Multi-stage 3D Gravity Inversion Scheme for Maximum Optimization of the Subsurface Basement Model at Gebel El-Zeit Basin, Southwestern Gulf-of-Suez, Egypt

Relevance and purpose of the work . Due to its basement fault block pattern in the sedimentary basin, the Southwestern Gulf of Suez’s Gebel El-Zeit basin is one of Egypt’s most desirable hydrocarbon concessions. However, salt diapers in sedimentary layers have hindered seismic interpretations in this area, making it challenging to build a 3D central primary basinal structure. This study uses Bouguer gravity anomalies to input basement complex lateral density model assumptions to determine the optimal three-dimensional basement depth for the study area. Research methodology . Based on the concept of sequential 3D spectral layered-earth inversion approaches, through trials with the Oldenburg and other forward models, many forward optimization strategies and parameterization sequences with variable constraint parameter assumptions were used to regulate the inversion operations within a proposed three-stage gravity inversion scheme to identify the optimal depth-density solution with a minimal computational data misfit. This study statistically analyzes the basement’s relief and complicated lateral density distribution to determine the best parameters for a 3D depth-density model solution. Zero regional gravity offset and DC-shift, which forced the mean error to be zero, helped simulate the lateral density model’s best-possible constraining assumptions. Results and conclusions . Correlating depth data from many stratigraphical-control wells drilled in the inverted 3D basement model confirmed the basement relief optimality of the study area. Correlation analysis showed a good match between the predicted and measured depths, proving the resulting optimality of the basement complex’s lateral density distribution, minimizing the computational depth error to a minimal percentage.


Introduction
Gravitational anomalies inversely help in recovering sedimentary basins, tectonics, and petroleum-rich places.Given the source's depth, thickness, and shape, determining the basement's undulating surface morphology from gravity measurements is a nonlinear inverse problem.Different source assumptions may create discrepancies when determining sedimentary basin basement depth.The forward Fast Fourier Transform (FFT) method estimates undulating layer gravitational or magnetic influences [1,2].
The slab formula (g = 2πγΔρt) predicts sediment thickness at each gravity datum utilizing just the gravitational constant (g), density contrast (Δρ), and slab thickness (t).Iterative modeling shows nonlinearity [3].Later articles modified the technique by increasing iterations, converting to a densitydepth function instead of a constant density, and re-evaluating the fitting function.
The Bott's iterative procedure's step sizes was adjusted based on the model's ratio of observed to estimated gravity anomalies [4].Silva suggested testing the model if the L2 norm of the residual vector is lower than in the previous iteration to speed convergence [3].The density matched the gravity model (drill hole gravity data, gamma-gamma density, and saturated or unsaturated sample density measurements).Linear, quadratic, exponential, hyperbolic, and parabolic models reveal that density growth is most significant towards the surface [5][6][7][8].The environment affects sediment density.
Density data may not match the density contrast function from density measurements at a few basin locations, making depth-dependent density contrast challenging to establish [8].Gravity modeling in sedimentary basins may benefit from non-density contrast interpretation methods.
Backward computing on the model's iteration field yields the analytic solution for the gravity field of a two-dimensional polygonal body, a three-dimensional rectangular prism, or a complex undulating layer [3].Fourier-domain operations are faster than space-domain operations, as Bott's technique avoids matrix multiplications and inversions.Formulas for polyhedral bodies with a linear density contrast function, analytical formulas for prismatic bodies with a parabolic [9] or cubic polynomial [10] function, and algorithms for modeling the vertical variation of density contrast with depth all require an exponential or cubic polynomial fitting function [6,11,12].Jachens calculated the basement's growing density's gravitational impact and created measures to minimize it using Bott's approach [13].Phelps examined Nevada's Yucca Flat basin isostatic anomalies [8].Tikhonov's regularized inversion estimates basement geometry for interpreting gravity data [14].Inverting subsurface columns into prisms with known horizontal dimensions and densities predicts column thicknesses.The L2 norm of the discrete first-order derivative of the model's objective function helps regularize the solution.Martins used the L1 norm of the discrete derivative total variation function to avoid penalizing quick morphological changes during basement depth inversion [15].Sun employed nonlinear inversion to restore smoothness and blockness to the model [16].Two early inversions split the research area into smoothand blocky-density contrast zones.The last inversion reduces the Lp model norm.
