogosi and Okeigbo, negative magnetic anomalies ranging from −30 to −156 nT have been noted. The belt of quartzite, quartz-mica schist and granulitic migmatite encapsulated by the quartzite belt in the region is identified with this observation. This quartzite is part of the Okemesi quartzite member of the Effon Psammite formation (east of Ilesha) belonging to the Ife-Ilesha schist belt of the Precambrian basement complex of Nigeria (Loehnert [1985]; Adegbuyi et al. [1996]). The Ikogosi town (study location) has magnetic lows of −0.46 to −35 nT, extending westwards. This location is also part of the fractured quartzite unit in the formation.

One of the methods of examining thermal structure of the crust is the estimation of the CPD, using aeromagnetic data (Dolmaz et al. [2005]). Various studies have shown correlations between Curie temperature depths and average crustal temperatures, leading to viable conclusions regarding lithospheric thermal conditions in a number of regions around the world (Ross et al. [2006]). The mathematical model on which our analysis is based is a collection of random samples from a uniform distribution of rectangular prisms, each prism having a constant magnetization. Two fundamental methods serve as a basis of all subsequent analysis, first provided by Spector and Grant ([1970]), estimating the average depths to the top of the magnetized bodies from the slope of the log power spectrum and second by Bhattacharyya and Leu ([1975]) for obtaining the depth to the centroid of the causative body. The method can provide valuable information about the regional temperature distribution at depths not easily examined using other methods (Okubo et al. [1985]). The Curie temperature isotherm corresponds to the temperature at which magnetic minerals lose their ferromagnetism (approximately 580°C for magnetite at atmospheric pressure). Magnetic minerals warmer than their Curie temperature are paramagnetic and from the perspective of the earth’s surface are essentially nonmagnetic (Ross et al. [2006]). Thus the Curie temperature isotherm corresponds to the basal surface of magnetic crust and can be calculated from the lowest wavenumbers of magnetic anomalies, after removing the approximate regional field from the aeromagnetic data (e.g. Bhattacharyya and Morley [1965]; Spector and Grant [1970]; Mishra and Naidu [1974]; Byerly and Stolt [1977]; Connard et al. [1983]; Hamdy et al. [1984]; Blakely [1988]; Tanaka et al. [1999]; Salem et al. [2000]; Ross et al. [2006]).

We applied the methods of Spector and Grant ([1970]), Okubo et al. ([1985]) and Trifonova et al. ([2006]), which examined the spectral knowledge included in subregions of magnetic data for our analysis.

Spectral analysis

The earliest papers on Curie point depth determination based on spectral analysis of geomagnetic data are those of Byerly and Stolt ([1977]) where analyses for different areas of USA have been published. More recently, investigations have been made for parts of the territory of Japan (by Okubo [1985, 1989, 1994]), USA (by Mayhew [1985]; Blakely [1988]), Greece (Tsokas et al. [1998]; Stampolidis and Tsokas [2002]), Portugal (Okubo et al. [2003]), Bulgaria (Trifonova et al. [2006, 2009]) and Turkey (Dolmaz et al. [2005]; Maden [2009]). Authors consider the power spectrum of the total geomagnetic field intensity anomaly over a single rectangular block using the expression, which was first given by Bhattacharyya ([1965]). The equation was transformed into polar wavenumber coordinates (S,ψ), and the average depths to the top of magnetized bodies from the slope of the log power spectrum were calculated. The model has proven successful in estimating average depths to the tops of magnetized bodies (Trifonova et al. [2006]).

One principal result of Spector and Grant’s analysis is that the expectation value of the spectrum for the model is the same as that of a single body with the average parameters for the collection (Okubo et al. [1985]).

Equation 3 can be recognized as the spectrum of a dipole.

In effect, the ensemble average at these very low frequencies is that of a random distribution of point dipoles. What follows, therefore, is independent of the details of the body parameters (prisms, cylinders or whatever), provided that the dimensions in all directions are comparable. The method of Okubo et al. ([1985]) was used in estimating z_o from Equation 3:

If $\mathit{G}\left(\mathrm{S},\mathrm{\psi }\right)=\frac{1}{\mathit{s}}\mathit{F}\left(\mathrm{S},\mathrm{\psi }\right)$

For these approximations to make sense, the bodies must in general be large in depth compared to their horizontal dimensions. However, if the distribution of horizontal body dimension is very broad, a similar effect will be produced by variability in terms corresponding to the horizontal body dimensions.

The sampling interval used during the analysis of data in this work, 500 m (0.50 km), directly imposes a Nyquist frequency of 1 km on the data.

Conductive heat flow

In this equation, it is assumed that the $\raisebox{1ex}{$\mathrm{dT}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{dz}$}\right.$ is constant.

Tanaka et al. ([1999]) showed that any given depth to a thermal isotherm is inversely proportional to heat flow, where q is the heat flow. This equation implies that regions of high heat flow are associated with shallower isotherms, whereas regions of lower heat flow are associated with deeper isotherms (Ross et al. [2006]). An average surface heat flow value was computed using Equations 10 and 11 and was based on possible Curie point temperature of 580°C using a thermal conductivity of 2.5 Wm⁻¹°C⁻¹, given by Stacey ([1977]) as the average for igneous rocks.

