Introduction

The perpetual dependency of energy supply on fossil fuels in the Kingdom of Saudi Arabia (KSA) may not be a viable and sustainable route even as there is a steady economic growth in the kingdom. Development and growth go along with escalating energy demand, and sustainability must be handled in a way to avoid compromising the capacity of the future generations by the present, in the course of meeting the energy needs of the present (Hashem 2012). Much is still required to bridge the existing knowledge gap and the insufficiency of information regarding the potential of geothermal resources in the KSA. Despite previous studies (Lashin and Al-Arifi 2012, 2014; Hussein et al. 2013; Al-Amri et al. 2016; Alqahtani et al. 2022), more detailed and comprehensive studies are still needed to evaluate the country’s economic reserves for possible energy production, especially in the volcanically active regions (Lashin et al. 2015). So far, only limited amounts of exploration efforts have taken place in this regard (Al-Amri et al. 2016). It is projected that the peak energy demand in the KSA will reach \(1.21\times {10}^{8} \mathrm{kW}\) in 2032 (Hashem 2012). In 2016, KSA produced \(3.24\times {10}^{11} \mathrm{kWh}\) of electricity (covering 109% of its annual consumption needs), of this, just about \(1.0\times {10}^{6} \mathrm{kWh}\) emanated from renewable sources (for example, solar). The remainder of this is derived from non-renewable fossil fuels (Worldometer 2022). As of 2015, KSA consumption of electricity from oil and gas sources was estimated at 2.40 \(\times {10}^{11} \mathrm{kWh}\) (Lashin et al. 2015).

Like most regions of rifting and plate boundaries, KSA has experienced volcanic eruptions, including our study area. Accessible depths are relative to subsurface character and recorded temperatures (150–300 °C) are promising for power generation due to the convective movement of mass and heat through magma intrusions and fractures. Fluids and circulation pathways, along with underlying heat source, set the stage for geothermal systems formed by convective fluid flow inside the brittle regions of the Earth’s crust (Rowland and Sibson 2004; Pearson-Grant and Bertrand 2021). The three main categories of unutilized geothermal resources (Fig. 1) in the KSA include (Lashin et al. 2015):

  • medium enthalpy resources (hot springs), existing at the southwestern coast and along the western regions,

  • low enthalpy resources, symbolized by aquifers at depths accessible by deep oil wells and

  • high enthalpy resources (volcanoes (“Harrats” in local name)), portrayed principally by lava fields spanning ~ 80,000 km2, with fumarolic activity (e.g., Harrat Khaybar).

Fig. 1
figure 1

Cenozoic lava fields of western Saudi Arabia with their distribution of ages (modified from Moufti et al. 2013). The study area Harrat Rahat (inserted Yellow Square) is also shown

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A volcanic eruption recorded in 1256 A.D. at the Al Madinah city resulted in the formation of volcanic lava fields (Fig. 1). Consequently, activities of geothermal character similar to hot springs, shallow wells with hot waters and steam emissions were traced to these harrats (Roobol et al. 2007). Harrat Rahat forms a 50–75-km wide, 300 km long, \(\mathrm{N}20-25^\circ \mathrm{W}\) trending plateau (Berthier et al. 1981; Coleman et al. 1983; Abdelwahed et al. 2016). It is composed of four coalesced, smaller volcanic fields attaining an approximate area of 19,830 \({\mathrm{km}}^{2}\) and an estimated volume of 1999 \({\mathrm{km}}^{3}\) flows (Camp and Roobol 1989; Abdelwahed et al. 2016).

Similar to many basalt successions, Harrat Rahat forms a significant aquifer for groundwater resources. The aquifer sits at the topmost region of the underlying basement, comprised of fractured basalt and pre-basalt sands and gravels with a saturated thickness of 60 m (Al-Shaibani et al. 2007). The importance of Harrat Rahat arises because its northern extremities stretch toward the environs of the holy city of Al-Madinah Al-Munawarah (Abdelwahed et al. 2016). Al-Amri et al. (2016) ranked the harrats in the region according to geothermal potentials with Rahat chosen as among those with the highest potential. Further comparison with a geothermal field with a comparable setting in Mexico (Tres Virgines geothermal plant in Baja-California) implies that the faults together with corresponding seismicity may be connected with elated permeability. Renewable energy sources such as geothermal resources have continuously attracted interest in the KSA (Hashem 2012; Lashin et al. 2015; Al-Amri et al. 2016; Alqahtani et al. 2022), and with the existence of considerably viable geothermal potentials in the KSA, geothermal energy presents a promising prospective source of renewable energy (Hashem 2012). Ample technologies and methods abound for accessing geothermal targets (Comps and Muller 1973; Lashin et al. 2015).