Feng established a nonlinear inverse approach that minimizes an objective function by adjusting model smoothness in the target area using a composite regularizing function [17].Edge analysis or first-approximation models identify unique gravity anomalies.Nonlinear modeling estimates basement morphology and constant density contrast [18].Li and Portniaguine modeled sedimentary basins without basement estimators [19,20].Regularized inversion is problematic because objective function stabilizers impact Several basement depth measurements geologically confine ITRESC approaches, which approximate density depth or contrast function.ITRESC will be tested in Egypt's southwest Gulf of Suez El Zeit basin with results comparison.
A prior information and geological setting.The Gulf of Suez formed when the African and Arabian tectonic plates Root-mean-square deviation of the inversely estimated recovered depth-to-basement The initially hypothesized depth-to-basement's root-mean-square deviation coefficient of variation The inversely estimated recovered depth-to-basement's root-mean-square deviation coefficient of variation The initially hypothesized homogenous basement complex's density's root-mean-square deviation coefficient of variation The inversely estimated-recovered homogenous basement complex's density's root-mean-square deviation coefficient of variation The initially hypothesized basement complex's lateral density distribution's root-mean-square deviation coefficient of variation The inversely estimated recovered basement complex's lateral density distribution's root-meansquare deviation coefficient of variation    diverged in the late Oligocene and early Miocene [21,22].Low-angle listric normal faulting and dyke injection created eastward half grabens along the rift 's fault blocks [23].Th e subsidence moved the rift axis eastward into the asymmetric axial grabens in the middle to late Miocene.During the Pliocene through the Pleistocene/Holocene, the southern Gulf of Suez intra-rift structural block Esh El-Mallaha was faulted and raised [24,25].As shown in fi g. 1.1, a, Faults F1 and F2 follow the Gulf of Suez and run NW-SE in multiple wadis fi lled with Quaternary alluvium, juxtaposing Precambrian bedrocks [26,27].Deep tectonic faults give the Gemsa-El Zeit Bay Basin a profound structural complexity.Nubian Sandstone, El Mallaha Formation, Raha Formation, Th ebes Formation, Nukhul Formation, Lower/Middle Miocene Rudeis and Kareem layers, Sabkhas, and salt marshes comprise it [25,[28][29][30][31].Metamorphic, granitic, and Dokhan volcanic rocks dominate the study area's eastern and western fl anks, Gebels El Zeit and Esh El-Mallaha [32].
Gravimetry can enhance Earth model computations by investigating the potential field without the direct     (1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984) proposal to develop a gravity map of Egypt by establishing a national base net covering the whole country and augmenting all foreign companies' surveys.Th e Egyptian Academy of Scientifi c Research and Technology supervised it.Remeasurements ensured correctness.Raw data were exported in x, y, and z dimensions, gridding at 1000 m intervals.
Th e contour map of the research area was colored using Bouguer anomalies (Fig. 1.1, b).Remarkable doublet Western gravity highs suggest local transfer faults intersect Gebel Esh El-Mallaha.Gebel El Zeit and Esh El-Mallaha display complicated basement outcrops east and west of Gemsa-El Zeit Bay, with a vast sedimentary basin in the middle as shown in fi g. 1.1, a, b, c.
The Litho-stratigraphic geological column of southern Gulf of Suez including the study area of Gebel El Zeit is represented in fig.1.2 [33].
