Introduction

Interpretation and enhancement of magnetic data are utilized for delineating the deep and shallow geologic structures (Sharma 1997). Moreover, the edge and texture detection allowed enhancing and identifying geologic contacts like lithologic boundaries and faults (Eldosouky et al. 2017).

Mapping and detecting the edges of magnetic sources, lateral magnetic variations, is a fundamental method for mapping the geologic contacts of magnetic data. Outlining these edges is similar to constructing a geologic map with the same lithologic units, whose edges are represented as geologic contacts. For aeromagnetic grids, there are many factors that can cause a lateral variation in magnetization other than the change in lithologies like the variation in mineral composition, metamorphism, and geologic structures, and it can reveal the alteration and deformity history of the region. Nevertheless, the edge delineation of magnetic data is a significant procedure for mapping various geologic units. Generating geologic maps from aeromagnetic data is essential in regions of overburden and large till cover. In the regions of well-exposed bedrock, the interpreters can trace connected magnetic assemblages between distinguished outcrops based on calibrated associations between lithology and anomaly shape by investigating the magnetic map. In till-covered regions, the geologic map is based particularly on interpretations of the aeromagnetic derivatives along with geophysical data; thus, accurate detection of edges is required to the map-generating process (Pilkington and Tschirhart 2017).

Dogru et al. (2016) used the edge detection methods to delineate the subsurface structures in geophysics to evaluate iron ore reserves. They concluded that the mentioned edge method was implemented to field data and gave a big agreement for the determination of the structure location.

Yan et al. (2016) used edge detection technique to interpret the potential field data for exploring the mineral, energy resources, and regional tectonics. Oliveiraa et al. (2017) proposed an algorithm to locate the edges of anomalies automatically in potential field data and to estimate the width and depth of causative sources. This algorithm found that the suggested approach presents reliable estimates for the objective parameters when compared with Euler deconvolution.

Samr El-Qaa area was studied by many authors. Said (1962) and El-Gaby (1983) illustrated the geology and tectonic setting of the study area. Bayoumi and Boctor (1970) and Abdel-Rahman and El-Etr (1980) used potential field data to detect the structural trend and the depth to the basement at Samr El-Qaa area.

The aim of the present study is to detect the edges from aeromagnetic data for delineating deep and shallow fault systems of Samr El-Qaa region using recent theta and HTAD techniques and to deduce the geologic information from the geophysical data, improve the existing edge-detection techniques, efficiency, edges continuity, reducing noise influences, and limiting the effects of variable depth to the body and source dip.

Geology of the study area

Samr El-Qaa area is located at the North Eastern Desert of Egypt, near the western side of the Gulf of Suez, to the west of Ras Gharib City (Fig. 1). The area extends between latitudes 28° 05′ 38″ N and longitudes 32° 04′ 36″ and 32° 40′ 22.76″ E, covering an area about 2400 km2. Various lithologic associations ranging in age from the Precambrian to the Quaternary describe the exposed rock units in Samr El-Qaa area.

Fig. 1
figure 1

Map of Egypt showing the area of Samr El-Qaa in the NED

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Samr El-Qaa area is dissected by several valleys, which mostly are structurally controlled and flow towards the east in the Gulf of Suez. The study area is characterized by rugged topography in its eastern part which mainly occupied by mountains of basement complex (mostly formed of granitic and volcanic rocks), while the western part is covered by sedimentary rocks, which is less complicated and mountainous than the eastern part (Hassanein and Soliman 2009).

Stern and Hedge (1985) illustrated the Eastern Desert (ED) of Egypt distinguished by three important basement zones, i.e., south (SED), north (NED), and central (CED). The CED is separated from NED by a boundary characterized by the dextral strike-slip fault (dipping NW) (Greiling et al. 1994; Stern and Hedge 1985). Stern and Hedge (1985), depending on radiogenic ages and field associations of the most types of rock units in the Eastern Desert, concluded that the NED is discriminated by the youngest rocks, while the oldest rocks are predominant in the CED and SED. The predominance of Ediacaran non-metamorphosed volcano-sedimentary sequences (590–630 Ma), including Hammamat sediments and Dokhan volcanics (Ressetar and Monard 1983), is the main character of the NED (Breitkreuz et al. 2010).