Previous works

A geothermal development roadmap for the KSA was provided by Hashem (2012) which identified some potentially rich geothermal locations and proposed a holistic avenue for efficient utilization of geothermal energy. Geo-scientific studies are the first step toward ascertaining geothermal resources including surface geological mapping to determine the depth, lateral extents of functioning geothermal systems and exploration drilling (Hashem 2012). George and Shorbaji (1987) and Al-Shaibani (2003) reported a mean temperature of the groundwater system beneath northern Harrat Rahat of 36 °C, about 4 °C higher than average groundwater measurements of Bob et al. (2015) from 20 wells in the Madinah City area.

Lashin et al. (2015) made preliminary assessments on the geothermal capability of some hot springs located at Lith and Jizan sites using mixed geological and geophysical methods. Their geothermometer estimations of the reservoir temperatures place the values within 130–220 °C and heat flow range at 120–210 μW/m2. Their results estimated the wet geothermal systems’ capability to produce about \(23\times {10}^{9} \mathrm{kWh}\) of electricity. Deep mantle structures relating to plumbing and crustal structure of the Harrats were analyzed by inverting high-quality arrival-time information from teleseismic events and local earthquakes (Abdelwahed et al. 2016). Their tomographic images reveal intense heterogeneities identified with low velocity zones stretching below the A.D. 1256 volcanic center and the 1999 seismic swarm region.

An inversion of gravity field from northern Harrat Rahat guided by the examination of aeromagnetic data by Langenheim et al. (2019) indicated a wide depression of the basement surface that appears deeper along the primary vent axis of the eastern and southwestern parts of the volcanic field. A less dense basement underneath the vent axis in the field was also identified and suggested to have arisen from lithological deviations in the basement that occurred prior to predating Cenozoic volcanism. Aboud et al. (2022) analyzed data from four boreholes (total depths ranging between 206 and 460 m) spread within the northern Rahat region with additional evaluations of gravity and magnetic data, to provide insights on noticeable surface thermal anomalies in some water wells in the region. Their results indicated a geothermal anomaly at depths of 3–4 km within a region of approximately 35 \({\mathrm{km}}^{2}\) beneath the historical eruption site. Alqahtani et al. (2022) inverted gravity and magnetic anomalies toward the determination of basement relief at the Harrat Rahat volcanic field. Their primary aim was to assess the geothermal prospects inherent in the northern Harrat Rahat region. Results from their analysis, using a global optimization technique of Particle Swarm Optimization (PSO) for depth varying density contrast to portray geological scenarios, indicated varying depths to the basement ranging between 0.10 and 624 m. Locations with higher prospects for geothermal energy exploration were also suggested. A set of factors affect the potential for exploration and use of geothermal power just like every other type of energy choice.

The present study focuses on the region within the Harrat Rahat identified from previous studies (Al-Amri et al. 2016; Alqahtani et al. 2022) as possessing higher subsurface heat flow. This deduction has been derived from cross-correlation of ambient seismic noise background on the young volcanics and the analysis of gravity and magnetic data. The aim of this study is to further examine the geothermal potential areas within the Harrat Rahat and perform 3D modeling of the subsurface geological structures aiming to provide an outlook on the nature of the subsurface. 3D modeling techniques have turned into a desirable tool for observing and analyzing the Earth and have found wide applications in several trades. 3D geological model assists geoscientists by providing a powerful communication tool that can be used to help explain the structure, composition and geological processes that makes up the Earth’s crust (Yan-lin et al. 2011).