Inversion Scheme General Outline.Douglas Oldenburg and others in the three-stage inversion scheme quantifi ed the El-Zeit basin's geologic attributes.Th e Oasis Montaj program's GM-SYS extension sub-routine (Geosoft Inc., Toronto, ON, Canada) uses a popular spectral layered-earth inversion algorithm for data reduction, fi ltering, and optimization, resulting in the best inversion solution for basement relief delineation.It also determines the appropriate average density for the sedimen-tary-basement layers, their density diff erence, depths to the basement, and sedimentary section thickness under the study area.Its inversion results were compared to others to establish if Oldenburg's constraining parameters produced the bestsolved and most reliable model.For time and eff ort reduction, the proposed inversion scheme employs a basic forward model and six optimization strategies to obtain the optimal initial and inverse models, three from forward modeling and three from inverse modeling.Th e parameterization fl owchart for the proposed scheme's forward and inverse modeling operations is shown in fi g. 2.1 with a legend in fi g. 2.2, and all parameterization abbreviations utilized within our research are listed in tables 2.1 and 2.2.
Stages of the Scheme.In the fi rst stage, three optimization strategies have been proposed: one for forward depth modeling that uses the unconstrained initial forward constant mean depth surface within the 3D depth model guess trials; another for forward density modeling that uses the initial forward density constraint assumptions of the 3D homogenous two-layered density model guess trials; and a third for depth inverse modeling that incorporates both of those for recovering Oldenburg's model with the lowest possible error.Stages of the Scheme.In the first stage, three optimization strategies have been proposed: one for forward depth modeling that uses the unconstrained initial forward constant mean depth surface within the 3D depth model guess trials; another for forward density modeling that uses the initial forward density constraint assumptions of the 3D homogenous two-layered density model guess trials; and a third for depth inverse modeling that incorporates both of those for recovering Oldenburg's model with the lowest possible error.
In the second stage, three further optimization strategies are proposed: One is forward depth modeling, where the initial forward variable depth surface has been used within the 3D depth model guess trials with varying depth guessing errors, imposing error reduction constraint assumptions from trial to trial for parameterization sequences' constraining; another strategy for forward density modeling that applies constraints to the density contrast guess trials of the initial 3D constant mean density contrast interface is to separate several guess trials of a homogeneous two-layered density model; and a third for density inverse modeling that incorporates both of those second stage's aforementioned forward strategies for recovering the densities best possible solutions.
The third final stage used three additional optimization strategies: one for forward depth modeling, which uses an unconstrained version of the forward variable depth constraint assumptions derived from the trials of inverted 3D possible depth models with varying errors in depth calculations; another for forward density modeling, which uses the constrained version of second stage's inverted lateral density possible models; and third strategy for the inverse depth modeling, which makes use of these constraint versions sought to evaluate the best possible density and density contrast model solutions, leading to the best possible basement depth model solution with the minimal inaccuracies.We achieved this low error by repeatedly refining depth-density model solutions inside the density contrast constrained-unconstrained optimization scenario between the second and third stages of the proposed inversion approach.In the second stage, three further optimization strategies are proposed: One is forward depth modeling, where the initial forward variable depth surface has been used within the 3D depth model guess trials with varying depth guessing errors, imposing error reduction constraint assumptions from trial to trial for parameterization sequences' constraining; another strategy for forward density modeling that applies constraints to the density contrast guess trials of the initial 3D constant mean density contrast interface is to separate several guess trials of a homogeneous two-layered density model; and a third for density inverse modeling that incorporates both of those second stage's aforementioned forward strategies for recovering the densities best possible solutions.
Th e third fi nal stage used three additional optimization strategies: one for forward depth modeling, which uses an unconstrained version of the forward variable depth constraint assumptions derived from the trials of inverted 3D possible depth models with varying errors in depth calculations; another for forward density modeling, which uses the constrained version of second stage's inverted lateral density possible models; and third strategy for the inverse depth modeling, which makes use of these constraint versions sought to evaluate the best possible density and density contrast model solutions, leading to the best possible basement depth model solution with the minimal inaccuracies.We achieved this low error by repeatedly refi ning depth-density model solutions inside the density contrast constrained-unconstrained optimization scenario between the second and third stages of the proposed inversion approach.
