Magnetic data interpretation to determine the depth of basement rocks and structural elements of Mandisha village , El-Bahariya Oasis , Western Desert , Egypt

Relevance. The study area is located at Mandisha village, El-Bahariya Oasis, Western Desert, Egypt. It is suffering from lack of surface water. So it’s important to search for another source of water (as groundwater) that important for everything for live. Based on the literature studies; the main aquifer in the study area is located in the Nubian sandstone aquifer, which located directly on the upper surface of the basement rocks. So the depth of the lower surface of the Nubian sandstone aquifer is equal to the depth of the upper surface of the basement rocks in the study area. Objectives of the study. This study is used the analysis and interpretation of magnetic data to determine the depth of the basement rocks and the structural elements that affected on the basement rocks at Mandisha area in El-Bahariya Oasis, Western Desert, Egypt. Research methodology. The Magnetic methods were applied to achieve these goals. One hundred and seventy four magnetic stations were acquired by Overhauser magnetometer instrument (GSM-19 “V7.0”). The magnetic data were processed by using Geosoft Oasis Montaj program. 2D Magnetic Profiles and 3D Magnetic Modeling were established to construct basement relief map in the study area. First Vertical Derivative Technique, Source Edge Detection Method and 3D Euler Deconvolution method were established to determine the locations and directions of faults that affected on the Basement Rocks in the study area. Work results. The most important results of this study: 1. The depth of the basement rocks in the study area ranges from 1200 m to 2000 m. 2. The northeastern, northwestern and western parts of the study area are characterized by shallow depth of the basement rocks, while the southern and eastern parts of the study area are characterized by deep depth of the basement rocks. 3. Deep faults (more than 2000 m) were located at northern part of the study area. 4. The main direction faults in the study area are NE–SW and E-W direction.


I ntroduction
Th e study area is located at Mandisha village in El-Bahariya Oasis, Western Desert, Egypt. It is located between latitudes 28° 16`22``N-28°19`14``N and longitudes 28°55`40``E-28°59`50``E with an area of 36.13 km 2 (Fig. 1). Th e study area is suff ering from lack of surface water. So it's important to search for another source of water that important for living and everything for live as groundwater. Based on the literature studies; the main aquifer in the study area is located in the Nubian sandstone aquifer (Cenomanian age), which located directly on the upper surface of the basement rocks [1]. So the depth of the lower surface of the Nubian sandstone aquifer is equal to the depth of the upper surface of the basement rocks in the study area.
Th e analysis and interpretation of magnetic data were used for mapping the relief of the basement rocks in the study area. So, the main purpose of this study is to analyze and interpret the magnetic data for determining the depth of basement rocks in the study area and the structural elements (Faults and/or cracks) that aff ected the study area.
Our pattern recognitions criteria are based on the interpretation of magnetic data that applied on the total intensity magnetic map reduced to the pole (RTP Map). Th e interpretation of magnetic data includes fi ve techniques which applied by Geosoft program: these techniques including First Vertical Derivative Technique, Source Edge Detection Method, 3D Euler Deconvolution, 2D Magnetic Profi ling and 3D Magnetic Modeling. Aft er that; the Magnetic interpretations have been compared with each other to determine the location of faults with high resolution.
Geology of the study area Th e geology of the study area was described from the geological map of El-Bahariya Oasis and the stratigraphic succession of well No. 1 (Box-1) that located at El-Bahariya Oasis. Th ese geological study includes surface and subsurface geology of the study area. a) Th e surface Geology of the study area has been described from the geological map of Egypt, Sheet No. (NH 35 SE BA-HARIYA) with a scale of 1 : 500 000 [2]. It was built by the Egyptian General petroleum Corporation in 1986 (Fig. 2). Surface Geology of the study area refers to the upper Cretaceous "Cenomanian age" and Quaternary age: 1. Upper Cretaceous deposits were represented by Bahariya Formation (Early Cenomanian age). It has deposited at widespread of the study area. Bahariya Formation consists of fi ne to coarse Ferruginous Sandstone intercalated with Shale. 2. Quaternary deposits were represented by 8 Fig. 3).
Methodology In this study, the magnetic data were analyzed and interpreted for determining the depth of the basement rocks and the structural elements that affected on the basement rocks of the study area.
