1 Introduction

Geothermal activity in Egypt has been recognized in several areas, whether in the Eastern or the Western Deserts. Due to tectonic activity, geothermal potentiality is concentrated along the Gulf of Suez and the Red Sea in the Eastern Desert. However, limited geothermal resources can be found in the Western Desert near the oasis (Bahariya and Dakhla). Thus, numerous comprehensive geophysical and geothermal studies have been done in the Eastern Desert for the purpose of geothermal exploration to identify key structures for geothermal activity (Ravat et al. 2011; Abdel Zaher et al. 2011a, b, 2012; Saleh et al. 2013; Lashin 2013; Atef et al. 2016). Most studies on the Western Sahara have been interested in groundwater exploration and structural investigation. For instance, Abdel Ati (2002) completed detailed hydrogeological studies on the Nubian Sandstone Aquifer of the Bahariya and Farafra depressions. He examined that NE–SW faults are the predominant trend at Bahariya area while the NW–SE faults are the second common trend and have relatively low throws than NE–SW faults. Hamdan et al. (2012) evaluated hydrogeochemical characteristics of the different Nubian aquifer horizons in order to identify the previous hydrochemical processes affecting the quality of the groundwater in the Bahariya oasis. In addition, Moustafa et al. (2003) studied the structural settings and tectonic evolution of the Bahariya Depression and indicated extraordinary similarity to the deformation of the structurally unstable area of the northern Western Desert where several hydrocarbon fields have been found. While, Abdel Zaher et al. (2014) outlined significant surface and subsurface structures to assess the structural system that controls the geometry of subsurface aquifers in the southern part of the Western Desert of Egypt. They showed that the main structure trend is ENE–WSW, while the lineaments of NE–SW are the oldest trend in the study area and its existence in the Paleocene and Eocene rocks probably indicate reactivated faulting. In contrast, there have only been few attempts to investigate geothermal resources in Western Desert. Abd El All et al. (2015) outlined subsurface structures at the Bahariya oasis utilizing two geophysical techniques: geomagnetic and geothermal surveys. Subsurface temperature contour map explained that the Bahariya oasis has geothermal groundwater reservoirs. In addition, Mohamed et al. (2015) developed a new predictive model to estimate geothermal gradients in the northern Western Desert based on bottom-hole temperature (BHT) and aerogravity data using an artificial neural network (ANN) approach. The predicted geothermal gradients map showed that the northern Western Desert of Egypt has low regional temperature gradients (30 °C/km), however several potential nearby geothermal fields were found (> 40 °C/km) and Bahariya oasis is one of them. Abdel Zaher et al. (2018) used 3D inversion on aerogravity data to delineate the depths of basement rocks in the Siwa oasis and to estimate its Curie point depth (CPD), geothermal gradient and heat flow maps using spectral analysis of aeromagnetic data. The got geothermal gradients run from 21 to 27 °C/km and the heat-flow values extend from 49 to 64 mW/m2.

The present work aims to study the geothermal resources, as well as the subsurface structural features affecting the basement rocks and to define the thermal structure of the Earth in the Bahariya oasis. Aeromagnetic data in the form of RTP map is used to achieve these objectives as well as subsurface stratigraphic data of well BOX-1, which extended to the basement surface. In addition, two dimensional modelling along four profiles was applied to display the surface basement, and the spectral analysis of the aeromagnetic data was used to estimate the Curie point depth (CPD), geothermal gradient and heat flow. Evaluating the varieties of the Curie depth in a territory can provide important information on both regional and local temperature distribution, as well as complement geothermal data in regions where deep boreholes are unavailable.

2 Geology and Structural Setting

Bahariya oasis is located in the north-central part of the Western Desert of Egypt. It is located between 27° 48′–28° 30′ N and 28° 35′–29° 10′ E and occupies the hinge line between the stable-unstable shelfs as stated by Said (1962) (Fig. 1 ). The morphology of the Bahariya depression (after Embabi and El-Kayali 1979) includes plateau surfaces, escarpments, residual hills, volcanic cones, alluvial fans, sabkhas and sand dunes. The stratigraphic section of the Bahariya oasis is dominantly clastic, reflecting its proximity to the Upper Egypt highlands, which in the past have shed sediment northward into the Western Desert and Nile Delta. The majority of the sequences become progressively sandier towards these highlands. Northward, numerous transgressed shales or marine carbonates allow for the subdivision of strata into main sequences and formations (Ball and Beadnell 1903; Hermina 1957; El-Bassyouny 1961; Said 1962; El-Akkad and Issawi 1963; El-Bassyouny 1972).