Geological setting

Harrat Rahat is elongated in a N–S direction of about 310 km in the direction of the Makkah-Madinah-Nafud (MMN) volcanic line and is comprised four smaller harrats forming an elongated shield-like shape with noticeable linear vents in the central area (Al-Amri et al. 2016). The basic component of the harrats is alkaline Olivinitic basalt, taking the shape of naturally roofed feeder route of lava flows (lava tubes) and with a partial solid surface. As the lava flows away from the eruption point, the margins of the flow gradually becomes stagnated, leading to the creation of a central channel at the starting regions of the flow (Roobol et al. 2002). A variation of the basalts comprises alkaline olivine to hawaiite and also olivine transitional basalt, while the connected changed rocks of mugerarite, benmoreite and trachyte basically exists as dome and tuff cones containing lava flows (Moufti et al. 2010, 2012; Abdelwahed et al. 2016). Harrat Al-Madinah basalts were moreover divided into upper and lower Madinah basalts (Camp et al. 1987; Camp and Robool 1989, 1991). The northern divide of Harrat Rahat is also referred to as Harrat Al-Madinah (Moufti et al. 2012; Abdelwahed et al. 2016). Three flow units (Fig. 2) constitute the upper Madinah basalts, namely, Qm1 (~ 1.7–1.2 Ma), Qm2 (~ 1.2–0.9 Ma), and Qm3 (~ 0.9–0.6 Ma), whereas four flow units, Qm4 (~ 0.6–0.3 Ma), Qm5 (~ 0.3 Ma–4500 BP), and Qm6 (~ 4500–1500 BP), constitute upper Madinah basalt (Camp et al. 1987; Camp and Robool 1989, 1991; Aboud et al. 2015). Proterozoic rocks comprising younger volcanic sedimentary sequences and volcanic arc rocks overlain and lapped onto by the Cenozoic volcanic rocks of the region. The magmatic activities in the last 30 Ma are evidenced in the lava fields (Camp and Robool 1991; Aboud et al. 2022). A basalt aquifer system covering 2000 km2 has been defined in the northern region of Harrat Rahat close to Al-Madinah Al-Munawwarah (Al-Shaibani et al. 2007).

Fig. 2
figure 2

Geological setting of the area covered by this study (Alqahtani et al. 2022)

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Data sources

Figure 3 shows the topographic map of the study area. In applied geophysics, local anomalies in the gravity field are mostly due to near-surface mass distributions and topography (Pirttijärvi 2014). Topography may not be the only factor influencing geothermal convection; however, its contribution is on a larger scale as compared to what is mostly surmised (Pearson-Grant and Bertrand 2021). The topography shows higher elevation to the east reaching ~ 1100 m toward the southeast and ~ 930 m toward the northeast. An average elevation of ~ 850 m is noted for the study area. Multiple volcanic vent systems exist within the study area as plotted in Fig. 3. Such settings, with multiple volcanic vents have been considered as pointers to volcanic centers hosting very large high-temperature reservoirs (Aboud et al. 2022).

Fig. 3
figure 3

Topographic map of the study area. Inscribed profile lines (AA′, EE′, FF′, VV′) correspond to profiles of previously collected data used in this study. Inserted black squares represent volcanic vents mapped in the region

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The gravity data utilized here was acquired from Alqahtani et al. (2022). Measurements at 149 gravity stations at a spacing of 0.2–1 km were corrected to create a residual Bouguer anomaly map (Fig. 4; Alqahtani et al. 2022).

Fig. 4
figure 4

Residual Bouguer anomaly map. “A” labels within the map represent the Al-Madinah Al-Munawwarah region while the numbers beside it represent locations within the Al-Madinah Al-Munawwarah region (Alqahtani et al. 2022). Within the central area lies a negative gravity anomaly which has its largest magnitude to the east (A11 and A13)

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Detailed processing including the various corrections applied to the data has been explained by Alqahtani et al. (2022). Data from Fig. 4 were used for further examination in this study.

