Introduction

The area under study is located to the west of the Nile River, within the northeastern portion of the Western Desert of Egypt. It lies between latitudes 29°00′ and 30°00′N and Longitudes 30°00′ and 31°18′E (Fig. 1), covering a total surface area of about 14,350 km2.

Fig. 1
figure 1

Locaion map of the study area

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The surface geology of the north Western Desert, in general, is characterized by almost featureless terrain of simple geologic nature. The exposed rocks are generally of Tertiary age interrupted by some spots of Cretaceous outcrops around Abu Roash area and Bahariya Oasis.

Because the north Western Desert tract is located within the unstable belt of Egypt, there are a number of folding and faulting structures within its sedimentary section that caused lateral variations in compositions and thicknesses of the affected sequences.

In general, the geophysical magnetic method is mainly based on the measurements and analysis of small variations in the earth’s magnetic field within any area. An aeromagnetic map is a reflection of the distinctions in the magnetic properties of the underlying rocks. Therefore, these variations encountered in the measured magnetic field are attributed to the distribution of the subsurface magnetically polarized rocks.

The sedimentary rocks are of weaker magnetic properties than the underlying basement rocks, especially the mafic rocks. Therefore, the magnetic methods are used to delineate the structural and lithological configuration of the basement rocks. Estimating the depths to the basement surface with basement determination methods is comparable to the calculation of the thicknesses of the overlying sedimentary rocks. That is important for hydrocarbon exploration, since the hydrocarbons can be found mainly in the sedimentary section, where the configuration of the basement rocks reflects the size and shape of any sedimentary basin and ridge that form the source rocks and trapping elements.

The main type of available geophysical data for the current study is an aeromagnetic map showing the distribution of the total intensity magnetic anomalies within the study area (Fig. 3). The current study involves the qualitative analysis of the available aeromagnetic data.

Fig. 2
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Geological map of the study area (Geological Survey of the Egypt 1981)

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Geologic setting

The distribution of the different rock types exposed in the area under study is shown in the geological map (Fig. 2), which was compiled from the Egyptian Geological Survey and Mining Authority (1981). This map reveals that, the exposed outcrops of this area range in age from Eocene to Recent.

Fig. 3
figure 3

Total intensity aeromagnetic of the study area

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The Eocene rocks are composed of limestone with some flints, mainly blanketing most of the southwestern portion of the study area, around the Faiyum Depression. Meanwhile, the Miocene deposits mainly cover the northwestern portion of the area. The Miocene deposits are separated from the Eocene rocks by narrow belt of Oligocene rocks outcropping north of Birket Qarun and are composed of cross-bedded sandstones and gravels with interbeds of shales and limestones. To the east, the Pleistocene–Recent sediments mainly cover the narrow strip of the Nile Valley, around the cultivated lands, with local Pliocene outcrops covering the older rocks. Surficial deposits in the form of sand dunes running generally in a north northwesterly direction also represent the Pleistocene–Recent rocks. Basaltic flows and sheets, which are believed to be of Late Oligocene–Early Miocene age, are exposed in some localities in this area, e.g., Gabal Qatrani, south of Cairo, and west of the Nile Valley. Gabal Qatrani is situated to the north of the study area.

Geomorphologically, the studied area, as a part of the north Western Desert of Egypt, is generally a rocky platform of low altitude, which has been characterized through its recent history by arid climatic condition. Therefore, its main geomorphologic features are primarily due to the wind action (Said 1962). The area exhibits a vast peneplain, which is covered in many places by wind-blown sands, sand sheets, and gravels.

Generally, the main geomorphologic features of the north Western Desert are: the absence of well marked drainage lines, the presence of some parallel belts of sand dunes of different lengths running mainly in a NNW direction, the presence of plateaus that are capped by resistant Eocene and Miocene limestone, and the presence of numerous extensive and deep-in depression, e.g. Bahariya Oasis, Faiyum and Wadi El-Rayian depressions. The second and third depressions are located in the study area.

Structurally, the north Western Desert has been extensively described by many workers, e.g. Said (1962), Youssef (1968), Meshref and El-Sheikh (1973), El-Gezerry et al. (1975), El-Sirafe (1985), Meshref (1980), Abu El-Ata (1988), Hantar (1990), Meshref (1990), and others.

The north Western Desert, where the area under investigation lies, is dominated by faults, many of which are step normal faults having a NE–SW, E–W, NW–SE and N–S trends. Some of these faults suffered strike-slip movements during a part of their history. There are also a large number of hanging faults affecting the shallower parts of the section and usually of limited throw. These faults are common in the northern part of the region.

