1 Introduction

The Moho is a clear boundary that marks the transition between the crust and the uppermost mantle. This boundary is particularly important as it marks a significant shift in rheology, velocity of seismic and chemical composition, also characterized by a significant change in elastic properties, which is caused by a substantial difference in the types of rocks present (Abdelwahed et al. 2013). By map** the depths of the Moho, we can acquire information about the thickness of the crust, the way continental plates are balanced in terms of weight, and the distribution of abnormal heat patterns.

Gravity is effective in Moho boundary geometry studies because of the strong-density contrast on this interface between the mantle and the crust from 2900 kg m−3 to 3300 kg m−3, about 400 kg m−3 density contrast (Gaber et al. 2022). One of the essential issues to model the entire earth heat flow and investigating the total hydrocarbon elements is to understand accuracy the deep structure (Bouman et al. 2015; Hantschel and Kauerauf 2009). In this study, the Moho depth and crustal thickness will be modeled to get better understand for the earth’s interior, beneath Egypt, using an integration approach of seismic and gravity data (Fig. 1).

Fig. 1
figure 1

Egypt's shaded digital elevation model developed from the etopo1 (Amante 2009), showing the location of seismology stations, cyan points indicating to the seismology stations (Hosny and Nyblade 2016), red points indicating to the hot springs (Zaher et al. 2018)

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Egypt can be divided into four units based on its geomorphology (Rushdi 1990): western desert, cultivated land, eastern desert and Sinai Peninsula (Fig. 1). The dynamics of Egypt’s lithosphere are governed by the drift of three major plates: Africa, Arabia and Eurasia, generating a complicated geodynamic setting (Saleh et al. 2006). Multiple studies investigated Egypt's Moho depth, gravity, seismic refraction, deep sounding, receiver function, seismological time inversion, Rayleigh wave and spectral ratio technique. (Sobh et al. 2019) estimated crustal thickness in Egypt using inverse and 3D forward gravity modeling, concluding it ranged from 25 to 45 km. (Gaber et al. 2022) evaluated the crustal thickness and structural patterns of the Sinai Peninsula using 3D density modeling of aeromagnetic and earthquake data. (Abdelwahed et al. 2013) developed 3D structural models of the Conrad and Moho discontinuities across Egypt's different tectonic domains. This paper deals with investigation of the Mohorovii (Moho) discontinuity characteristics using seismically constrained inversion of satellite gravity data. Our mission is to identify higher geothermal potential zones in Egypt based on crustal thinning and Moho nearer the earth's surface, confirming this with location of hot springs (Zaher et al. 2018) (Table 1) and high land surface temperatures. This study serves as essential for future geothermal investigation in Egypt. Several models: the global relief (Etopo1) model, the (Crust1) and many others, along with earlier seismic research, provide constraints on the geometry and physical parameters that affect the gravity inversion.

Table 1 Location and temperatures of hot springs in Egypt, obtained from (Zaher et al. 2018)
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2 Geological setting

Egypt is situated at the border between Africa and Asia, with a geographically square territory of around 1,000,000 km2. The Mediterranean Sea forms the northern boundary, and the Red Sea lies at the eastern border. Egypt is flanked by three active tectonic plate boundaries: the Afro-Eurasian boundary, the Red Sea boundary, and the Aqaba-Dead Sea fault, as shown in Fig. 2. As a result, Egypt undergoes complex and essential tectonic interactions that encompass compressional, extensional and shear movements. Egypt has seven primary geographical areas: (1) the Nile valley and delta, (2) El Fayum, (3) the Suez Canal, (4) the Western Desert, (5) the Eastern Desert, (6) the Sinai Peninsula and (7) the islands in the Red Sea (Ball 1939).

Fig. 2
figure 2

The Surface Geology map of Egypt modified after (Hosny et al. 2014); the geologic units are illustrated through a colored legend; red solid lines delineate the tectonic boundaries. Red Sea Axial rift and the recent major faults modified after (Abou Elenean 2007; Abdelwahed 2013), and the black lines show the faults

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Recent global positioning system observations reveal Africa's northwestward movement relative to Eurasia at a rate of 6 mm per year. The Red Sea's spreading rates range from 14 mm per year to 5.6 mm per year. The southern Aqaba-Dead Sea fault experiences left-lateral strike-slip motion. These tectonic events cause secondary deformation and insignificant earthquake activity (McClusky et al. 2000 and 2003; Wdowinski et al. 2004).

