1 Introduction

G. (Gebel, mountain) El-Maghara has an economic importance in Sinai Peninsula, Egypt because it has the only Egyptian coal mine. It represents one of the largest anticlines in northern Sinai, along with G. Yelleg and G. Halal. It extends several tens of kilometers long (c. 60 km) with width of 13–17 km. Structurally, it is composed of four main asymmetric anticlines (Maghara, Hamayir, Um Mafruth, and Um Asagil) trending in NE–SW direction [1, 2]. The origin of the NE–SW trending anticlines in the region including El-Maghara fold has been explained by two different hypotheses. The suggested scenarios for the formation of these structures in Egypt's unstable shelf include vertical uplift stresses and lateral compression [3].

The gravity method which measures the changes in the gravitational field has various applications. These applications range from deep to near surface studies, including the study of Earth's crustal structure, basement depth calculations, geothermal exploration, environmental and engineering surveys, and archeological investigations [4,5,6,7,8,9,10,11,12,13,14,15,16]. Edge detectors as tools of potential field data interpretation have become essential for subsurface structural mapping of contacts, faults, dykes, and ore bodies [17,18,19,20]. Generally, gravity signal amplitudes show a large dynamic range which depends on the sources’ depths, geometries, and density values [21]. Therefore, the use of advanced edge detection techniques can help in imaging the boundaries of gravity sources of week amplitudes.

Both horizontal and vertical derivatives of the potential field are the most prominent used for edge detection. Over the last decades, different filters have been developed to precisely delineate the edges of the potential field sources. They reflect a significant increase in the quality and the accuracy of edge location and a considerable reduction in inherent noise. Among these filtering techniques are: the total horizontal gradient (THD) [22], analytical signal (AS) [23], tilt angle derivatives (TDR) [24], total horizontal derivative of the tilt angle (THD_TDR) [25], Theta map (also called Cos theta) [26], horizontal tilt angle (TDX) [27], tilt angle of the horizontal derivative amplitude (TAHG) [21], tilt angle of the analytic signal amplitude (\({T}_{AS}\)) [28], NTilt [29], STDR and it total horizontal derivative (THD_STDR) [20], improved analytical signal (IAS) [30], Softsign Function (SF) [31], normalized Harris filter (NHF) [32], and improved horizontal tilt angle (impTDX) [33].

The study area is situated between latitudes 30°37` and 30°46`N and longitudes 33°09` and 33°27`E in northern Sinai Peninsula (Fig. 1). The main goal of the current study is to characterize the structural architecture and evaluate the tectonic settings of the investigated area using gravity data. Firstly, the effectiveness of various edge detection techniques was tested on synthetic data, then the most suitable filters were applied to the gravity data of G. El-Maghara area.

Fig. 1
figure 1

Satellite images from the Google Earth show the location of the study area. Imagery ©2022 Landsat/Copernicus, used in accordance with the Google Maps/Earth terms of service for research purposes

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2 Geological and Structural Settings

Generally, the area of G. El-Maghara is covered by a sedimentary sequence with a highest thickness of about 2000 m (Fig. 2a) representing the Jurassic-Cretaceous age and considered the most complete Jurassic exposure in Egypt [34]. It is represented by six formations arranged descending from top to base: Masajid (Late-Jurassic), Safa, Bir El-Maghara (Middle Jurassic), Shusha, Rajabia and Mashaba formations (Early Jurassic) (Fig. 3). Lithological settings of such formations show three depositional cycles of sea transgressions and regressions [35]. Stratigraphically, sedimentary rocks in G. El-Maghara (particularly the limestones) have been affected by several tectonic stages controlling their geomechanical and petrophysical characteristics [36].

