Salt geometry influence on present-day stress orientations in the Nile Delta: Insights from numerical modeling

Journal of African Earth Sciences 114 (2016) 96e109

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Salt geometry influence on present-day stress orientations in the Nile Delta: Insights from numerical modeling Andreas Eckert*, Weicheng Zhang Department of Geosciences and Geological and Petroleum Engineering, Missouri University of Science and Technology, Rolla, MO, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 August 2015 Received in revised form 12 November 2015 Accepted 13 November 2015 Available online 1 December 2015

The offshore Nile Delta displays sharply contrasting orientations of the maximum horizontal stress, SH, in regions above Messinian evaporites (suprasalt) and regions below Messinian evaporites (subsalt). Published stress orientation data predominantly show margin-normal suprasalt SH orientations but a margin-parallel subsalt SH orientation. While these data sets provide the first major evidence that evaporite sequences can act as mechanical detachment horizons, the cause for the stress orientation contrast remains unclear. In this study, 3D finite element analysis is used to investigate the causes for stress re-orientation based on two different hypotheses. The modeling study evaluates the influence of different likely salt geometries and whether stress reorientations are the result of basal drag forces induced by gravitational gliding or whether they represent localized variations due to mechanical property contrasts. The modeling results show that when salt is present as a continuous layer, gravitational gliding occurs and basal drag forces induced in the suprasalt layers result in the margin-normal principal stress becoming the maximum horizontal stress. With the margin-normal stress increase being confined to the suprasalt layers, the salt acts as a mechanical detachment horizon, resulting in different SH orientations in the suprasalt compared to the subsalt layers. When salt is present as isolated bodies localized stress variations occur due to the mechanical property contrasts imposed by the salt, also resulting in different SH orientations in the suprasalt compared to the subsalt layers. The modeling results provide additional quantitative evidence to confirm the role of evaporite sequences as mechanical detachment horizons. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Gravity gliding Salt Nile Delta Stress orientations Finite element analysis

1. Introduction The offshore Nile Delta is the largest clastic wedge in the Mediterranean Sea region and represents a typical tertiary delta. It was created by an influx of clastic sediments from the Nile River since the late Miocene (Badawy, 2005). Due to the tectonic activity since the Cenozoic, the Nile Delta is composed of two separate clastic delta systems: an inert Jurassic-Miocene delta system located in the lower part and an active PlioceneeHolocene delta system deposited in the upper part (Sestini, 1989). An unconformity comprised of Messinian evaporites isolates the two systems (Marten et al., 2004). As a result the offshore Nile Delta is characterized by both typical deltaic structures (e.g. listric-growth faults

* Corresponding author. Department of Geosciences and Geological and Petroleum Engineering, Missouri University of Science and Technology, 129 McNutt Hall, 1400 N. Bishop Av, Rolla, MO 65409-0410, USA. E-mail address: [email protected] (A. Eckert). http://dx.doi.org/10.1016/j.jafrearsci.2015.11.014 1464-343X/© 2015 Elsevier Ltd. All rights reserved.

and rotational block faults) and salt-associated structures (such as normal and strike-slip faults, folds, collapsed depocenters, and polygonal mini-basins), which have been discovered in sequences above Messinian evaporites (Loncke et al., 2006). Due to their low shear strength, evaporite layers in sedimentary basins have been considered to act as a mechanical detachment layer (e.g. Davis and Engelder, 1985; Bell, 1996; Bowers, 2007; Tingay et al., 2011), decoupling the stress regimes in the overlaying (termed suprasalt) and underlaying (termed subsalt) sequences. Data available from the North Sea (Grollimund et al., 2001), the Jeanne D'Arc Basin offshore Canada (Courel and Bell, 1996) and the North German Basin (Roth and Fleckenstein, 2001) show different stress orientations of sedimentary regions structurally attached vs. regions structurally detached from the basement rocks. Yet, as summarized and stated by Tingay et al. (2011), most of these data sets only represent suprasalt sequences and hence conclusive evidence to support this hypothesis was not present. In their study, Tingay et al. (2011) presented stress orientation data of the maximum

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horizontal stress, SH, from 44 wells in the offshore Nile delta showing sharply contrasting stress orientations (~90
variations) in supra-vs. subsalt layers. Wells drilled through sequences with evaporates either show a NNEeSSW suprasalt SH orientation in field A (i.e. margin-normal; Fig. 1a), but an ESEeWNW subsalt SH orientation (i.e. margin parallel; Fig. 1a), or show ESEeWNW SH in suprasalt sequences (i.e. margin-parallel; Fig. 1b), but a NNEeSSE SH below the Messinian evaporites in field B (i.e. margin-normal; Fig. 1b). These data sets provide the first major evidence that evaporite sequences can act as mechanical detachment horizons (Tingay et al., 2011, 2012).