Most folds owe their origin to compressional movements, which affected the area during the Late Cretaceous–Early Tertiary tectonic event. These folds have an ENE–WSW trend and a periclinal geometry. In addition, there are other folds, which owe their origin to normal or horizontal displaced faults (Hantar 1990).

Main concepts

There are some principles should be taken into consideration when working with the magnetic data. The interpretation of magnetic data is not unique, because it is controlled by many factors; for example, depth to top of the causative feature, its shape, its azimuth, its magnetic susceptibility, that is mainly related to its petrographical composition. Such factors are related to the subsurface anomalous features that produce their magnetic signatures at the surface. The availability and use of some of these factors during the interpretation reduce the ambiguity in the magnetic interpretation. Such factors can be taken from the available well data and regional geology of the area. The available magnetic data for this study have been corrected for the diurnal variations, instrument drift, and for the errors in positioning and height keeping.

Insights on the original magnetic data

The close study of the total intensity aeromagnetic map (Fig. 3) indicates that most of the observed anomalies show ENE–WSW trend patterns with some sharp gradients at varying locations. Since the magnetic maps are related directly to the basement rocks’ features, therefore, this indicates the presence of a basement relief change. This is because any sudden change in the magnetic contour spacing over a relative short distance suggests a discontinuity in the basement rocks, lithological variations within the basement rocks, or both.

The analysis of Fig. 3 (total intensity magnetic map) shows the existence of a major ENE–WSW low magnetic anomaly parallel to Birket Qarun, bounded between two magnetic highs at the northwestern and southeastern portions of the study area, with some superimposed smaller anomalies. The magnetic gradient to the northwestern portion is rather gentler than that of the southern one. The effects of the sub-topographic relief of the dissected basement surface and/or the small variations in susceptibility of its composing rocks caused such magnetic highs and lows. The occurrence of some basement intrusions into the sedimentary cover of the study area complicated the aeromagnetic pattern. The combined effect of these anomalies with the regional field of the geomagnetic field produced such observed aeromagnetic data. Therefore, the aeromagnetic map can be described in terms of the following parameters, the anomaly’s areal extension, shape, amplitude in gammas and the gradient.

Analysis of the magnetic data

The processing of the aeromagnetic anomalies is based on the analysis of the computer-digitized information using different processing techniques at different altitudinal levels from the compiled aeromagnetic data shown in Fig. 3. These techniques involve; first the reduction to the north magnetic pole. The reduced to the north magnetic pole digitized data were used for further investigative techniques that helped integratively to deduce the structural set-up for the basement of the considered area.

Reduction to the north magnetic pole

Since the study area is positioned within a low-latitude region in the northern hemisphere, the original aeromagnetic data subjected to reduction to the north-pole. A reduction-to-pole (RTP) transformation is standardly applied to the aeromagnetic data to minimize the polarity effects. These effects are manifested as a shift of the main anomaly from the center of the magnetic source and are due to the vector inclination of the measured magnetic field. The RTP transformation usually involves an assumption that, the total magnetizations of most rocks align parallel or anti-parallel to the Earth’s main field (declination = 3.439°, inclination = 43.279°, and IGRF total intensity value = 42,989 nT, for the study area). This assumption probably works well for the Tertiary units in the surveyed area, which are the focus of interpretation. The RTP aeromagnetic data, computed from the grid of total-field magnetic data, are shown in Fig. 4. This figure shows a kind of general northward shift of the magnetic anomalies, with the appearance of some sort of sharper magnetic gradients in the central part of the study area with a general ENE–WSW trend; in addition to a shorter N–S trend at the middle-eastern side of the study area.

Fig. 4
figure 4

Reduction to the Pole (RTP) map for the study area

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Upward continuation

Because of the potential nature of the potential fields (like in Gravity and Magnetic), they can be calculated at any elevation above (and in some cases below) the level of measurements, that is, if there is neither gravity nor magnetic sources between these two levels. This procedure is called the upward continuation of potential field. It is generally a useful and physically meaningful filtering operation. It allows smoothing the field and eliminating small anomalies (noises) in the form of noises from the near surface objects. In the spectral domain, upward continuation can be written as:

$$ \begin{gathered} F(u,v) = s(u,v) \times f\left( {u,v} \right) \hfill \\ F(u,v) = \frac{s(u,v)}{{1 + \alpha s(u,v)^{2} }} \times f(u,v) \hfill \\ \end{gathered} $$
(1)

where f(u,v) is the spectrum of the field to be transformed. F(u,v) is the spectrum of transformed (upward or downward continued) field. s(u,v) is the spectrum of the transformation and the small regularization parameter.