Results and discussion A Comparison of the best-possible models in three stages.We identifi ed that for three best-possible forward models, we could obtain three best-possible inverse models, resulting in minimal error optimal solutions constrained by the three initial best-possible mean depth error guessing trials, as highlighted in fi g. 3, 4, 5.Each stage uses a diff erent strategy to generate forward models and locate their matching inverse solutions.Th e model's optimality in minimizing calculational error validated its reliability and effi cacy based on an inversion results analysis conducted on the entire study area and individual locations.
Th ese forward models were started with the optimal forward initial parameterization guessing sequences, which included these parameters for the fi rst stage: Z₀ -3470 m, ρb₀ 2.77 g/cc, ρs₀ 2.34 g/cc, Δρ(ρb-ρs)₀ 0.43 g/cc, Δd₀ 37.65 mGal, Dc shift 37.652 mGal, fi lter LHC limit 14000 m, fi lter UHC limit 7500 m, convergence limit 0.01 mGal, and regional off set Quantitative interpretation.Fig. 6, 7, 8 show the best forward initial guesses and inverse estimates for the proposed inversion scheme's first, second, and third stages.Using a quantitative interpretation of the inverse outcomes, we were able to conclude the following about the optimality of the key and constraint model parameters that make up the inverse optimal parame-  0 mGal.Th ese inputs started the forward modeling guesswork process with 43.6% inaccuracy.For the second stage, these parameters were included: Z₀ -3536 m, ρb₀ 2.67 g/cc, ρs₀ 2.21 g/cc, Δρ(ρb-ρs)₀ 0.46 g/cc, Δd₀ 42.661 mGal, Dc shift 42.661 mGal, fi lter LHC limit 10000 m, fi lter UHC limit 9600 m, convergence limit 0.0054 mGal, and regional off set 0 mGal, with 1.78% error in forward modeling guessing.Finally, for the third stage, these parameters were included: Z₀ -3536 m, LDDb₀ 2.6706 g/cc, ρs₀ 2.21 g/cc, Δρ(LDDb-ρs)₀ 0.4606 g/cc, Δd₀ 42.670 mGal, Dc shift 42.670 mGal, fi lter LHC limit 20000 m, fi lter UHC limit 15000 m, convergence limit 0.0001 mGal, and regional off set 0 mGal, with 1.78% error in forward modeling guessing.
We subsequently linked the three-stage best-possible inverse parameterization estimates and their errors to assess our scheme's overall optimality in minimizing computational error within this gradual improvement (fi rst, 6.4; then, 1.78; fi nally, 1.63%) from the fi rst to the third stage.Th is error sequence resulted from iteratively optimizing in the presence of zero regional off sets used as a data-misfi t constraint within the three stages, the mean depth key parameter (fi rst, -3513; then, -3536; fi nally, -3534.6 m), the mean density contrast key parameter (0.43; 0.4606; 0.4606 g/cc), the fi lter LHC limit constraint parameters (14000; 10000; 20000 m), the fi lter UHC limit constraint parameters (7500; 9600; 15000 m), the convergence limit constraint parameter (0.01; 0.0054; 0.0001 mGal), and the DC shift constraint parameter (37.652; 42.661; 42.670 mGal).
