The study presented in this research concerns the evaluation of the total field aeromagnetic anomalies for estimation of Heat flow in the Northern part of the sedimentary Nupe Basin using spectral analysis. The basin, which has in the past received limited attention from geologists and especially geophysicists partly due to lack of immediate geologic and economic values is fast becoming an important study area for geoscientists in view of increased efforts to explore for new and more energy locations in Nigeria. Moreover, geophysical studies in the basin are minimal and with no record of crustal temperature studies. Heat flow assessment of the area would significantly, compliment the geophysical information of the adjoining basins to the gap of missing crustal temperature information of the central part of Nigeria.
Useful two-dimensional (2-D) techniques for spectral analysis of aeromagnetic
anomalies have been described by Bhattacharyya (1966),
Spector and Grant (1970) and Shuey
et al. (1977). Bhattacharyya (1966) derived
an expression for the power spectrum of the total magnetic field intensity over
a single rectangular block, which was generalized by Spector
and Grant (1970) by assuming that the anomalies on an aeromagnetic map are
due to an ensemble of vertical prisms. They demonstrated that contributions
from the depth, width and thickness of a magnetic source ensemble could affect
the shape of the energy spectrum. The dominant term, which controls this shape,
is depth factor. The depth estimates could be made using the equation (Spector
and Grant, 1970; Hahn et al., 1976):
where, E(r), h and r are the spectral energy, depth and frequency, respectively.
Graphs of the logarithms of the spectral energies against frequencies are plotted
and linear segment from the low frequency portion of the spectra, representing
contributions from the deep-seated causative bodies could be drawn from each
graph. The gradient of the linear segment is therefore, evaluated and the equation
(Spector and Grant, 1970; Hahn et
al., 1976) below used to calculate the depth to the causative bodies:
where, m is the gradient.
Spector and Grant (1970) also showed that another factor,
(1-e-tr)2 contributes thickness in the energy spectrum;
where, t is the thickness. Smith et al. (1974)
and Boler (1978) used the effect of the factor to find
the thickness of the deepest magnetic layer. The parameter t plays a rather
interesting role in shaping the power spectrum. When combined with the depth
factor e-2hr (for not too large values of r), the effect of (1-e-tr)2
is to produce a peak in the spectrum whose position shifts toward smaller
wavenumbers with increasing values of t. When this peak occurs (significant
maximum), it indicates that the source bottoms are detectable. The frequency
fmax of the spectral peak, the mean depth h to the source tops (depth
to deep-seated causative bodies) and the mean depth d to the source bottom (Curie
depth) are related by (Boler, 1978; Connard
et al., 1983; Salem et al., 2000):
where, d = h + t.
Whether the sources appear to be depth limited or not depends very much on the size of the map. If there were no restrictions upon either the size of the map or size of the computer, then presumably the Curie-point isotherm could be observed. Therefore, estimates of heat flows in the crust maybe made using this depth and thickness information. The Curie point temperature at which rocks lose their ferromagnetic properties provides a link between thermal models and models based on the analysis of magnetic sources.
The magnetic susceptibility and strength of the materials that make up the continental crust are factors controlled by temperature. For temperatures higher than the Curie point, magnetic ordering is loose and both induced and remanent magnetization vanish, while for temperatures greater than 580°C those materials will begin to experience ductile deformation. The basic relation for conductive heat transport is Fouriers law. In one-dimensional case under assumptions that the direction of temperature variation is vertical and the temperature gradient (dT/dz) is constant; Fouriers law takes the form:
where, qz is heat flow and k is thermal conductivity.
The Curie temperature θc can also be defined as:
where, d is the Curie-point depth (as obtained from the spectral magnetic analysis).
Provided there are no heat sources or heat sinks between the earths surface and the Curie-point depth, the surface temperature is 0°C and dT/dz is constant. The Curie temperature depends on magnetic mineralogy. Although the Curie temperature of magnetite (Fe3O4), for example, is at approximately 580°C, an increase of titanium (Ti) contents of titanomagnetite (Fe2-xTixO3) causes a reduction of the Curie temperature. A Curie-point temperature of 580°C and thermal conductivity of 2.5 W m-1 °C-1 as average for igneous rocks is used as standard (Stacey, 1977) in this study.