Despite Hammamat sediments are not eternally linked to Dokhan volcanics, the northernmost appearances in the NED, including Gabal Samr El-Qaa, are represented singly by Dokhan volcanics and lack of the intercalations of Hammamat sediments. Further, plutons of the Younger Granite and dikes are dominant in the NED, whereas there is a prevailing lack of ophiolites. Older volcanics (≈ 750 Ma) (Ali et al. 2009) occur further southward in the SED and CED and are grouped into Older and Younger metavolcanics, which are assumed to be ophiolitic and island arc volcanics respectively (Stern 1981).

Various lithologic units, including many types of sedimentary, metamorphic, and igneous rocks, are the main characteristics of Samr El-Qaa area. In addition, the location of the Gulf of Suez at the eastern side of Samr El-Qaa area in the NED of Egypt gave the area more significant setting. Accordingly, the area has been studied by several authors (Bayoumi and Boctor (1970), Ammar et al. (2003), and others). The geology of Samr El-Qaa area is derived from sheet no. (NH36SW, Beni Suef, CONOCO 1987). The geologic map of the study territory (Fig. 2) describes that the area is occupied by various types of the basement and sedimentary rock units.

Fig. 2
figure 2

Geologic map of Samr El-Qaa area (after Conoco, 1987)

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The geologic map of Samr El-Qaa district (Fig. 2) reveals that the eastern region of the studied territory is occupied by basement rocks. Younger granites (pink), Older granites (red), and metavolcanics are the main units of these basement rocks. Meanwhile, various types of sedimentary deposits cover the western portion of the area differing in age from the Paleozoic to Cenozoic. They consist of Araba Formation (sandstones), Samr El-Qaa Formation (shale), Wadi Qena Formation (sandstones), Galala Formation (limestone), Esna Formation (shale), Thebes Formation (limestone), Mokattam Formation, Sudr Formation, Rakhiyat Formation, Hawashiya Formation, Umm Omeiyid Formation, and Quaternary (Undifferentiated Sediments). The contact zone between the basement and sedimentary sequences is considered as an unconformity boundary (CONOCO 1987).

According to Bayoumi and Boctor (1970), the regional structure of Samr El-Qaa area is the NE-SW direction, perpendicular to the prevailing trend system of the fault systems, making horsts and grabens. Whereas Nossair (1981 and 1987) illustrated that the NE-SW, NNE-SSW, and NNW-SSE are the major structural sets and the NE-SW, NW-SE, and N-S are the predominant joint trends affecting Samr El-Qaa area.

Aeromagnetic data and methodology

In this study, reduced to the pole (RTP) data of Samr El-Qaa district was used after subtracting the International Geomagnetic Reference Field (IGRF) using the Gesoft Oasis packages (Geosoft 8.3.3 V) (Fig. 3), which is provided by the Aero Service Company (1984) for the Egyptian Mineral Resources Authority. The airborne geophysical scanning was done with a 32.8 N inclination, 1.9 E declination, and with a flight height of 120 m. Therefore, the TMI map was processed using the RTP method (Kearey and Michael 1994) after subtracting the International Geomagnetic Reference Field (IGRF) using the Gesoft Oasis packages (Geosoft 8.3.3 V).

Figure 3
figure 3

RTP map of Samr El-Qaa area

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Reduction to the pole

Pole reduction is a technique which makes the magnetic bodies appear as if observed at the pole and takes anomalies and changes their asymmetric pattern to the symmetric style (Baranov 1957). The domain of frequency is given by:

$$ {A}^{\prime}\left(u,v\right)=\frac{A\left(u,v\right)}{{\left(\sin \theta +i\cos \theta \sin \left(\varphi +\alpha \right)\right)}^2} $$
(1)

where the amplitude is A(u,v), α is tan−1(v/u), and φ and θ are the magnetic declination and inclination.

Theta derivative

Various enhancements were practiced to appear weak anomalies of aeromagnetic maps, i.e., automatic gain control (Cooper 2009) and tilt derivative (Miller and Singh 1994). Theta derivative can produce noise in results less than the other filters when applied to downward and upward continued data (Cooper 2017).

Theta derivative was introduced by Wijns et al. (2005) for detecting the edges of magnetic anomalies. It is the ratio between the horizontal gradient magnitude (HGM) (Blakely and Simpson 1986) and the analytic signal (AS) (Roest et al. 1992) and is given by:

$$ \mathrm{Theta}\ \left(\cos \theta \right)=\left(\frac{\mathrm{HGM}}{AS}\right) $$
(2)

Where:

$$ AS\left(x,y\right)=\sqrt{{\left(\frac{\partial A}{\partial x}\right)}^2+{\left(\frac{\partial A}{\partial y}\right)}^2+{\left(\frac{\partial A}{\partial Z}\right)}^2} $$
(3)
$$ \mathrm{HGM}\left(x,y\right)=\sqrt{{\left(\frac{\partial A}{\partial X}\right)}^2+{\left(\frac{\partial A}{\partial y}\right)}^2} $$
(4)

and \( \frac{\partial A}{\partial x} \), \( \frac{\partial A}{\partial y} \), \( \frac{\partial A}{\partial Z} \) are the two horizontal gradients in x and y directions and the vertical gradient respectively.

