Introduction

Due to the scarcity of water, the desert, which makes up the majority of Egypt, offers significant difficulty for the government. The population of Sinai has recently improved their living conditions, which has resulted in excessive demand for water. In order to irrigate a desert area and thereafter establish significant agricultural zones for sustainable development, particularly in the south Sinai Peninsula, shallow groundwater excavation is urgently required. Groundwater resources are essential for urban growth and attract investment to the Sinai Peninsula. Many others have examined these resources in Sinai, particularly in the southern section (Elewa and Qaddah 2011; Arnous and Omar 2018; Yousif and Hussien 2020; El-Badrawy et al. 2021; Ibrahim et al. 2021; Zarif et al. 2021; Elshalkany et al. 2022; Soliman et al. 2022).

Geophysical research is necessary and productive in the investigation of shallow groundwater. Several authors investigated geophysical groundwater in Sinai's west-central, south, southeastern, and southwest regions (Nigm et al. 2001; Rabeh 2003; Youssef 2006; Aboelkhair et al. 2020; Basheer and Alezabawy 2020; Zarif et al. 2021; Shebl et al. 2022). Furthermore, near the study area, other studies were conducted by many authors including Youssef (2010, 2016), Ghoneimi et al. (2020), and Zarif et al. (2021).

Ras Gara is located in Egypt's Sinai Peninsula (Fig. 1a), between latitudes 28°08′38″ and 28°09′20′ N and longitudes 33°45′37″ and 33°46′36′ E (Fig. 1b). It is bounded to the northwest by El-Tor City, and to the west and south by the Gulf of Suez.

Fig. 1
figure 1

(a) Google map of Sinai Peninsula. (b) Location map of the study area including the vertical electrical sounding (VES) sites along five main profiles in the study area. (c, d) Geologic and hydro-geologic map of Sinai Peninsula (Elewa and Qaddah 2011)

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When using a single geophysical technique in regions with complicated geology, such as the Sinai Peninsula, it is difficult to determine the precise hydrogeological condition. The goal of integrating two or more geophysical techniques is to resolve ambiguities in the interpreted data, obtain a more reliable final model, and offer a more precise representation of the subsurface distribution (Yusoh et al. 2018; Daniel et al. 2019). Therefore, by merging the inversion data from the two methods, the subsurface interpretation can be improved. To determine the subsurface profile without affecting the environment, electrical resistivity and seismic refraction methods have become popular site investigation techniques (Razak et al. 2015).

In the present study, vertical electrical sounding (VES) of DC resistivity and shallow seismic refraction surveys were used to measure the depth and thickness of subsurface layers holding the shallow Quaternary groundwater aquifer in Ras Gara, southwestern Sinai.

The primary goals of our study are to (1) define shallow structural features, such as subsurface composition, the depth of basement rocks, and faults found, (2) examine shallow aquifer characteristics in the studied area, such as its depth, thickness, and extension depending on the use of various geophysical techniques, and (3) apply one-dimensional lateral constrained (1D-LCI) inversion on VES data to improve resolution for output models with slow lateral variations, (4) apply two-dimensional (2D) inversion to DC and seismic data to obtain better images of the subsurface layers, and (5) prepare true resistivity, velocity, and top depth image maps for the water-bearing horizons of the Araba Formation to determine the lateral extension and top depth of this aquifer.

Many authors (Auken et al. 2005; Wisén et al. 2005; Schmalz and Tezkan 2007; Lin et al. 2019; Ourania 2021; Genedi et al. 2021) have applied the 1D-LCI inversion technique to various geophysical data types, such as DC resistivity data, electrical resistivity tomography (ERT) data, and electromagnetic data. Using the Fortran code of the Schlumberger array, a 2D inversion approach is applied to the DC resistivity data (Tripp et al. 1984; Genedi et al. 2021). Additionally, resistivity and refraction seismic data are likewise subject to the 2D inversion approach (Gallardo and Meju 2003; Cardarelli et al. 2010; Hellman et al. 2017).

Because the study area's subsurface is not homogeneous and is highly complicated and impacted by secondary structures, there will be some uncertainty (ambiguities) in the model results. In order to address the non-uniqueness of the model interpretation and obtain well sharp boundaries, the key original aspect of this research is the application of lateral constraints on the 1D model parameters, such as resistivity and depths, at the VES site locations along the same profiles.