MATERIALS AND METHODS
Location and geology of the study area: The area of study is bounded
by latitudes 8°30' and 10°00' North and longitudes 4°30' and 6°00'
East. It is an area of about 27,200 square kilometres situated at the West of
Central Nigeria. The Nupe Basin (also known as the Middle Niger Basin or Bida
basin) is an elongated NW-SE trending depression perpendicular to the main axis
of the Benue Basin of Nigeria. The entire basin is bounded by latitudes 8°00N
and 10°30N and longitudes 4°30E and 7°30E and
covers an area of approximately 90 750 km2 (Fig. 1).
The area is marked by two distinct climatic conditions. The rainy season lasts
usually from May/June to September/October every year depending on the rainfall
pattern for the particular year. The mean annual rainfall is 1560 mm. The dry
season is usually heralded annually by the dry, cold Harmattan winds and occurs
between November and March. After the departure of the Harmattan and in the
absence of rain, the hot sunny season with temperatures exceeding 27°C sets
in (Balogun, 2000). The mean annual temperature of the
area is 20°C.
The vegetation, which is predominantly of the Savannah-type, is characterised by giant grasses and few trees. Short feathery grasses form an almost continuous ground cover during the wet season. The Niger River and its tributaries mainly water the area. The height above sea level is about 100 m along areas bordering the River Niger and its tributaries but rises to about 200-300 m in other areas. The soil cover in the area is mainly lithosols and alluvial along River Niger areas and its tributaries.
The geology of the Nupe Basin (Fig. 1) is believed to be
a gentle down-warped shallow trough filled with Campanian-Maestrichtian marine
to fluviatile strata. The strata are believed to be more than 300 m thick (Adeleye,
1973, 1974, 1976). Those
with marine affinity, the limestones, often form cappings (under variable thickness
of laterites) to the means of the basin. Some form prominent intermediate breaks
of slope along the mesa walls.
map of Nigeria showing the surveyed area
Murat (1972) reported that the basin might be regarded
as Northwestern extension of the Anambra basin, which is found in the Southeast,
both of which were major depocenters during the second major sedimentary cycle
of Southern Nigeria in the Upper Cretaceous time.
Data acquisition and analysis: Airborne magnetometer survey maps of
contours of total magnetic field intensity of sheets 160, 161, 162, 181, 182,
183, 202, 203 and 204 published by the Geological Survey of Nigeria (GSN) Agency,
Airborne geophysical series (1976) on a scale of 1:1000,000 were used as basic
data for determining the nature of magnetic anomalies over the area. The contour
interval is variable at 5, 10, 25 and 50 nT. The survey was carried out along
a series of North-South lines with a spacing of 2 km and an average flight elevation
of 152 m above the ground level. The average magnetic inclination across the
survey area was from 9° in the north to 0° in the south. Since one common
problem in automated data interpretation is to select digitisation spacing and
minimum length of data profile in order to minimize aliasing error, selecting
a digitisation interval of 0.875 km is found to solve the problem in this study
(Khurana, 1981). Therefore, the maps were carefully hand
digitised at an equal spacing of 0.875 km yielding 4096 values per sheet and
36,864 values for the 9 sheets used in this study. Although hand digitisation
is the most elementary and least efficient method of digitisation, its accuracy
when carefully done, compares favourably with other more sophisticated methods
(Bath, 1974). The spacing interval of 0.875 km imposes
a nyquist frequency of 0.57 km-1.
In view of the simplicity in the trend of the magnetic field in the survey
area, the regional anomaly was removed from the observed data by fitting a plane
polynomial surface to the data. The study area does not have complex geology
and it has spatial extent, therefore, it seemed adequate and reasonable to assume
that the regional field is a first-degree polynomial surface (plane trend).
All the regional fields were, therefore, evaluated as a two-dimensional first-degree
polynomial surface. The expression for the regional field of the study area
is therefore, calculated and given as (Nwankwo, 2006):
Residual data were then obtained as the deviations from the total intensity data from the fitted plane surface. Upward continuation technique was also utilized to suppress short wavelength components of the residual magnetic anomalies in the study area. The continuation was carried out at a height of 0.282 km.