Geophysical investigations conducted in Egypt have revealed three significant tectonic trends: the Mediterranean trend (E-W), the Red Sea trend (NW–SE) and the Gulf of Aqaba trend (NE-SW) (Yousef 1968; Saleh et al. 2024). Tectonic forces are very complicated, so most of Egypt's seismic activity is limited to four areas: the Levant-Aqaba band, the Northern Red Sea-Gulf of Suez-Cairo-Alexandria region, the eastern Mediterranean Cairo-Fayum zone and the Mediterranean Coastal Dislocation Belt (Kebeasy 1990; Abou Elenean 1997).

Egypt has stable and unstable shelfs, separated by the Hinge zone. The stable shelf features moderate tectonic deformations and sedimentary layers, with a narrow sequence near the Arabian-Nubian Shield (Said 1962). The Hinge Zone, which lies between the unstable shelf and the miogeosynclinal basinal region, shows a significant rise in sediment thickness from the Oligocene to the Pliocene period. Significantly, this zone corresponds with the modern Mediterranean shoreline region. However, certain granitic outcrops in southern Egypt have been recognized as a component of the extremely ancient Saharan Metacraton. Figure 2 simply illustrates the Egyptian geological map and its major characteristics. The Keraf shear zone divides the Neoproterozoic terrains and the Metacraton from east to west, respectively; the Precambrian Basement is overlain by Phanerozoic sedimentary strata spanning the majority of Egypt's land. On the opposite side, Paleozoic shales and sandstones represent the foundation of the sedimentary group, which is frequently topped by Mesozoic sediments, followed by Paleogene and Neogene sediments and topped by the unconsolidated Quaternary deposits (Abdelsalam et al. 1998; Abdelsalam and Stern, 1996).

The sedimentary cover in Egypt encompasses the entire Phanerozoic Eon, with representation from all geologic periods. As indicated in Egypt's basic geological map (Fig. 2), volcanics and Phanerozoic sediments span around 90% of the territory, while the basement constitutes approximately 10% of the region. However, many earlier sedimentary rocks, particularly Paleozoic formations, are hidden within very deep basins beneath more recent rock strata. Underground investigation has greatly improved our grasp of Egypt's geological past. Phanerozoic volcanic activities are geographically and temporally broad, invading both the basement and the sedimentary overlay. These volcanic activities are related to crustal processes. Nonetheless, the country has frequently exhibited stable cratonic behavior throughout the Phanerozoic Eon. Egypt's geology is split into four major rock groups: the Basement, Paleozoic, Mesozoic and Cenozoic. The Mediterranean Sea and its progenitor, the Tethys Ocean, gave particular consideration to the sedimentary cover and its geological history (El Shazly 1977).

Hot springs in Egypt are natural occurrences resulting from geothermal activity and have a notable impact on the country's hydrothermal system (Bilim 2017; Lashin 2013). Egypt's geology, which stands out for having a complex tectonic past and a wide variety of geological structures, is closely related to the occurrence of hot springs in the country. Hot springs are predominantly located in regions characterized by ongoing faulting and volcanic phenomena, such as the rifting of the Red Sea and the Gulf of Suez. These places have tectonic regimes that are characterized by extension. This creates fractures and fault networks that allow geothermally heated water to move upward (Bektas 2013; Zaher et al. 2018). Additionally, areas with higher permeability, such as cracked basement rocks that make it simple for geothermal fluids to circulate, are frequently associated with hot springs. The geological structures, such as fault systems and permeable rock units, serve as pathways for the movement of fluids from deep underground. Geothermal gradients and natural increases in temperature with depth heat these fluids. Geothermal springs, which are distinctive for their high temperatures and mineral-rich water, are the result of this phenomenon (Zhang et al. 2017). An analysis of the distribution of hot springs in Egypt offers useful information on the geological processes, tectonic activity and geothermal resources of the country. This analysis helps us gain a deeper understanding of Egypt's geodynamic evolution and its potential for sustainable energy use. Although the exact nature of the interaction between these two parameters is not yet completely known, multiple studies have indicated a possible connection. The depth of the Moho has an important impact on controlling the thermal structure and heat movement in the Earth's crust, which can affect the accessibility of geothermal energy. Geological features related to the Moho depth, like fault networks and porous rock units, can also help geothermally heated fluids move, which leads to the formation of hot springs (Huang et al. 2002). By examining the relationship between hot springs and Moho depth, we can obtain useful knowledge on the characteristics, distribution and potential resources of geothermal systems.