Fig. 1
figure 1

modified from El-Akkad and Issawi (1963), c subsurface sequence of the BOX-1 Well (after Moustafa et al. 2003)

a Map of Egypt showing the location of Bahariya Oasis in the Western Desert, b the geologic map of the Bahariya oasis

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The subsurface sequence in the area, which was drilled by the Sahara Petroleum Company in 1957 and recorded in well BOX-1 at a depth of 1841 m (Moustafa et al. 2003), is consistent from the bottom to the top of the Precambrian basement (Fig. 1c). It is composed of a sedimentary section from the Cambrian era, resting upon a metamorphosed igneous basement. This section is composed of intercalated siltstone, sandstone, and clay. Cretaceous rocks lay on top of Cambrian deposits of undifferentiated sandstones, composed of sands and clays intercalated with each other. The top the lower Cenomanian (Bahariya Formation) consists of intercalations of sandstone, sands and clays.

Structurally, the Bahariya oasis occupies an area of the Syrian Arc anticline running SW–NE, passing the main hills of the depression to the southern part of the oasis, and seems to continue south to include the Farafra oasis. Upper Cretaceous reservoirs which constitute the Bahariya Formation are also well exposed typical of the Syrian Arc orogenic event (Said 1962). Oligocene basalts unconformably overlay the Bahariya Formation over most of the oasis, and two lines of folds are developed along the east and west sides of the Bahariya anticline. Three fault systems are distinguished in the Bahariya oasis, trending NE–SW, NW–SE and E–W with variable throws (Korany 1984).

3 Materials and Methods

The geophysical data used in the present study is in the form of a reduction to the pole (RTP) aeromagnetic map, obtained from the GETECH Group PIC., ‘African Magnetic Mapping Project’ (AMMP). The survey was done in 1964 by Getech, PGW and ITC. It is in the form of a unified 1-km grid of total magnetic intensity (TMI) at a mean terrain clearance of 1000 m, produced from aeromagnetic and ground measurements, as well as Magsat data, with 10 nT contour intervals and line spacing of 3000 m (Getech 1992; Green et al. 1992). Subsurface stratigraphic information was obtained from deep well BOX-1, which was drilled by the Sahara Petroleum Company in 1957 (Moustafa et al. 2003), this well is reach to the basement rock at a depth of 1841 m from the surface.

3.1 Qualitative Study of Aeromagnetic Data

Qualitative interpretation of the RTP map of the study area (Fig. 2a) indicates the existence of different anomalies, with main positive anomalies seen in the northern and southwestern parts, and a negative anomaly seen in the southern parts. The positive and negative anomalies are possibly due to uplift and subsidence of the basement rock and its associated structures. Linear anomalies also occur as belts in the middle part of the study area, extending in E–W, NE and NW directions. These linear belts reflect faults that affect the basement rocks.

Fig. 2
figure 2

a RTP aeromagnetic map of the Bahariya oasis (Getech 1992; Green et al. 1992); the black lines indicate the location of selected profiles used for 2D forwarded modelling; b low-pass filtered regional RTP map (cut-off wavenumber = 0.003 cycle/km); c high-pass filtered residual RTP map (cut off wavenumber = 0.003 cycle/km); d tilt gradient map of RTP aeromagnetic data

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The RTP map was filtered at several cut-off wavelengths to obtain the best regional and residual anomaly maps. These cut-off values were obtained from the power spectrum of aeromagnetic data. After that, the effective cut-off wavelength was selected, which was 0.03 cycle/km. The low and high pass filters with a cut-off of 0.03 cycle/km were then applied on the RTP map to separate the regional anomalies that reflect the deep-seated structures from the local ones, which indicate shallow structures. This technique was applied using Geosoft oasis Montaj version 6.4.2. On the low-pass filter map (Fig. 2b), one positive anomaly alternating with other negative anomalies are observed with a range of 104 to − 103 nT. The two anomalies trending closely in the ENE–WSW direction, in combination with the regional structural trend in the Bahariya oasis, has been discussed by several authors as the Syrian arc anticline. The differences in the magnetic relief between the two anomalies refer to the variation in lithology and are related to the basement faulting structure. The high pass filter map (Fig. 2c) shows numbers of small and local anomalies reflecting shallow and local structures and/or geologic features. Most of these local anomalies extend in the E–W, NE–SW and NW–SE directions.