Fig. 2
figure 2

(a) Geological and surface structural lineaments map of G. El-Maghara area and its surrounding, northern Sinai Peninsula, Egypt (reproduced after [41]). Rose diagrams representing the azimuth frequency of the structural lineaments trends according to their numbers (b) and lengths (c)

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Fig. 3
figure 3

Litho-stratigraphic column representing the exposed formations at G. El-Maghara area (modified after [38])

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Masajid Formation is composed of pale-gray limestone with nodules of chert and stylolitic structures with small shale interbeds. Its thickness ranges from 300 to 500 m [37]. Safa Formation includes about eleven seams, only two of them are minable and economic: the upper coal seam (UCS) and the main coal seam (MCS) with thickness of 130–190 cm at Maghara area [38]. Thus, this formation is highly important due to its content of coal bearing seams. Based on exploration well data, its geologic coal reserve is estimated to be 52 Mt [39]. Such coals formed in lagoons or lakes adjacent to the coastline [40]. The lower part of this formation consists of alternations of sandstone, shale with hematitic sands alternated with sandy shale and many lenticular coal seams. Bir El-Maghara Formation is sub-grouped into three members: Mahl Member (94 m) of highly oncolitic packstone bioturbated, and shale containing few fossils of corals and gastropods, Bir Mowerib Member (132 m), and Bir El-Maghara Member (216 m) consisting of clays with interbeds of hard coralline grayish algal limestone with gastropods, brachiopods, ammonites, bivalves, and corals [35]. This formation reveals a shallow subtidal depositional environment with some high terrigenous input [36]. Shusha Formation is composed of intercalation of continental cross bedded sandstone, shales (sideritic concretions), and clays. Rajabia Formation represents interbeds of brownish sandstone and yellow marl representing the lower part of the formation. Its middle part consists of dolomitic limestone with intercalations of thin beds of sandy limestone and sandstone. Its dominant environments are an extension of the depositional environments found in the upper parts of Mashaba Formation [42]. Mashaba Formation is made up of about 100 m thick of cross bedded sandstones with clay, sandy limestone interbeds. It is distinguished by mottled appearance because of its high content of iron oxides [43] and is sub-grouped into two members: lower of shallow marine, tidal and fluvial deposits, and upper consisting of fossiliferous lagoonal limestones with interbeds of deltaic sandstones [34].

Lower Jurassic formations differ greatly in thickness from place to another in the study area depending on the structural settings and facies lateral changes [36]. Most of the Jurassic section was described to have rich potential source rocks exceeding 1.5% Total Organic Carbon (Toc) in Masajid, Safa, Bir-Maghara and Shusha formations [44].

Structural evaluation of the northern Sinai folds has been carried out by several researchers [1,2,3, 45, 46]. These folds are commonly asymmetric, with a steeper southeastern flank and a gentle northwestern flank (dipping about 5°–20°). During the Senonian time, Jurassic basins were formed and then inverted along the African and Arabian margins [47, 48]. This tectonic inversion developed a zone of intensively folded and faulted mountains on these margins, forming the Syrian Arc System [49]. The northern extension of the Syrian Arc inversion structures into the southeastern Mediterranean region is considered the North Sinai offshore area. The northern and central parts of Sinai were shallow shelf (with low relief) and coastal plain, dissecting the continental shield of Arabo-Nubian to the south from Tethyan Sea to the North [43].

G. El-Maghara is a large, breached anticline with a gently sloping north flank and a steep (often vertical) to over-turned southern flank. It is also considered as an anticline with an asymmetric doubly plunging which directed with the same trend of the Syrian Arc System at northern Sinai area, while the core of El-Maghara region seems like a dome [39]. Some reverse faults with dipping angles of more than 45° in few folds in northern Sinai were mapped [1]. However, these reversed faults were reported to be with low angle thrusts. The surface reverse faults in northern Sinai show a similar northwestward dip, implying a southeastward vergence [45]. Structural deformation at the area corresponded by huge subsurface anticlines affecting hydrocarbon potential and geological history of the region was mentioned by [43].

