Influence of Inherited Brittle Fabrics on Continental Rifting: Insights From Centrifuge Experimental Modeling and Application to the East African Rift System

The presence of pre‐existing fabrics at all lithospheric scales has been proven to be of primary importance in controlling the evolution of continental rifts. Indeed, observations from natural examples show that even in conditions of orthogonal rifting, when extension should result in simple fault patterns dominated by normal faults orthogonal to extension vectors, inherited fabrics induce complex arrangements of differently‐oriented extension‐related structures. This paper explored the influence of inherited fabrics on rift‐related structures by using a series of analog models deformed in a centrifuge. The models reproduced a brittle‐ductile crustal system and considered the presence of pre‐existing discrete fabrics in the brittle crust in conditions of orthogonal narrow rifting. These fabrics were reproduced by cutting the brittle layer at different orientations with respect to the extension direction. Modeling shows pre‐existing fabrics have a significant influence on rift‐related faults, provided that the angle between inherited fabrics and the rift trend is less than 45°. In these conditions, fabrics cause prominent segmentation of rift‐related faults and induce the development of isolated depocenters. Pre‐existing fabrics strongly influence the geometry of extension‐related structures, resulting in curved fault patterns and en‐echelon arrangement of oblique faults. These findings provide insights into the development of continental rift systems in nature: our modeling shows indeed significant similarities (i.e., peculiar fault architecture and geometries) with the faults in different sectors of the East African Rift System (e.g., the Magadi and Bogoria basin, Kenya Rift), testifying that reactivation of inherited fabrics is a paramount process in shaping continental rifts.

dominated by normal faults orthogonal to the extension vector (see for instance the complex fault pattern characterizing the orthogonal southern Main Ethiopian Rift in East Africa; e.g., Corti et al., 2022).However, how the pre-existing fabrics are reactivated and the influence on the rift-related faults and structures during rifting still need to be understood in detail and evaluated quantitatively.
We implemented these previous works by presenting the first centrifuge models (i.e., deformed in an enhanced gravity field) designed to reproduce and investigate the influence of pre-existing brittle fabrics on the development and structural pattern of narrow continental rift valleys.In addition to well-known advantages described when performing centrifuge models (e.g., a better distribution of the stress field and the possibility to employ stronger materials and better reproduce ductile deformation), in this specific case, the centrifuge apparatus allowed the use of more cohesive brittle materials than those commonly used in normal gravity experiments, implying better resolution (i.e., sharpness and definition) in the resulting fault pattern, which is key to highlight and investigate fault reactivation in detail.The models were designed to reproduce a brittle/ductile crustal scale system and consider conditions of orthogonal rifting; pre-existing vertical weaknesses in the brittle layer simulate inherited fabrics (e.g., inherited faults or narrow shear zones) that typically characterize natural rifts (e.g., Le Turdu et al., 1999;Saalmann et al., 2016;Smith & Mosley, 1993).We focused on the influence of these heterogeneities on the characteristics (evolution, geometry, segmentation) of boundary and internal faults of continental rifts, and our results aimed to test how the obliquity of pre-existing fabrics influenced reactivation during rifting, causing curvature of the rift-related faults or complicated geometry of rift-related structures.Finally, we compared our results to natural examples from the East African Rift System.