Quantitative interpretation.Fig. 6, 7, 8 show the best forward initial guesses and inverse estimates for the proposed inversion scheme's fi rst, second, and third stages.Using a quantitative interpretation of the inverse outcomes, we were able to conclude the following about the optimality of the key and constraint model parameters that make up the inverse optimal parameterization sequence in the inversion scheme's third-last stage: 1.As illustrated in maps A and A' in fi g. 8, the third stage's optimal inversion process's initial forward depth model
2. Th ird stage of our inversion scheme's optimal inversion process started with optimal initial forward density guessing parameters of (Mean LDDb₀ 2.6706, Max.LDDb₀ 2.7558, Min.LDDb₀ 2.5935, and SD LDDb₀ 0.0294 g/cc) as a 1.74% error constraint assumption, resulting in the best possible

63% error in the estimation of the basement depth (maps A and A`), the complex basement density (maps B and B`), the basement-sedimentary density contrast interface (maps C and C`), and the data misfi t residual Bouguer anomalies (maps D and D`). For ease of comparison, each parameter's forward-guessed and inversely estimated maps share the same legend Рисунок 8. Последний третий этап нашей схемы инверсии оптимально инициировал упреждающие предположения и их суммарные оптимальные оценки для четырех параметров с ошибкой 1,63% в оценке глубины фундамента (карты A и A`), комплексной плотности фундамента (карты B и B`), границы контраста плотности фундамента и осадочных пород (карты C и C`) и несоответствия данных остаточным аномалиям Буге (карты D и D`). Для простоты сравнения карты каждого параметра с прямой и обратной оценкой имеют одну и ту же легенду
13 lous misfits after recovering the optimal inverse-estimated model's solutions.Map D's linear color legend shows the minimal mean data misfit estimations of 0.0045 mGal, covering practically the whole study area between estimated and observed Bouguer anomalies with means of de = -24.9139and da = -24.9094.The mean Bouguer anomaly's misfit optimality is bounded by 14.2795 and -4.9724 mGal.Map D in Fig. 7 shows how the substructure of elongated basins in the sedimentary layer above the basement complex along two significant normal faults provided the first viable migration and oil accumulation zones.These extended basins produced low Bouguer anomalies on Map D. These basins formed when the graben system's two main normal faults squeezed sedimentary layers over a basement complex.Over the middle El-Zeit basin, fault compression forms subsidiary sedimentary basins.5.These best constraint parameters of Dc shift 42.6709 mGal, filter LHC limit 20 000 m, filter UHC limit 15 000 m, convergence limit 0.0001 mGal, and regional offset 0 mGal maximally constrained the third last stage's inverse-estimated parameteri-НАУКИ О ЗЕМЛЕ А. Г. М. Хассан и др./ Известия УГГУ.2023.Вып.4(72).С. 19 deviation difference between the last two iterations' data misfit is less than the fifth convergence limit parameter, which equals 0.0001 mGal.The fourth and fifth constraint parameters help estimate the optimal inverse model solution with minimal computational errors.Th ese estimates produced a density solution with a default 1.63% computed depth inaccuracy.Th e initial 2.6706 mGal mean density parameter on Map B' in fi g. 8 suggests that granitic basement rocks dominate the basement complex's lateral mean density distribution in the study area.Th e second and third LDDbe density parameters (minimum 2.5935 and maximum 2.7558 g/cc) describe acidic igneous rock densities in which the basement depth laterally confi nes and best matches prior information.Working in that density space helps recover the optimal inverse estimated depth model.Basement rocks outcrop at zero depth (Fig. 8), map B' .

3.
In addition, the basement-sedimentary interface in the study area has been interpreted as a density contrast constraining assumption within the optimal sixth inverse depth modeling trial of our inversion scheme's third stage, with the following parameters: Mean 0.4606, Max 0.5458, Min 0.3835, and SD 0.0294 g/cc.Th e optimal initialized forward modeling, incorporating initially limited forward density contrast parameters (Mean 0.4606, Max 0.5458, Min 0.3835, and SD 0.0294 g/cc), yielded these optimum inverse density contrast assumptions.As shown in Map C' of fi g. 8, the mean lateral density contrast (Mean ∆ρ(LDDb-ρs)e 0.4606 g/cc) was confi ned to optimize distribution on the sedimentary section-basement complex interface in the research area, with maximum and minimum Indirect usage of the first and second controls reflects a forward-initiated unconstrained model without strong depth constraints, inverting the lateral 3D optimal final depth solution with minimal error.This strategy works better with less prior information and considers applying the proposed inversion scheme to a new domain requiring more data for reliable predictions.bounds of 0.5458 and 0.3835 g/cc, respectively.Th ese optimized density contrast parameters and its best constraint assumption at the interfaced surface provided an optimal El-Zeit sedimentary-basement basinal depth model in the study area with a mean minimum error of 1.63% in delineations.
