Introduction

The M’Rara region is located at the Northeast Algerian Sahara basin, which is seriously affected by several natural hazards1,2. To exploit the Albian aquifer and supply M’Rara town with drinking and irrigation water a hydraulic drilling was realized in 1960 (Fig. 1). The stratigraphic column revealed presence of salt layer with a thickness of 11 m and located at a depth between 947 and 936 m (Fig. 2). After ten years of exploitation, in the 70s, the drilling began to debit 1200 l/mn of salt water (315 g/l). Following this, the drilling was sealed with cement plug. Near this drilling, there is fenced building that served as a cooling system for de hot water rising from the Albian. Inside this building, a land subsidence circular form with diameter of 5 m. It would seem the existence of a cavity below. North-east of this hydraulic drilling, at 117 m, a collapse appeared (Fig. 2a). Its shape is elliptical, approximately 10 m length by 5 m width and elongated in the N80° (± 20°) direction. It constituted the beginning of cavity elongated in the same direction and deep of 8 to 10 m. Another collapse appeared North-west of the hydraulic drilling and located at 1.3 km from the first collapse (Fig. 2). This cavity has an elliptical shape, but less pronounced than in the first-one. It presents 5 m length by 4 m width, oriented N100° to 110° and deep of 10 to 15 m. In addition of these collapses and land subsidence, an important fissure exists in the Plio-Quaternary agglomerates, at 770 m southwest of the hydraulic drilling. It is quasi-rectilinear, sometimes sinuous, presents more than 50 m length and oriented around the N°080°. It is a rosary of small deep hollows between 10 and 20 cm with a few centimeters wide, whose continuity defines fissure3.

Fig. 1
figure 1

(a) and (b) Location map of the study area, superimposed (in b) on the topographic relief map from ETOPO1 1-min global relief in m (www.ngdc.noaa.gov). (c) gravimetric dataset collected in this study. The displayed projection system is geographic (East longitude and North latitude) and Cartesian coordinates (WGS84, UTM zone 31 N in meters).

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Fig. 2
figure 2

(a) Surface cavities observed during data acquisition. (b) Geological map of the M’Rara region and its surroundings. (c) The lithostratigraphic column of the hydraulic borehole, located in the center of M’Rara city.

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Currently, gravimetric surveys are used in diverse fields, such as geotechnical engineering, environmental and engineering studies, hydrological and geothermal investigations, archaeological exploration, and geotectonic research4,5,6,7,8,9,10,11. Gravimetric results, or gravimetric anomalies, provide images of the masses distribution and/or densities variation within the basement12,13,14,15. These images do not directly indicate the presence of masses or voids but show apparent variations in densities caused by these masses or voids. Therefore, by analysis of this density distribution, we can identify their origins, such as cavities, decompressions, or geological faults16,17,18,19,20. The gravimetric method allows us to image the underground geological structures and to distinguishes the underlying formation. This significantly enhances our understanding of the internal processes responsible for natural resources and geological risk structures.

In this work, we would like to understand the phenomenon of the land subsidence, collapses and fissures that appeared around the sealed Albian drilling. Especially, its relationship with presence of eventually cavity located at the salt layer. To achieve this, we conducted gravimetric survey in the M’Rara region to image the density distribution and interpret the abnormal zones in relationship with the presence of cavities.

Geological setting

Surface geology

The M’Rara region is located Northeast of the Algerian Sahara, in the Oued Rhir area. It is situated at 100 km West of El Oued, 65 km Northwest of Tougourt and 32 km West of Djamâa (Fig. 1). It is a rural agglomeration surrounded by agricultural land. The region has a Saharan arid climate, characterized by hot, dry summers and milder winters. It is in Plio-Quaternary basin, at an altitude with about 100 m. It covers an area of ~ 15 km², surrounded by Mio-Pliocene hills. It belongs to the Saharan platform domain, which was structured into several basins during the upper Paleozoic separated by shoals21. It stayed relatively stable in the Meso-Cenozoic, except the compressive phase in the late Aptian (lower Cretaceous), which produced anticlines with N-S axis, and a compressive phase of the Cenozoic. The outcrops can be seen on the geological map (Fig. 2b). From the oldest to the most recent, the outcrops are dominated by:

  • The Pontian (transition from Miocene to Pliocene), surrounding the M’Rara city,

  • The continental Pliocene, constituted by pudding and lacustrine limestone,

  • The continental Quaternary, formed by ancient alluvium and terraces,

  • The recent dunes,

  • The actual alluvium, including small sebkhas and gypsum-saline crusts.