3 Materials and methods

The primary data sources for this study were two gravity datasets and the Level-2 Land Surface Temperature (LST) product from the Sea and Land Surface Temperature Radiometer (SLSTR) on the Sentinel-3B (Table 2).

Table 2 Description of the used datasets
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3.1 Land surface temperature (LST) map**

The Sea and Land Surface Temperature Radiometer (SLSTR) is a temperature radiometer that operates in low Earth orbit at an altitude of 800–830 km. It uses dual-view scanning to measure the temperature of both the sea and land surfaces. The instrument is installed on both the Sentinel-3A and Sentinel-3B satellites, which are now in operation as part of the Copernicus program. The SLSTR instrument on Sentinel-3 plays a major role in this operational mission. The efficacy of the SLSTR's Land Surface Temperature (LST) algorithm is contingent upon various elements, such as the biome type, the diurnal cycle, the fraction of vegetation cover and the viewing zenith angle. Regarding daylight data, the technique has been evaluated and shown to have 1.8 K resolution and 1.2 K sensitivity. This is attributable to substantial thermal fluctuations commonly observed across land surfaces (Pérez-Planells et al. 2021).

3.1.1 Used data

LST, land surface temperature product from the Level-2 of the above-mentioned satellite, was used in this investigation to acquire land surface temperatures at a resolution of 1 km. The temperature measurements were later used to calculate the amount of heat produced on the surface. A total of forty-four images spanning from September 29, 2021, to September 30, 2022, were collected from an open access source (https://www.onda-dias.eu), specifically focusing on MISSIONS: Sentinel-3B, PRODUCT: SL-2-LST, LEVEL: L2 and INSTRUMENT: SL-STR. The collected images underwent processing and compression, resulting in the generation of eight consolidated images for further analysis.

3.1.2 LST data processing

The data were processed using the Sentinel Applications Platform's snap software in three steps: First, the measure was converted from kelvin to degrees Celsius using the formula (K°− 273.15), and then the data were projected using raster technology (GIS referenced). The impact of clouds obscuring the image is then eliminated during the masking step by employing the function (confidence in summary clouds).

3.2 Gravity data

3.2.1 Used data

This study made use of two separate gravity databases. The initial dataset consists of unprocessed gravity data acquired by the GOCO06S spherical harmonic model, which solely relies on measurements from the GOCE mission (Kvas et al. 2019). The GOCO06S version, derived from the European Space Agency's GOCE effort (Ince et al. 2019), generates the Moho depth model, providing accurate Knowledge about Earth's interior structure and identifying longer wavelength anomalies associated with deeper crust and shallower mantle layers.

This work includes the XGM2019 integrated model, which combines satellite and terrestrial gravity measurements for improved accuracy. It is particularly useful for forward modeling due to its superior accuracy at shorter wavelengths, enhancing resolution of shallower formations like sediments and top crust (Zingerle et al. 2020).

3.2.2 Gravity data processing

It is necessary to get rid of any unwanted signals and concentrate on the desired data before applying the Moho inversion. The Bouguer anomaly is used in our study as the key piece of information for this reason. To ensure the accuracy of the results, a number of effects were eliminated during the data processing stage. Tesseroids, an open-source program that divides the research region into spherically shaped prisms, was utilized for processing (Uieda et al. 2016; Farag et al. 2022); we provided our updated version of the processing software within the supplementary materials. Throughout the processing steps, the study area was expanded by five degrees in all directions to reduce edge effects (Szwillus et al. 2016). The GOCO06 data underwent a series of processing steps that included the following to clean up the dataset and get it ready for Moho inversion analysis:

  1. 1.