4. We investigated the data-misfi t parameters (Mean 0.0045, Max 14.2795, Min -4.9724, and SD 1.3111 mGal) to in-terpret the optimal model's Bouguer response.Fig. 8 illustrates the lateral distribution of linear and normal-colored Bouguer anomalous misfi ts aft er recovering the optimal inverse-estimated model's solutions.Map D's linear color legend shows the minimal mean data misfi t estimations of 0.0045 mGal, covering practically the whole study area between estimated and observed Bouguer anomalies with means of de = -24.9139Graph A8 shows the re-estimated optimal depth misfit sequences relative to the six constraint wells' actual mean basement depth, showing the percentage coefficients of variation for each well.For example, the sixth optimal depth misfit sequence in the first stage is re-estimated by W8 12.0, W13 13.2, W15 -0.07, W17 -5.0, W18 -7.9, and W19 -2.0%, while in the third stage, W8 1.7, W13 -3.0, W15 -1.1, W17 -0.9, W18 1.1, and W19 -0.5%.
Through extraction of 2D gravity models at seismic lines' locations 5. Our inversion scheme's 3D gravity inverse optimal depth-density model solution's fifth quality control test generated 2D gravity model cross sections at 2D seismic line locations along the El Zeit basin's underlying basement relief.Fig. 10.1, 10.2, and and da = -24.9094.Th e mean Bouguer anomaly's misfi t optimality is bounded by 14.2795 and -4.9724 mGal.Map D in Fig. 7 shows how the substructure of elongated basins in the sedimentary layer above the basement complex along two signifi cant normal faults provided the fi rst viable migration and oil accumulation zones.Th ese extended basins produced low Bouguer anomalies on Map D. Th ese basins formed when the graben system's two main normal faults squeezed sedimentary layers over a basement complex.Over the middle El-Zeit basin, fault compression forms subsidiary sedimentary basins.
5. Th ese best constraint parameters of Dc shift 42.6709 mGal, fi lter LHC limit 20 000 m, fi lter UHC limit 15 000 m, convergence limit 0.0001 mGal, and regional off set 0 mGal maximally constrained the third last stage's inverse-estimated parameterization sequence's optimality, resulting in the optimal model's minimal errored solutions.Th e fi rst constraint parameter (DC shift = 42.6709mGal) was utilized to predict the forward initial mean depth parameter (Mean DTB₀ = -3536 m), estimating the inverse mean depth parameter (Mean DTBe = -3534.6m).Th e second constraint parameter (fi lter LHC limit = 20 000 m) smoothed the optimal inverse-estimated mean density-depth model and its calculated mean Bouguer anomaly response.Th e third constraint parameter (fi lter UHC limit = 15 000 m) optimized the impact of the second constraint.Th e second and third parameters govern the model's solution and their data calculation smoothness and non-smoothness.Th e calculated and observed Bouguer anomalies are best fi t with a mean misfi t ∆de = 0.0045 mGal when the fourth regional off set constraint parameter is zero aft er recovering the optimal inverse model's solutions in the study area.Th e inversion run stops when the standard deviation diff erence between the last two iterations' data misfi t is less than the fi ft h convergence limit parameter, which equals 0.0001 mGal.Th e fourth and fi ft h constraint parameters help estimate the optimal inverse model solution with minimal computational errors.had nineteen wells, and a gravity inversion was used to get the optimal 3D basement estimated depth.Th e DC shift , convergence limit, regional off set, and fi lter lower and upper high cut limits were adjusted to manage the misfi ts of calculated data and model solutions from the constraints of actual measured values.Aft er inversion, basement constraint wells were used as a fi rst quality control test to ensure the inverse depth values stayed inside the analytic depth domain.As a second quality control, we checked whether the optimal inverted depth to the basement was more profound than the total depth of the thirteen unreachable basement constraint wells.

Evaluation of the inversion stages Th rough indirect analysis of drilled-well data
Indirect usage of the fi rst and second controls refl ects a forward-initiated unconstrained model without strong depth constraints, inverting the lateral 3D optimal fi nal depth solution with minimal error.Th is strategy works better with less prior information and considers applying the proposed inversion scheme to a new domain requiring more data for reliable predictions.3. We examined lateral basement density and basement-sedimentary density contrast in the fourth control test to assess our inversion scheme's inverse density estimations.Th is control test determined whether a lateral density model could optimize the basement-sedimentary density contrast and determine the basement depth with minimal depth estimate error.Graphs B1, B2, B3, B4, B5, and B6 in fi g. 9.1 show the results of this test.