A tilt derivative filter (TDR) was also applied to delineate the vertical and inclined lithologic and/or structure contacts. The TDR results are presented as a contour map (Fig. 2d). From this map it can be seen that the TDR values range between − 1.4 and 1.2 radians. These values refer to the location of structural edges, where the positive anomalies values correspond with being present over the sources, and become negative outside of the source region (Miller and Singh 1994). On the other hand, tilt derivatives display zero crossings of anomalies located close to the edges of structures. This means that the subsurface faults can be traced from the zero contour lines on this map. The detection of fault trends from the RTP map and its derivative maps was considered from the zero contour lines as traces of faults. The magnetic fault trends traced from the aeromagnetic maps of the study area are shown in Fig. 3.

Fig. 3
figure 3

Structure lineaments traced from the aeromagnetic maps of the study area and the corresponding azimuth frequency diagram; a RTP aeromagnetic map; b low-pass filtered regional RTP map; c high-pass filtered residual RTP map; d tilt gradient map

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3.2 Two-Dimensional (2D) Magnetic Modelling

To study and determine the basement surface depth and outline the general structural framework of the study area, four regional magnetic profiles are modelled using GM-SYS through the oasis Montaj Programs (2007). Two profiles extending from west to east were named P2P′2, and P4P′4, while the other two profiles were named P1P1′ and P3P3′, extending from south to north and from southwest to northeast, respectively (Fig. 4). The subsurface stratigraphic data of well BOX-1, in which the basement surface was recorded at a depth of 1841 m from the surface, was used as control reference in verifying the modelling processes. The four profiles were taken on the RTP map in different directions, distributed to cover most of the study area, and crossing the BOX-1 well, with the expected profile of P4–P4′ being parallel to profile P2–P2′ and intersecting profiles P1–P1′ and P3–P3′ at distances of 47,713 and 20,869 m from the start, respectively. The depth to the basement at the intersection points is 3777 and 2100 m, respectively. These two points were used as control points for the present model (P4–P4′).

Fig. 4
figure 4

2D forwarded aeromagnetic models along profile P1, P2, P3 and P4; the locations of these profiles are shown in Fig. 2. The x-axis refers to the distance in metres along the profile; the y-axis refers to the magnetic field in nT. The sections indicate the geological model results from fitting the observed (dotted line) and calculated (solid line) data. The densities are in kg/m3 while the magnetic susceptibilities are in cgs-system units

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Magnetic susceptibility of rocks is an extremely important property for magnetic exploration methods. It is usually depend on the magnetite content of the rocks, with rocks that have significant concentrations of ferro-and/or ferri-magnetic minerals tending to have the highest susceptibilities. Table 1 displays the susceptibility of rocks according to Parasnis (1986), Sharma (1986), and Telford et al. (1990). The subsurface sequence in the study area, as recorded in well BOX-1 up to a depth of 1841 m, is composed of sedimentary sections that belong to the Cambrian and rest upon the metamorphosed igneous basement. Accordingly, the magnetic susceptibility of the basement rocks was assumed to be constant with a value of 0.088 SI units (equals 0.007 cgs units). This parameter was used in the modelling of the magnetic profiles. The results of the modelling of this magnetic data are shown in Fig. 4.

Table 1 Susceptibility of rocks (k × 106 rationalized SI units) to convert to the unrationalized c.g.s units, divide by 4π (Parasnis 1986; Sharma 1986; Telford et al. 1990)
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The magnetic field of the study area used in the geologic modelling process was computed by using a magnetic declination of 2.33° east and a magnetic field inclination of 40°. The resulting regional magnetic field intensity was 41,849 nT. The effect of remanent magnetization neglected; however, measurements on rock samples demonstrate that the susceptibility plays the dominant role of the total magnetization due to a clear predominance of the induced magnetization over the remanent magnetization. Generally, the orientation of the remanent magnetization vector is in the same direction of the present earth magnetic field (Mattsson et al. 2004), and this will mainly influence the amplitude of the modelled anomalies, and it will not essentially influence their shape. On the other hand, the densities of the sedimentary cover consist of three values according to the subsurface sequence record in the BOX-1 well (Fig. 1), which are 2430, 2300 and 2430 kg/m3.