    The calculation of gravity disturbance eliminates normal earth's influence (γ) using the closed-form algorithm, revealing residual gravitational anomaly due to terrain, sediment and elevation changes (Li and Gotze 2001) (Fig. 3a).

  2. 2.

    The topography was corrected for gravity disturbance using the etopo1 model and crust1 model (Amante and Eakins 2009; Laske et al. 2013). The correction assumed uniform density distribution, with 2670 kg representing top continental crust and 1630 kg representing ocean waters. The topographical impact (Fig. 3b) was removed to create the Bouguer map (Fig. 3c).

  3. 3.

    The Bouguer anomaly and Moho effect are distinguished by removing gravitational influence from sedimentary layers (Fig. 3d). The gravity impact is estimated independently using three sediment layers with distinct densities (Laske et al. 2013).

  4. 4.

    Gravity correction assumes irregular Moho clearance is the sole remaining component (Rathnayake et al. 2021; Tenzer and Chen 2019) all corroborate this notion.

Fig. 3
figure 3

a Free air anomaly map of Egypt; b the gravitational effect of topography of Egypt; c the Bouguer anomaly of Egypt; d the gravity correction of Egypt’s sedimentary cover; e final Bouguer map of Egypt; with a resolution of 0.1 arc degrees

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(Farag et al. 2022) described the entire Bouguer gravity disturbance mathematically as:

$${g}^{B}={g}^{dis}-{g}^{T}- {g}^{T. \delta \rho }- {g}^{B}- {g}^{MS}- {g}^{IS}- {g}^{C}$$
(1)

where \({g}^{B}=\text{the gravity anomaly without effect of sediments}\), \({g}^{dis }=\text{the gravity disturbance}\), \({g}^{T}=\text{the gravitational effect of topography}\), \({g}^{T. \delta \rho }=\text{the abnormal}-\text{topographic correction}\), and \({g}^{B}=\text{the bathymetric}\), \({g}^{MS}=\text{the marine sediment}\), \({g}^{IS}=\text{the inland sediment}\), \({g}^{C}=\text{gravity of the solidified crust}\). (Fig. 3e) depicts the final processed Bouguer map.

3.3 Gravity inversion and Moho depth estimation

To characterize the architecture of the crust and figure out Moho depth, both an inversion technique and a 2D forward density modeling approach were employed. The Moho depth was initially estimated through the inversion of satellite gravity data obtained from the GOCO06 dataset. Subsequently, the obtained results were compared with five profiles derived from forward gravity modeling using the combined gravity model XGM2019e_2159.

To characterize the architecture of the crust and figure out Moho depth, both an inversion technique and a 2D forward density modeling approach were employed. The Moho depth was initially estimated through the inversion of satellite gravity data obtained from the GOCO06 dataset. After that, the results were compared with five profiles that were made using the combined gravity model XGM2019e_2159 and forward gravity modeling.

This study employs a nonlinear inversion method with gravity and seismic data, utilizing the Gauss–Newton formula and tesseroids to address the ill-posedness of the inverse problem (Sobh et al. 2019; Uieda and Barbosa 2017); we provided our modified version of the inversion code in the supplementary materials. The technique also incorporates Earth curvature and uses a Tikhonov regularization factor (Farag et al. 2022). The inversion technique determines three critical parameters: regularization parameter, Moho discontinuity reference depth (Zref) and crust-mantle density difference (Δρ). It involves calculating the regularization value and performing inversion for different density contrast and reference depth values.

To ensure robust comparisons and obtain reliable predictions, the inversion process was constrained by seismic data, as indicated by the distribution of seismic points shown in Fig. 1. A variety of values were tested, with increments of + 50 kg/m3 for the density disparity (ranged from 200 to 500 kg/m3) and + 2.5 km for the reference Moho depth (ranged from 10 to 50 km). The final model was determined based on the best fit to the seismic data points. Subsequently, the inversion step was performed for various combinations of density contrast and reference depth values.