Stratigraphy

The stratigraphic column revealed by the water borehole (Fig. 2c), located in the M’Rara city (see position in Fig. 1), shows from bottom to top:

  • Albian unit with a thickness of 141 m and composed by sand, sandstone, and sandy clay,

  • Vraconian unit corresponds to dolomites, limestone, and clay,

  • Cenomanian unit presents a thickness of 182 m and constituted of clays, marls, and anhydrites,

  • Turonian unit with a thickness of 74 m and composed by marly or dolomitic limestone, marls, and dolomites,

  • Lower Senonian unit with a thickness of 468 m and dominated by massive anhydrites sometimes to gypsum, with intercalation of dolomites, marls, and dolomitic limestone. At the bottom of this unit a massive salt layer with a thickness of 11 m and located at a depth between 947 and 936 m,

  • Upper Senonian unit with a thickness of 267 m and composed mainly by marls, dolomitic limestone, and anhydrites,

  • Eocene unit with a thickness of 73 m and composed by marls, dolomitic and marly limestone, anhydrites, and dolomites,

  • Mio-Pliocen unit with a thickness of 48 m and corresponds to an alternation of lacustrine limestone, marls, sands, and clays, with gypsum sometimes.

Aquifer system

The M’Rara area hosts two major aquifer systems. The first-one system, known as the complex terminal (CT), consists of two main levels separated by semi-impermeable to impermeable layers. The upper level is the superficial aquifer situated in the Mio-Pliocene sands. The lower level is the aquifer found in the limestone of the late Eocene and early Senonian carbonates22. The CT aquifer is utilized through artesian wells and more recently by hydraulic drilling. The second-one aquifer system, the deep Continental Intercalary (CI), is one of the largest groundwater systems in the world, covering an area of approximately 600,000 km²23. This aquifer consists of sand, sandstone, and sandy clay continental formations deposited between the end of the Paleozoic and the Upper Cretaceous marine episodes. The useful reservoir is situated in the Albian layer, which is the primary target of the boreholes drilled to supply water to the M’Rara city.

Gravimetric evidence

The gravimetric measurements were collected using a terrestrial Scintrex CG3 gravimeter. The dataset is composed of 225 gravity measurements. They were collected, arranged in a nearly regular pattern over a 5 × 5 km² square grid (black circles, Fig. 1c). Where, the hydraulic drilling represents the center of this grid. These gravimetric stations measurements were illustrated by 11 East-west profiles, with a 5 km long and separated by 500 m. Each profile contains 20 gravimetric stations, spaced by 250 m between them, resulting in a measurement density of approximately 15 gravimetric stations per km². To ensure measurement quality, we re-measured 25 gravimetric stations. The gravimetric readings were linked to absolute gravity through a reference point located within the study area (blue triangle, Fig. 1c). For gravimetric corrections, the coordinates and altitude of each gravimetric station were determined using a bi-frequency differential GPS, Ashtech-Z12.

The prospected area altitudes vary from + 98.70 to + 126.92 m. The Eastern part of the altitudes map is characterized by a NW-SE topographic depression (Fig. 3a). Otherwise, the Western part of the map is represented by a decrease in altitudes from West to East. The extreme NE of this map is illustrated by an increase in elevation values from West to East. In addition, we notice a topographic relief in the southern part, with a peak of about of + 117 m. Geomorphologically, the M’Rara town is located within watershed with alternating limestone and gypsum facies3.