Model Setup
The analog experiments were performed in an artificial gravity field of ∼18g using the large capacity centrifuge available at the TOOLab (Tectonic Modelling Laboratory) of UNIFI-DST (Department of Earth Sciences, University of Florence, Italy) and CNR-IGG (Institute of Geosciences and Earth Resources, National Research Council of Italy).The models, simulating the extension of a brittle-ductile continental crust, were built inside a transparent rectangular Plexiglas box (with internal dimensions of 25 × 16 × 7 cm) and confined by two moveable side walls (Figure 1a).Models were set up with a two-layer structure, corresponding to the brittle upper crust (UC) and ductile lower crust (LC), floating on a low-viscosity layer (LVL), which helped the model to expand laterally and provided the isostatic support to the deforming crust.The analog LC was characterized by the presence of a weak zone (Weak Lower Crust (WLC)) in the central area, in order to localize the extension and give rise to a symmetric orthogonal rift system.
The centrifuge was used to produce an artificial enhanced gravity field and induce extension on the models.By removing rectangular Plexiglas blocks (i.e., the so called "spacers"; Figure 1a) at the sides of the moving walls in the model setup, we allowed the centrifuge force to push the model orthogonally to its surface (simulating an enhanced gravity force), and consequently allowing the LVL at the bottom to flow laterally, driving the lateral  Maestrelli et al. (2021b) and the text for details).Milazzo et al., 2021;Philippon et al., 2015;Zwaan et al., 2020), the UC was simulated by using a FS900SF K-feldspar sand characterized by a linear increase in strength with depth to reproduce natural brittle behavior (Del Ventisette et al., 2019).The LC was modeled by using a ductile mixture of Polydimethylsiloxane (PDMS) and plasticine with a % weight ratio of 100:45, hereafter referred to as PP45.The WLC was simulated by using a mixture of Dow Corning 3179 putty, corundum sand, and oleic acid with a 100:70:05% weight ratio.For the basal LVL a mixture of Dow Corning 3179 putty, corundum sand, and oleic acid with a 100:70:20% weight ratio was used.Parameters and detailed physical properties of these materials are reported in Table 1.By using the above-described materials, we approximated the typical Christmas-tree strength profile that characterizes the continental lithosphere in nature (Figure 1a, Corti, 2012).
The brittle sand layer was cut vertically with a knife at regularly spaced intervals (average of 2 cm) to reproduce the inherited fabrics (with a width of ca. 2 mm for regular cuts, and ca. 4 mm for the wider cuts) within the UC, a technique which has been widely used in previous analog models (e.g., Bellahsen & Daniel, 2005;Bonini et al., 2021;Corti et al., 2007Corti et al., , 2020;;Maestrelli et al., 2020Maestrelli et al., , 2021aMaestrelli et al., , 2021b;;Viola et al., 2004;Zwaan et al., 2021b).Creating weak zones in the sand produces reorientation of particles and variation of their original compaction, inducing a reduction of the coefficient of friction of about 10%-40% compared to undisturbed sand (e.g., Bellahsen & Daniel, 2005;Sassi et al., 1993;Zwaan et al., 2021b) and therefore producing a local weakening of the sand mixture.Notably, Morley et al. (2004) and Morley and Nixon (2016) suggested that variation in the strength of inherited fabrics may also affects the degree of their activation.Bellahsen and Daniel (2005) estimated a ≈35% drop in cohesion for inherited fabrics cut through the sand (as done in our models) and we can therefore expect a drop close to that value in our experiments.In this study, we defined a parameter α to represent the angle between the rift axis and the trend of the cuts (Figure 1c).The experimental series was performed by varying the value of this parameter from 0° to 90° with the interval of 15°, in order to systematically explore the influence of obliquity of the inherited fabrics on the rift-related structures (Table 1).Out of 39 models performed, we present the results of nine experiments that were considered representative of the experimental series.Each model was replicated at least twice, to guarantee reproducibility of results.

Scaling
Scaling the models down to natural conditions to make sure the similarity of geometry, kinematics, and dynamics is critical to ensure the reliability of analog modeling (Hubbert, 1937;Ramberg, 1981;Weijermars & Schmeling, 1986).For this experimental series, the models were built with a geometric scale ratio of ca. 10 −6 , which means that 1 mm in the experiments corresponded to 1 km in nature.This allowed modeling the lateral displacement of up to 30 km for the 30-km-thick crust in nature.The 2-4 mm wide cuts corresponded to vertical inherited fabrics with 2-4 km width, in the range with what observed in nature (e.g., ∼2-6 km for the Aswa Shear Zone system in East Africa; e.g., Le Turdu et al., 1999;Westerhof et al., 2014).According to the dynamic-kinematic similarity relationships among gravitational, viscous, and frictional stresses in the modeling system, the velocity of lateral extension in the models (∼1.5 × 10 −5 m•s −1 ) scaled to the natural values of ∼5.0 mm yr −1 , which is in good consistency with what observed in the different natural examples (e.g., 0.8-5.2mm yr −1 for the East African Rift System, Saria et al., 2014; 15-20 mm yr −1 for the Red Sea, McClusky et al., 2010).Details of the scaling parameters are reported in Table 2.