3.3 Curie Point Depth (CPD) of the Bahariya Oasis

The thermal structure of the Earth’s crust varies in different geological environments and can be determined by using magnetic data, where the magnetic minerals change from a ferromagnetic to a paramagnetic state at a temperature of 550 °C ± 30 °C (Hsieh et al. 2014; Nwankwo and Shehu 2015). In the present study, the Centroid method (Bhattacharyya and Leu 1975; Okubo et al. 1985; Tanaka et al. 1999) was used to compute the CPDs from the spectral analysis of the observed aeromagnetic data in the Bahariya oasis. For more details on the theory of power spectral density of total magnetic fields, see Blakely (1995). The Bahariya oasis covers an approximate area of 1800 km2. This area is very small and not useful for calculating the Curie point depth. To overcome this problem, the area was extended and data from outside of the study area was used. The RTP aeromagnetic map of the extended area was divided into twenty (20) overlapping 75% adjacent blocks, and each block had a dimension of approximately 73 × 55 km2. The Curie depth point is considered at the centre of the blocks as shown in Fig. 5.

Fig. 5
figure 5

Twenty overlapping blocks (75%) used for estimating CPD on the RTP map (approximately 55 × 75 km2), and Curie depth point is located at the centre of the blocks

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The power spectrum of the RTP data for each block was calculated by plotting the spectrum against the wavenumber, k (Fig. 6). Then, the top (Zt) and the centroid (Z0) depths of the magnetic sources were calculated by applying the technique from Okubo et al. (1985), where the centroid depth (Z0) of the deepest magnetic source is derived from the slope of the longest wavelength of the spectrum and divided by the wave number. The previous step was repeated again to derive the depth to the top of the magnetic source Zt from the slope of the high wave number portion of the power spectrum. Finally, from these slopes, the lower bound of the magnetic source can be computed (Okubo et al. 1985; Tanaka et al. 1999) as Zb = 2Z0 − Zt. These steps were carried out within the Geosoft oasis Montaj software version 8.3 (2014).

Fig. 6
figure 6

Example of the radial power spectrum from the aeromagnetic anomaly data of block no. 2. The CPD was calculated from the slope of the part of the longest wavelength of the spectrum

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The Curie point depth values obtained for each block were then contoured in a Curie point depth map of the study area (Fig. 7). To provide an idea about the geothermal resources present in the Bahariya oasis, the geothermal gradient and heat flow were calculated from the Curie point depth (Zb). Using a Curie point temperature of 580 °C, the geothermal gradient between the Earth’s surface and the Curie depth (Zb) can be calculated using the equation dT/dz = 580 °C/Zb (Tanaka et al. 1999; Stampolidis et al. 2005; Maden 2010). Then, the heat flow was calculated by using the formula: q = λ (dT/dZ) = λ (580 °C/Zb), where λ is the coefficient of thermal conductivity. Based on the measurements of thermal conductivity for the rocks forming the stratigraphic section of the northern Western Desert (Morgan et al. 1983), the average thermal conductivity was assumed to be 2.6 W/m °C in the present study.

Fig. 7
figure 7

Map of the Curie depths of Bahariya oasis obtained by gridding the resultant CPD (Zb) in Table 1

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4 Results

The trend analysis of the RTP map, in addition to its derivative, is used in visualizing the common structural trends affecting the study area. The magnetic lineaments deduced from aeromagnetic maps indicated that the most predominant trends are the NE (running parallel to Bahariya anticline), NW, and ENE to E–W trends. From the 2D models that cover most of the study area, a map of the depth to basement surface has been contoured (Fig. 8).

Fig. 8
figure 8

Basement relief image as interpreted from the 2D aeromagnetic modelling. The map shows that the northeastern and southwestern parts correspond to the Heiz, Ghorabi and Sandston Hill anticlines, where depths to basement are 500–2000 m

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All results obtained from 2D modelling on the aeromagnetic data were combined to construct a new map describing the structure of the basement surface. The structure map and the corresponding azimuth frequency diagram are shown in Fig. 9. Two sets of faults are recognized; the first set is the NE–SW trend fault that runs parallel to the anticline of the Bahariya oasis and represents the most common fault trend. The second set is the NW–SE structural trend, which is second-most predominant in regards to basement trends. Additionally, E–W trending faults are the least common in the area.