Northern Sinai has been affected tectonically by four phases of deformation: (i) Paleozoic–Triassic extensional tectonics due to the divergence between the Afro-Arabian and Eurasian plates and opening of the Tethys. In this phase, deep-seated faults trending ENE–WSW were reactivated [44], (ii) the Late Cretaceous–Early Tertiary extensional tectonics resulting in forming the Syrian Arc System. This event produced a series of asymmetrical doubly plunging anticlines trending in NE to ENE direction. The Syrian Arc folds in northern Egypt include both inversion and non-inversion folds [50]. Locally, the boundaries to these folds are formed by faults oriented in the ENE–WSW and E–W directions [2], (iii) the Late Oligocene–Early Miocene compressional tectonics due to the convergent movement between the Afro-Arabian and Eurasian Plates. Normal faults trending NNW–SSE are dominating in this tectonic phase [51], and (iv) the Late Miocene–Recent tectonics due to the divergence of African and Arabian plates. It is associated with the Dead Sea transform's sinistral strike-slip movement [1].

A statistical analysis was conducted to examine the trends of the surface structural lineaments in the study area, which were identified from the geological map (Fig. 2a). The findings were graphically presented through rose diagrams, illustrating the frequency of azimuths for both the number (Fig. 2b) and length (Fig. 2c) of the structural lineaments. The results show prominent prevalence of surface structural trends oriented in the NE–SW to ENE–WSW directions, corresponding closely with the well-known Syrian Arc System observed in northern Egypt.

3 Data and Methods

3.1 Remote Sensing Data

This study employed imagery from the Landsat 8 satellite's Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS) for analysis. The OLI sensor captures images in the visible, near-infrared (NIR), and short-wave infrared (SWIR) spectra, while the TIRS sensor is specifically designed for thermal infrared imagery. The imagery used in this study was acquired from Path 175 and Row 39 on July 22nd, 2022. The data were obtained from the Earth Explorer data portal, a platform maintained by the United States Geological Survey (USGS) and accessible at https://earthexplorer.usgs.gov/. The downloaded data were provided in the Universal Transverse Mercator (UTM) projection, utilizing the WGS 84 World Geodetic System. The Landsat 8 image utilized in this study consisted of eleven bands with varying wavelengths and resolutions, as outlined in Table 1. In the field of geology, the optical bands (OLI) ranging from the Coastal aerosol (Band 1) to the panchromatic band (Band 8) are widely utilized [52,53,54]. In the ongoing research, the OLI image is being utilized to map the structural lineaments [55, 56], as their analysis enables the identification of highly faulted zones [57].

Table 1 Landsat 8 satellite’s spectral bands
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Principal Component Analysis (PCA) is a widely employed technique for analyzing Landsat data. It offers valuable insights into the information contained within multispectral images captured by Landsat satellites. PCA allows researchers to extract meaningful patterns and reduce the dimensionality of the data, facilitating easier interpretation and visualization [58, 59]. The application of Principal Component Analysis (PCA) technique in false color composites (FCC) enhances contrast in images. Specifically, the contrast is more pronounced in white and black versions [60]. Figure 4 displays the PCA image obtained from Landsat 8 data. Among the principal components, PC1 was identified as the most suitable for mapping lineaments in the study area. The lineament extraction process involved automatic extraction using the LINE tool in PCI Geomatica 2013 software. This algorithm improves data edges by employing specific parameters such as edge detection, thresholding, and curve extraction [61]. For this study, default parameters of the algorithm were utilized. The results of the automatic extraction technique for lineaments, as shown in Fig. 5a, reveal that the primary lineament system exhibits orientations ranging from ENE–WSW to E–W directions (Fig. 5b, c) which coincide with the faults trends surrounding the folds of the study area mentioned by [2]. The majority of lineaments are concentrated in the central and western regions of the study area.