Radiogenic heat generation

The presence of thorium-rich accessory minerals, such as monazite, zircon and rutile is usually linked to micaceous zones in radio-active porphyritic and coarse granite (Ragland and Roger [1961]; Gerard and Kappelymeyer [1987]). Such granitic rock bodies are found to be suitable nuclear resources including the uraniferous sandstone and marginal marine sediments. Using the scanning electron microscope to determine the spot chemical composition and empirical formulae of nearly all rock-forming minerals in the rocks of the basement complex of southwestern Nigeria, Oyinloye ([2011]) discovered the mineral, monazite. He concluded that this mineral was present as a notable accessory mineral in all the crystalline rocks of the basement complex in Ilesha area even in the amphibolites which is supposed to be igneous. Monazite is a phosphate of the rare earth elements, especially the light ones. The petrogenetic implication of the presence of monazite in the crystalline rocks of southwestern Nigeria is that the initial magma from which the precursor rocks were formed contains some input from the crustal or sedimentary source. There is therefore the possibility of a uranium/thorium bearing unit at a vertical depth in the micaceous-quartzite rock unit of the Ikogosi Warm Spring area (Adegbuyi and Abimbola [1997]). The majority of the continental heat flow originates from the decay of radioactive isotopes in the crust, thus finding areas with high isotope concentration can be equal to finding areas with high heat flow (Holmberg et al. [2012]).

Map division into overlapping subregions

In the estimation of depths to the Curie temperature in Oregon, for example, Connard et al. ([1983]) divided a magnetic survey into overlapping cells (77 × 77 km) and calculated for each cell a radially average power spectrum. However, the spectrum of the map only contains depth information to a depth of length (L)/2π (Shuey et al. [1977]). If the source bodies have bases deeper than L/2π, the spectral peak occurs at frequency lower than the fundamental frequency for the map and cannot be resolved by spectral analysis (Salem et al. [2000]).

Our method has evolved from published methods. Rather than dividing the aeromagnetic data into overlapping subregions of equal dimension on a uniform grid, we selected subregions of dimension 55 × 55 km across the entire magnetic map and additional random blocks at prominent magnetic anomaly regions. We ensured at least 50% overlap of the blocks and our choice of 55 × 55 km dimension was adopted from the size of each of the four map sheets incorporated for the total field intensity map. The number of overlapping blocks of 22 was discretionary, guided by the concentration of prominent magnetic anomalies on the map. The coordinates at the centre of each block, representing the sampled point, were noted for the CPD location. We adopted the current method to enable sampling of more data points. Given the location of the Ikogosi Warm Spring (7°35′N, 5°00′E) at the centre of the aeromagnetic map investigated, our method enabled adequate probing of the warm spring area. Figure 4 shows the sampled points for the CPD analysis realized from our method.

For simplification of the approach used in our CPD analysis (Bhatacharyya and Leu [1975, 1977]; Okubo et al. [1985]), we resolve these steps to Equation 16 for deriving the depth to the centroid (z_o) and Equation 17 for estimation of the depth to the top boundary (z_t) of that distribution:

$ln\left[\frac{\mathit{P}{\left(\mathit{s}\right)}^{1/2}}{\left|\mathit{s}\right|}\right]=ln\mathit{A}-2\mathrm{\pi }\left|\mathit{s}\right|{\mathit{z}}_{\mathrm{o}}$

(16)

$ln\left[\mathit{P}{\left(\mathit{s}\right)}^{1/2}\right]=ln\mathit{B}-2\mathrm{\pi }\left|\mathit{s}\right|{\mathit{z}}_{\mathrm{t}}$

(17)

where P(s) is the radially averaged power spectrum of the anomaly, |s| is the wavenumber, A is a constant and B is a sum of constants independent of |s|. Then the basal depth (z_b) of the magnetic source is calculated from Equation 2. The obtained basal depth of a magnetic source is assumed to be the CPD. FFT was used to convert the space domain grid data to the Fourier domain. The radially average log power spectrum of each block was computed using MAGMAP filtering program (GEOSOFT MAGMAP [2007]). The radially averaged energy represents the spectral density (energy) averaged for all grid elements at the wavenumber. Figure 5 shows the example of the radially averaged power spectrum plot for block 5 of the 22 blocks. From the centroid depth of 7.60 ± 0.06 km and depth to the top of 0.78 ± 0.02 km, CPD is calculated as 14.42 ± 0.53 km with percentage uncertainty at 3.7 for this block. The 22 estimated CPD values of the study area range from 11.5 to 21.9 km. Table 1 and Figure 6 shows the CPD values and CPD map of the study area, respectively.

In the terrestrial continental crust, the average heat flow is between 65 mW/m² and 48 mW/m². For our calculations, we assumed a surface heat flow value of 65 mW/m² for continental lithosphere (Pollack et al. [1993]). We adopted the concentrations of U, Th and K in surface rocks collected from the Ikogosi Warm Spring region, given in average concentration values of 6.68 ppm U, 27.19 ppm Th and 5.77% K for both quartzite and schistose rock types (Adegbuyi and Abimbola [1997]). Equation 13 was applied in Equation 19 with the average density of quartzite taken as 2650 kgm^− 3 (Marciniszyn et al. [2013]).