Horizontal tilt angle derivative

The horizontal tilt angle derivative (HTAD) was presented by Cooper and Cowan (2006) as a method for detecting the magnetic edges. It is expressed by:

$$ \mathrm{HTAD}={\tan}^{-1}\left(\frac{\mathrm{HGM}}{\frac{\partial A}{\partial Z}}\right) $$
(5)

Upward continuation

Upward continuation is recognized as a distinct filter because it provides practically no side effects that may require the utilization of other enhancements to correct. It decreases the effects of higher wave number (shorter wavelength) elements associated with more local, shallower anomaly bodies; thus, it can be used as a powerful smoothing procedure for the departure of anomalies due to deeper origins. Moreover, the obtained data from upward continuation may be represented numerically and with modeling software. This is not the character for many other filter methods. The Geosoft formula to determine upward continuation is:

$$ L(r)={e}^{- hr} $$
(6)

where (h) is the distance to the continuation level and (r) is the wave number (Dobrin and Savit 1988).

Results

The methods of edge analysis (AS, HGM, theta, HTAD) were applied to RTP data.

AS and HGM of RTP data (Figs. 4 and 5) show the general fault trends affecting Samr El-Qaa territory. These two maps illustrate that the most predominant structural trends are NNE, NE, N-S, NNW, WNW, E-W, and NW directions. Moreover, the contact between the sedimentary deposits in the western part of the study region and the basement rocks in the eastern part is revealed in the HGM map of RTP (Fig. 5). However, the boundaries of faults could not be detected sharply in the results of AS and HGM of RTP data because their responses include the effects of deep structures.

Fig. 4
figure 4

AS map of RTP data of Samr El-Qaa area

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Fig. 5
figure 5

HGM map of RTP data of Samr El-Qaa area

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The results of theta and HTAD maps (Figs. 6 and 7) provide detailed information about the geologic units and fault boundaries of Samr El-Qaa region. The fault edges and rock boundaries are well delineated in the theta and HTAD of RTP maps. These maps (Figs. 6 and 7) clearly mapped the NE-SW fault trend direction which scattered the study area starting from the north part of Wadi Hawashiya to the northeastern part of the study region along the Alkali-feldspar granite. Moreover, the boundary between the basements to the east and the sedimentary cover to the west is sharply mapped. The edges of metavolcanics and Dokhan volcanics in the southeastern corner of the study area are clearly distinguished to be controlled along the NW, E-W, NE, NNW, and N-S directions. The good inspection of these maps showed that the eastern section (basement rocks) is more complicated in its structural pattern than the western part (sedimentary cover), where the NW, NE, NNW, E-W, N-S, and NNE directions are the main structural trends affecting the basement rocks (eastern part), while the sedimentary cover (western part) is controlled by the NW and NE directions.

Fig. 6
figure 6

Theta map of RTP data of Samr El-Qaa area

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Fig. 7
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HTAD map of RTP data of Samr El-Qaa area

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The upward continuation (UC) was applied to RTP map of Samr El-Qaa area at 3 km to reveal the basement at this altitude as shown in Fig. 8. The upward continued data reveal increasing attenuation and broadening of the high wave number anomalies with increasing altitude above the investigated area.

Fig. 8
figure 8

UC map of Samr El-Qaa area (3 km level)

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The same methods of edge analysis (AS, HGM, theta, and HTAD) were applied to the UC data. The response of AS and HGM of UC (3 km) (Figs. 9 and 10) from deep sources does not provide the assumed sharp slope over the magnetic edges. They give a general picture of the subsurface faults.

Fig. 9
figure 9

AS map of UC (3 km) of Samr El-Qaa area

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Fig. 10
figure 10

HGM map of UC (3 km) of Samr El-Qaa area

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Otherwise, the theta and HTAD maps (Figs. 11 and 12) of UC (3 km) give more information about the subsurface geologic rock units of the area. Theta map (Fig. 11) delineates deep fault edges well. The N-S, ENE, NW, NNE, and NE are the main deep fault patterns at Samr El-Qaa. HTAD map (Fig. 12) of UC (3 km) sharply outlined and mapped the edges and boundaries of deep geologic units. The golden-yellow line in Fig. 12 represents the magnetic edges of deep units and structures.