Geologic setting of the study area

Geomorphological setting

The Sinai Peninsula is divided into four main geomorphological units: the southern elevated mountains (Precambrian unit), El-Egma and El-Tih Plateau units in central Sinai, the northern mountainous and hilly units (Hammad 1980), northern coastal plain and Gulf of Suez coastal plain. The Gulf of Suez coastal plain is home to the current study of Ras Gara area, which is distinguished by its low relief and brief wadis.

Geological setting

The research area is broadly covered by rock exposures dating from the Precambrian to the Quaternary (Fig. 1c), including Paleozoic rocks (Araba Formation) which include Cambro-Ordovician basal sandstone, post-Cambrian granite, basic dykes, and Quaternary sediments (Shata 2002, 2004; Elewa and Qaddah 2011). The wadi deposits that occupy the majority of the study region serve as a representation of the alluvial Quaternary sediments of aeolian sand sheets and dunes.

Structural setting

The main structural features of Sinai were studied by many authors such as Meshref (1990), Rabeh (2003), and Moustafa (2010). Ras Gara area and its surroundings have overlapping imprints of the Suez and Aqaba rifts' tectonic domains. It is located at the apex of the conjugated branches of these rifts. These areas are dissected by numerous minor and major faults with variable trends and types. Most of these faults are strike-slip and normal faults (Shata 2002), which are mainly aligned in the direction of the Gulf of Suez's main trend, which is northwest to southeast.

Hydrogeological setting

There are five different groundwater aquifers identified in Sinai (Fig. 1d), including the shallow Quaternary aquifers in northern Sinai, the valley aquifers, which are recharged from heavy storms and rainfall, the Miocene sandstone aquifer along the Gulf of Suez coast, the deep Lower Cretaceous aquifer in western Sinai, and the crystalline basement rock aquifer in southern Sinai (Elewa and Qaddah 2011).

Depth to water table factor

The water level depth is mostly determined by the area's hydrogeological conditions, topography, and rainfall pattern. The shallow Quaternary aquifer has a water table depth of 15 m or less below ground level (bgl). The valley aquifer, Miocene aquifer, and crystalline basement rock aquifer have depths ranging from 16 to 45 m bgl while the deep Lower Cretaceous aquifers have depths of more than 61 m bgl (Elewa and Qaddah 2011). As illustrated in Fig. 1d, the water table depth in the Quaternary aquifer decreases towards the northern and southern Sinai, but it increases towards the central and eastern Sinai in the lower Cretaceous aquifer (Elewa and Qaddah 2011).

Materials and methods

Data acquisition

Twenty-seven vertical electrical soundings (VES) sites were collected in the study area along five main profiles (Fig. 1b) following the DC resistivity survey utilizing the Schlumberger array, which is oriented parallel to the profile direction. This array's current electrode separation (AB) can be as far apart as 1200 m, allowing it to investigate a shallow Quaternary groundwater aquifer with an expected top depth of < 15 m (Fig. 1d). The study area's topography is flat, and the distance between VES sites ranges from 275 to 630 m. At the same VES sites, 27 shallow seismic refraction spreads were carried out. The spreads were conducted in two main directions (N–S and E–W) and have a length of 115 m with an inter-geophone spacing of 5 m, as illustrated in Fig. 1b. Field layouts were designed to include offsets from both sides, forward, split and reverse shots.

1D-LCI method and its inversion theory on DC resistivity data

Introduction

The one-dimensional lateral constrained inversion (1D-LCI) approach is a profile-oriented technique for inverting DC resistivity data along a single profile line in order to minimize the common objective function. It encourages the selection of the structures that follow the line direction, while the adjoining lines are ignored (Auken et al. 2005; Christiansen et al. 2007). It is an example of model space smoothing based on the least-square method. The 1D-LCI solution is adequate in sedimentary environments where the subsurface is structured with laterally stable layers (Auken et al. 2002; Auken and Christiansen 2004).

The 1D-LCI conducts 1D parametrized inversion of the raw datasets and many separate models. As part of the inversion, lateral constraints on model parameters like the resistivities and depths are used to link adjacent models (Auken and Christiansen 2004; Wisén et al. 2005). The lateral constraints are part of the inversion at which all data sets are inverted simultaneously and the final models are balanced between the constraints and the data-model fit. These constraints can be considered as prior information on the geological variability within the study area. The constraint becomes more rigid as the expected variation of a model parameter decreases (Wisén et al. 2005). The inverted models were subjected to sensitivity analysis of the output model parameters to get proper quality control, and the subsequent geological interpretation was refined.