Fig. 4
figure 4

The PCA image of the study area

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Fig. 5
figure 5

(a) Lineaments map extracted from the PCA image of the Landsat 8. Azimuth frequency rose diagrams representing structural trends of obtained lineaments according to their numbers (b) and lengths (c)

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3.2 Gravity Data

The gravity data of G. El-Maghara area and its surrounding have been digitized from the Bouguer gravity map of Egypt produced by [62] with a scale of 1:100,000 and a contour interval of 1 mGal. The obtained Bouguer gravity map of the study area (Fig. 6) shows gravity values range from − 34.62 to 16.30 mGal. Two distinguished gravity zones can be noticed. Positive gravity zone to the northwest with a maximum gravity value of 16.3 mGal and negative gravity zone to the southeast with a gravity value of − 34.62 mGal.

Fig. 6
figure 6

Bouguer gravity map of the study area

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3.3 Digital Edge Detection Filters

Using edge detection techniques became common in interpretation of gravity anomalies [18]. Nine filters have been chosen to be applied to dataset produced by synthetic modeling study. The outcomes of these filters have been compared and evaluated then some of them which gave good results have been further applied on real gravity data. These edge detectors are THD, AS, TDR, Theta map, TDX, TAHG, STDR, THD_STDR, and SF.

The THD filter shows maximum values over the body`s edges where it helps to enhance the body's edges [22]. The THD filter is given by Eq. (1):

$$THD = \sqrt {\left( {\frac{\partial f}{{\partial x}}} \right)^{2} + \left( {\frac{\partial f}{{\partial y}}} \right)^{2} }$$
(1)

where f is the gravity field, \(\frac{\partial f}{\partial x}\) and \(\frac{\partial f}{\partial y}\) are the derivatives of the gravity field in x and y directions, respectively.

The AS was introduced by [23] through Eq. (2) where the maxima of AS form an anomaly of bell-shaped over the causative body.

$$AS = \sqrt {\left( {\frac{\partial f}{{\partial x}}} \right)^{2} + \left( {\frac{\partial f}{{\partial y}}} \right)^{2} + \left( {\frac{\partial f}{{\partial z}}} \right)^{2} }$$
(2)

where \(\frac{\partial f}{\partial y}\) is the vertical derivative of the gravity field. A disadvantage of this filter is that it could not detect body`s boundaries of weak anomalies, therefore there would be a diffusion in detection the edges of the source [63, 64].

The TDR was proposed by [24] using Eq. (3):

$$TDR = \tan^{ - 1} \left( {\frac{\partial f/\partial z}{{THD}}} \right)$$
(3)

The TDR function has a range of − 90 to + 90°. The highest TDR values overlie the body, while the lowest values are located outside it, and the zero values are found over the body’s edges. However, the TDR filter is unable to distinguish very closely spaced bodies [27]. It also causes ambiguous display for the edges of deep sources [21].

By using the ratio between the THD and the AS (Eq. 4), the Theta map edge detector was introduced by [26] as follow:

$$Theta map \left( {{\text{Cos}} \theta } \right) = \left( {\frac{THD}{{As}}} \right)$$
(4)

The TDX filter (Eq. 5) has been suggested by [27]. Its maximum values correspond to the edges of the causative sources. Results from applying TDX filter are similar to those obtained from Theta map filter as they both diffuse and give wider estimation for the detected edges than their true locations [21, 65].

$$TDX = \tan^{ - 1} \left( {\frac{{\sqrt {\left( {\frac{\partial f}{{\partial x}}} \right)^{2} + \left( {\frac{\partial f}{{\partial y}}} \right)^{2} } }}{{\left| {\frac{\partial f}{{\partial z}}} \right|}}} \right)$$
(5)

The TAHG filter has been introduced by [21] in a trial to avoid the disadvantages of previous edge detectors. It is expressed by the following equation (Eq. 6):

$$TAHG = \tan^{ - 1} \left( {\frac{{\frac{\partial THD}{{\partial z}}}}{{\sqrt {\left( {\frac{\partial THD}{{\partial x}}} \right)^{2} + \left( {\frac{\partial THD}{{\partial y}}} \right)^{2} } }}} \right)$$
(6)