Other data utilized for this study were drawn from previous regional geophysical studies (Abdelwahed et al. 2016; Langenheim et al. 2019; Alqahtani et al. 2022). Profiles AA′ and FF′ (Fig. 5) were from Abdelwahed et al. (2016), and represent vertical cross sections from P-wave tomography evaluations. Cross-section AA′ passes from north to south intersecting the historical 1256 AD eruption site. Shallow low velocity anomalies (6–40 km depths) are visible below the historical and trachytic domes with lateral off-shooting dipping steeply to the south (Abdelwahed et al. 2016). Cross-section FF′ was constructed further south of our study area (Figs. 3 and 5c) and runs perpendicular to cross-section AA′. However, the part of this cross-section falling within our study area indicates low velocity anomalies almost encapsulating the high-velocity anomalies. For our geothermal potential modeling, we choose a depth 10 km on the selected profile cross sections (Fig. 5). This section traverses the seismic swarm region and the trachytic volcanic centers (Fig. 5a). Prominent shallow low velocity anomalies are notable in both shallowly and at depth marked-out upper 10 km within the study area (Fig. 5d). These low velocity anomalies coincided with the location of the 1999 seismic swarm. Profile EE′ (Fig. 6) was extracted from Langenheim et al. (2019) and represents a horizontal cross-section running across our study area in the northern part. This profile was adapted from the Abdelwahed et al., (2016) model by Langenheim et al. (2019), utilizing density data and mapped geological relationships. Model of Profile EE′ was performed by Langenheim et al. (2019) and a modified density distribution restricted to the upper 20 km of the initial model was created. However, for the purposes of our study, we extracted the upper 10 km. Profile VV′ (Fig. 7) has been taken from Alqahtani et al. (2022) and the cross section utilized to evaluate the upper subsurface structures to a depth of ~ 2 km. The cross section originated from a two-dimensional forward modeling outcome of magnetic and gravity data. Although the depth extent from Profile VV′ falls short of our set model depth extent, Profile VV′ examined in 3D, the nature of the upper part of the considered area. 3D visualization can provide people with an instinctive feel about a subject matter (Yan-lin et al. 2011).

Fig. 5
figure 5

Vertical cross sections of P-wave velocity tomography below the Harrat Al-Madinah. Locations of the profiles are displayed on the inset map (a). The blue and red colors denote high and low velocities, respectively. The velocity perturbation (in %) scale is also shown. SLV and DLV represent shallow low velocity and deep low velocity, respectively. The purple and red triangles denote the trachytic lava domes and basaltic cones, respectively. Inserted red square (a), represents the study area whereas the black squares (b and c) represent the study area extent on the profiles and extracted depth to the upper limit of 10 km. d displays the extracted sections from (b) and (c), respectively

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Fig. 6
figure 6

a Cross-section of profile E−E′ as adapted from Langenheim et al. (2019). (D represents modified density distribution limited to the upper 20 km). d, density in kg/m3, S, magnetic susceptibility in 10−3 SI units. Inserted black square represents part of the cross-section traversing our study area. b displays the extracted sections from (a)

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Fig. 7
figure 7

A hypothetical geological cross-section resulting from gravity\(-\)magnetic data at Profile VV′ (Alqahtani et al. 2022)

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Estimating density from gravity data

A variety of geochemical (geothermometer) and geophysical methods utilized in geological investigations and hydrocarbon explorations in the oil industry can be used for geothermal potential explorations (Al-Arifi et al. 2012). Information from these methods is always useful for modeling a geothermal system and appraising the potential of such resources. Density, \(\rho\) (kg/m3 or g/cm3) is the petrophysical parameter analyzed in gravity studies and relates to variations in composition and structure (material properties) of soil and rocks. Therefore, the gravity method grants an indirect procedure to investigate the geological setup of the Earth (Pirttijärvi 2014). Gravity interpretation is an inverse problem, but gravity data cannot be interpreted uniquely. The purpose is to use density modeling and inversion to build a density distribution to interpret the measurements.

The modeling in this study was achieved with inversion techniques through the application of Singular Value Decomposition (SVD) (Press et al. 1988) and Occam optimization (Constable et al. 1987; deGroot-Hedlin and ConsTable 1990). The gravity anomalies were modeled in 3D using the Bloxer (Version 1.6e) and Grablox (Version 1.6e) computer programs. The optimization procedure was achieved in stages commencing from the base optimization, density optimization, Occam density optimization, height optimization, and Occam height optimization. These optimizations are conducted with the objective of decreasing errors between model and measurement data, toward obtaining the right model (Titi and Minarto 2017). The outcomes of the 3D modeling of gravity anomalies are shown in Fig. 8. In this study, the acquired gravity data was gridded on 100 rows \(\times\) 96 columns, with a grid spacing of 202 m on both axes to achieve a final gravity field data of 9600 data points. Both inverse and forward modeling can be performed using the Grablox program. The height of individual blocks and respective density values are optimized by the inversion method. The roughness of the resulting model is also minimized using Occam’s principle. The density distribution in the resultant block model could consequently be utilized for geological interpretations.