The study area was divided into eighty-one overlapped blocks for the purpose
of spectral analysis as shown in Fig. 2. Each block covers
a square area of 45 by 45 km, which represents a square grid of 16 by 16 upward-continued
residual field points. These were cosine-tapered before spectral evaluation
for heat flow assessments were carried out. Graphs of the logarithms of the
spectral energies against frequencies obtained for various blocks were obtained.
Linear segments from the low frequency portion of the spectra, representing
contributions from the deep seated causative bodies could be drawn from each
graph. The gradient of the linear segment was evaluated and the Eq.
2 was used to calculate the depth to causative bodies. Equation
3 was subsequently used to calculate the thickness and hence, the curie-point
depths (Nwankwo et al., 2008, 2009
may be checked for details). The Fouriers law Eq. 4
was eventually used to calculate the heat flow by means of Eq.
showing overlapped blocks of the study area used for spectral analysis.
Gray numbered blocks do not have data
RESULTS AND DISCUSSION
Graphs of the logarithms of the spectral energies against frequencies obtained
for the various blocks were obtained. Some of the graphs with spectral peak
are shown in Fig. 3a-f. The occurrence of
a significant peak in the spectrum indicates that the Curie-depths, which define
the source bottoms, are detectable.
spectra for depth estimations of some of the blocks, (a) block 4.6, (b)
block 4.7, (c) block 4.8, (d) block 5.5, (e) block 6.4 and (f) block 6.8
Gradient map of the study area. Contour interval is 1.0°C km-1
Two linear segments could be drawn from each graph. However, the gradients
of the low frequency linear segment were evaluated and the Eq.
2 was used to calculate the depths to top of the causative bodies (deep
sources) while Eq. 3 was used to calculate the thickness and
hence the curie-point depths. The deeper sources depth has previously been estimated
and found to vary from a thickness of 0.52 to 4.38 km (Nwankwo
et al., 2008) while the Curie-point depth varies from a thickness
of 12 to 30 km (Nwankwo et al., 2009). Using
a Curie-point temperature of 580°C and the derived curie-point depths (Nwankwo
et al., 2009), geothermal gradient variations in the area were obtained
and shown in Fig. 4. Furthermore, thermal conductivity of
2.5 Wm-1 °C-1 (Stacey, 1977)
was subsequently used to estimate the corresponding heat flow anomalies in the
study area. The heat flow is shown in Fig. 5.
The result show that the geothermal gradient varies between 19 and 46°C
km-1 while the ensuing heat flow varies between 30 and 120 mW m-2.
Figure 5 shows that in the southeast and southwest of the
study area heat flows were found to be less than 60 mW m-2 while
flows more than 100 mW m-2 are found in the northeastern and northwestern
parts. All the current literature states that the Curie point depth and of course
heat flows are greatly dependent upon geological conditions. Heat flow is the
primary observable parameter in geothermal exploration. Generally, the units
that comprise high heat flow values correspond to volcanic and metamorphic regions
since these two units have high heat conductivities. Additionally, tectonically
active regions affect heat flows significantly (Tanaka et
al., 1999). The average heat flow in thermally normal continental regions
is reported to be above 60 mW m-2. Values in excess of about 80-100
mW m-2 indicate anomalous geothermal conditions (Jessop
et al., 1976). Anomalous high heat flow values (above 100 mW m-2)
have been observed in the study area.
The study area has in the past received limited attention from Earth Scientists
partly due to lack of immediate geologic and economic values however, in view
of increased efforts to explore for new and more energy locations in Nigeria
it is fast becoming an important study area. Since, geophysical studies in the
basin are minimal and with no record of crustal temperature studies, the result
from this studies would definitely act as an added data.
Flow map of the study area. Contour interval is 5 mW m-2
Therefore, heat flow assessment of the area would significantly, compliment
the geophysical information of the adjoining basins to the gap of missing crustal
temperature information of the central part of Nigeria. This not withstanding,
the study has shown that a possibility of geothermal resource exist in Nupe
Basin, Nigeria. Therefore, the anomalous heat flow areas observed in this study
maybe recommended for further investigation.
The authors are grateful to the Geological Survey Agency of Nigeria for releasing the aeromagnetic maps. The authors would also thank the Federal Government of Nigeria Scholarship Board and University of Ilorin for partial sponsorships awarded to one of them.