Monitoring of the Experiments
Top-view photos of the models were taken at defined stages during deformation (extension of 3 mm, 6 mm, 9 mm, and the final stage at 10 mm) in order to monitor the evolution of surface deformation.Digital Elevation Models (DEMs) were reconstructed to obtain the surface topography of each model at the extension of 10 mm.Digital Elevation Models (DEMs) were generated by taking 3D perspective photos (with a Canon EOS 1300D reflex camera; Figure 1d) and implementing photogrammetric techniques (e.g., Donnadieu et al., 2003) using  the software Agisoft Metashape and following the procedure described in Maestrelli et al. (2021aMaestrelli et al. ( , 2021b)).3D rendering of model surfaces obtained from DEMs are shown in Figure A1.

Evolution and Characteristics of the Reference Models
Top-view photos and fault interpretation of model NPFC-1 and NPFC-4 (Table 1) are shown at bulk extensions of 3 mm, 6 mm, and 10 mm (Figure 2), illustrating the geometric characteristics and differences at different stages of the deformation process.Model NPFC-1 represents a homogenous setup where no pre-existing fabrics were simulated, while model NPFC-4 bears pre-existing "standard" fabrics (2 mm) trending at 30° to the direction of the rift axis (α = 30°).The evolution of these two models is described in detail as they are considered reference models for this experimental series; their description serves indeed as a reference for comparing with models bearing pre-existing fabrics trending at various α angles, afterward (see Section 3.2).
All the top-view photos, DEMs, line-drawing, and raw data are free to download from the data set by Zou et al. (2023).

Model NPFC-1 (Homogenous Model, No Pre-Existing Fabrics)
Model NPFC-1 (Figure 2) was a homogeneous model with no pre-existing fabrics and its evolution showed a deformation process typical of orthogonal rifting.At an extension of 3 mm (Figure 2a), the border faults appeared while no evidence of marginal grabens and axial faults was observed.After 6 mm of extension (Figure 2b), the border faults had grown, propagating to form a well-developed boundary faults system.Additionally, some antithetic faults began to develop to form two lateral grabens parallel to the boundary fault system and delimited a non-deformed axial horst.At the end of model deformation (10 mm; Figure 2c), the border faults further  (Bonini et al., 2001;Mulugeta, 1988;Ramberg, 1981).Ramberg number R m is obtained via the following equation: R m = (ρ•g•h 2 )/(η•v) (Weijermars & Schmeling, 1986).increased displacement and length, causing hard and soft linkage among different segments.Similarly, the antithetic faults experienced significant propagation and growth and led to the subsidence of the two lateral grabens.

Table 2 Characteristics of Experimental Materials and Scaling Ratios for the Analog Models
In parallel, the axial horst started to be affected by axial faults that caused its further subsidence defining a longitudinally continuous depocenter (Figures 2c and 3a).