1. Magnetic data acquisition One hundred and seventy four magnetic stations were measured to cover the study area (Fig. 4, a). Magnetic data were carried out using one Overhauser magnetometers for both field survey and base station recordings. The model of Overhauser magnetometer, which used for magnetic acquisition, is ((GSM-19) V7.0), made in Canada (since 1980), with sensitivity 0.022 nT (Fig. 4, b and Fig. 4, c) [5]. Magnetic stations were measured in the study area every 300-500 m. The base station was recorded every 3-5 hours during field measurements. It was located at the Eastern part of the study area with longitude 28°59'30.99"E and latitude 28°17'57.4"N with an absolute value of 42592.5g.    Magnetic readings were stored in the memory of Overhauser magnetometer, after that; all data were loaded from Overhauser magnetometer to the computer ( Table 2) for preparing magnetic data for necessary corrections and interpretations.
2. Magnetic data processing Magnetic data were corrected for daily variations correction before starting the interpretation. Daily variations in the Earth's magnetic field sometimes had an amplitude more than 10 gammas (which caused by sunspots). Therefore, the base station was used for magnetic correction. The daily variations of the geomagnetic field were subtracted from the Magnetic field data. The corrected magnetic values were contoured by Geosoft program with contour interval 2 nT [6] and represented by the total intensity magnetic map (Fig. 5, a).
Total Intensity Magnetic Map (TIM Map). TIM Map is a reflection of lateral changes in the magnetic properties of the Basement Rocks in the study area ( Fig. 5, a). Thus, the magnetic expression of various structural features depends on the existence and magnitude of their magnetic contrasts. The qualitative interpretation of the Total Intensity Magnetic Map begins with a visual inspection of the forms and directions of the main magnetic anomalies. TIM Map has magnetic anomaly values between 42 500 nT and 42 620 nT. The high magnetic anomalies indicate that the depth of basement rocks is shallow depth, so the thickness of sedimentary cover is thin. The high magnetic anomalies are represented at Northeastern part of the study area. On the other side, the low magnetic anomalies indicate on a deep basement rocks (thick sedimentary cover). The low magnetic anomalies are located at the Southeastern part of the study area. Generally, the magnetic anomaly increases from Southeastern part to Northeastern part of the study area, which indicate that the depth of basement rocks increase from Northeastern part to Southeastern part of the study area.  The Total Intensity Magnetic Map Reduced to the Pole (RTP Map). The total intensity magnetic data were reduced to the magnetic pole (Fig. 5, b) to overcome the distortion in anomaly appearance. This appearance depends on the magnetic latitude of the survey area and depends on the dip angle of the magnetization vector in the body using magnetic parameters such as inclination angle (41.2177°), declination angle (3.9282°), magnetic field strength (42488.2 nT) and the height of device's sensor from earth surface (1 m). This mathematical procedure was first described by [7][8][9][10][11].
A general outlook to the magnetic map reduced to the magnetic pole (Fig. 5, b) in comparison with the total magnetic intensity map (Fig. 5, a) reflects the northward shift in the positions of the inherited magnetic anomalies due to elimination of inclination of magnetic field at this area. The RTP map exhibits different magnetic anomalies while ranging from 42 512 nT to 42 607 nT. The northeastern and northwestern parts of the study area reveal high magnetic anomalies where the eastern, southern, and southeastern parts exhibit low magnetic anomalies.

Magnetic data interpretations
Interpretation of magnetic data includes five Techniques which applied by Geosoft program to determine the structural elements (Faults) and the depths of the upper surface of the basement rocks that caused the magnetic anomalies in the study area. FVD Technique acts as a filter. FVD Technique emphasizes the expression of local features of magnetic anomalies and eliminates the effect of regional anomalies. The first vertical derivative map was applied on RTP Map. In FVD Map (Fig. 6), zero contour lines show the contact lines between highly polarized sources (which indicate that the depth of basement rocks are shallow) and less polarized sources (which indicate that the depth of basement rocks are deep) at the same level of measurement. These Zero contour lines indicate on the faults that affected on the basement rocks in the study area. The main directions of these faults are N-S, NE-SW and NW-SE directions. Negative magnetic values show deep basement rocks, which located at the Eastern and Northwestern parts of the study area. Where, the positive magnetic values show shallow basement rocks, which located at northeastern and western parts of the study area. b) Source Edge Detection Method (SED Method). The source edge detection (SED) system is used to locate the approximate edges and down-gradient directions of source bodies from magnetic or gravity gridded data sets [18]. Blakely   used SED Method to calculate reduction to the pole grid and total horizontal derivative grid from the total magnetic field grid [18]. The Geosoft program was used to calculate RTP Grid and its horizontal gradient. Two maps were created by applying SED Method: First map is horizontal gradient Map of RTP Grid, which containing on oval-shaped magnetic anomalies and their axes indicate on the direction of faults that appeared in the study area (Fig. 7, a). Second Map is geological contacts Map (faults) that detected on RTP Map. This map shows the locations and directions of faults in the study area. The main directions of faults are NE-SW and E-W directions (Fig. 7, b). c) 3D Euler Deconvolution. Recently, 3D Euler Deconvolution method has been widely used in the automatic interpretation of Magnetic and Gravity data. It has emerged as a powerful tool for direct determination of depth of the gravity and magnetic bodies. Also, it uses for determination the dykes and contacts with remarkable accuracy [19][20][21][22][23][24].