Applying 1D-LCI to DC resistivity data has multiple advantages, including reducing interpretation uncertainties brought on by equivalence issues where the subsurface borders between rock units are artificial, as would be predicted from 1D conventional inversion. As a result, this method provides an accurate assessment of the study area's water-bearing zone. The 1D-LCI produced a model that was laterally smooth with distinct layer boundaries and provided better model parameter analysis. Finally, findings of 1D-LCI inversion more accurately depict the true subsurface than 1D standard inversion smooth models (Auken et al. 2005).

Inversion theory

The 1D-LCI inversion algorithm and the actual application of the restrictions are both thoroughly described in Auken and Christiansen (2004) and Auken et al. (2005). The steps of the Aarhus algorithm are represented in the following flowchart (Genedi et al. 2021) as shown in Fig. 2.

Fig. 2
figure 2

Flowchart of Aarhus algorithm (Genedi et al. 2021)

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The constraints value reflects the subsurface geological changes in the field area. Only lateral constraints are used in the 1D-LCI technique, not vertical constraints. Large model changes are allowed only in case of strong constraints, as this approach produces an extremely smooth inversion model without losing local information, and vice versa (Auken et al. 2005). Based on the model calculations with synthetic data, a decent starting point for constraint values ranges from 1.1 to 1.3, where the model parameters differ by 10–30% between nearby models, respectively. These constraints were ideally determined for each data set (Auken et al. 2005). The constraints during 1D-LCI inversion are represented by 1 and − 1 values, with zero values in all other places, in the covariance matrix (CR) and roughness matrix (R) (Auken et al. 2005).

Equations (1 and 2) depict the model estimate and the model estimate minimization, respectively. Here, (G´) indicates the joint between the Gacobian (G) and roughening (R) matrices, (δd´) implies the joint matrix that includes the parameters and the delta observation data, (A) represents the number of constraints, (N) represents the number of data, and (C´) represents the covariance matrix for the joint observation error:

$$\delta m_{{{\text{est}}}} = \left( {G^{\prime T} \cdot G^{\prime - 1} \cdot G^{\prime } } \right)^{ - 1} G^{\prime T} \cdot G^{\prime - 1} \delta d^{\prime } ,$$
(1)
$$Q = \sqrt {\frac{1}{N + A}\left[ {\delta d^{\prime T} \cdot C^{\prime - 1} \cdot \delta d^{\prime } } \right]} .$$
(2)

Parameter analysis of the 1D-LCI inverted model

The sensitivity analysis of the final model parameters is used to improve the 1D-LCI inversion model's resolution and confirm the accuracy of the inversion results. The STDF factor on the model parameters is derived using Eq. (3), where Cest stands for the covariance matrix of the estimation error, due to the logarithmic representation of the model parameters. The range values of the STDF, which are depicted in the following Table 1, are dependent on different cases of the model resolution (Auken et al. 2005):

Table 1 The range values of the STDF and its resolution cases (Auken et al. 2005)
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$$\mathrm{STDF }\left({m}_{\mathrm{s}}\right)=\mathrm{ exp }\left(\sqrt{{C}_{\mathrm{est},\mathrm{ss}}}\right).$$
(3)

Result and discussions

DC resistivity data interpretation

First, all DC resistivity data were interpreted using a traditional 1D inversion utilizing the IPI2WIN technique (Bobachhev et al. 2001), and the Marquardt approach is utilized to tackle the inversion problem. Second, using the Aarhus algorithm, designed by the Aarhus University in Denmark, 1D-LCI inversion code is applied to DC resistivity data (HGG 2012). The Fortran code of the Schlumberger array (Uchida algorithm) was used to create a 2D inversion of the DC resistivity data (Uchida and Maurakami 1990).

1D-LCI inversion results of DC resistivity data

According to three factors; the conventional 1D inversion results from the IPI2WIN algorithm, the number of geological profile units, and the 1D-LCI sensitivity analysis of model parameters, five layers were produced in the 1D-LCI section. The 1D-LCI model provides a clear and accurate description of the layer interfaces between different geological units. Between the resistivity and depth interfaces of the adjacent VES sites along the same profile, the lateral constraint factor of 0.3 is applied.

According to a comparison of the inversion results of the DC resistivity data along profile four from conventional 1D and 1D-LCI (Fig. 3), the layer boundaries are unrealistic in the 1D inversion model while they are extremely sharp and smooth in the case of the 1D-LCI inversion model after the later constraints are applied to the model parameters from the 1D inversion results. This suggests that the issue of data non-uniqueness was overcome via 1D-LCI inversion.