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For a clearer understanding of the data presented by Tingay et al. (2011, 2012), the typical stress field characteristics of a clastic wedge in a deltaic region is reviewed and illustrated (Fig. 2a; adopted from Tingay et al. (2012)). For such systems, the delta shelf province (on the continental side) has an extensional stress regime, where SH orientations are margin-parallel and normal faulting prevails, and the delta toe province (on the sea side) has a compressional stress regime, where SH orientations are margin-normal and thrust faulting exists (Bell, 1996; King
, 2010; Tingay et al., 2011, 2012). Stress data from the and Backe Nile delta supports this model for wells in the eastern Nile Delta

Fig. 1. a) SH orientations for field A showing suprasalt margin-normal and subsalt margin-parallel orientations (data from Tingay et al., 2011). b) SH orientations for field B showing suprasalt margin-parallel and subsalt margin-normal orientations (data from Tingay et al., 2011). c) Map of the offshore Nile Delta (from Tingay et al., 2011) showing stress orientation data from the World Stress Map (Heidbach et al., 2008) and from Bosworth (2006). Suprasalt stress data are shown in yellow, subsalt orientations in dark blue. The map also features the outline of the Messinian evaporites and the zone of gravitational gliding containing typical growth faults. The line A e A0 represents the approximate cross-section featured in the finite element models. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 2. a) Typical stress field distribution of a deltaic system showing margin-parallel SH orientation in an extensional stress regime for the delta shelf region (near the continent) and margin-normal SH orientation in a compressive stress regime for the delta toe region (Figure adapted from Tingay et al., 2011). b) Conceptual gravity-gliding model on top of a salt layer introduced by Tingay et al. (2012). In this model the salt acts as a mechanical detachment horizon decoupling the principal stresses in the supra- and subsalt layers. The gravitational gliding is thought to induce basal drag forces in the suprasalt layer, increasing the margin-normal principal stress component, and hence resulting in different stress orientations (Figure adapted from Tingay et al., 2012).

where evaporites are not present. For the SH orientations observed in wells drilled through the Messinian evaporites, Tingay et al. (2012) present a stress detachment model shown in Fig. 2b and postulate 2 hypotheses in order to explain the predominant margin-normal stress orientations in the suprasalt layers and margin-parallel stress orientations in the subsalt layers (i.e. for the case of field A). In the first hypothesis the margin-normal stress orientations could be the result of down slope gravity sliding of salt bodies inducing basal drag forces in the sediments above. As stated by Tingay et al. (2011, 2012) it remains unclear whether such a mechanism is plausible and whether it can explain the observed stress orientations. Analog modeling of gravitational gliding (Cobbold and Szatmari, 1991) suggest the development of different structural domains with different stress regimes. In the second hypothesis the scattered stress orientations could be explained by mechanical property contrasts imposed by the Messinian evaporites. Such contrasts result in localized stress variations as observed in the central North Sea and the Gulf of Mexico (Bell, 1996; Yassir and Zerwer, 1997). Yet, as stated by Tingay et al. (2011) the margin-normal stress orientations are observed up to 2500 m above the

evaporites and may not be just a localized phenomenon. Moreover, to account for such material contrasts the geometry of the evaporate layers, which is currently not known in sufficient detail, should be considered. Despite these two hypotheses, it remains unclear what controls the stress orientations observed in suprasalt sequences. While Tingay et al.'s (2011) conceptual detachment model accounts for the suprasalt margin-normal SH orientations (Fig. 1a), the margin-parallel suprasalt SH orientations (Fig. 1b) in field B are not discussed in greater detail. In this study, 3-dimensional finite element analysis (FEA) is used to simulate the total stress distribution in the offshore Nile Delta featuring evaporite sequences. In order to evaluate the influence of the geometry of the Messinian evaporites, several different salt sequence geometries are considered. As suggested by Healy et al. (2012), this study aims to provide a better understanding of how salt sequences can act as a mechanical detachment layer, resulting in contrasting stress orientations in suprasalt and subsalt layers. The numerical modeling results are used to evaluate if possible basal drag forces induced by gravitational gliding or if mechanical property contrasts imposed by the evaporites show significant spatial variations in the resulting

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stress orientations.

2. Modeling approach

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a) Continuous slightly dipping salt sheet (Fig. 3b) b) Isolated salt pyramids below growth faults (Fig. 3c) c) Continuous salt sheet and salt pyramids below growth faults (Fig. 3d)

2.1. Model geometries The models represent a 100 km long, 5 km wide, and 10 km deep cross section (along line A e A0 in Fig. 1, which is approximately perpendicular to the maximum horizontal stress orientation on the northern African continent) and represent simplified geometries based on the structural elements in the eastern Nile delta after an interpretation by Marten et al. (2004). Since the detailed geometry and spatial distribution of Messinian evaporites is not known in sufficient detail (Tingay et al., 2011) for a realistic and correct representation in a numerical model, several salt geometries typical for deltaic sequences (e.g. Montgomery and Moore, 1997; Warren, 1999) are investigated (Fig. 3). All model geometries considered represent the following units of the Nile Delta system: Pliocene continental shelf; Miocene and Oligocene units; suprasalt sediment cover (Blocks 1e4); Messinian evaporites; basement rock; water load imposed by the Mediterranean Sea (Fig. 3a). Listric growth faults separating the suprasalt sediments and a low angle detachment fault of the clastic wedge below the Pliocene unit are implemented as frictional interfaces with a friction coefficient of 0.6. The following different geometries are considered (e.g. Montgomery and Moore, 1997; Warren, 1999):