Fig. 11
figure 11

Theta map of UC (3 km) of Samr El-Qaa area

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Fig. 12
figure 12

HTAD map of UC (3 km) of Samr El-Qaa area

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Discussion

Figure 13a and b represents the interpreted structural maps derived from shallow and deep theta and HTAD maps of Samr El-Qaa territory to illustrate the prevailing tectonic pattern in the study area.

Fig. 13
figure 13

Shallow structural map (a) and deep structural map (b) of Samr El-Qaa area

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The delineated structural elements in the shallow structural map (Fig. 13a) are statistically investigated by considering the azimuth and the number of aeromagnetic lineaments in each 10° and are displayed in the form of the rose diagram as shown in Fig. 14a. The shallow rose diagram (Fig. 14a) shows that the most dominant trends are arranged in the NNE, ENE, NNW, N-S, E-W, and WNW directions.

Fig. 14
figure 14

Shallow rose diagram (a) and deep rose diagram (b) of Samr El-Qaa area

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The deep structural map (Fig. 13b) and the deep rose diagram (Fig. 14b) indicate that the ENE, N-S, E-W, NNW, and NW directions are the main subsurface structural trends controlling Samr El-Qaa area. Moreover, NNE direction was the dominant trend in the geologic and shallow structural maps and appeared as a minor trend in the deep altitudes indicating that it is the youngest structural trends controlling Samr El-Qaa district.

According to Meshref and El-Sheikh (1973), the NNE (Aqaba) trend is the prevailing tectonic trend and Sinai and the Gulf of Aqaba. It is probably a common shallow cross-trend in the Red Sea and Suez Gulf fault block mosaic. While the N-S (East-African) trend was considered as one of the oldest fractures in the Egyptian Eastern Desert (EED) (Tealeb 1979), moreover, the E-W (Tethyan) trend was considered as the oldest fault pattern in Egypt and the oldest tectonic fault affecting the basement of Egyptian (El-Shazly 1966). The N-S and E-W trends were the predominant tectonic faults affecting the study region as shown in the shallow and deep structural maps (Fig. 14a, b).

Theta and HTAD edge detector methods were applied for enhancing magnetic anomalies for sharp detection of magnetic features and source edges of Samr El-Qaa territory that equalize signals from ear surface and deep sources. The effectiveness of the approach is estimated by correlating it with other edge detection techniques that have been earlier described in the literature and that make application of derivatives. The results confirm that theta and HTAD are less sensitive to the depth variation of the sources and that they map the location of the causative body edges in an extra accurate way when compared with previous AS and HGM methods, also for anomalies due to multiplied interfering origins. These results display that the theta and HTAD methods are useful tools for interpreting the magnetic data qualitatively.

Calculated edge locations estimated from these methods appear sufficiently accurate, less sensitive to noise, and continuous, and detailed outcomes to afford a stable basis on which the mapping operations were based and achieved successfully.

Conclusions

AS, HGM, theta, and HTAD methods were applied to RTP and upward continued (UC) (3 km) data of Samr El-Qaa area to define the edges of surface and deep geologic units and fault boundaries. AS and HGM maps of RTP data illustrated that the most predominant shallow structural trends are arranged in the NNE, ENE, NNW, N-S, E-W, and WNW directions, but the response of AS and HGM of UC (3 km) from the deep sources does not provide the assumed sharp slope over the magnetic edges.

The theta and HTAD maps of RTP and UC (3 km) data provide more information about the shallow and subsurface geologic rock units. Theta map successfully delineated fault edges, while HTAD map sharply outlined and mapped the edges and boundaries of geologic rock units.

As a general conclusion, it can be concluded that the AS, HGM, theta, and HTAD techniques were successfully applied for outlining the edges of aeromagnetic data at Samr El-Qaa territory.

The present study illustrated that the estimated edge positions calculated from the theta and HTAD techniques are sufficiently reliable and continue to give a solid basis on which the mapping operations were based and accomplished successfully. The theta and HTAD approach used in this study are broadly suitable to other parts of the Egyptian Eastern Desert and other districts with related geological conditions in Africa and the world which can be used for mineral and oil/gas exploration.