The upward continuation of the reduced to the pole data to an altitude above the measurements level will eliminate the effects of possible near-surface noises that may result in misleading responses. In the same time, upward-continued maps reflect the general configuration of the main sources of the magnetic anomalies, which is mainly the surface of basement rocks. This will, definitely, reduce the resolution of the magnetic anomalies.

In the current study, the upward-continued magnetic response was determined at three levels, 1 km (Fig. 5), 2 km (Fig. 6) and 3 km (Fig. 7) above the level of measurements. A closer look at those three maps showed that Fig. 5 exhibits more resolvable anomalous features than in Figs. 6 and 7. That is expected, since we are going further away from the magnetic sources, the smaller sources will be reduced in their responses. The upward-continued map at 1 km shows relative smaller anomalies superimposed on the wider regional magnetic responses. The two levels of 2 and 3 km upward-continued maps are showing more general pattern for the basement surface. This reflects that, there is a major plutonic uplift trending ENE–WSW within the study area. In addition, it can be noticed that, the big negative anomaly in Fig. 5, at the northwestern part of the study area, is reduced in its areal extension and amplitude, as shown in Fig. 7.

Fig. 5
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Upward-continues RTP map to 1-km level

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Fig. 6
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Upward-continues RTP map to 2-km level

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Fig. 7
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Upward-continued RTP map to 3-km level

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Downward continuation

Downward continuation highlights the high frequency content of a gridded magnetic data set, just as if the data had been acquired at a lower survey height. Theoretically, the field can also be continued downwards until the continuation level does not cross any field sources. However, it has been proved that, this operation is unstable because it greatly magnifies the existing noise and makes the field unusable.

To deal with this problem; some relaxation (regularization) techniques can be used. In the current study, that can be done through the use of Tikhnonov regularization parameter. The Tikhonov regularization parameter β (Tikhonov and Arsenin 1977) is important in the optimization process. Kristofer and Yaoguo (2007) explained that, in order to find the optimal data misfit, a Tikhonov parameter, β, is chosen based on the optimal model weighting. The regularization parameter is chosen, so the optimal solution is neither over-smoothing nor under-smoothing the data (i.e. fitting the noise or the signal). Several values for this parameter were tried to find the best for the data under study. This parameter was chosen such that the resulted data using the selected parameter’s value show some sort of similarity (in its overall representation) to the pattern of the original data to be downwardly continued.

The reduced-to-pole data (Fig. 4) is subjected to the downward continuation, with Tikhonov regularization parameter of 10−4, to transform the studied data to be as taken at lower levels. Downward-continued data to a relatively shallow depth will emphasize the residual components (of shallower sources) making the map noisier (as shown in Fig. 8). While, downwardly continued data to deeper depths will show less noisy-manifestations. Knowing that the average depth to the basement surface in the study area is in the range of about 4.5 km as known from some deep wells, the reduced-to-pole data were continued downwardly to three levels 1, 3, and 5 kilometers, as shown in Figs. 8, 9, and 10, respectively. As we are going deeper, below the original level of measurement, such downward-continued maps reflect the combined effect of the strikes of the subsurface structural elements, direction of magnetization, as well as the susceptibility contrasts between the sedimentary section and the underlying/surrounding basement. These structural features shown on such maps are slightly different, and will be discussed separately.

Fig. 8
figure 8

Downward Continued RTP Map at Level 1-km

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Fig. 9
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Downward Continued RTP Map at Level 3-km

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Fig. 10
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Downward Continued RTP Map at Level 5-km

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For the downward-continued map to 1 km depth

This map (Fig. 8) shows that, a −125 gamma contour line is located at the southeastern portion of the study area, while a +250 gamma contour lines are located within the middle portion of the study area with an ENE–WSW trend and accompanied by a number of smaller or local anomalies in a scattered fashion. This reflects the irregular nature of the closer-to-surface causative features; except the northwestern portion of the study area which shows some sort of less heterogeneity. The contour gradient is sharper in the middle portion of the study area and towards the south, but shows gentler behavior at the northern part of the study area. Many smaller wavelength local anomalies can be seen in this map, revealing the existence of limited small subsurface features, in either their composition and/or their altitude.