2.2. Material parameters Two different constitutive laws are used: salt is modeled as a linear visco-elastic Maxwell material, similar to e.g. Schultz-Ela (2003), Luo et al. (2012), and Nikolinakou et al. (2012); all other rocks are modeled as linear-elastic materials. For the salt, the visco-elastic constitutive behavior is given by (e.g. Luo and Liu, 2009):

_ þ ½Q 1 fsg f_εg ¼ ½D1 fsg

(1)

3 1v v v 0 0 0 6 v 1v v 0 0 0 7 7 6 6 v E v 1v 0 0 0 7 7 6 D¼ 0 0 0:5  v 0 0 7 ð1 þ vÞð1  2vÞ 6 7 6 0 4 0 0 0 0 0:5  v 0 5 0 0 0 0 0 0:5  v 2

(2)

Fig. 3. a) Basic model geometry of the Nile Delta system as incorporated in the finite element models. All models include Pliocene, Miocene, Oligocene, and basement rock layers. The shelf is characterized by a series of 4 growth faults (included as frictional interfaces) separating 4 blocks of suprasalt sediments. The offshore sediments are loaded by the equivalent water pressure of the Mediterranean Sea. Different geometries of the Messinian evaporites are included to test the influence of salt geometry. b) Messinian evaporites are featured as a continuous salt sheet. c) Messinian evaporites are featured as isolated salt pyramids below the growth faults. c) Messinian evaporites are featured as a continuous salt sheet plus pyramid shaped salt pillows below the growth faults.

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2

½Q 1

1 6 3 6 6 6 1 6 6 6 6 16 1 ¼ 6  h6 6 6 6 6 0 6 6 6 0 4 0

0

0

0

0

0

0

1

0

0

0

1

3 07 7 7 7 07 7 7 7 7 07 7 7 07 7 7 07 5

0

0

0

1

1 6 1 3 1  6 0

1  6 1  6 1 3 0

0 0



(3)

_ the stress rate vector, fsg the where f_εg is the strain rate vector, fsg stress vector, [D] and [Q] are the material matrices related to Young's modulus, E, Poisson's ratio, n, and viscosity h. Table 1 lists the material properties, which are assigned to the different model units. Without detailed knowledge about the elastic properties of the Nile Delta sequences, a homogeneous distribution with slight changes in Young's modulus and density is chosen. This material distribution minimizes the effects of the elastic properties and lateral density variations on the stress state and hence enables to isolate the impact of the salt on the resulting state of stress. 2.3. Boundary conditions and loading steps It is obvious that the model boundary conditions have a significant impact on the model results. A correct application of model boundary conditions in a 3D numerical model is necessary to benchmark or calibrate the resulting stress magnitudes (Buchman and Connolly, 2007; Hergert and Heidbach, 2011; Eckert and Liu, 2014). Unfortunately, quantitative stress and pore pressure magnitude measurements in the Nile Delta have not been published due to confidentiality constraints and only qualitative observations are available (Tingay et al., 2012). Extensional stress regimes exist in normally pressured sequences, transtensional stress regimes in moderately overpressured sequences and strikeslip stress regimes in highly overpressured sequences. Horizontal stresses are anisotropic and interpreted not to be the cause for the variable stress orientations (Tingay et al., 2012). Since the majority of stress regimes is extensional (i.e. s1 being vertical) it is clear from the tensor based concept of pore pressure stress coupling that both the minimum horizontal and maximum horizontal stress are affected to a similar degree by the pore pressure (Altmann et al., 2014). This means that the subsurface pore pressure distribution is unlikely the cause for the observed change in stress orientations. Since information about the pore pressure distribution is unknown, and since the main focus is on the resulting stress orientation, total stress is analyzed. Hence, for the model geometries and parameters considered, salt creep, and faulting induced slip are the main causes for stress magnitude variations. As the sequences overlying the Messinian evaporites suggest predominantly extensional stress regimes with anisotropic horizontal stresses (Tingay et al., 2012), an exemplary stress state of Sh ¼ 0.67SV and SH ¼ 0.75SV near the MioceneePliocene interface at ~4000 m depth is chosen. In this