3.4 2D forward modeling with GM-SYS

To complement our inversion model, a gravity modeling which is a 2D forward technique was carried out utilizing the GM-SYS version of the Oasis Montaj software. We assigned the following forward density values: 2400 kg/m3, 2700 kg/m3, 2900 kg/m3, 3300 kg/m3 at sediment, upper crust, lower crust and upper mantle, respectively (Makris and Wang 1994; Ginzburg and Ben-Avraham 1987). The objective of this modeling approach was to further investigate the subsurface structure and provide supplementary evidence for our study. The 2D modeling process encompassed five distinct profiles (P1 to P5) strategically positioned across different regions within the study area. These profiles played an essential role in characterizing the geometries of significant underground boundaries, including the Basement interface, the Conrad interface and the Moho interface.

For the forward modeling, Bouguer data extracted from the XGM2019e_2159 dataset were employed. This dataset combines satellite gravity data from GOCO06 and terrestrial data, resulting in enhanced resolution of shorter wavelengths associated with shallower depths. By utilizing this powerful dataset, our aim was to gain detailed vision about the subsurface structure and improve our understanding of the geological characteristics specific to the studied area.

4 Results and discussion

4.1 Surface thermal anomalies map

The high-quality imagery (Figs. 4 and 5) presented in this study was acquired during periods characterized by milder weather conditions, specifically toward the end of winter and throughout the spring season. The selection of these timeframes was motivated by the reduced impact of cloud masking and limitations related to satellite image dimensions. Figure 4 provides an overview of the land surface temperature (LST) evolution observed in February, while Fig. 5 depicts the LST patterns recorded in May. To explore the potential relationship between hot springs and temperature anomalies detected in the LST data, a straightforward overlay analysis was conducted using the geographical coordinates of various hot springs identified in (Zaher et al. 2018) (Table 1). Notably, the primary objective of this investigation is to assess whether the observed LST variations are influenced by factors such as Moho depth and crustal thickness. Specifically, we aim to determine whether regions characterized by a thinner crust and a shallower Moho are more likely to experience higher surface temperatures due to the elevated thermal impact exerted by the asthenosphere. Subsequent sections of this study will address this critical concern and acquire perspective on this relationship.

Fig. 4
figure 4

LST map of Egypt using sentienel-3B, a LST (27/2/2022); b LST (6/2/2022), c LST (1/2/2022); d an overlay between a, b and c to strength the thermal anomalies, red dots show the locations of hot springs (Table 1) by (Zaher et al. 2018)

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Fig. 5
figure 5

LST map of Egypt using sentienel-3B, a LST (29/5/2022); b LST (25/5/2022), c LST (24/5/2022); d an overlay between a, b and c to strength the thermal anomalies, red dots show the locations of hot springs (Table 1) by (Zaher et al. 2018)

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The findings of our study align with the conclusions of (Al-Aghbary et al. 2022; Zaher et al. 2018). We confirmed that regions with a thinner crust and a shallower Moho tend to experience higher surface temperatures due to the increased thermal impact of the asthenosphere. Moreover, our research yielded novel view of the relationship between land surface temperature (LST) variations and Moho depth, as well as crustal thickness. (Al-Aghbary et al. 2022) used a random forest regression model to estimate geothermal heat flow across Africa, finding that the Gulf of Aden, the Red Sea and the East African Rift System are the locations which regarded to have highest values of the geothermal heat flow. These regions, characterized by a thin crust and a shallow Moho, allow for the heat from the asthenosphere to reach the surface more easily. Similarly, (Zaher et al. 2018) conducted GIS-based analysis to identify geothermal resources in Egypt, identifying the significant prospective locations for geothermal growth, which also exhibit a thin crust and a shallow Moho.