Fig. 8
figure 8figure 8

3D model density results from the inversion of gravity anomalies in the study area. a The final model after the 3D inversion. b–g Model slices across the model block from the southern region of the map toward the north. h Final 3D model result after removing the background density from (a)

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Results

We present results from the 3D inversion modeling of the gravity anomalies (Fig. 8). Profile slices on the density model are compared with cross sections extracted from Abdelwahed et al. (2016) at the same location and presented in Fig. 9. The 3D visualization of data extracted from the computations of Abdelwahed et al. (2016) for our study coverage area is presented in Fig. 10. Figure 1 shows 3D visualization of data from Langenheim et al. (2019) for the northern region of our area of coverage, whereas Fig. 1 shows the 3D visualization of data from Alqahtani et al. (2022) that traverses the central region of our study area. Leapfrog geothermal software was utilized for the final visualization of these data. Figure 13 displays a combination of 3D visualization of data derived from the three previous studies considered in this study. The intent is to compare with our initially derived 3D density model from gravity anomalies.

Fig. 9
figure 9

Profile slices of the density model at the locations of the cross section extracted from Abdelwahed et al. (2016). a Profiles AA′ and FF′ taken on the density model from the gravity data inversion. b Vertical cross sections of P-wave velocity tomography considered for this study. Inserted black square represents the cross-section boundary for this study

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Fig. 10
figure 10

3D visualization of P-wave velocity tomography beneath the study area derived from vertical cross sections of P-wave velocity tomography computed by Abdelwahed et al. (2016). a The traversing profile data (AA′ and FF′) extracted from the P-wave velocity tomography. b Visualization sequence of the various subsurface structures. c Final 3D visualization of data from the cross sections. d Final 3D visualization result with topography-draped geological map

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Discussion

The topography of our study area (Fig. 3) shows increasing elevations from the western toward the eastern regions at 750–1100 m. The eastern region shows an elevated topographic trend with densely concentrated vents. The high elevated topography may be related to the N–S trending concentration of volcanic scoria cones in the area. The region proposed by Alqhatani et al. (2022) for further geothermal examination possesses elevations ranging between 900 and 980 m and is not directly located within the highly elevated scoria cones of the study area. Subsurface hydraulic pressure gradients can focus fluid flow, bringing about favorable recharge in the regions of high topography and discharge in regions of low topography (Graven 1995; Pearson-Grant and Bertrand 2021). However, it is surmised that topographic forces are important only at shallow depths and are small relative to buoyancy forces that drive fluids vertically through fractures toward the surface (Chi and Xue 2011). In this study, we postulate that the topography of the region has potential effects on the recharge and discharge dynamics of subsurface fluid flow. With preferential discharges occurring especially at the identified geothermal active location (with lower elevations). Fluid pathways (permeability) are key for geothermal fluid flow. Geological models, which can be derived from density distributions, provide the first indication of a possible permeability distribution and are a key first step in geothermal exploration.

Inversion of gravity anomalies (Fig. 8) shows the various density anomalies in the study area. A significant isolated density structure is observed at the center of the study area with densities around 2820 \({\mathrm{kg}/\mathrm{m}}^{3}\) encapsulating structures with much lower densities (< 2300 \({\mathrm{kg}/\mathrm{m}}^{3}\)). Density model slices in Fig. 8b–g shows the various stages of the resultant 3D density model with the various slices revealing the nature of the secluded anomaly within the region. We hypothesize that the Isolated Anomalous Structure (IAS) could well represent a heat source for possible geothermal reservoir feeding from an inherent magma chamber at a depth. Shallow magmatic intrusions are common features in volcanic areas (Burchardt 2019; Faizy 2021). These intrusions form as a result of magma rising and cooling on a shallow depth after it arrives at the upper crust (Faizy 2021). An analysis of the young volcanics within the study area by Al-Amri et al. (2016) indicates elevated subsurface heat flow. The Rahat is one of Makkah-Madinah-Nafud (MMN) lines of active volcanism. From assessment of the elemental composition of the basaltic rocks in the region, Camp and Roobol (1992) proposed that the lava along the MMN line was conjugated from greater degrees of partial melting at shallower depths of melting. Figure 8h shows a model result after filtering of background density. The IAS is adequately revealed. Our interpretation also shows that the geothermal reservoir could be reached at starting depths of ~ 1.3 km, whereas its effect could be accessed at depths of less than 1 km.