scenario, Sh reflects uni-axial strain conditions under hydrostatic pore pressure conditions and a SH which is slightly elevated. Each model features a static pre-stressing load step that gravitationally equilibrates the stresses (e.g. Buchmann and Connolly, 2007; Eckert and Liu, 2014; Eckert et al., 2014) and applies displacement boundary conditions resulting in the desired stress regime. In the second load step visco-elastic salt relaxation is modeled until the von Mises stress within the salt bodies decays below 1 MPa (e.g. Fredrich et al., 2003; Luo et al., 2012). In the salt relaxation load step uni-axial strain boundary conditions are applied (i.e. only in-plane displacements are allowed at the model boundaries). The commercial finite element software ABAQUS™ is used to solve the models. 3. Results It should be noted that the static pre-stressing load step for all geometries results in margin-parallel maximum horizontal stresses on the continent and the delta shelf regions and in margin-normal maximum horizontal stresses at the delta toe, and is hence consistent with the conceptual model of deltaic stresses shown in
, 2010; Tingay et al., 2012). Once the salt Fig. 2b (King and Backe relaxation is simulated localized stress reorientation occurs, which is described separately for each model geometry. The parameters presented for the results analysis include the principal stress orientations, the resulting displacement field and the slip magnitudes on the fault surfaces. All results are presented in the xez coordinate plane. 3.1. Continuous salt sheet Fig. 4a shows the resulting displacement vectors plotted on the contours of positive displacement along the x-axis for the region of the suprasalt sediments. The results show that the sediments of Blocks 2, 3, and 4 are gravitationally gliding along the x-axis on the salt layer. Average positive displacements of 1.5e2.8 m are observed, with Block 1 and the layers below the salt moving marginally in the opposite direction (gray contours). This represents a first indication of the mechanical detachment imposed by the salt layer on suprasalt and subsalt rocks. Fig. 4b shows the inplane (tangential) slip on the growth faults implemented in the model. The results show that all faults are slipping with maximum displacements of 1.5e1.7 m occurring near the bottom of the faults. The results also show that the first growth fault not underlain by the evaporite layer shows significant less slip (~0.75 m). Fig. 5 shows the orientations of the principal stress components for the regions of the continental shelf (Fig. 5b), the region containing the growth faults (Fig. 5c) and the delta toe sediments (Fig. 5d). As expected for the chosen stress regime, the vertical stress is the maximum principal stress, s1, for all model regions below ~1 km depth (Fig. 5bed). In Fig. 5b, the stress orientations near the continent show that the principal stress component, which is oriented along the x-axis (i.e. margin-normal), is either the minimum principal stress, s3, or the intermediate principal stress,

Table 1 Material parameters used in the finite element models. Unit

Young's modulus (GPa)

Poisson's ratio

Density (kg/m3)

Viscosity (Pa s)

Pliocene Miocene Oligocene Basement Suprasalt sediments Messinian evaporites

40 40 40 40 40 30

0.25 0.25 0.25 0.25 0.25 0.25

2500 2600 2600 2600 2300 2000

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Fig. 4. a) Resultant displacement vectors plotted on top of contours of positive displacement along the x-axis for the continuous salt sheet model showing that gravitational gliding occurs in the suprasalt Blocks 2e4. Since the subsalt layers move in the opposite direction a first indication of mechanical detachment is given. b) In-plane (tangential) fault slip magnitudes showing that the growth faults on top of the salt layer have much larger slip than the growth fault not underlain by salt.

s2, near the surface (with the vertical stress being s3). This indicates that the maximum horizontal stress for the continent is always margin-parallel, consistent with the margin-parallel maximum horizontal stress reported by Tingay et al. (2011, 2012). For the region containing the growth faults underlain by the salt layer (Fig. 5c) a similar distribution of the principal stress orientations is evident, i.e. the salt layer does not result in any stress reorientations in the suprasalt sequences of Blocks 1e3. Slight variations can be observed below the northern tip of the salt layer (red box in Fig. 5c), where the margin-normal principal stress component becomes s2. For the sediments in Block 4 (Fig. 5d), which also features the largest displacements, the horizontal suprasalt stress orientations are opposite from the subsalt sequences. In the suprasalt rocks (with the vertical stress being s1) the marginnormal principal stress is s2, and in the subsalt rocks the margin normal principal stress is s3. This corresponds to the horizontal stress variations observed for the Nile Delta. 3.2. Isolated salt pyramids Fig. 6a shows the resulting displacement vectors plotted on the contours of negative displacement along the x-axis for the region of the suprasalt sediments. The results show that the sediments of Blocks 1, 2, and 3 are not gravitationally gliding towards the delta toe, but rather are a reaction to the slip of the growth faults. As a result mostly negative displacements in the order of 0.1e0.5 m occur. In comparison to the continuous salt sheet model fault slip is reduced (i.e. maximum slip magnitudes are ~1.38 m; Fig. 6b). Also, when the fault is in contact with the salt pyramids, slip magnitudes are reduced to ~ zero displacement. Here, deformation is accommodated by the creep deformation of the salt pillow. As a result of the imposed gravitational load (i.e. the downward fault slip) the salt pillow is squeezed laterally, as indicated by the displacement

magnitudes of opposing signs (Fig. 6a; gray contours indicate positive displacement along the x-axis; colored contours indicate negative magnitudes along the x-axis) next to the salt pyramids. Only Block 4 gravitationally glides towards the delta toe, yet as it is not underlain by salt in this model, a mechanical detachment of the displacement field is not observed here (i.e. both the sediment cover and the basement rocks move towards the delta toe as indicated by the gray contours of displacement in Fig. 6a). Fig. 7 shows the orientations of the principal stress components for specific regions of interest in the model. As for the continuous salt sheet model, the vertical stress is the maximum principal stress, s1, for all model regions below ~1 km depth (Fig. 7bed). Near the continent (Fig. 7b) the same behavior as for the continuous salt sheet model is observed, i.e. the marginnormal principal stress is either s3, or s2 (near the surface). For the region containing the growth faults underlain by the salt pyramids (Fig. 7b) significant re-orientations of the principal stresses are evident. The regions between the salt pyramids (extending vertically up to 1.5 km from the bottom of the salt; red insets in Fig. 7b) are characterized by horizontal stress orientations being opposite from the subsalt sequences. In these regions (with the vertical stress being s1) the margin-normal principal stress is s2, and in the subsalt rocks the marginnormal principal stress is s3. This corresponds to the horizontal stress variations observed for the Nile Delta. Margin-normal s2 orientations are also observed for the delta toe region (Fig. 7d). In contrast to the continuous salt sheet model these orientations are observed both for the sediments of Block 4 and the underlying basement rocks (red inset in Fig. 7d). Since no salt layer separates these units a mechanical detachment is not present, which is also evident from the continuous positive displacements along the x-axis for these units (Fig. 6a). These observations do not coincide with the observations from the Nile Delta.