For the downward-continued map to 3 km depth

This map (Fig. 9) shows more relative regular contour lines with local features of different trends and amplitudes. As this map shows a downward-continued picture, it is clear that as we approaching the basement surface, so the magnetic effect will get bigger (in its positivity and negativity). Therefore, the middle portion of the study area shows relative high magnetic values (up to +750 gammas at the eastern part), while also the negativity increased in the northern part of the study area down to −250 gammas). The many localized features, in some localities, are signs that the basement surface still not reached yet. Sharper contour gradients can be seen especially at the southern half of the study area. Such gradients illustrate the presence of sharp contacts between the subsurface causative features. These contacts are most likely of fracturing effect.

For the downward-continued map to 5 km depth

This map (Fig. 10) shows smoother contour lines with higher amplitudes that reached +750 gammas, while also the negative contours are showing amplitudes of −750 gammas and less (down to −1,250 gammas). The smoothness of these contours gives an indication that this level is within the basement rocks and this reflects the combined effect of the structural elements and/or the lithological variations within the basement rocks. The gradients in those two maps are gentler than the previous map (Fig. 8), reflecting more homogeneity.

Extracting the magnetic sources using matching band-pass filtering

The RTP magnetic data of the study area can be used to illustrate this process. The shallow geologic units produce weak, short wave length magnetic anomalies. The deeper geologic units produce stronger magnetic anomalies with longer wavelengths. This is reflected by varying slops in the Fourier power spectrum of the aeromagnetic data, which has been averaged for all azimuths as illustrated in Fig. 11. The first step in designing a filter (using program MFDESIGN of Phillips 1997), is to fit only the short wavelength end of the spectrum with a straight line representing the spectrum of a thin magnetic layer containing a near-surface source layer (Fig. 11a). The effect of this layer is subtracted from the spectrum, and the intermediate wavelengths of the residual spectrum are fit with another straight line representing the spectrum of the intermediate source layer (Fig. 11b). This process is continued until the long wavelength end of the spectrum is fit with the deepest equivalent source layer (Fig. 11c). At this point, the combined spectrum of all the equivalent layers should approximately match the spectrum of the data (Fig. 11d). Fourier bandpass filters for extracting the magnetic signals of each of the equivalent layers are computed as the spectrum of the individual equivalent layer divided by the combined spectrum of all the equivalent layers (Fig. 11e).

Fig. 11
figure 11

In matched filtering, the radial power spectrum, is fit by series of linear curves representing the power spectra of simple equivalent magnetic layers

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The filters are applied to the observed data (using program MFFILTER of Phillips 1997) to separate the magnetic anomalies by apparent source depth. Figure 12 contains RTP magnetic anomalies produced by shallow geologic sources with equivalent dipole layer for this band-pass located at 0.30 km. The intermediate wavelength map (Fig. 13) involves RTP anomalies produced by geologic sources at intermediate depths. The equivalent RTP half-space for this band-pass is located at 1.18 km. Moreover, the long wavelength map (Fig. 14) includes the anomalies from the deepest and broadest features of the geology. Therefore, the equivalent magnetic half space for this band-pass is located at 3.9 km depth.

Fig. 12
figure 12

Short-wave length component of RTP magnetic data using matching filtering

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Fig. 13
figure 13

Medium-wave length component of RTP magnetic data using matching filtering

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Fig. 14
figure 14

Long-wave length component of RTP magnetic data using matching filtering

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Horizontal gradient maps

The horizontal gradient (HG) method is considered as the simplest approach to delineate the contact locations (e.g. faults). It requires a number of assumptions about the sources: (1) the regional magnetic field is vertical, (2) the source magnetization is vertical, (3) the contacts are vertical, (4) the contacts are isolated, and (5) the sources are thick (Phillips 1998). In contrast, the method is the lease susceptible to noise in the data, because it only requires the two first-order horizontal derivatives of the magnetic field. If T(x, y) is the magnetic field and the horizontal derivatives of the field are (∂T/∂x and ∂T/∂y), then the horizontal gradient HG (x, y) is given by:

$$ {\text{HG}}\,(x,y)\, = \,\sqrt {\left( {\frac{\partial T}{\partial x}} \right)\, + \,\left( {\frac{\partial T}{\partial y}} \right)} $$
(2)

Once the field is reduced to pole, the regional magnetic field will be vertical and most of the source magnetizations will be vertical, except for sources with strong remnant magnetization such as basic volcanic rocks. This technique has been carried out to the downward-continued data, along the three depth levels, 1, 3, and 5 km, below the surface of measurement. This resulted in three maps showing the distribution of the HG features, as shown in Figs. 15, 16, and 17. These horizontal-gradient maps are vivid, simple, and intuitive derivative products, which reveal the anomaly texture and highlight anomaly-pattern discontinuities. These maps contour the steepness of the anomaly relief’s slope. Horizontal-gradient maxima occur over the steepest parts of potential-field anomalies, and minima over the flattest parts. Short-wavelength anomalies are also enhanced.