4. Th is study compared the calculated and actual Bouguer anomalies at nineteen easily accessible control wells.A tertiary control test performed across the region may provide a mean data misfi t near zero by terminating the inversion process at regional null off sets.Th is scenario shows a minimal data misfi t consistent with the best solution of the depth-density model.Fig. 9.1, graphs C1, C2, C3, and C4, provide proof of this.Fig. 9.2, graphs (A2 and A4) demonstrate that the mean basement depth model's sixth optimal inverse trial produced the lowest model calculation error for the fi rst stage of our inversion scheme.First-stage optimality shows a correlation between the actual and estimated basement depths of the six constraint wells in the following order: W8 -333.6,W13 -87.8, W15 2.0, W17 138.8, W18 221.2, and W19 55.7 m, as a result of depth estimates in the following sequence: (W8 -2910.6,W13 -1216.68,W15 -3767, W17 -2023.1,W18 -2686.7,and W19 -3995.3m).In the third stage of our scheme, we adjusted the basement depth model by minimizing the misfi t with the best correlation to actual depths using an estimated depth sequence (W8 -2624, W13 -1044.2,W15 -3738.7,W17 -2135.4,W18 -2938.3, and W19 -4035.5 m) with a more signifi cant reduction of the depth misfi t sequence (W8 -46.9, W13 84.7, W15 30.2, W17 26.5, W18 -30.2, W19 15.4 m).Th e depth misfi t sequence shows that the optimal depth model in the third stage of our scheme is more accurate.
Th rough extraction of 2D gravity models at seismic lines' locations 5. Our inversion scheme's 3D gravity inverse optimal depth-density model solution's fi ft h quality control test gen-erated 2D gravity model cross sections at 2D seismic line locations along the El Zeit basin's underlying basement relief.Fig. 10.1, 10.2, and 10.3 show minimal Bouguer misfi ts for the 2D optimal solutions of the basement complex lateral density distribution, the basement-sedimentary density contrast interface, and the basement depth.
As shown in fi g. 10.1 map A, indicator lines A-A'; B-B'; C-C', and D-D' (width 14056, 14977, and 19066 m * length 25805 m) indicate the asymmetrical basin's width along the northwest-southeast axis, estimated for the southern, middle, and northern parts of the basin.Delineating the optimal basement relief, which depicts the basement-sedimentary density contrast interface, shows this optimal sedimentary basin depth model.Fig. 10.1B, 10.2, and 10.3 show two-dimensional gravity inversion results along the research area's six seismic lines.Our research area's optimal three-dimensional gravity model was the sixth inverse model trial in the inverse parameterization sequence for the third fi nal stage of our inversion scheme, from which the optimal two-dimensional gravity models were inversely modeled.Th e approximately minimal calculated inverse data misfi t error from this sixth optimal trial validates the 2D extracted model's optimal key parameter values.
Conclusions Th e present study employs the GM-SYS-3D inversion code to conduct a multi-dimensional three-stage gravity inversion within the Gebel Zeit area of the southwestern Gulf of Suez.Th ree strategies are utilized to parameterize the forward modeling process by providing initial approximations and optimizing inverse modeling estimates through multiple iterations.Th e depth-to-basement, lateral density distribution of the basement complex, and lateral density contrast at the basement-sedimentary interface were estimated using the 3D depth-density model.
A total of six stratigraphic wells, which were accessible with total depths to the basement, were utilized as control measures.Th e estimated depths to the basement for these basement control wells exhibited an overall 1.63% coeffi cient of variance in correspondence with their actual total depths to the basement.Th e discrepancies in depth ranged from -1.24% to 8% relative to the measured mean depth of the basement and from -1.24% to 3.8% relative to the total measured depth of each well's basement.