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Fig. 5. a) Model geometry of the continuous salt sheet model featuring 3 regions of specific interest, including the continent, the region containing the growth faults and the delta toe region, for which detailed stress orientation results are presented in Fig. 4bed. b) Principal stress orientations for the continent region showing that SH is always margin-parallel (i.e. SH ¼ s2 at depth with Sh ¼ s3, and SH ¼ s1 near the surface). c) Principal stress orientations for the region of the growth faults. Supra and subsalt regions show the same orientations as for the continent. Local variations occur near and below the end of the salt sheet (indicated by the red box). Here, stress reorientations result in margin-normal SH below the salt, while the suprasalt SH is margin-parallel. d) Principal stress orientations for the sediments of Block 4. A clear separation of suprasalt and subsalt stress orientation is present. For the suprasalt sediments SH is margin-normal (red inset); for the subsalt sediments SH is margin-parallel. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3.3. Continuous salt sheet plus salt pyramids Fig. 8a shows the resulting displacement vectors plotted on the contours of positive displacement along the x-axis for the region of the suprasalt sediments. The results show that the sediments of Blocks 2, 3, and 4 are gravitationally gliding towards the delta toe (along the x-axis). Average positive displacements of 2.5e4 m are observed with a maximum of up to 7 m occurring at the bottom of the last growth fault. Block 1 and the layers below the salt move marginally in the opposite direction (gray contours). Same as for the continuous salt sheet model, the salt layer represents a

mechanical detachment horizon. As a result of the enhanced gravitational gliding (compared to the continuous salt sheet model) fault slip magnitudes are higher (Fig. 8b; maximum slip is ~2.75 m); slip also reduces to ~ zero when the fault comes into contact with the salt. The resulting stress orientations are presented in Fig. 9 for the regions of specific interest in the model. The stress orientations on the continental shelf (Fig. 9b) show a margin-parallel maximum horizontal stress (either s1 or s2) and hence are equal in all three model geometries considered. The subsalt regions below sediment Blocks 1, 2, and 3 separated by the growth faults (Fig. 9c) are

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Fig. 6. a) Resultant displacement vectors plotted on top of contours of negative displacement along the x-axis for the isolated salt pyramids model. Gravitational gliding does not occur in the suprasalt sediment Blocks. The vertical load results in a lateral squeezing of the salt as indicated by the opposing signs of the displacements along the x-direction (gray contours indicate positive). b) In-plane (tangential) fault slip magnitudes showing that the growth faults have less slip compared to the continuous salt sheet model. Also, slip magnitudes approach 0 near the salt pillow.

characterized by stress orientations where the maximum horizontal stress (i.e. s2) is margin-parallel. In the suprasalt sequences the maximum horizontal stress becomes margin-normal directly above the evaporites (extending vertically for up to 1 km) before rotating back to become margin-parallel again. The suprasalt sediments of Block 4 (Fig. 9d) also features opposing maximum horizontal stress orientations compared to the subsalt layers. In the suprasalt rocks the maximum horizontal stress (s2 here) is marginnormal (extending vertically for up to 4 km from the top of the salt), and in the subsalt rocks the maximum horizontal stress is marginparallel. Hence, the observations from Fig. 9c and d also correspond to the horizontal stress variations observed for the Nile Delta. 4. Discussion Numerical modeling studies have shown that salt relaxation can significantly affect the state of stress of surrounding rock units (Fredrich et al., 2003; King et al., 2012; Nikolinakou et al., 2012). In this study, numerical models (based on 3D FEA) of different likely salt geometries of the Messinian evaporites of the Nile Delta system show great variability in the orientation of SH and perpendicular orientations of the horizontal stresses below and above the salt sequences are the result. These observations provide additional evidence to support the conclusion that salt, under specific conditions, acts as mechanical detachment. From the results presented, it is clear that the salt geometry has a large impact on the resulting stress orientations and the different models are evaluated with respect to the hypotheses postulated by Tingay et al. (2011) in order to determine the cause for the different stress orientations. Synoptic figures are presented in order to provide a conceptual explanation of the various stress re-orientations in the different models. 4.1. Localized stress variations Tingay et al. (2011) list the influence of mechanical property contrasts imposed by the Messinian evaporites as one possibility to