Fig. 3
figure 3

The upper plot (a) shows the results of a conventional 1D inversion model of DC resistivity data with five geo-electrical layers and unrealistic boundaries along profile four, while the lower plot (b) represents a 1D-LCI inversion model with sharp boundaries along the same profile after applying lateral constraints to the model parameters (resistivity and depth)

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Figure 4 depicts the 1D-LCI inversion models of DC resistivity data and the parameter analysis along profile one, while Fig. 5 depicts the same along all remaining profiles. The main resistivity regime's lithologies range from unconsolidated to consolidated wadi deposits (surface clastic deposits), a saturated sand aquifer of the Araba Formation with fresh and brackish water, and basement rocks.

Fig. 4
figure 4

The upper plot (a) depicts the findings of a 1D-LCI inversion model using DC resistivity data with five geo-electrical layers along profile one. The lower plot (b) shows the 1D-LCI sensitivity analysis of the final model parameters associated with this profile (resistivity; Res.1–Res.5 and thicknesses; Th.1–Th.4) for all profiles. STDF factor = 1 indicates a well-resolved parameter with red color coding, whereas STDF factor = 1.2 indicates a moderately resolved parameter with blue color coding

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Fig. 5
figure 5

The left plots depict the results of a 1D-LCI inversion model using DC resistivity data with five geo-electrical layers along profiles two (a), three (b), four (c), and five (d). Along with these profiles in order (e–h), the right plots show a 1D-LCI sensitivity analysis of the final model parameters

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All profiles comprise five geo-electrical layers (Fig. 4a; upper side and Figs. 5a–d; left side), which are summarized as three geological units with smooth transitions in sensitivities and layer boundaries. In the model section, the top layer with a thin thickness is invisible. The first geological layer on the surface was separated into two geo-electrical layers. The first represents unconsolidated wadi deposits with resistivity ranging from 243 to 1158 Ω.m, while the second represents consolidated wadi deposits with resistivity ranging from 12 to 198 Ω.m.

There are two zones in the second conductive geological layer. The first zone (third geo-electrical layer) has low resistivity values (8.7–26.7 Ω.m) along the main profiles, with just a few VES sites (5, 6, 8, 14, 17, 18, 27) having high conductivity values (5–7.5 Ω.m) due to some clay lenses or sea water invasion into this zone. This zone's thickness spans from 5.1 m to 13.4 m. Its top depth varies along the profiles, ranging from 2.4 m (VES-06) in the south to 15.6 m (VES-13) in the north. The second zone (fourth geo-electrical layer) shows high conductivity values (0.9–3 Ω.m) along the main profiles and a low resistivity value (14.4 Ω.m) that is only slightly lower than VES-04. Its thickness ranges from 1.8 to 26.8 m. Its depth spans from 8.7 m below VES-06 to 28.5 m below VES-13. The effect of a shallow Quaternary aquifer in the saturated sandstone layer (Araba Formation) in the studied area is responsible for the drop in resistivity values in these zones compared to the upper and lower layers. The third geo-electrical layer reflects a fresh groundwater zone, whereas the fourth geo-electrical layer represents a saline groundwater zone that is invaded from the west via a seawater intrusion from the Gulf of Suez. The basement complex in the studied region is represented by the final third geological (fifth geo-electrical) layer with higher resistivity (637–935 Ω.m). These findings are consistent with the depth to groundwater map at southwestern Sinai (Elewa and Qaddah 2011), where the Quaternary aquifer begins at a depth of < 15 to 30 m (Fig. 1d).

According to the parameter analysis plots (Fig. 4b; lower side and Fig. 5e–h; right side), the STDF factor ranges between 1.01 and 1.24 along all profiles, indicating that the parameters are well-resolved in most areas of these profiles. The layer boundaries along the 1D-LCI models are particularly sharp due to the constraints. As a result, the 1D-LCI generates a laterally smooth model that characterizes the horizontal interfaces of the different geological units.

2D inversion results of DC resistivity data

The 2D Fortran code of Uchida and Murakami (1990) was used to do a 2D inversion of DC resistivity VES data along all profiles, with this algorithm interpreting all VES data simultaneously by one conductivity model. A forward calculation is performed at each VES data point using the initial model, which is considered to be 30 Ω.m homogeneous earth. In this area, these models account for the topographical effect.