Model NPFC-4 (Pre-Existing Fabrics, α = 30°)
Model NPFC-4, was designed with a pre-existing fabric trending at 30° to the direction of extension (α = 30°).The model showed high similarity in its architecture when compared with Model NPFC-1, but with crucial differences in the geometry of specific features.During the incipient stages of deformation (3 mm of extension, Figure 2d), the initial border fault segments showed a slight bend when approaching the location of the inherited fabrics.At 6 mm of extension (Figure 2e), the bending of the border faults became more visible, and slight curvature could also be observed for newly-formed antithetic faults.When the extension reached 10 mm (i.e., end of model deformation, Figure 2f), a remarkable complexity could be observed in this model, if compared with model NPFC-1: in areas close to the location of inherited fabrics, the boundary faults experienced evident curvature toward the fabric trend and diffused occurrence of relay ramps.This influence could be also observed on the antithetic faults and in newly-formed axial structures (Figure 2f): for example, larger faults showed at their tip some "J"-shape or "S"-shape trajectories following the trend of pre-existing fabrics, while smaller axial faults developed following the trend of the discontinuities.Notably, in its final stage, the axial portion of the model was characterized by separated depocenters whose segmentation corresponded to the location of where pre-existing fabrics (Figures 2f and 4a).

Evolution and Characteristics of the Models With Pre-Existing Fabrics
In order to analyze the influence of the pre-existing fabrics trending at different angles, as well as the effect of an increased fabric width on rift architecture, we describe the models by showing their topography (i.e., DEMs) and fault interpretation at 10 mm extension (Figures 3-5).This will help to focus on the interaction between rift-related faults and the pre-existing fabrics, which became mature and evident at the end of model deformation.Despite model NPFC-1 and NPFC-4 were described in Section 3.1, they are also shown here (Figures 3a and 4a) for completeness.
When α = 0° (Model NPFC-2; Figure 3b), both border faults and antithetic faults developed longer and more continuous than those of Model NPFC-1 (i.e., with no pre-existing fabrics).More importantly, deformation was also highly localized in a system of straight conjugate axial faults defining a well-developed central graben which was not observed in Model NPFC-1.
Overall, all the main faults exhibited an extremely marked longitudinal continuity and linearity, with no anomalous top-view pattern (i.e., the above mentioned "J" and "S"-shaped geometries), nor significant segmentation.When α = 15° (i.e., low obliquity; Model NPFC-3, Figure 3c) or α = 45° (i.e., moderate obliquity; Model NPFC-5, Figure 4b) curvilinear fault patterns (mainly "J"-and "S"-shaped) widely occurred where rift-related faults intersect pre-existing fabrics.Relay ramps were especially common in areas where the fabrics intersected with border faults or antithetic faults; these areas also defined segmentation of the depocenter of the axial graben (Figures 3c and 4b).

High Obliquity (α ≥ 60°)
We define high obliquity models those bearing pre-existing fabrics trending to the direction of extension with an angle higher than 60°.Models NPFC-6, NPFC-7 and NPFC-8 (Figures 4c, 5a, and 5b) simulated pre-existing fabrics trending at 60°, 75° and 90°, respectively.The variability in terms of fault architecture for these models was not prominent and, in general, the structural patterns mimicked those of the homogenous reference model (NPFC-1; Figures 2c and 3a).In fact, all these models showed a reduced effect of the pre-existing fabrics on the geometry of rift-related faults: although the interaction between rift-related faults and pre-existing fabrics at their intersection still existed, the degree of influence exerted by this latter was greatly reduced.Specifically, the fabrics simply led to slight curvature of the border faults, rather than inducing their prominent segmentation and formation of soft linkages (i.e., relay structures).Antithetic faults were not offset by pre-existing fabrics nor became strongly curved: contrarily, especially in models where α was very high (e.g., NPFC-7 and NPFC-8, Figures 5a  and 5b), antithetic faults propagated to crosscut pre-existing fabrics showing no visible interaction.The effect on the depocenter segmentation was also reduced.