explain localized variations in the maximum horizontal stress orientations. Such property contrasts have an influence on the state of stress where the salt geometry/body imposes loads on the adjacent rocks due to salt relaxation and creep (Fredrich et al., 2003; Luo et al., 2012). Since such localized variations are directly dependent on the geometry of the salt layer, the different model geometries are investigated in this respect. Localized stress variations can be observed pre-dominantly in the model featuring the isolated salt pyramids. In particular affected are the regions between the growth faults, where the resulting displacement field (Fig. 6a) shows that gravitational gliding is not occurring. Yet, the maximum horizontal stress switches from margin-parallel in the subsalt sequences to margin-normal between and above the salt pyramids. The resulting displacement field (Fig. 6a), showing positive displacements along the x-axis to the right and negative displacements along the x-axis to the left of these salt pyramids, provides an explanation for these stress variations. As the salt pyramid is gravitationally loaded, the salt is “squeezed out” laterally and hence compresses the adjacent sediments (Fig. 10a). This compression results in the stress magnitudes along the x-direction, Sxx, becoming larger than the stress magnitudes along the y-direction, Syy, as the salt relaxation progresses with time (Fig. 10b). The subsalt sediments are not affected by this compression and thus do not show Sxx becoming larger than Syy (Fig. 10c). While this scenario does not represent a decoupling of suprasalt and subsalt layers it provides a possible explanation for the predominantly marginnormal suprasalt stress orientations (Fig. 1a). Localized stress variations also occur in the model featuring the continuous salt sheet. Directly at and below the end of the sheet facing the continent the maximum horizontal stress becomes margin-normal, while the maximum horizontal stress in the suprasalt sediments is margin-parallel. This can also be explained by the resulting displacement field of the model (red (in the web version) arrows in Fig. 10d). As the suprasalt sediments of Blocks 2e4 gravitationally glide towards the delta toe, the continent end of the salt sheet is gravitationally loaded and also moves towards the continent (negative x-displacement) and hence compresses the

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Fig. 7. a) Model geometry of the isolated salt pyramids model featuring 3 regions of specific interest, including the continent, the region containing the growth faults and the delta toe region, for which detailed stress orientation results are presented in Fig. 4bed. b) Principal stress orientations for the continent region showing that SH is always margin-parallel (i.e. SH ¼ s2 at depth with Sh ¼ s3, and SH ¼ s1 near the surface). c) Principal stress orientations for the region of the growth faults show that SH is margin-normal between the salt pillows (red insets), while for the subsalt sediments SH is margin-parallel. d) Principal stress orientations for both the sediments of Block 4 and the basement rock (red inset) show that SH is margin-normal. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

adjacent rock (Fig. 10d). This scenario represents the opposite reorientation as seen for the isolated salt pyramids and could explain margin-normal orientation in subsalt sequences as observed for Field B (Fig. 1b). 4.2. Basal drag forces induced by gravitational gliding The conceptual model by Tingay et al. (2011, 2012) resulting in margin-normal stress orientations in suprasalt layers and marginparallel stress orientations in subsalt layers is based on the gravitational gliding of the suprasalt sediments on the evaporite layer. During the gliding process basal drag forces are induced in the suprasalt layers elevating the margin-parallel principal stress

component. The displacement field results presented in this study show that gravitational gliding occurs for both the continuous salt sheet model (Fig. 4a), and for the model featuring the salt pyramids on top of a continuous salt sheet (Fig. 8a). In the model of the continuous salt sheet stress the sediments in Block 4 feature suprasalt maximum horizontal stress orientations (margin-normal), which are opposite from the subsalt sequences (margin-parallel). It is worth noting that while the gravitational gliding zone extends delta-toe-wards from the second growth fault, the margin-normal principal stress is not increased in the region between the growth faults (i.e. for Blocks 1e3). This is shown in Fig. 11a which shows the contours of the differential stress SxxSyy. It is important to repeat that for the initial stress regime of the

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Fig. 8. a) Resultant displacement vectors plotted on top of contours of positive displacement along the x-axis for the model featuring the continuous salt sheet showing and the salt pyramids below the growth faults. The displacement vectors show that gravitational gliding occurs in the suprasalt Blocks 2e4. The subsalt layers move in the opposite direction indicating the mechanical detachment. b) Due to the enhanced gravitational gliding in-plane (tangential) fault slip magnitudes of the growth faults on top of the salt layer have larger slip than the growth faults for the continuous salt sheet model.

model the margin-parallel principal stress, Syy, is larger than the margin-normal principal stress, Sxx (i.e. Sxx ¼ 0.67SV and Syy ¼ 0.75SV). After the salt relaxation Fig. 11a shows that Sxx is increased for the sediments of Block 4 (positive differential stress), with the compression increasing towards the non-moving model boundary. It is important to note that the non-moving model boundary condition does not induce an artificial stress increase, but rather represents the presence of the Eratosthenes seamount which restricts the gravitational gliding (Tingay et al., 2012). In Blocks 1e3 Sxx remains smaller than Syy. The stress magnitude evolution over time (inset graph in Fig. 11a) shows that Sxx is even further reduced compared to Syy between the growth faults. Fig. 11b summarizes these observations and depicts the causes for the resulting stress fields for the different suprasalt regions. Since the first growth fault near the continental shelf is not slipping (Fig. 4b) and the majority of Block 1 moves in the negative x-direction (Fig. 4a), the slipping of the growth faults of Blocks 2 and 3 results in a stress release in Blocks 2 and 3. In Block 4 the gravitational gliding of the sediments on the salt layer induces basal drag in the suprasalt sediments, which results in the margin-normal principal stress, Sxx, overcoming Syy. In contrast to the continuous salt sheet model, the model featuring the salt pyramids on top of a continuous salt sheet shows that margin-normal maximum horizontal stresses in the suprasalt regions do not only occur in Block 4, but also in Blocks 1e3. This can be explained by the particular salt geometry of this model. From the resulting displacement field (Fig. 8a) it can be seen that gravitational gliding occurs in Blocks 2e4. The majority of Block 1 is moving in the negative x-direction. Hence, the increased Sxx magnitudes in Block 1 can be attributed to the lateral squeezing of the salt pyramids depicted in Fig. 10a. For Blocks 2e3 the gravitational gliding induces basal drag forces and results in increased Sxx magnitudes. Instead of being released as in the continuous salt sheet model, Sxx magnitudes overcome Syy to become the maximum horizontal stress, as shown by the positive magnitudes