Fig. 9
figure 9

Basement tectonic map of the Bahariya oasis, as interpreted from the depth to basement map and the corresponding azimuth frequency diagram (Fig. 5); the NW–SE and NE–SW structural trends are predominant as subsurface (basement) structural trends

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The values of the Curie point depths estimated from spectral analysis of the aeromagnetic data vary from 17 km in the western parts and increase to 29 km towards the eastern and southwestern parts of the Bahariya oasis, with an average of 25 km, which are agree with previous studies in the Western Desert (Mohamed et al. 2015; Elbarbary et al. 2018). The geothermal gradient and heat flow maps of Bahariya oasis were constructed from the map of CPDs as shown in Fig. 10. The estimated geothermal gradients show values ranging from 20 to 35 °C/km and an average of approximately 30 °C/km. The heat flow map illustrates that the value of heat flow ranges from 52 to 90 mW/m2 with an average of approximately 66 mW/m2. The calculated Curie point depths, geothermal gradient and heat flow values for each block on the RTP aeromagnetic map of Bahariya are shown in Table 2.

Fig. 10
figure 10

a Temperature gradient map of the Bahariya oasis estimated from a Curie temperature of 580 °C and the obtained curie depths from the aeromagnetic data. b Heat flow map of the Bahariya oasis using an average thermal conductivity of 2.9 W/m °C

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Table 2 Lists of the derived CPD, geothermal gradients and heat flow values from the power spectrum analysis of aeromagnetic map for 20 blocks in the study area
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5 Discussion

The results obtained from the basement surface map show that the thicknesses of sedimentary cover increase and decrease in the form basins and uplift within the area ranging between 0.5 m, reflecting the presence of uplifting to more than 2.0 km and indicating basins. For example, a basin is seen in the middle part with a sedimentary thickness of 4000 m, which corresponds to the El-Hefhuf syncline. Meanwhile, anticlinal uplifts are observed in the northeastern and southwestern parts of the area and correspond to the Heiz, Ghorabi, Ris and Sandston Hill anticlines where depths to the basement vary from 500 to 2000 m. Both basins and uplifts are controlled by fault zones extending mainly in the NE and NW directions. The locations of the faults derived from 2D modelling on the aeromagnetic data represent optimal sites for exploration of the geothermal potentiality of the Bahariya oasis, especially in the northern direction where the depth to basement is shallow. For example, the El-Bawiti fault is well exposed at “the Hot and Gold” spring in El-Bawiti. All of these fault trends are considered good pathways for groundwater movement and hydrochemical facies.

The CPDs are strongly dependent upon geological conditions. This means that the CPD in the study area is related to topographic relief to the basement surface as well as to subsurface structures in the study area. A shallower CPD of 17 km agrees with the high relief basement with a depth of 0.6–2.0 km. Tanaka et al. (1999) and Aydin and Oksum (2010) expected that shallow Curie point depths (CPDs) represent the regions which have geothermal potential, such as young volcanisms and areas of thin crust.

6 Conclusion

From the analyses and processing of the RTP aeromagnetic map and its derivative maps, in addition to the spectral analysis of the aeromagnetic data, it is shown that:

  1. 1.

    The trend analysis of the aeromagnetic maps shows that the most predominant trends are the NE (running parallel to the Bahariya anticline), NW, and ENE to E–W trends. These trends agree with the general structural features of the Bahariya oasis.

  2. 2.

    The depth to basement over the studied area ranges from 0.6 to 4.0 km. The thickness of sedimentary rocks decreases in the northeastern and southwestern parts of the area.

  3. 3.

    The basement structure map shows that the main tectonic trends are NE as the first order, while NW and ENE to E–W trends comprise the second order.

  4. 4.

    Curie point depth varies from 17.0 km in the western parts and increases to 29.0 km, with an average of 25.0 km, towards the central and eastern parts of the Bahariya oasis.

  5. 5.

    The geothermal gradient and heat flow maps of the Bahariya oasis are computed and contoured as maps from the Curie point depths, and the thermal conductivity is assumed to be 2.6 W/m °C. The geothermal gradient values are found to be in the area range from 25 to 35 °C/km with an average of 30 °C/km. Additionally, the heat flow map illustrates that the value of heat flow ranges from 52 to 90 m W/m2, with an average of 66 m W/m2.

  6. 6.

    The correlation between maps (basement structure, CPD, geothermal gradient and heat flow maps) display an abundance of geothermal resources where there is high heat flow, namely, at shallow Curie depths, and may represent promising regions for future geothermal exploration.