Usually the locations and depths of any sources (x 0 , y 0 , z 0 ) can been determined by using the following equation (2): where ƒ is the observed field at location (x, y, z) and B is the base level of the field [regional value at the point (x, y, z)] and SI is the structural index or degree of homogeneity [19]. The equation (2) is solved for the source position by least-squares inversion of a moving window of data points. To obtain an accurate estimation of the source location, the field data used must adequately sample the anomalies present in the data.
In the present study, the 3D Euler Deconvolution technique was applied to determine the locations and depths of the faults in the study area. The obtained solutions of the interpretations of 3D Euler Deconvolution of magnetic data are shown in Fig. 8. Euler solutions were applied on RTP Grid by structural indexes 0, 1, 2, and 3 to select the best solution. Structural index zero "SI = 0" indicates on Contact/Step (Fig. 8, a), structural index one "SI = 1" indicates on Sill/Dyke (Fig. 8, b), structural index two "SI = 2" indicates on Cylinder/Pipe (Fig. 8, c) and structural index three "SI = 3" indicates on Sphere/Barrel/Ordnance (Fig. 8, d) [6]. The structural index SI = 0 gives better solutions than the structural indices 1, 2 and 3, because the data is concentrated in the study area (Fig. 8, a). d) 2D Magnetic Profiles. 2D magnetic profiles were applied by GM-SYS program on RTP Map [25]. GM-SYS program provide an easy interface for creating and managing models to fit observed magnetic data.
GM-SYS program was used to estimate the depth of the upper surface of the basement rocks using the following parameters:  and Remanence Declination = 3.9282° (Fig. 9). Seven magnetic profiles were applied on RTP Map (Fig. 4, a). The first profile (P1) passes through well (BOX_2) with direction from South to North and other profiles (P2, P3, P4, P5, P6 and P7) were oriented from West to East. Profile "P1-P1 \ " is perpendicular on other profiles; it has a direction from South to North with a length of 6130 M. This profile passes through the borehole (Box_2), which is located at 28° 19 \ 27.5 \\ N and 28° 58 \ 00 \\ E with depth of Basement rocks 1822 M. The depth of Basement Rocks along profile P1-P1 \ varies from 1822 m to 1963 m (Fig. 9).
The other profiles (P2, P3, P4, P5, P6 and P7) were oriented from West to East. The second Profile "P2-P2 \ " has a length 7187 M. Profile P2 passes through Profile P1 with depth of Basement 1929 M. The depth of Basement Rocks along Profile P2 ranges from 1820 m to 1998 m (Fig. 10, a). The third Profile "P3-P3 \ " has a length 7161 M. Profile P3 passes through profile P1 with depth of Basement 1960 M. The depth of Basement Rocks along Profile P3 ranges from 1630 m to 2150 m (Fig. 10, b). The fourth Profile "P4-P4 \ " has a length 7174 M. Profile P4 passes through Profile P1 with depth of Basement 1847 M. The depth of Basement Rocks along Profile P4 ranges from 1580 m to 1996 m (Fig. 10, c). The fifth Profile "P5-P5 \ " has a length 7161 M. Profile P5 passes through profile P1 with depth of Basement 1957 M. The depth of Basement Rocks along Profile P5 ranges from 1714 m to 2065 m (Fig. 10, d). The sixth Profile "P6-P6 \ " has a length 7161 M. Profile P6 passes through profile P1 with depth of Basement 1701 M. The depth of Basement Rocks along Profile P6 ranges from 1588 m to 1742 m (Fig. 10, e). The seventh Profile "P7-P7 \ " has a length 7174 M. Profile P7 passes through profile P1 with depth of Basement 1500 M. The depth of Basement Rocks along Profile P7 ranges from 1274 m to 1564 m (Fig. 10, f).