Figure 6 depicts 2D-DC inverted models along with all profiles (a, b, c, d, and e). Different geo-electrical layers are presented in this area, with different resistivity values governed primarily by variations in lithology, which consists primarily of sands, gravels, clays, and silts of the Pleistocene deposits.

Fig. 6
figure 6

Two-dimensional (2D) inversion models of VES sites along five main profiles

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These inverted sections demonstrate that the upper layer of decreasing resistivity values (about between 10 and 100 Ω.m) may indicate the presence of a shallow aquifer in this area. At shallow and intermediate depths, a high conductivity zone (< 10 Ω.m) is represented in the eastern portion of the study area along profiles one (Fig. 6a) and two (Fig. 6b), and the western part along other profiles, particularly below VES sites (4–6, 10–14, 18, 20–21, 23–24, and 26–27). These conductivity anomalies reflect the aquifer's saline zone, which is affected by seawater invasion. The fresh-saline water contact is around 50–100 m in elevation.

Some sections with very high resistive anomaly (> 500 up to 40,000 Ω.m) are characterized at deep depths based on the correlation between 2D models along all major profiles (Fig. 6). These anomalies can be found in the western part of the study area along profile two (VES-07, VES-08, VES-09, and VES-10) and the eastern part along profile three (VES-16 and VES-17), profile four (VES-22), and profile five (VES-25, VES-26 and VES-27). These anomalies indicate the fractured basement (500–1000 Ω.m) and fresh basement (1000–40,000 Ω.m) that dominated in Ras Gara area, as well as their top depths at elevations of up to 50 m. A considerable number of anomalies with resistivity values (100–1000 Ω.m) are also seen at deeper areas of profile one (VES-01, VES-02, and VES-03), indicating the accumulation of dry sand and conglomerates.

A lateral change in resistivity values of these sections from west to east is observed due to the presence of some clay lenses at shallow parts and the effect of basement uplifting at deeper parts, particularly below VES sites (7–10, 17, 22, and 25–27) caused by normal faults that trend generally N–S or NW–SE. The basement location on profiles one and two differs from that on the other profiles. This difference in behavior could be due to the projected strike-slip faults between profiles two and three. These faults are mainly E–W trending. A comparison of the observed DC data and the calculated apparent resistivity data from 1D-LCI and 2D inversion results for the selected VESes sites along profile four is presented in Fig. 7, where a good fit was established.

Fig. 7
figure 7

Comparison between the observed and synthetic data from 1D-LCI and 2D inversion results of the selected VES sites along profile four

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Seismic refraction data interpretation

Seismic refraction measurements are primarily used to delineate subsurface layering and to determine the top depth of boundary borders. The geologic background of the Araba Formation, which is predicted to be a water-bearing formation, is the primary focus of this study. This formation is bounded by wadi deposits and basement rocks.

The seismic data were processed in the form of picking the first arrival, building time distance (T–D) curves, inversion techniques, and calculated depth velocity models. The Seisimager algorithm (Winsism 2009) was used to process and interpret seismic data, resulting in a two-dimensional earth model with good lateral and vertical direction within the subsurface layers. The seismic refraction travel-time data is inverted into depth-velocity values via delay time inversion.

2D inversion results of seismic refraction data

The objective of seismic refraction data interpretation is to determine the velocities and depths of the subsurface layers. These findings are provided in two forms: depth-velocity models that show the vertical and lateral distribution of the second sand layer (Araba Formation) along spreads, and velocity and depth contour maps that show the aerial distribution of this layer throughout the study area.

Geo-seismic cross-sections

In the study areas, twenty-seven spreads were built along two main directions: N–S and E–W. Figure 1b illustrates the locations of the above mentioned spreads. Along each spread, geoseismic cross-sections or depth-velocity models (Fig. 8) were built. Figure 8 presents the interpreted depth-velocity sections of these spreads, which demonstrate that two and three layers dominate in the study area. The velocity range of the first geo-seismic layer is 400 to 1100 m.s−1, corresponding to unconsolidated wadi sediments. The lowest velocity value of this layer is recorded at spreads (S24 and S27) in the investigated area, while the highest velocity value (1100 m.s−1) is observed at spreads (S9, S12, and S18). The Araba Formation, which is considered the water-bearing horizon in this area, is the second geo-seismic layer. It is composed of different clastic rocks, including sandstone with siltstone, conglomerate, and clay. This formation exhibits P-wave velocity values (1200–1900 m.s−1), with the maximum velocity recorded under spreads S26 and S27, and the minimum velocity overlying spreads S2, S7, and S25. The depth of the top of this layer ranges from (3.7–20.5 m), with the maximum depth seen beneath spread (S13) and the minimum depth observed at spreads (S26 and S23) in this area. The third geo-seismic layer is represented by the basement, which has a velocity range of 2400 m.s−1 under spread (S4) to 5400 m.s−1 under spread (S5). The top depth of this layer is between (17.3–34.3 m), with the minimum depth presented under spread (S17) in the eastern part of this area and the greatest depth shown under spread (S17) in the western part of this area (S10).