A similar geothermal field as the Harrat Rahat, located in Mexico (the Tres Virgines geothermal plant in Baja California, Mexico) with same geological settings (Al-Amri et al. 2020) produced water temperature of 280 °C at drilled exploration well depths of between 1290 and 2500 m (Ocampo-Diaz et al. 2005). A case study from a conceptual example for a basalt\(-\)related geothermal system on the Mountain Home AFB, Idaho, USA, indicates a temperature of \(93^\circ{\rm C}\) recorded at a depth of 1207 m with estimated thermal gradient of 69 °C/km. This suggests that temperatures at depths of 1500–1800 m are elevated and may have the potential for binary cycle power generation (Nielson et al. 2019). Roobol et al. (2007) reported higher water well temperatures (\(\ge 53^\circ{\rm C}\)) within the Harrat Rahat, indicating geothermal processes.

Given the limitations resulting from ambiguity in gravity data interpretations, constraints from ancillary observations (for example, geology and/or geophysical) could assist in effective solution for gravity investigations (Hinze et al. 2013). Therefore, we compare the density model with data from other geophysical studies (Abdelwahed el al. 2016; Langenheim et al. 2019; Alqhatani et al. 2022) conducted in the region. Applying multiple methods of analysis over the same anomaly profile also increases the interpretation of results. Figure 9a displays regions of lower densities encapsulated by higher densities from the two profiles (AA′ and FF′) traversing our study area derived from Abdelwahed et al. (2016). The low density regions take approximate size, shape, and location with identified regions of shallow low velocity (SLV) from P-wave velocity tomography (Fig. 9b), with expected minimal deviation. The close reconcilability of identified anomalies from the two perspectives further strengthens our deductions in this study. The existence of an IAS, extending at depth, has been confirmed in Fig. 10. Results from P-wave velocity tomography at the shallow low velocity (SLV) zone (Abdelwahed et al. 2016) within our area of study depict contrasting anomalies having two basic velocity perturbations \({\mathrm{V}}_{\mathrm{P}} (\mathrm{\%})\), ranging between − 2.5 and 2.5, respectively (Fig. 10c). These anomalous velocity structures may be due to high temperatures and zones of magma when compared with the surrounding crust (Al-Amri et al. 2016). The final subsurface structure is located in a similar area with the same approximate size, shape, and depth elongation as subsurface structural outcome achieved with the 3D gravity inversion results at the same location, hence confirming the reliability of our computations. Superimposing the regional geology on the 3D visualization data (Fig. 10d) indicates that the structural body appears as possible magmatic intrusion and may have contributed (partly) to the eruption that occurred within the study area. We posit that the IAS holds some geothermal properties which could be further explored for additional information. Magmatic dikes intruded the harrats with the tip of the dikes ascending to a depth of less than 2 km from the surface leading to earthquakes and surface ruptures (Pallister et al. 2010; Baer and Hamiel 2010; Koulakor et al. 2014, 2015; Al-Amri et al. 2020). The young tephra and lava deposits, and documented historic and near eruption evidence are constant reminders of active magmatic systems underlying the harrats, with significant geothermal energy exploitation potentials (Al-Amri et al. 2020).

Figure 11a shows 3D visualization procedure on the cross section derived from Langenheim et al. (2019), within the region of our study. The result is from a profile (EE′) which is located at the northern edge of our study area and was able to capture an intruded subsurface structure within the area. The intruded subsurface structures with densities 2796 and 2818 \({\mathrm{kg}/\mathrm{m}}^{3}\) have also been identified from results of the 3D gravity anomaly inversion (Fig. 8h), therefore, adding some confidence to our modeling result. The final 3D visualization result is clearly seen in Fig. 11b and its location with respect to the surface geology is presented in Fig. 11c. Profile data for analyzing the internal structure of this model was lacking hence the deficiency of information at the center of the model.