of the differential stress SxxSyy (Fig. 12a). This can be attributed to the continuation of the salt sheet into the salt pyramids below the next growth fault. This geometry results as a local barrier to the gravitational gliding hence resulting in the increase of Sxx. The increased Sxx in Block 4 result from the induced basal drag forces. 4.3. Implications for hydrocarbon production in the Nile Delta In the context of the recent discovery of the 30 trillion cubic feet supergiant “Zohr” gas field (Eni, 2015), the observations by Tingay et al. (2011) and the results of this study may have several geomechanical implications considering drilling and production in the Nile Delta region. Applications including (but not limited to) wellbore stability of deviated production wells, seal breach by fault reactivation, and preferred perforation orientations to mitigate sanding are depending on a thorough understanding of the prevailing stress orientations. For deviated wells in an extensional and transtensional stress regime wellbore stability varies depending on the drilling direction (Hillis and Williams, 1993). While drilling along the minimum horizontal stress direction represents the most stable drilling direction, the maximum horizontal stress direction represents the least stable direction, and the borehole is more prone to breakouts or drilling induced tensile failure. Hence, deviated or horizontal wells drilled in regions in the Nile Delta, where stress reorientations occur laterally may result in wellbore stability problems, as the wellbore may experience variations of stable to unstable conditions. Seal breach by fault reactivation is another concern in the offshore Nile Delta. The majority of faults present in the offshore Nile delta are extensional growth faults with a fault strike being approximately margin-parallel. In the extensional stress regime present, these faults are favorably oriented for reactivation, which is also confirmed by the numerical modeling results presented (Figs. 5, 7 and 9). However, in order to quantify the likelihood of the

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Fig. 9. a) Model geometry of the continuous salt sheet model plus the salt pyramids below the growth faults. 3 regions of specific interest are highlighted (black boxes), including the continent, the region containing the growth faults and the delta toe region, for which detailed stress orientation results are presented in Fig. 4bed. b) Principal stress orientations for the continent region showing that SH is always margin-parallel (i.e. SH ¼ s2 at depth with Sh ¼ s3, and SH ¼ s1 near the surface). c) Principal stress orientations for the region of the growth faults show that SH is margin-parallel for the subsalt sediments and rotates to become margin-normal in the suprasalt sediments directly above the evaporates (red insets). SH rotates back to become margin-parallel near the surface. d) Principal stress orientations for the sediments of Block 4. A clear separation of suprasalt and subsalt stress orientation is present. For the suprasalt sediments SH is margin-normal (red inset), while for the subsalt sediments SH is margin-parallel. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

fault reactivation risk, the critical pore pressure difference with respect to the failure envelope needs to be calculated based on the principle of pore pressure stress coupling (Altmann et al., 2014; Eckert et al., 2015). Since stress magnitude and pore pressure measurements are currently not available for the Nile Delta region (Tingay et al., 2012) such an analysis is beyond the scope of this contribution. Perforation stability and related sand production are complex processes which can create serious problems in weakly consolidated reservoirs. It has been shown that depending on the effective

s0

s0

stress ratios K 0H ¼ sH0 and K 0h ¼ s0h different optimal perforation oriV V entations, ranging from parallel to the minimum horizontal stress to parallel to the maximum horizontal stress, are recommended to mitigate sand production (Santarelli et al., 1991). For extensional stress regimes where s’h > 0.5 s0 V (as for the numerical models for the Nile Delta presented in this study) the maximum horizontal stress direction represents the optimal perforation orientation (Santarelli et al., 1991). This finding agrees with a study by Morita and McLeod (1995), who report a field study where wells with orientated perforations along the maximum in-situ stress direction

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Fig. 10. a) Synoptic diagram showing that the vertical load imposed on the salt pyramids squeezes the salt laterally, hence compressing the regions between the salt pyramids. b) This lateral compression results in stress magnitudes along the x-direction, Sxx, overcoming stress magnitudes in the y-direction, Syy. c) Sxx in the subsalt layers do not become larger than Syy, since they are not compressed by the salt. d) Synoptic diagram showing the cause for the margin-normal SH orientations at and below the end of the continuous salt sheet. The salt is both loaded vertically (by the gravitational gliding of the sediments) and laterally (the resulting displacement vectors show that the salt is pushed laterally along the negative x-direction) resulting in a region that undergoes localized compression.