Fig. 15
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Horizontal gradient map for 1-km downward-continued map

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Fig. 16
figure 16

Horizontal gradient map for 3-km downward-continued map

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Fig. 17
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Horizontal gradient map for 5-km downward-continued map

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Tectonic inferences of the basement discontinuities

The results and information obtained from the fore-mentioned critical analysis and interpretation were integrated with the general available geologic features to construct the predominant tectonic elements affecting the basement discontinuities of the study area (Fig. 18).

Fig. 18
figure 18

Map showing integrated basement structure discontinuities

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These tectonic features are either high trends (expressing anticlinal zones or swell-like belts) or low trends (referring synclinal zones or trough-like belts) and fault trends (throwing from the high trends to the low trends).

Accordingly, the basement surface is configured by three major swell systems and two trough belts. The northern high belt (swell) system trends mostly ENE–WSW with N–S splitting at the west end, which represents the Camel Pass–Abu Roash high (Abu El-Ata 1990).

While, the second swell orients mostly NE–SW (El Faras–El Faiyum High trend), with mostly E–W bifurcation at its western part (El-Sagha high trend) and other two small E–W, NNE–SSW bifurcations at its central part. The main trend of this belt represents the El Faras–El Faiym high trend.

The southwestern small third high belt (Camel-Pass belt), that starts in NW–SE direction and ends in the mostly N–S with E–W bifurcation at its southern end.

Moreover, the major central trough zone (Qatrani-El Gindi low trend) that run mostly ENE–WSW with N–S split at its western part and NW–SE split at its central part throughout Qarun lack. While, the southeastern trough belt orients NE–SW with two N–S and NNW–SSE splits at its southern end. In addition, a series of separated ENE–WSW and N–S small troughs are observed at the northern and southwestern parts of the map, beside a series of moderate N–S and NE–SW swells observed at the northwestern and southwestern corners.

These high and low trends are bounded and dissected by major and minor faults, in the form of horst blocks, graben blocks, or step-like blocks.

Horizontal gradient maps aided in defining the location of linear features, which in turn are related to the trend of the structural manifestations in the area. Faults can be traced easily along these linear features.

Results and conclusions

Through the downward-continued maps, it can be deduced that, some of the magnetic anomalies shown in Fig. 4, have sources within the sedimentary section, overlying the deep-seated basement rocks. The types, magnitudes, areal extensions, and distributions of such sources are expected to be in close relation with the basement rocks (i.e., supra-basement features).

It seems that, the whole area is portrayed as a part of a major sedimentary basin interrupted by several discontinuities in the form of smaller highs and lows. This reveals the complexity of the stress effects and directions exerted on the area, in form of compressional and tensional stresses. The predominant tectonic trends as delineated through N60°E with intermittent N–S directions. Such basement surface can be illustrated as being of several swells and troughs with zones of displacement of different reliefs, areal extensions and mainly oriented northeasterly. Block faulting could be the most prominent structural style.

Through integrating the whole set of maps together with the horizontal gradient maps, the faults were traced along these maps. The resulting set of lineaments was compared with the available well data that reached the basement surface, to determine the relative highs and lows in the basement rocks. Based on the integrated magnetic anomaly pattern from the different processed techniques used in this work, a number of magnetic highs (swells) and lows (troughs) features were delineated. Such swells and troughs are in the form of uplifted and down-faulted blocks within the basement. The illustrations showed, the major trends of the basement features are ENE–WSW, NE–SW, E–W and NNE–SSW trends. These major trends are interrupted by number of minor N–S trending faults with shorter areal extensions.

The fore-mentioned tectonic elements are shown in the basement tectonic map, and named related to Abu El-Ata (1990), Camel Pass–Abu Roash high, El-Sagha high, El-Faras-El-Faiym High as well as Qatrani-El Gindi low trends.