Fig. 8
figure 8

Interpreted geo-seismic cross-sections (velocity-depth models) by the ABC method at some VES sites along different spreads such as spreads; S5 (a), S9 (c), S17 (e), S18 (g) at E–W direction and spreads; S4 (b), S8 (d), S24 (f) and S21 (h) at N–S direction

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Comparison between inversion results from DC and seismic data

Figure 9 displays an example of inversion model sections derived from 1D-LCI and 2D inversion results for DC resistivity along profile four, as well as 2D inversion data for seismic refraction spreads at two VES site locations along that profile. After the inversion process, the resistivity and seismic refraction images were generated, which were based on resistivity (ρ, Ω.m) and compressional wave velocity values (Vp, Km.s-1), respectively. The color legend was set to be the default value, and it serves as an indicator of resistivity and velocity values.

Fig. 9
figure 9

1D-LCI and 2D inversion results of DC resistivity data along profile four (a, b). 2D inversion results of seismic refraction data along two spreads at the center of two VES sites (VES-18 and VES-21) on the same profile (c, d)

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Since the geology of the study area consisted of wadi deposits, Araba Formation sandstone layers, and basement rock, 1D-LCI inversion results of DC resistivity data show five geo-electrical layers with sharp layer boundaries, which are interpreted into three geological layers. The wadi deposits are separated into surface consolidated and unconsolidated layers, with resistivity ranging from (261.4–1121 Ω.m) to (12–198 Ω.m), respectively. The saturated sandstone layer is divided into fresh and saline water zones with resistivity ranges of (10.2–11 Ω.m) and (0.9–1.9 Ω.m), respectively, and is located at elevations of roughly 120 m (2.3–12.3 m depth) and 110 m (9.9–23.4 m depth).

The freshwater zone has only a low resistivity value of 6.1 Ω.m at the site (VES-18), which could be attributable to the accumulation of clay or the invasion of seawater within this zone. The last geological layer of the basement complex has a resistivity value of (830–840.5 Ω.m) and is found at an elevation of roughly 90 m.

Figure 9b shows the electrical resistivity image obtained from 2D-DC inversion results with resistivity values ranging from (0–1000 Ω.m). The sandstone layer (Araba Formation) is divided into two zones: upper freshwater (up to 30 Ω.m) and lower saline water (1–10 Ω.m), with the fresh-saline water contact lying between 50 and 100 m elevation. Its top depth decreases toward the west.

The resistivity value of fractured basement rock ranges from 800 to 1000 Ω.m, where it is located at approximately 50 m in elevation in the portion below VES-22, and its depth decreases toward the west. Figure 9c, d shows the seismic section image from two seismic speeds at the center of two VES sites (VES-18, left side, and VES-21, right side) along profile four based on 2D inversion results of seismic refraction data. The overall velocity ranges between 700 and 3000 m.s−1. At two sites, the velocity of the soft, less compacted wadi deposits ranges between (700–1000 m.s−1) and is located at an elevation of 115–130 m. The velocity of the second porous and saturated, moderately compacted sandstone layer, which is located at 100–120 m elevation, ranges between (1400–1700 m.s−1). The third hard, denser, and very compacted basement layer has a velocity of 3000 m.s−1 at the site (VES-18), and its top depth (from 115 to 95 m) decreases towards the west.

The results of seismic refraction inversion only defined the subsurface layering and the depth boundaries between these layers. Some similarities between DC resistivity and seismic refraction results were noted; there were two to three major layers, surface wadi deposits at the top, sandstone layer in the middle, and basement rock at the bottom, with the depth decreasing toward the west. The DC resistivity method, on the other hand, produces a different image section than the seismic method, as the saturated second sandstone layer is located and divided into fresh and saline water zones differently than the seismic refraction inversion results because DC resistivity method is sensitive to some factors such as porous water-bearing horizons inside groundwater aquifers, and compaction and consolidation of the layers, where the geological layers are divided into sub-geo-electrical layers.