Fig. 11. a) Contours of positive differential stress SxxSyy indicating that Sxx has overcome Syy in Block 4. The inset for the stress evolution between the growth faults shows that Sxx is further decreased, thus indicating stress release. b) Synoptic diagram (on top of displacement contours along the x-axis, U1) showing the causes for the observed stress field variations. The region between the growth faults is characterized by a stress release (i.e. lower Sxx magnitudes), which is caused by the gravitational gliding of sediment Blocks 2 and 3 towards the delta toe. As Block 1 is marginally moving in the opposite direction, extension occurs resulting in the horizontal stress release. For the sediments of Block 4 the gravitational gliding results in basal drag forces in the suprasalt layers which increase the margin-normal principal stress component.

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Fig. 12. a) Differential stress SxxSyy contours showing increased Sxx (i.e. Sxx > Syy) in all suprasalt sedimentary blocks. b) Synoptic diagram (on top of displacement contours along the x-axis, U1) showing the causes for the observed stress field variations. For Block 1 lateral salt squeeze induces compression along the x-axis. For Blocks 2 and 3 basal drag forces are induced. The salt pyramid geometry acts as a barrier, thus preventing stress release due to the gravitational gliding. In Block 4 Sxx is increased due to the basal drag forces.

exhibited significantly reduced sanding problems compared to the surrounding wells. Tronvoll et al. (2004) also studied a field case from the Varg Field in the North Sea where oriented perforation based on 180
phasing (in order to avoid less favorable perforation orientations) reduced the sanding risk substantially. Hence, for the offshore Nile Delta, depending on the prevailing stress orientations, different perforation approaches may need to be considered. 5. Summary and conclusions The contrasting orientations of the maximum horizontal stress, SH, which is predominantly margin-normal in suprasalt layers and predominantly margin-parallel in subsalt layers in the offshore Nile Delta, provide the first major evidence that evaporate sequences can act as mechanical detachment horizons (Tingay et al., 2011, 2012). The numerical modeling results presented in this study show that such opposing stress directions can be caused by different salt geometries including continuous salt layers and isolated salt pillow geometries. The modeling results are in agreement with both hypotheses postulated by Tingay et al. (2011). When salt is present as a continuous layer gravitational gliding occurs and basal drag forces induced in the suprasalt layers result in the margin-normal principal stress becoming the maximum horizontal stress. As the margin-normal stress increase is confined to the suprasalt layers, the salt acts as a mechanical detachment horizon, resulting in different SH orientations in the suprasalt compared to the subsalt layers. The modeling results provide additional quantitative evidence to confirm the observations from Tingay et al.'s (2011) study. When salt is present as isolated bodies (i.e. pyramid shaped salt pillows below growth faults in this study) localized stress variations occur due to the mechanical property contrasts imposed by the salt. For the case of the salt pyramids below the growth faults, compressional stresses are induced between the growth faults, also resulting in different SH orientations in the suprasalt compared to the subsalt layers. For the case of the isolated end of the continuous salt sheet margin-normal SH orientations occur in the subsalt layers, while SH remains margin-parallel in the suprasalt layer.

This example shows that both variations of stress orientation data (Fig. 1aeb) can be explained. Observations from field B (margin-parallel in suprasalt layers and margin-normal in subsalt layers) are likely caused by localized stress variations imposed by mechanical property contrasts. Observations from field A (marginnormal in suprasalt layers and margin-parallel in subsalt layers), which represent the predominant orientations occurring in the Nile delta. Tingay et al. (2011), can be explained consistently by models featuring gravitational gliding and associated basal drag stress increases. It is important to remark that the numerical model presented in this study do not try to exactly replicate/simulate the data presented by Tingay et al. (2011). As suggested by Healy et al. (2012), the study rather aims to provide conceptual models resembling the mechanical conditions of the offshore Nile Delta in order to provide possible explanations for the contrasting stress orientations and their implications for hydrocarbon production. Acknowledgments The authors would like to thank Mark Tingay for his valuable and constructive review, which greatly improved the manuscript. Mark Tingay is also acknowledged for kindly providing high resolution images for Fig. 1. References Altmann, J.B., Müller, B.I.R., Müller, T.M., Heidbach, O., Tingay, M.R.P., Weißhardt, A., 2014. Pore pressure stress coupling in 3D and consequences for reservoir stress states and fault reactivation. Geothermics 52, 195e205. Badawy, A., 2005. Present-day seismicity, stress field and crustal deformation of Egypt. Journal of Seismology 9, 267e276. Bell, J.S., 1996. Petro geoscience 1. In situ stresses in sedimentary rocks (part 2): applications of stress measurements. Geosci. Can. 23, 135e153. Bosworth, W., 2006. North Africa-Mediterranean present-day stress field transition and implications for fractured reservoir production in the eastern Libyan basins. Geol. East Libya 4, 123e138. Bowers, G.L., 2007. Effect of inelastic sediment behavior on near-salt stresses and pore pressures. Lead. Edge (Tulsa, Okla.) 26, 1462e1465. Buchmann, T.J., Connolly, P.T., 2007. Contemporary kinematics of the Upper Rhine Graben: a 3D finite element approach. Glob. Planet. Change 58 (1), 287e309.

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