4.2 Final derived Bouguer map

Various factors contribute to the positive or negative effects on gravitational force, including the presence of mountains, rifts, sedimentary basins and intrusive igneous bodies. In the case of Egypt, the gravity anomalies are complex and result from a combination of these factors. Additionally, the most significant gravity anomalies in Egypt stem from the presence of mountains, rifts and sedimentary basins. The study area analyzed Bouguer anomaly values, as depicted in Fig. 6, ranging from − 100 to 300 mGal, reflecting density variations and the geological structure of the underlying rocks. The onshore region, encompassing the Nile River and southwest Egypt, exhibits negative values of Bouguer anomaly because of existence of granitic crust, known for its lower density compared to oceanic crust.

Fig. 6
figure 6

Egypt’s sediments-free Bouguer map; resolution (0.1)

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Conversely, the offshore areas including the Mediterranean coastline, the northern portion of the Nile Delta and the Red Sea, display positive Bouguer anomaly values. This occurrence can be attributed to the existence of mafic oceanic crust, which possesses higher density than continental crust. The variations observed in Bouguer anomaly values offer helpful understanding about the geological composition and tectonic history of the study area.

In contrast, the study identifies significant high gravity values within the continental crust of Egypt, predominantly concentrated in the Western Desert. These findings align with prior investigations conducted by (Sobh et al. 2019; Abdelwahed et al. 2013) on earth gravity. Nevertheless, this study introduces a novel perspective by exploring the correlation between these reduced gravity values and the depth of the Moho. The outcomes indicate a reduction in crustal thickness, implying the proximity of the mantle to the Earth's surface. This association between decreased crustal thickness, areas with hot springs and elevated surface thermal anomalies brings new revelations derived from this research.

4.3 Moho depth derived from the inversion model.

The inversion process utilized sediment-free Bouguer gravity data and seismic constraints as input, leading to the generation of 25 Moho models with minimal mean square error. The most favorable outcome was attained when adopting 35 km as a reference depth of Moho and a density difference of 500 kg/m3 (Fig. 7). The gravity residuals exhibited a value of -0.10 mgal as a mean and a value of 4.40 mgal as a standard deviation. The resulting models portrayed varying Moho levels ranging from 20 to 40 km, as illustrated in Fig. 8. Additional information can be found in the supplementary materials.

Fig. 7
figure 7

The relation between the three gravity inversion parameters. The reference Moho depth (\({Z}_{ref}\)); 35 km, the density disparity (Δρ); 500 kg/m3, and the regularization parameter; (1\({e}^{-10}\)). The colored contours show the mean square error. The grey rectangular indicates our optimum fitting model

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Fig. 8
figure 8

The optimum Moho depth map; derived with 35 km depth and 500 kg/m3 density disparity

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Figure 8 showcases the final depth model of Moho, generated through the gravity data inversion, which produced the least mean square error. This model holds great significance in studying the Moho depth and the underlying crustal structure, particularly in areas where the Moho boundary approaches the surface. It offers important details about the characteristics of the region's geological composition and aids in further exploration and analysis.

The results of our study, as well as the studies by (Sobh et al. 2019; Abdelwahed et al. 2013), show that the depth of the Moho in the Eastern Desert estimated to be approximately 20 km, 22 km and 21 km, respectively, while the Moho depth in the Western Desert is estimated to be around 30 km, 33 km and 32 km, respectively. Furthermore, our study, along with (Sobh et al. 2019; Abdelwahed et al. 2013), suggests a Moho depth of approximately 40 km, 43 km and 42 km, respectively, in the Nile Valley. These additional details further support the robust Moho depth model, which serves as an important tool for studying Africa's crustal structure, identifying geothermal resource potential and enhancing earthquake prediction capabilities.