Maxima of TAHG reveal the edges of sources. Despite the fact that it is efficient for detecting the source edges very precisely, it is not suitable for discrimination between closely spaced bodies. Consequently, the resolution of the results would be significantly reduced [20]. To overcome the problem of anomaly edge`s diffusion during the process of field potential data interpretation, the STDR filter was proposed by [20]. It is calculated using Eq. (7):

$$STDR = \tan^{ - 1} \left( {M\frac{{\frac{{\partial^{2} f}}{{\partial z^{2} }}}}{{\sqrt {\left( {\frac{\partial THD}{{\partial x}}} \right)^{2} + \left( {\frac{\partial THD}{{\partial y}}} \right)^{2} } }}} \right)$$
(7)

where \(\frac{{\partial }^{2}f}{\partial {z}^{2}}\) represents second-order vertical derivative of the gravity field. M is a positive number set by the interpreter. In gravity, it represents the absolute gravity value in the study area. The STDR shows positive values over the causative body. It also equalizes the intensity of shallow and deep sources and has the ability to distinguish between adjacent sources. In order to detect the boundaries with sharp edges, [20] suggested the calculation of the THD of the STDR function (Eq. 8).

$$THD\_STDR = \sqrt {\left( {\frac{\partial STDR}{{\partial x}}} \right)^{2} + \left( {\frac{\partial STDR}{{\partial y}}} \right)^{2} }$$
(8)

The SF filter (Eq. 9) was introduced by [31] using the function of softsign and the horizontal gradient derivatives in attempt to balance the signals generated by geological structures at different depths without any spurious locations of boundaries.

$$SF = \frac{{k \times THG_{z} - \left( {k + 2} \right) \sqrt {\left( {THG_{x} } \right)^{2} + \left( {THG_{y} } \right)^{2} } }}{{\sqrt {\left( {THG_{x} } \right)^{2} + \left( {THG_{y} } \right)^{2} } + \left| {k \times THG_{z} - \left( {k + 1} \right)\sqrt {\left( {THG_{x} } \right)^{2} + \left( {THG_{y} } \right)^{2} } } \right|}}$$
(9)

where \(TH{G}_{x}\), \(TH{G}_{y}\), and \(TH{G}_{z}\) are the gradients of potential field`s total horizontal gradient in x, y, and z directions. k is a positive real number decided by the interpreter. The maximum values of SF are located over the source’s boundaries. The radian was demonstrated as the unit of the SF filter’s outcome by [31] but it worth mentioning here that the SF has no unit (refer to Eq. 9).

3.4 Synthetic Modeling Study

A synthetic model study has been carried out to evaluate the efficiency of several published edge detection techniques. The model presumed the existence of three prism bodies G1, G2, and G3 located at different depths 3 km, 9 km, and 15 km, respectively (Fig. 7a). The geometry and the physical parameters of these bodies are shown in Table 2. Two synthetic gravity datasets with a grid of 100 km × 100 km were produced from the synthetic modeling, one is free of noise and the other is contaminated with Gaussian noise. The gravity map (Fig. 7b) generated by the three sources shows that the gravity values range from 0.8 to 19.2 mGal.

Fig. 7
figure 7

(a) 3-D view of the synthetic model showing the three bodies (prisms) G1, G2, and G3 located at depths of 3, 6, and 15 km, respectively. (b) gravity anomaly map resulted by the three gravity sources within a grid of 100 × 100 Km2. The black lines refer to the true boundaries of the gravity bodies