Increased Width of the Pre-Existing Fabrics
In order to test the effect of the increased width of pre-existing fabrics (i.e., a higher strength contrast with respect to the surrounding brittle crust), in model NPFC-9 we reproduced wider pre-existing fabrics (ca. 4 mm instead of the standard ca. 2 mm, Figure 5c) with a constant obliquity (α = 30°).This may better simulate non-discrete fabrics and rather corresponded to larger inherited weak zones or shear zones in nature.As in Model NPFC-4 (Figure 4a), these pre-existing fabrics had a remarkable impact on fault pattern and linkage, leading to a larger scale and stronger influence than in models with a standard width.Where border faults and pre-existing fabrics intersected, the pattern of the extensional structures was more complex, being marked by a more prominent segmentation and top-view curvature; a larger number of antithetic and axial faults tended to parallelize the pre-existing fabrics and the axial graben depocenter was more markedly segmented.
As a result, wider pre-existing fabrics overall exerted a more prominent control on the architecture of boundary and intra-rift faults, as well as on the segmentation and geometry of the axial graben and, hence, associated depocenters.

Statistical Analysis of Faults
Statistical analysis of models was performed with the free software FracPaQ (Healy et al., 2017) for MATLAB™, allowing quantitative analysis of the fault pattern (e.g., fault trace length and orientation) resulting from the extension.In this analysis, the fault traces and fault segments were derived from the fault line drawing of model faults, and the length of a single fault trace was defined as the sum of fault segment lengths.Consequently, in

Orientation of Faults Segments
The rose diagrams and frequency histograms of fault distribution, calculated from the orientation of different fault segments, are illustrated for the different models in Figure 6.Fault distribution is described in the geographical reference system (assuming the topmost side of the figure is the local North direction).
Models NPFC-1 (homogenous model, Figure 6a) and NPFC-2 (α = 0°, Figure 6b) showed a uniform distribution of faults, with histograms and rose diagrams characterized by a symmetrical distribution and a main peak delineating dominance of N-S faults.Notably, model NPFC-2 was characterized by a narrower distribution of fault orientation, related to a more localized deformation and a lower number of rift-related faults (see below).
Models with low to moderate obliquity (15° ≤ α ≤ 45°, i.e., models NPFC-3, NPFC-4, NPFC-5, NPFC-9, Figures 6c-6e and 6i) still displayed a dominance of N-S faults, but both histograms and rose diagrams showed a larger scatter in fault distribution; diagrams were characterized by an asymmetric shape, with an increase in the number of faults characterized by a NNE-SSW to NE-SW trend.The graph asymmetry denoted a higher number of fault segments with orientation close to the trend of the pre-existing fabric.
To better highlight the influence of pre-existing fabrics on rift faults, we performed the analysis of fault distribution in 4 cm × 4 cm target and restricted areas (see Figures 3-5) highly influenced by inheritance in four selected models (NPFC-3, NPFC-4, NPFC-5, NPFC-9, Figure 7).This analysis showed a more marked asymmetry of both rose diagrams and frequency histograms, with a large scatter of fault orientation and an overall shift toward the strike of pre-existing fabrics.This was emphasized in model NPFC-9 (Figure 7d), where the wider fabrics had a more pronounced influence on rift-related faults.
This phenomenon was more evident when plotting the average value of the fault segment trend against the α values (Figure 8a).The tendency of the fault segment trend average values presented a peak shape when 15° ≤ α ≤ 45° (with the highest value for α = 30°).In this range, the values greatly exceed the reference value of the homogenous model (Figure 8a), while when α = 0° and α ≥ 60°, their values were significantly lower than that of the homogenous model.Compared with the entire modeling area, the analysis undertaken on restricted target areas (i.e., black inset in Figures 3-5) showed higher fault segment strike values when 15° ≤ α ≤ 45°.Thicker pre-existing fabrics (square symbol in Figure 8a) led to greater fault segment re-orientation, being their control on rift-related structure more effective.
Standard deviation σ could provide a measure of the dispersion of a data set: Here,   is the average value of the finite data set x 1 , x 2 , …, x N , and a higher σ value means a more scattered data set.The standard deviation of the segment trend data set was calculated for each model to characterize the dispersion of fault segment trends.The plot of standard deviation versus α (Figure 8b) showed maximum dispersion for 15° ≤ α ≤ 45 with the highest value when α = 30° indicating a strong effect of pre-existing fabrics on controlling rift-related fault development.