The comparison of 1D-LCI and 2D inversion results of DC resistivity data shows non-similarity at some portions of its section, which could be attributable to the presence of some structures in the area where the 2D section is well defined. As a result, the area is afflicted by a typical type of dip-slip fault between the VES-21 and VES-22 sites, which may strike in the N–W or NW–SE direction.

Furthermore, the top depth of the saline-water zone decreases toward the west (sea direction) while increasing toward the east, far away from the invasion of seawater from the Gulf of Suez. The fresh-saline water contact is located at an elevation of about 110 m based on 1D-LCI results and between (50–100 m) based on 2D-DC results.

True resistivity and depth-colored image maps

Resistivity and depth colored image maps

The lateral fluctuation of true resistivity of the fresh and saline zones of the shallow aquifer in the second layer of saturated sand (Araba Formation) is illustrated in Fig. 10a, b. These variations are determined from the 1D-LCI inversion of DC resistivity data at all VES sites in the investigated area. In addition, Fig. 10d, e displays the top-depth fluctuations of these two zones as a result of this inversion.

Fig. 10
figure 10

True resistivity and top depth maps of the freshwater zone (a, d) and saline-water zone (b, e) in the saturated sandstone layer (Araba Formation), respectively which calculated from 1D-LCI inversion results of DC resistivity data. Velocity map ( c) and top depth map (f) of the saturated sandstone layer (Araba Formation) that calculated from 2D inversion results of seismic refraction data

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The resistivity values of the fresh-water zone (Fig. 10a) range from (8.7 to 26.7 Ω.m) in the study area, but only at VES sites (5–6, 8, 14, 17–18, 27), they were low (5–7.5 Ω.m). These values have higher contents in the north-central, southern, eastern, and southwestern directions of the map than in the other directions, particularly at VES sites (1–2, 4, 12–13, 20–22). This increase in resistivity values could be attributed to an accumulation of dry sands and conglomerates inside the aquifer zone underneath these sites. The recorded decreasing resistivity values towards the northeastern, southeastern, and northwestern directions, particularly below VES sites (5–6, 8, 14, 17–18, 27), may be due to the accumulation of clay contents within the groundwater zone below these VES sites or to the invasion of seawater into this zone. The fresh-zone top depth (Fig. 10d) ranges from 2.4 to 15.6 m and increases towards the north-central (VES-21), eastern (VES-12 and VES-22), western (VES-13), and southern (VES-04) parts of the map. This depth zone begins to decline in other parts of the map, particularly in the north (VES-24 and VES-25), northeast (VES-27), northwestern (VES-18 and VES-23) and southeastern (VES-05 and VES-06). The saline-water zone resistivity values (Fig. 10b) vary from (0.9 to 3 Ω.m) in the study area, with high values (14.4 Ω.m) only at the site (VES-04). These values are high in the map's northern, eastern, western, southern, and north- and south-western quadrants, particularly underneath VES sites (1–2, 4–5, 7, 9, 13, 22–23, 25). These values drop in the north-, southeastern, and southern directions, particularly below sites (6 and 27), highlighting greater salinity as a result of seawater intrusion into this aquifer.

The saline-zone top depth (Fig. 10e) ranges from 8.7 to 28.5 m. This depth increases in the map's north-central (VES-19 and VES-20 and VES-21), eastern (VES-12 and VES-22), western (VES-13), southern (VES-03), and southwestern (VES-01 and VES-02) regions. This depth zone begins to decline in other areas of the map, particularly in the north (VES-24 and VES-25), northwestern (VES-18 and VES-23), north- (VES-27), and southeastern (VES-05 and VES-06).

Finally, there is good agreement between the top depth zone of the shallow aquifer from the inversion results and the earlier hydrogeological data, with the top aquifer depth beginning at 15 m bgl or less (Elewa and Qaddah 2011).

Velocity and depth-colored image maps

The data for the areal distribution of model parameters are collected from the interpreted models of the different spreads. The X and Y coordinates of velocities and depth values at these locations are used to grid the data for the second layer's velocity and depth maps (saturated sand aquifer of the Araba Formation). The primary focus of this study is the P-waves velocity colored image map of the second layer (Fig. 10c). Its velocity measurements range from 1200 to 1900 m.s−1, reflecting the effect of the water-bearing horizon inside the Araba Formation. Maximum velocity readings (1900 m.s−1) inside this layer are indicated at the central, western, north- (S26 and S27) and south-eastern, and north- and south-western regions of the examined area. This increase in velocity numbers reflects the increase in sandstone compaction. On the other side, the lowest values (1200 m.s−1) are observed in the southern (S2 and S7), northern (S25), and south-western regions of this area. This decrease in velocity values implies a decrease in sandstone compaction as well as an increase in siltstone, clay, and conglomerates within the formation.