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Table 2 Physical and spatial parameters of the presumed synthetic model’s gravity sources
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The outcomes of applying different filters (i.e., THD, AS, TDR, Theta, TDX, TAHG, STDR, THD_STDR and SF) on both noise-free and noise-contaminated datasets of the synthetic models are displayed in Figs. 8 and 9. Figures 8a and 9a illustrate the results of applying the THD filter which acts well with shallow anomalies and shows high anomaly over the body G1 but with larger width. The filter did not succeed in detecting the boundaries of intermediate (G2) and deep (G3) gravity sources. However, the THD filter shows less sensitivity to noise. Although the AS maps (Figs. 8b and 9b) present high gravity anomalies over the causative bodies, the AS filter can not detect the sources’ edges. The TDR filter (Figs. 8c and 9c) gives a better imaging for the sources at shallower depths than deeper ones which means that its efficiency decreases with depth. A false anomaly between G2 and G3 was generated. Therefore, the boundaries were diffused and could not be defined precisely. Both filters Theta map (Figs. 8d, d) and TDX (Figs. 8e and 9e) exhibit edges of the sources wider than the actual ones. The outcomes show the intermediate (G2) and the deep (G3) bodies as one large anomaly. Thus, they can not distinguish the boundaries of neighboring sources. The TAHG filter (Figs. 8f and 9f) demonstrates well detection of sources’ edges at different depths, but it shows higher sensitivity to noise than the previously mentioned filters. Edges of deep sources were not detected clearly. The STDR filter (Figs. 8g and 9g) exhibits high values over the causative gravity bodies. However, it acts precisely over the shallow sources and gives a wider estimation for the boundaries of deep sources. Moreover, the THD_STDR filter yields sharp results over the boundaries (Figs. 8h and 9h). The STDR and the THD_STDR show a considerable sensitivity to noise. Using k = 2, the SF filter (Figs. 8i and 9i) displays good results for both shallow and intermediate sources, but it gives incomplete boundaries for deep source (G3) which is one of the disadvantages of this filter besides its high sensitivity to noise. In order to enhance the edge detection and overcome the problem of noisy data, upward continuation filter at two different heights (1 km and 2 km) was applied to the STDR, THD_STDR and SF noisy gravity data (Fig. 10). The results demonstrate a considerable reduction of noise, especially for the STDR map when it has been continued up to 2 km.

Fig. 8
figure 8

(a) THD, (b) AS, (c) TDR, (d) Theta, (e) TDX, (f) TAHG, (g) STDR, (h) THD_STDR, and (i) SF maps of noise-free gravity data

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Fig. 9
figure 9

(a) THD, (b) AS, (c) TDR, (d) Theta, (e) TDX, (f) TAHG, (g) STDR, (h) THD_STDR, and (i) SF maps of contaminated gravity data

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Fig. 10
figure 10

(a) STDR, (b) THD_STDR, and (c) SF maps of gravity data upward continued to 1 km. (d) STDR, (e) THD_STDR, and (f) SF maps of gravity data upward continued to 2 km

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4 Results of Modeling Applications to the Study Area’s Gravity Data

Wavenumber filters have been used to separate the Bouguer gravity map into its regional and residual gravity components [66]. The Bouguer gravity data (Fig. 6) were subjected to low-pass (0.0542 km−1), band-pass (0.0542–0.12916 km−1), and high-pass (0.12916 km−1) filters based on results of the radially averaged 2D power spectrum analysis (Fig. 11). Depth Calculations carried out on three segments of the obtained power spectrum show that the average depth values for deep, intermediate, and shallow gravity sources are 9, 3.4, and 1 km from the survey level, respectively. Figure 12 illustrates the regional (Fig. 12a), the intermediate (Fig. 12b), and the shallow (Fig. 12c) gravity anomalies.