Fig. 3
figure 3

(a) The altitudes map and (b) the Bouguer anomaly (BA) map of the M’Rara area. The data were uniformly reduced using a Bouguer correction density of 2400 kg/m3. The displayed projection system is geographic (East longitude and North latitude) and Cartesian coordinates (WGS84, UTM zone 31 N in meters).

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Bouguer anomaly

The relative difference of the corrected device readings, converted into absolute gravity values, allowed the calculation of measured gravity. This calculation was done after adjusting for tidal effects and instrumental drift. The lunar-solar correction was computed directly from the tidal potential using the formula proposed by Longman24 and further developed by Gemael25 and Amarante and Trabanco26. For the gravimeter drift, we assumed it to be linear and distributed it proportionally across all readings based on the observation time27,28. The primary document for interpreting gravimetric data is the complete Bouguer gravity anomaly map. It represents the difference between the measured gravity and a model value at the same point. This model value is based on the normal gravity of a reference ellipsoid and is corrected for the effects of elevation above the reference ellipsoid and the mass of rock between the point and the ellipsoid15. So, the complete Bouguer anomaly values are given following relationship (1):

$$g_{b} = {\text{ }}g_{{mes}} {-}g{\text{ }}(f){\text{ }} + {\text{ }}\left( {0.3086{\text{ }}h_{s} } \right){-}\left( {0.0419{\text{ }}d.h_{s} } \right)\, + \,g_{T}$$
(1)

gb = gmes – g (φ) + (0.3086 hs) – (0.0419 d.hs) + gT (1).

Where, gmes is the station measured gravity, g (φ) represents the theoretical gravity calculated within the IUGG1967 system, hs is the station elevation, d represents the density correction and gT is the topographic correction. The data was uniformly reduced with a density of 2400 kg/m3 for the Bouguer correction.

The Bouguer anomaly map is based on a regular grid of interpolated values using the minimum curvature method, with equidistant contour lines at 0.05 mGal intervals (Fig. 3b). The Bouguer anomaly values vary between − 55.590 and − 54.400 mGal. The BA map reveals three major anomalies: two high-value anomalies (A1 and A2, Fig. 3b) and one low-value anomaly (A3, Fig. 3b). The first high anomaly (A1) is located at the North and is roughly circular, with Bouguer anomaly values around − 54.570 mGal. The second high anomaly (A2) is situated to the south and consists of a series of high anomalies aligned North-south, with a Bouguer anomaly value of approximately − 54.400 mGal. The high anomalies (A1) and (A2) correspond to the Pontian and they seem to be connected by a North-south positive axis and correspond to the Pontian. The third major anomaly (A3), characterized by low values, is found in the Northeast, with Bouguer anomaly values around − 55.514 mGal. This gravimetric anomaly is associate to Quaternary continental deposits. In addition to these long-wavelength variations, several short-wavelength circular anomalies are also observed.

Separation of anomalies

The Bouguer anomaly map shown in Fig. 3b incorporates effects from superficial, deep, and intermediate sources. To isolate and analyze only the local (residual) anomalies, it is necessary to separate these effects. We use the polynomial method of various orders to eliminate the regional effect12,29. This technique approximates the measured field using a polynomial in x and y, with the order chosen based on the preferred pattern representing the regional effect. Polynomials of orders 1, 2, and 3 have been removed from the measurements, as described in Eq. (2).

$$\:P(x,y)={\sum\:}_{i=0}^{n}{a}_{i}{U}_{i}(x,y)$$
(2)

In this context, \(\:{U}_{i}(x,y)\) refers to the basic function which is the product of two orthogonal polynomials and represents the real coefficients of the polynomial. Selecting the appropriate residual polynomial is crucial for interpretation, making it important to choose wisely which polynomial to remove. Since the objective is to highlight superficial structures, this study focuses on presenting the residuals of orders 2 and 3 (Fig. 4a and b). The residual of order 2 map is obtained by retrieving polynomial of order 2 following Eq. (3):

Fig. 4
figure 4

(a) The residual map of order 2 obtained by subtracting a polynomial of order 2. (b) The residual map of order 3 obtained by subtracting a polynomial of order 3. (c) The horizontal gradient (HG) map of the Bouguer anomaly. (d) The vertical gradient (VG) map of the Bouguer anomaly. The displayed projection system is geographic (East longitude and North latitude) and Cartesian coordinates (WGS84, UTM zone 31 N in meters).