The findings from the Moho inversion process align with previous studies by (Al-Aghbary et al. 2022; Zaher et al. 2018), indicating that the typical African Moho depth fluctuates between 20 and 40 km including certain regions, such as the Red Sea and the East African Rift, exhibiting shallower Moho depths. The final Moho depth model provides specific measurements across Africa, revealing that the Eastern Desert has the shallowest Moho at approximately 20 km, followed by the Western Desert at around 30 km, while the Nile Valley exhibits the deepest Moho reaching about 40 km. These variations in Moho depth distribution can be attributed to the complex tectonic history of the continent, as the ongoing building of the juvenile East African Rift System contributes to its shallower Moho, and the tectonically stable Western Desert accounting for its relatively deeper Moho. Beyond studying crustal structure, the final Moho depth model serves as a beneficial resource for identifying regions with thin crusts and close proximity to the asthenosphere, holding potential as geothermal resources. Moreover, the model aids in the understanding of Africa's tectonic history and facilitates future earthquake prediction.

4.4 Forward modeling

For verification of the reliability of our inversion model, we utilized 2.5D forward gravity profiles employing Bouguer data derived from the XGM2019e_2159 combined model. Forward gravity modeling, owing to the significant density contrast associated with the Moho boundary, proved to be a suitable technique for determining the Moho depth. To ensure full coverage, we selected five profiles (Fig. 9a) oriented in different directions: E-W for profiles P1 and P2, NW–SE for profiles P3 and P5 and NE-SW for profile P4. These profiles, by fitting the observed and calculated Bouguer gravity data, provide significant geometric information about the basement interface, Conrad boundary and Moho boundary while minimizing data error.

Fig. 9
figure 9

a Sediments-free Bouguer map extracted from XGM model; red lines present the positions of the density model profiles P1, P2, P3, P4 and P5, b the Moho depth map revealed from inversion; red lines present the positions of the Moho depth inversion model profiles I1, I2, I3, I4, I5 and I6

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To strengthen the credibility of our findings, we constructed forward cross sections using reference data obtained from previous research. This approach enhances the evidential support for our results and reinforces the overall robustness of our investigation.

In our study, the visual representing of the 2D profiles with density-based coloring illustrate the correlation between observed and calculated gravity values (Fig. 10). Furthermore, the figure includes an assessment of the error percentage, enabling a comparison of the Moho depth between the inverse and forward models. This comparative analysis validates the accuracy and reliability of the inversion methodology employed in our study.

Fig. 10
figure 10

2D cross sections of sediments-free Bouguer map extracted from XGM model and equivalent depth profiles extracted from the inversion model, obtained in Fig. 9. The cross sections letters (from a to e) positions are shown in Fig. 9

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The cross sections unveil an increase in crustal thickness from west to east, with the Moho depth progressively deepening from 30 km in the west to 35 km in the east. Profiles P1 and P2 exhibit variations in sediment thickness, while profiles P3, P4 and P5 provide discoveries on the structure beneath the Sinai Peninsula and the diagonal structure of Egypt.

4.5 Model uncertainties

To assess the impact of inversion parameters, reference depth (Zref) and density contrast (Δρ) on the estimation of Moho depth, we conducted an analysis of uncertainties. For (Zref), we employed a value of 35 km with a step increment of 2.5 km for the inversion range. Regarding the density disparity (Δρ) at the reference depth 35 km, we calculated values by subtracting 450 kg/m3 and adding 50 kg/m3.

The uncertainties and their corresponding results are summarized in Table 3. Figures (9b and 10) present a cross-comparison between the Moho depth obtained from the inversion and the other which are derived from forward density modeling. This comparison demonstrates the consistency between the forward model and the inverted model.

Table 3 Uncertainties calculation
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Figure 11 illustrates the misfit in Moho estimation, comparing between the seismic-based and gravity-based model. The frequency differences range from -5 to 5 km, with 0.10 km mean and 4.4 km standard deviation.

Fig. 11
figure 11

a Differences in Moho depth between gravity derived and seismic derived, b the misfit histogram between gravity and seismic data with -0.10 km mean and 4.40 km standard deviation

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4.6 Moho depth correlated to hot springs.

Our objective was to investigate any possible links or associations between the subsurface Moho boundary and thermal anomalies in the research area by considering the data on Moho depth and the spatial distribution of hot springs as depicted in Fig. 12. This approach involved merging the Moho depth estimates obtained from the inversion process, based on the least mean square error, with the distribution of hot springs (thermal anomalies). The purpose was to establish a conclusive relationship between these two factors.