Fig. 11
figure 11

2-D averaged power spectrum of the gravity data

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Fig. 12
figure 12

(a) Regional gravity map of the study area produced by low-pass filter. (b) gravity map of gravity sources at intermediate depths produced by band-pass filter. (c) Residual gravity map produced by high-pass filter

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The modeling study reveals that the TAHG and SF filters exhibit edges that are closer to the real edges compared to other filters. However, the TAHG filter struggles to isolate intermediate and deep bodies, while the SF filter produces incomplete boundaries for deep bodies. In contrast, the STDR filter and its horizontal derivative prove to be the most effective filters, although they yield wider boundaries than reality, they successfully provide clear and distinct bodies. Consequently, these filters were selected for the application to the regional and residual gravity data of G. El-Maghara to delineate the structural settings in the study area. Figure 13 exhibits the outcomes of performing the STDR and THD_STDR filters on the three gravity maps in Fig. 12. After the regional gravity data upward continued to 1 km to reduce the noise in the data, the outcome of applying the STDR (Fig. 13a) and the THD_STDR (Fig. 13b) filters were obtained. The results of applying these filters on intermediate (Figs. 13c, d) and shallow (Figs. 13e, f) gravity components show a main NE–SW tectonic trend.

Fig. 13
figure 13

(a) STDR and (b) THD_STDR of regional gravity data upward continued to 1 km (Fig. 11a). (c) STDR and (d) THD_STDR of gravity data of Fig. 11b, (e) STDR and (f) THD_STDR of residual gravity data of Fig. 11c

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Interpreting and analyzing the obtained outcomes of the filtering process led to constructing three structural maps at three depth levels: deep (Fig. 14a), intermediate (Fig. 14b) and shallow (Fig. 14c). Rose diagrams representing the interpreted structural lineaments were created based on their lengths and numbers (Fig. 15) to identify the tectonic directions of the traced lineaments. According to the statistical trend analysis of the rose diagrams, the main tectonic trends in the region at deep depths are WNW–ESE and ENE–WSW. The NE–SW represents the main trend at intermediate depths, while at shallow depths the NE–SW, E–W, and NW–SE trends are dominating.

Fig. 14
figure 14

Interpreted structural maps at (a) deep (b) intermediate, and (c) shallow depths

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Fig. 15
figure 15

Azimuth frequency rose diagrams depicting structural trends of the deep lineaments according to their numbers (a) and lengths (b). Azimuth frequency rose diagrams representing structural trends of lineaments at intermediate depths according to their numbers (c) and lengths (d). Rose diagrams representing the azimuth frequency of the structural lineaments trends at shallow depths according to their numbers (e) and lengths (f)

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5 Discussion

A synthetic modeling study has been performed using several filters published in the geophysical literature. The comparison between THD, AS, TDR, Theta, TDX, TAHG, STDR, THD_STDR and SF filters shows that the STDR filter and its total horizontal derivative are superior to other filters although they show high sensitivity to noise in the data. The other filters exhibit several drawbacks such as the disability to detect the edges of deep sources (e.g., THD, AS, and TDR), the failure to distinguish between adjacent sources (e.g., Theta map and TDX), and the detection of incomplete source boundaries (e.g., TAHG and SF). Thus, the STDR and THD_STDR filters were selected to be applied to the gravity data of the study area. In order to reduce the influence of the noise, upward continuation filter has been applied to the gravity data before applying the chosen filters.

The study area is characterized by a thick sedimentary sequence ranging from Triassic to Quaternary [3, 67]. The Jurassic and Cretaceous rocks outcrop extensively in the area (Fig. 2). Based on the power spectrum, three gravity maps representing deep, intermediate and shallow gravity sources were created using low-, band-, and high-pass filters. The STDR and THD_STDR filters have been applied to these maps in order to construct their corresponding structural maps at several depth levels. The tectonic trends in the study area have been determined by drawing rose diagrams of the deduced structural elements.

The WNW–ESE direction (Figs. 15a, b) represents the main tectonic trend of deep levels in the study area which agrees with the Triassic trend determined by [68]. The main trend affecting the intermediate and shallow depths as deduced from gravity data is the NE–SW (Fig. 15c, d, e, f). This direction is in agreement with the Late Cretaceous–Early Tertiary NE to ENE trend of [50] and [68] which resulted from the convergence between the Eurasian and African plates. In comparison with the geological and structural map of the area (Fig. 2), a good agreement between these inferred shallow lineaments and their extensions to intermediate depths (Figs. 14a, b) and the known faults/contacts (Fig. 2) are noticed especially in the areas of the main anticlines of El-Maghara fold. The structural trends derived from Landsat images (ENE–WSW to E–W) and the structural and geological map (NE–SW to ENE–WSW) exhibit a consistent agreement with the structural trends identified from shallow gravity sources (NE–SW and E–W) within the tectonic trend range spanning from NE to E. These trends align with the orientation of the anticlines, as well as their associated faults and contacts in the area, as previously described by references [1,2,3].