The results of 2D magnetic profiles were used to construct a depth map of the basement rocks in the study area by Geosoft program with contour interval 20 m (Fig. 11). The depth of the basement rocks in the study area is ranging from 1300 m to 2100 m. The northeastern, northwestern and western parts of the study area are characterized by shallow basement rocks, while the southern and eastern parts of the study area are characterized by deep basement rocks. Thus, the depth of basement rocks is increasing from northeastern, northwestern and western parts toward eastern part of the study area (Fig. 11). е) 3D Magnetic Modeling. 3D Magnetic modeling was carried out on RTP Grid by GMSYS-3D software. GMSYS-3D is a package for 3D modeling of gravitational and magnetic grids. The model is determined by number of surface layers, with its density, magnetic susceptibility and Remanence magnetization that distributed and defined for each layer [26].
The GMSYS-3D program is used to perform 3D magnetic modeling in order to obtain the relief of the basement rocks and relief of the earth's surface relatively to sea level using the following parameters: 1. The used parameters for Earth's surface layer are: average Density 2.5 gram/cm 3 , Magnetic Susceptibility = 0 CGS, Remanence Magnetization = 0 emu/cm 3 , Remanence Inclination = 0° and Remanence Declination = 0° (Fig. 12, a). 2. The used parameters for Basement Layer are: average density 2.8 gram/cm 3 , Magnetic Susceptibility = 0.00075 CGS, Remanence Magnetization = 0.00398 emu/cm 3 , Remanence Inclination = 41.2177° and Remanence Declination = 3.9282° (Fig. 12, c). After applying 15 iterations by GMSYS-3D software, the results of 3D Magnetic Modeling shows that the thickness of the sedimentary layer in the study area is ranging from -1200 m to -2000 m. The thin thickness of the sedimentary layer is located at the northeastern, northern and western parts of the study area (the depth of the basement rocks is more than -1450 m). While the thick thickness of the sedimentary layer is located at the eastern part of the study area (the depth of the basement rocks is less than -1700 m) (Fig. 12, b).

Discussion
In this study, the depth of the basement rocks determined by 2D magnetic profiles and 3D magnetic modeling. The matching between the Basement Depth Map (Fig. 11) and 3D magnetic modeling (Fig. 12, b)   3D magnetic modeling shows that; the deep depth of the basement rocks are located at the eastern part, and many places in the southern part of the study area. But the shallow depth of the basement rocks are located at northeastern, northern and western parts of the study area.
The basement rocks in the study area were affected by many faults that determined by First Vertical Derivative technique (FVD), Source Edge Detection method (SED) and 3D Euler Deconvolution method. The integration between results of SED method and RTP Map shows that; the down-through of faults were directed to low values of magnetic anomalies of RTP map (Fig.  13, a). The Results of FVD method and 3D Euler Deconvolution with structural index (SI) = 0 determine the locations of faults in the study area (Fig. 13, b). Zero contour lines at FVD Map are show the contact lines between shallow and deep basement rocks at the same level of measurement. These Zero contour lines indicate on the locations of faults that affected on the basement rocks in the study area. 3D Euler Deconvolution with structural index (SI) = 0 also used to determine the locations and depths of these faults in the study area. The results show high matching between two methods. The main direction of these faults in the study area are NE-SW and E-W directions (Fig. 13, b).
The comparing between 3D Euler's Deconvolution with a structural index = 0 and Basement Depth Map is showing that; many faults are deep faults (their depth more than 2000 m) and reaching to the basement rocks. These deep faults were determined at northern part of the study area (Fig. 13, c).

Results
As mentioned in this research, the most important results of this study: 1. The depth of the basement rocks in the study area ranges from 1200 m to 2000 m. 2. The northeastern, northwestern and western parts of the study area are characterized by shallow depth of the basement rocks, while the southern and eastern parts of the study area are characterized by deep depth of the basement rocks. 3. Many faults are deep (their depth more than 2000 m) and dissect the basement rocks, these faults located at northern part of the study area. 4. The main direction faults in the study area are NE-SW and E-W direction. a c b Figure 13. Integrations between the interpretation methods. a -integration between SED technique and RTP Map; b -integration between FVD method and 3D Euler Deconvolution with a structural index = 0; c -integration between 3D Euler Deconvolution with a structural index = 0 and Basement Depth Map. Рисунок 13. Интеграции между методами интерпретации. а -интеграция между SED методом и магнитной картой RTP; б -интеграция между методом FVD и 3D методом деконволюции Эйлера со структурным индексом = 0; в -интеграция между 3D методом деконволюции Эйлера со структурным индексом = 0 и картой глубины залегания фундамента.