Length and Number of Fault Traces and Segments
For each model, we also calculated other key parameters of faults, including the average length of fault trace (L ta ), the number of fault traces (N t ), the ratio of the average length of fault traces to fault segments (L ta /L sa ), as well as the ratio of the number of fault traces to fault segments (N t /N s ).These fault parameters have the potential to characterize the degree of complexity of the fault pattern and quantitatively describe faults linkage.Comparing models with at the same amount of extension, the shorter L ta and the larger N t mean that the extensional deformation was accommodated by more and shorter faults, rather than fewer and longer faults, which reflected a more complex geometry of the fault pattern.Similarly, a decrease in L ta /L sa and an increase in N t /N s indicated that fault segments or independently nucleated short faults were more difficult to link into a coherent and long fault trace, implying a greater probability of occurrence of complex rift-related structures (e.g., relay structures).
The above parameters also showed a significant functional relationship with the α value (Figure 9), and the fitted curve characteristics of these fault parameters were similar to those of the average fault segment strike (Figure 8a) and standard deviation (Figure 8b), presenting typical spoon shapes.In detail, when 15° ≤ α ≤ 45°, these fitting curves showed peak or valley shapes, and the values had maximum difference from the reference value of the homogeneous model.When α ≥ 60°, these curves and parameter values approached the reference value of the homogenous model.This confirmed that when the obliquity of the pre-existing fabric was in the range of 15°-45°, the inherited fabrics strongly affected the degree of fault linkage and of fault system complexity.
Results of our models confirm this and indicate that the inherited fabrics have an important impact on rift-related faults provided that the obliquity of these fabrics is α ≤ 45°.In these conditions, the most prominent effect is the segmentation of major extension-related faults and the axial depocenter; major faults are characterized by a local re-orientation, with these faults tending to curve and parallelize the pre-existing fabrics.As a consequence, the fault pattern is typically characterized by S-shaped, J-shaped, or zig-zag geometries and/or isolated short faults parallel or nearly parallel to the fabrics (Figures 3c, 4a, and 5c).Overall, the higher segmentation and complexity of the fault pattern are documented by a decrease in the average length of fault traces and a significant increase in the number of fault traces (Figures 9a and 9b), indicating that the rift structure is controlled by more and shorter faults.Also, the lower ratios of the average length of segments and the higher ratios of the number of fault traces to fault segments indicate that the linkage of faults is less developed in these models (Figures 9c and 9d).This is related to the influence of the pre-existing fabrics, which make it difficult for many isolated short faults or fault segments to link and form large faults during the process of rifting.
Conversely, when α = 0°, pre-existing fabrics are strongly reactivated, focusing deformation on a few long, linear faults which may lead to the development of a deep, longitudinally continuous axial graben.