The influence of the collision between Asia and Africa in the Late Eocene–Early Oligocene time can be clearly discerned on the shallow gravity structural map where NE–SW, E–W and the NW–SE trends are dominating. The NW–SE trend could be related to the tensional stresses resulted in the Gulf of Suez rift during Late Oligocene to Early Miocene [51]. Such tectonic activity created favorable conditions for the deposition of rich source rocks and a heat regime that places these rocks in the hydrocarbon generation window [44]. Therefore, the study area may have a promising hydrocarbon potential. Moreover, the NE–SW trend of the structural lineaments is thought to be the most tectonic trend that controls the hydrocarbon resources in the area.

The findings reveal that the main tectonic trend of the deep structures (i.e., NW–SE) is different from the main tectonic trend of intermediate and shallow structural lineaments (i.e., NE–SW) which means that most likely that thin-skinned tectonics is responsible for the deformation of the area rather than thick-skinned tectonics suggested by [1]. Thus, the Late Cretaceous–Early Tertiary Syrian arc folding system is confirmed by gravity data in the study area.

The results of this study have significant implications for various sectors. In terms of industry, the identified tectonic trends can provide valuable insights for the exploration and production of natural resources, particularly hydrocarbons and minerals. Industries involved in resource extraction should consider the structural controls and orientations of these trends when planning their exploration and development activities. Furthermore, the knowledge of the dominant tectonic orientations can guide the sustainable management and utilization of underground resources, including groundwater and geothermal energy. Additionally, the findings of this study open avenues for future research and investigations in the region, encouraging more detailed analyses to gain a comprehensive understanding of the subsurface structures and their implications for various applications.

6 Conclusions

Using both synthetic noise-free and noise-contaminated gravity data, the efficiency of several previously published filters were compared and assessed. Among the filters used in this study, the STDR and THD_STDR filters exhibited superior performance. These filters were subsequently employed to construct structural maps for G. El-Maghara area. The power Spectrum technique was utilized to isolate gravity anomalies based on their wavenumbers and calculate the average depths of their gravity sources. Regional-residual separation of gravity anomalies was accomplished using low-, band-, and high-pass filters. The results illustrate that the gravity sources are situated at average depths of approximately 9 km, 3.4 km, and 1 km. The analysis of statistical trends in gravity maps, Landsat images, and structural geological maps has unveiled multiple tectonic orientations influencing the study area. These orientations include WNW-ESE, ENE-WSW, NE-SW, E-W, and NW–SE. Notably, the NE–SW trend is most prominent at shallow and intermediate depths, while the WNW–ESE trend dominates at deeper levels. This disparity in trends between deep and shallow depths suggests the possibility of thin-skinned tectonics occurring during the Late Cretaceous–Early Tertiary period.

The tectonic results obtained from this study contribute to our understanding of the geological development of the region. These findings have profound implications for industries engaged in natural resource extraction, particularly hydrocarbons and minerals, as they provide valuable insights into the underlying geological framework and structural controls. Furthermore, the knowledge gained from these tectonic orientations plays a vital role in promoting the sustainable management of underground resources, including groundwater and geothermal energy. Moreover, the outcomes of this study lay a solid groundwork for future research endeavors, enabling advancements in geophysical exploration techniques and fostering more effective resource management strategies. Overall, the findings presented in this study hold significance and are poised to facilitate long-term development and sustainable utilization of the region's natural resources.