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$$\:P(x,y)={c}_{1}+{c}_{2}x+{c}_{3}y+{c}_{4}{x}^{2}+{c}_{5}xy+{c}_{6}{y}^{2}$$
(3)

Where, C1 = -54.8716294, C2 = 0.0002110708, C3= -0.00003185, C4 = -0.000000029, C5 = -0.000000032 et C6 = 0.0000000036. This map shows more details than the Bouguer anomaly map. These values are ranging from − 0.404 to + 0.395 mGal and presents two positive sets (A1 and A2) separated by a NE-SW negative set (Fig. 4a). The two positives set correspond to Pontian and the negative-one represents Plio-Quaternary agglomerates. The collapse appeared near the hydraulic drilling is located between transition positive-negative anomalies. Whereas the second collapse appeared North-west of the hydraulic is located at the positive set (A1). The observed fissures are positioned within negatives anomalies (Fig. 4a).

The residual of order 3 map is obtained by retrieving polynomial of order 3, following relationship (4):

$$\:p(x,y)={c}_{1}+{c}_{2}x+{c}_{3}y+{c}_{4}{x}^{2}+{c}_{5}xy+{c}_{6}{y}^{2}+{c}_{7}{x}^{3}+{c}_{8}{x}^{2}y+{c}_{9}x{y}^{2}+{c}_{10}{y}^{3}$$
(4)

Where, C1 = -54.8805237, C2 = 0.0005062063, C3= -0.000030836, C4 = -0.000000227, C5 = -0.000000011, C6 = 0.0000000114, C7 = 2.84246e-011, C8 = -9.4941e-012, C9 = 5.37606e-012 et C10 = -2.7897e-012. This map represents anomalies caused by more superficial sources than the residual of order 2. The anomalies values of residual of order 3 map are ranging from − 0.328 to + 0.468 mGal. Two distinct areas are evident. The eastern and northern regions exhibit high values with positive anomalies, while the western part is characterized by low values and negative anomalies (Fig. 4b). The residual map of order 3 shows collapses, land subsidence, and fissures associated with negative anomalies. These negative anomalies indicate the presence of low-density masses, including cavities, in the subsurface. In contrast, positive anomalies suggest the presence of heavy, dense masses. Since the focus of our study is on detecting potential cavities, we will concentrate specifically on the negative anomalies (Ano1 to Ano4, Fig. 4b). The residual anomalies at various orders offer a qualitative interpretation into the distribution of densities in the subsurface. In the subsequent analysis, we use these residual anomalies to estimate the depths of the sources responsible for the observed gravity anomalies (see Sect. 4).

Gravimetric lineaments

We applied specialized processing techniques using vertical and horizontal gradient filters, to the Bouguer anomaly data to better identify the sources of the anomalies. These filters highlight gravity lineaments that correspond to faults or boundaries between geological structures. The magnitude of the horizontal gradient (HG) can be calculated as (5):

$$\:HG=\:\sqrt{{\left(\frac{\partial\:BA}{\partial\:x}\right)}^{2}+{\left(\frac{\partial\:BA}{\partial\:y}\right)}^{2}}$$
(5)

Whereas the vertical gradient (VG) can be calculated using the relation below (6):

$$\:VG=\:\frac{\partial\:BA}{\partial\:z}=\:{f}^{-1}\left\{\left|k\right|\:f\left(BA\right)\right\}$$
(6)

Where BA is the Bouguer anomaly, f and f− 1 are the Fourier and inverse Fourier transforms, respectively and |k| is the radial wave number (see13).