Fig. 11
figure 11

3D visualization of data derived from EE′ cross section (Langenheim et al. 2019) at the northern region of our study area. a Profile EE′ and derived cross section applied in the 3D modeling. b 3D visualization of data from the EE′ cross section. c 3D visualization of data with draped geology map on topography

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The Alqahtani et al. (2022) model was examined to a depth of ~ 2 km (Profile VV′ in Alqahtani et al. 2022) to examine the upper structural setup of the region. Figure 12a shows the cross section used in achieving the 3D visualization of data in Fig. 12b. We also modeled the two vents directly on the Profile VV′ and proposed possible locations for boreholes sitting as follows: RDH_1 \(\left(39.803^\circ \mathrm{E}, 24.251^\circ \mathrm{N}\right),\) RDH_2 \(\left(39.768^\circ \mathrm{E}, 24.240^\circ \mathrm{N}\right)\) and RDH_3 \(39.827^\circ \mathrm{E}, 24.240^\circ \mathrm{N})\), respectively. This proposal is also based on the results from Alqahtani et al. (2022). We hypothesize that depositional units and the upper region of the basement (Fig. 12) provide some sort of a cover for the anomalous subsurface structure within the area. Figure 12c indicates the surface geological map interactions with the visualized model result.

Fig. 12
figure 12

3D visualization of data from profile section VV′ (Alqahtani et al. 2022) to a depth of 2000 km. a Traversing profile VV′ across the study area. b Final 3D visualization results with depth slice along profile VV′. The two major vents falling directly on the VV′ profile are hypothetically modeled along with Recommended Drill Hole (RDH_1, RDH_2, RDH_3) locations. c 3D visualization result of cross-section VV′ with overlain regional geology map. “CS” denotes cross section and “map” denotes depositional basaltic lava flows derived from the surface geology map

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A combination of the 3D visualized data from the three previous studies considered earlier is shown in Fig. 13 and comparison of the final two results is shown in Fig. 14. Result from previous studies reveals very close proximity to the 3D model result from inversion of gravity anomalies. It is clear that the similarity in the model parameter distribution (despite differences in investigative geophysical parameters) confirms the existence of an IAS within the center of the study area. This isolated structure is interpreted to represent a possible magma body and could symbolize the presence of a geothermal reservoir within the study area. The geologically young development of a contemporary crustal magma chamber or chambers in the northern Harrat Rahat is consistent with differentiated rock types found in upper Madinah basalt (Al-Amri et al. 2016), therefore further exploration is recommended, for example, magnetotellurics (MT) to identify zones of partial melt and geothermal fluid. This study would provide the baseline and additional insights for the MT study. In addition, other future exploration studies in the region can also benefit from our reconnaissance study.

Fig. 13
figure 13

A combination of the 3D visualization of data from the three previous studies conducted in the region (Abdelwahed et al. 2016; Langenheim et al. 2019; Alqahtani et al. 2022). a Cross-sections combinations used for the modeling to achieve a final model combination result in b for the study area

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Fig. 14
figure 14

A comparison of the 3D visualization results at 10-km depth with the 3D density model result from computations on gravity anomalies from the study area. a 3D visualization data from a combination of previous studies. b 3D model result from computations on gravity anomalies

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Conclusion

Subsurface structural examination of the northern Harrat Rahat volcanic field shows the presence of an isolated subsurface structure within the basement. Initial modeling of gravity anomalies to a depth of 10 km shows varying density values ranging between 2000 and 3100 \({\mathrm{kg}/\mathrm{m}}^{3}\). An isosurface evaluation at a density of ~ 2858 \({\mathrm{kg}/\mathrm{m}}^{3}\) reveals a secluded subsurface structure of higher density enclosing lower densities (< 2500 \({\mathrm{kg}/\mathrm{m}}^{3}\)) almost at the center of the study area. The secluded structure is suggested to represent a possible geothermal heat source arising from shallow magmatic intrusion in the area. Further investigation of the study area with regard to previous studies in the region confirms the existence of the modeled subsurface magmatic intrusion. Given the identified location and depth extent of the modeled geothermal heat source, possible geothermal resources could be exploited at depths of ~ 1.3 km at designated locations (\(39.803^\circ \mathrm{E}, 24.251^\circ \mathrm{N}\); \(39.768^\circ \mathrm{E}, 24.240^\circ \mathrm{N}\); \(39.827^\circ \mathrm{E}, 24.240^\circ \mathrm{N}\)). Consequently, further geothermal exploration is recommended in the study area, especially at designated locations.