The top depth variation of the major target layer of this study is depicted in Fig. 10f (Araba Formation). The maximum depth value (20.5 m) is found in the western (S13) section of the researched region, while the smallest depth value (3.7 m) is found in the north-eastern (S26) and north-western (S23) sections. It displays the same gradual decrease in depth in this area towards the north- (S26 and S27) and south-eastern (S4 and S5), eastern (S17 and S22), and north- (S23) and south-western (S1).

Conclusions

Several geophysical techniques, including DC resistivity and shallow seismic refraction, were used in this investigation to identify water-bearing structures in the shallow Quaternary aquifer in the study area.

The DC resistivity models derived from the 1D-LCI inversion data reveal five geo-electrical layers that are interpreted as three geological units along all profiles. In comparison to the unrealistic boundaries produced by conventional 1D-DC inversion results due to data ambiguity, the 1D-LCI results provide a good smooth model with lateral constraints where layer boundaries between geologic layers are quite sharp. From top to bottom, the lithologies of the main resistivity regime differ between unconsolidated surface clastic wadi deposits (high resistivity layer, 243–1158 Ω.m), consolidated wadi deposits (moderate resistivity layer, 12–198 Ω.m), freshwater-bearing (low resistive) zone and saline water-bearing (high conductive) zone of the Araba Formation (0.9–26.7 Ω.m) and basement rocks (very high resistivity layer, 637–935 Ω.m).

The 1D-LCI inversion results divided the Araba Formation's second conductive geological unit into two water-bearing zones with lower resistivity values than the above and below layers. This highlights the importance of the shallow aquifer in this area. The general resistivity values of the third layer (first fresh-water zone) range from 8.7 to 26.7 Ω.m, with only relatively low values (5–7.5 Ω.m) at VES sites (5–6, 8, 14, 17–18, 27), which could be attributable to clay accumulation or seawater invasion. The resistivity values of the fourth layer (second saline-water zone) range from (0.9–3 Ω.m) to (14.4 Ω.m) at the site (VES-04). The thicknesses of the fresh and saline-water zones are (5.1–13.4 m) and (1.8–26.8 m), respectively, while the top depths vary between (2.4–15.6 m) and (8.7–28.5 m). The first low resistivity zone represents good quality fresh water-bearing groundwater formation, while the second high conductive zone represents saline water-bearing formation. The decrease in the resistivity value of the second zone reflects the incursion of seawater from the Gulf of Suez, particularly in this zone of extremely saline water. So, in this zone, the aquifer essentially deteriorates.

The 2D-DC inverted model generally reflects three main layers; the first shallow low resistivity layer (about 10–100 Ω.m) may reflect the fresh zone of the shallow aquifer in the study, and the second high conductive layer (< 10 Ω.m) may indicate the aquifer's saline zone. The fresh-saline water contact is between 50 and 100 m in elevation. High resistivity anomalies (500–40,000 Ω.m) represent fractured and fresh basement rocks at deep areas of these models with top depths of up to 50 m elevation. The influence of the basement uplifting at deeper parts is demonstrated by a lateral change in resistivity values from west to east.

From 2D-DC inversion results that correlate with previously known geology, certain normal faults (trending nearly N–S or NW–SE) and expected strike-slip faults (trending roughly E–W) were observed.

There is good agreement between the top depth of the fresh- and saline-water zones inside the aquifer from 1D-LCI and 2D inversion results of DC resistivity data and from hydro-geological map information in the southwestern Sinai where the Quaternary aquifer begins at < 15 to 30 m deep. From 2D inversion results of shallow seismic data, the depth-velocity models reflect dominant two and three geo-seismic layers in this area: the first layer (Vp = 400–1100 m.s−1) of unconsolidated wadi sediments, the second layer (Vp = 1200–1900 m s−1) of the Araba Formation water-bearing aquifer with depths ranging from (3.7–20.5 m), and the third layer (Vp = 2400–5400 m.s−1) of basement complex (17.3–34.3 m).

Finally, applying the 2D-LCI inversion on the DC resistivity data to determine the shallow aquifer is recommended. According to the study, the site locations in the eastern part of this area are ideal for drilling new water wells since they are far from the invasion of seawater.