The horizontal gradient filter is particularly effective in detecting horizontal boundaries of gravity sources13,30, revealing density variations in the horizontal plane (Fig. 4c). The vertical gradient filter (Fig. 4d) is useful for identifying local and shallow features31,32. Both the horizontal and vertical gradient maps show a series of NW-SE lineaments across almost the entire study area. This alignment corresponds to the path of Oued Retem and the flow direction of the Mio-Pliocene shallow water table. Tectonic deformation from the Pontian period, related to the tectonic events during the creation of the Atlas domain in the Cenozoic, is evident. This deformation is primarily visible on the outcrop scale, with joints that are nearly perpendicular to the stratification, some of which are filled with amorphous calcite.

Three-dimensional inversion

For more in-depth detailed information about the locations of various anomalies, a 3D three-dimensional inversion technique was used. The scope of this study is to emphasize the density contrast of the target area, with a particular focus on the cavities. Theses cavities are characterized by their lower density and can be detected accordingly. This helped in understanding the different shapes found in the enhanced 2D horizontal maps, highlighting several high anomalies. The more detailed understanding of this density deficient area encouraged the use of the licensed software GraMagInv3D33 to enhance this 3D inversion (https://www.gravmaginv.ru/). This software is based on a new method that has been devised to tackle the inverse problem of gravimetric exploration applied to grid models34. This approach integrates deep cells into the density model determination process, using a gradient descent rate that varies with depth35. This link between the exponent and shape of inhomogeneities echoes methods such as Euler deconvolution17, although unlike this method, the suggested algorithm directly generates a density distribution model. By using a priori data, it becomes possible to design more sophisticated gradient descent rate distributions, which consider not only depth, but also horizontal coordinates. What’s more, the efficiency of this method remains constant, irrespective of the size of the area studied and the dimensions of the space in which the density models are developed. With the aim of achieving the accomplishment of this 3D inversion using this software, we utilized a residual anomaly as described previously. The data for the residual anomaly was formatted in a grid. The 3D inverted model was then obtained after conducting several tests. The density contrast is represented by a set of contiguous cells of constant density in the 3-D model area. The inverse solution is obtained by finding the density distribution that minimizes a model objective function while reproducing the data.

The result revealed from this 3D model showcased the density contrast into the M’Rara region (Fig. 5). As mentioned above, we are seeking for the identification of cavities. So, we simply presented the low-density anomalies due to the desired necessity of the study. The highlighted 3D density model discloses the presence of multiple low-density bodies distributed across the study area. From the suggested 3D model, all the observed low-density bodies are located at depth < to 600 m.

Fig. 5
figure 5

(a) 3D Inversion results showing the low-density anomalies. (b) represents the observed anomaly and (c) the calculated-one.

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Conclusion

Surface geological observations show no evidence of large-scale collapses around the M’Rara hydraulic drilling site. Additionally, gravity data from the salt layer, located about 1000 m deep, does not reveal any anomalies beneath this drilling site. Although this suggests that the hydraulic drilling is not responsible for fissures or collapses, the study highlights a considerable risk in the area due to the presence of shallow cavities. These cavities likely form due to water circulation in the subsoil originating from the Retem valley. This issue is exacerbated by the continuous flow of water from the Albian aquifer, which is extensively used for crop irrigation through various boreholes. The observed collapses and subsidence on the surface tend to occur mainly at the edges of dense and consolidated formations, which act as barriers to underground water movement at shallow depths. As a result, water is redirected and affects less consolidated formations, leading to significant erosion and the transportation of materials elsewhere. This study demonstrates that the gravimetric method is a powerful tool for detecting cavities, with significant implications for urban planning and hazard mitigation. By pinpointing areas susceptible to subsidence or collapse, it enables planners to make informed decisions regarding land use, infrastructure development, and construction safety. Early detection facilitates the implementation of preventive measures, such as ground stabilization or rerouting critical infrastructure, thereby minimizing risks to human life and property. Furthermore, understanding the root causes of these hazards provides valuable insights for guiding policies and optimizing resource allocation for long-term risk management in vulnerable areas.