Th e quantitative analysis of the optimal inverse-recovered model in the third stage exhibited the best-possible correlation with geological data, with a minimal error of 1.63%.Th e inversion procedure was employed eff ectively to model the forward behavior of three depth-density scenarios inversely.Th is model successfully estimated the mean depth of the basement in the study area, which spanned from 0 to 6453 m beyond sea level.Th e resulting mean Bouguer anomaly misfi t was found to be 0.0045 mGal.Th e average density contrast at the interface between the basement and sedimentary layers is 0.4606 g/cc, exhibiting a lateral variation ranging from 0.5458 to 0.3835.Th e interface delineates the central basin of the research area.
Th e presence of salt diapers challenges basement delineation through seismic interpretation in two dimensions.Th e inverse problem of accurately recovering the optimal 3D depth-density model was handled through this model's solutions' evaluation at nine seismic lines, resulting in a well-char-acterized representation of the basement relief.The complete recovery of the residual Bouguer image depicts the effect of the high tectonics of the underlying basement relief on its overlaid thick sedimentary structure in the study area, yielding valuable deep geological insights into the advancement of petroleum resources.The results of this study revealed the presence of a graben system characterized by two prominent normal faults that intersect sedimentary strata, originating from a depth of 6500 meters within the Earth's crust and extending up to the surface.The Gebel Zeit and Esh-Mellaha ranges exhibit geological faults that result in the exposure of underlying basement rocks.The phenomenon of basement shallowing in this particular study area is of significant interest from both tectonic and hydrocarbon perspectives.
The 3D optimal inverse recovery suggests that the study area is characterized by three distinct basement blocks, which have been accurately estimated in terms of depth, density, and density contrast with the overlaid sedimentary blocks.The first block is a downthrown block located in the middle of the area and is covered by a substantial cover of sedimentary deposits.This block is responsible for forming a basin structure known as the El Zeit basin, which reaches a maximum depth of 6453 m.The other two blocks are located on the western and eastern flanks and are considered upthrown blocks.These blocks have zero depths and are associated with the roots of the Gebel Zeit and Esh-Mellaha ranges, respectively.Numerous fault traps can be generated along fault planes where minor half-grabens are formed due to the fault compression within sedimentary layers.This compression leads to the development of elongat-ed sub-basins above the basement complex.These sub-basins are adjacent to the basement complex, as the basement blocks uplift through the sedimentary layers and are separated from it by small anticlinal structures.These anticlinal structures increase the possibility for fault entrapment in the presence of an overlaid impermeable sedimentary layer above them.The tectonic characteristics of these sedimentary sub-basin structures are attributed to the vertical displacement of the underlying basement blocks, resulting in significant upward pressure and converging towards the central basinal region.The elementary basinal structure in El Zeit experienced tectonic activity, which played a significant role in shaping the Nubia sandstone and creating a deep reservoir formation with a substantial volume of hydrocarbons in the study area.The deep sedimentary column in the middle basinal area has the potential to serve as a source for migrating hydrocarbons through the fault planes where low pressures exist.This migration is best possibly entrapment along the hanging wall sedimentary block above the eastern and western fault planes, where small anticlinal structures can form between the compressed sedimentary structures and the fault planes.The basement foot wall block on the other sides of the fault planes laterally seals these anticlinal structures.The impermeable sedimentary layers' formations may also vertically seal them.

Figure 9 . 2 .
Figure 9.2.An extension of the preceding figure 9.1, together illustrating the three-stage inversion scheme's six basement total depth constraint wells' focused data analysis (shown in figures 9.1 and 9.2) illustrates the indirect constraining process of the three bestpossible models' solutions for the entire research area.Checks for quality control tests ensure that the best outcomes correspond as closely as possible to real constraints and desired solutions.The red, blue, and yellow sequences indicate the first, second, and third

Table 1
USA).Th e Bureau Gravimetric International (BGI) in Paris authorized the General Petroleum Corporation of Egypt's (GPC) ten-year A. G. M. Hassan / News of the Ural State Mining University, 2023, issue 4(72), pp.