Fig. 12
figure 12

The Moho depth revealed from inversion, red dots show the locations of hot springs (Table 1) by (Zaher et al. 2018)

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By incorporating the information regarding the Moho depth and the spatial distribution of hot springs, we aimed to uncover any potential connections or correlations between the subsurface Moho boundary and the occurrence of thermal anomalies in the study area. This integrated analysis can provide beneficial knowledge about the geodynamic processes and geological characteristics that contribute to the formation of hot springs, thereby contributing to a thorough understanding of the underlying mechanisms at play.

Our finding coincided with the previous estimation of the Moho’s depth, such as (Youssof et al. 2013), (Baranov et al. 2023) and (Alemu 2024). The findings of this extensive investigation have substantial ramifications for the exploitation of geothermal resources and the development of electricity in Egypt. The center section of the country, specifically between 25 and 30 N, contains strategic spots for targeted geothermal exploration and resource assessment. These places have been determined to have Moho depths ranging from 32 to 35 km.

On the other hand, the relatively shallow depths of the Moho in these areas indicate the existence of higher thermal gradients and greater heat transfer from the Earth's interior. Consequently, this suggests a greater probability of discovering usable geothermal resources that might be utilized for generating power or providing direct heat. This approved by (Zaher et al. 2018) when they related the hot springs in the center of the western desert with the heat flow due to the thinning of the crustal thickness in the area of hot springs. Additionally, this finding gives us a more comprehension of the fundamental geological and tectonic elements that govern the presence of geothermal resources, such as faulting process and sedimentary basins distribution that have been explained in (Meshref 2017), (El-Dakak et al. 2021) and (Abdel-Fattah et al. 2019).

5 Conclusion

The primary objective of this study was to identify potential geothermal locations in Egypt by analyzing the depth of the Moho boundary. The Moho is the boundary between the Earth's crust and upper mantle. It is known for having significant differences in physical attributes, such as temperature gradients. In the initial phase of this study, we examined thermal anomalies on the land surface alongside the distribution of hot springs. Subsequently, we performed a seismic constrained inversion of satellite gravity data using Bott's method with Tikhonov regularization to generate a Moho depth map of Egypt with minimum mean square error. To validate the results obtained from gravity inversion, we conducted 2D gravity forward modeling on five profiles.

To assess the uncertainty of our conclusions, we compared the seismic and gravity-derived Moho models. The mean difference is 0.10 km, indicating an excellent fit between the two. We also compared cross sections between the inversion and forward gravity-derived Moho models, resulting in an exact match between both.

The Moho depth model indicates that the southern and western regions of Egypt exhibit greater depths, whereas the eastern and northern areas, encompassing the Mediterranean, the Red Seas, display shallower depths. The Egypt’s southern shows that the Moho depth varies between 35 and 39 km, with a deepest point located at 39 km beneath the southwestern region. The Moho depth of Sinai Peninsula ranges from 35 km at the south to a shallower depth of 30 km at the north. The Moho depth of the Eastern Desert ranges from 31 to 35 km.

Our research shows that regions in the central part of Egypt, between 25 and 30 degrees north, that have a significant quantity of thermal activity and hot springs, are correlated with Moho depths ranging from 32 to 35 km. Regions in Egypt with shallower Moho depths are more likely to have higher thermal potential because of the thinning of the Earth's crust in those areas.. We suggest exploiting these regions with Moho depths ranging from 32 to 35 km to build geothermal power facilities. Exploiting Egypt's geothermal energy potential in these key areas might yield favorable environmental outcomes by mitigating emissions that contribute to global warming and societal benefits by delivering clean and dependable electricity to local populations. In summary, the findings of this study provide beneficial perspectives for future geothermal exploration and development endeavors in Egypt. Understanding geothermal resources' distribution and properties can provide valuable information for making policy decisions and develo** investment plans. This knowledge can help Egypt in its efforts to shift toward a more sustainable and renewable energy generation. To further explore the areas indicated, we will next compute their geothermal heat flow, which represents the transfer of heat from the interior of the earth to its surface.