Comparison With Previous Analog and Numerical Models
As stated in Section 1, several previous analog and numerical modeling works have been applied to the analysis of the influence of pre-existing brittle fabrics on rifting.A2 for detailed data.Some of these works (e.g., Corti et al., 2007) were designed to simulate specific geometries and patterns of pre-existing fabrics applied to selected natural examples (e.g., Western Branch of the EARS); these works did not systematically investigate the role of pre-existing brittle fabrics on rifting.Conversely, such a systematic analysis was performed in other analog (Bonini et al., 2023;Maestrelli et al., 2020;Zwaan et al., 2021aZwaan et al., , 2021b) ) and numerical (Deng et al., 2017(Deng et al., , 2018) models, whose results indicate a strong influence on rift-related faults of pre-existing fabrics with obliquity α ≤ 45°, in good agreement with our findings.
Previous analog models were deformed in normal gravity and used variable set-ups to simulate pre-existing fabrics in the brittle layers.Maestrelli et al. (2020) reproduced brittle heterogeneities by pre-cutting a sand package in brittle/ductile of rotational continental distributed extension.Despite the rotational nature of the setup, and the use of an elastic rubber band to distribute the deformation, their outcomes suggest a threshold angle of <45° for the reactivation of inherited structure, with the highest effect for pre-existing fabrics trending at 30° to the rift axis.Zwaan et al. (2021aZwaan et al. ( , 2021b) ) used both "seeds" (narrow stripes of thicker ductile layer; i.e., narrow stripes of thinner and weaker brittle crust) and cuts in the brittle layer to simulate inherited upper crustal weaknesses.Extension in these models was applied through a basal VD.Also in this case, their results showed that when α = 30°, the pre-existing fabric can be fully reactivated, having a significant impact on the architecture and morphology of the broadly distributed basins.In a recent paper, Bonini et al. (2023) examined the impact of pre-existing faults on the geometry and distribution of newly formed rift-related faults by reproducing precuts trending at different orientations and dips in purely brittle models made of clay, in which extension was driven by the movement of a basal VD.Their results showed that when the strike and dip of pre-existing faults are very close to those of an optimally oriented extensional fault, their influence on the development of the rifting basin is more significant.The discrete element numerical models by Deng et al. (2017Deng et al. ( , 2018) ) also showed that the crustal pre-existing faults in the extension background will experience full reactivation (α ≤ 30°), partial reactivation (α = 45°), and little or no reactivation (α = 60°).
Our modeling setup implements the previous analog modeling works in which extension was achieved by motion of basal plates imposing a VD (localizing boundary structures, e.g., Bonini et al., 2023;Zwaan et al., 2021aZwaan et al., , 2021b)), or stretching of an elastic foam or rubber bend (distributing deformation, e.g., Maestrelli et al., 2020), both approaches strongly affecting the stress distribution in the models and the evolution of structures.In our modeling, instead, the centrifuge forces impose a uniform stress field on the models and the different distribution of deformation is only imposed by lateral variation in strength and rheology due to the presence of the brittle and/ or ductile weakness zones (e.g., Corti (2012) for review).This allows the proper simulation of fault development and evolution in natural rift settings, by first nucleating boundary faults followed by antithetic faults forming marginal grabens, and then shifting the deformation toward the rift center to develop axial fault segments bounding a central (i.e., axial) basin (see Corti, 2012).Centrifuge modeling also implies a more natural architecture of the boundary faults, which are better able to freely propagate laterally: this in turn indicates that when the analog crust is efficiently perturbed by inherited fabrics, the resulting fault pattern surely reflects the influence of inheritance, rather than a possible control exerted by a basal VD.Moreover, the centrifuge allows the use of a stronger (more cohesive) sand, which implies better resolution (i.e., sharpness) in the fault pattern and in the simulation of pre-existing fabrics.Despite technical differences, all of the previous modeling results strongly agree with our outcomes, supporting a significant functional relationship between the influence intensity of the inherited fabrics and their obliquity.In addition to this evidence, our models suggest that inherited fabrics with low-to-medium obliquity could induce curvature in the rift-related faults trajectory, and contribute to complicating the structure of narrow rifts.
Besides the orientation with respect to the direction of extension, the relative strength/weakness of the pre-existing fabric with respect to the surrounding rock body may also play a role in reactivation, specifically in the amount of fault length that follows the pre-existing fabric (e.g., Morley & Nixon, 2016;Morley et al., 2004).This influence has not been investigated in our work and has yet to be addressed by analog modeling.

Comparison With Natural Examples From the Eastern African Rift System
We compare our models with the East African Rift System (EARS), a classic example of continental rift and a perfect location for the analysis of the influence of pre-existing fabrics on rift-related faulting (Chorowicz, 2005;Corti, 2009;Corti et al., 2007;Ebinger & Casey, 2001;Hodgson et al., 2017;Morley et al., 1999;Muirhead et al., 2016Muirhead et al., , 2019;;Rosendahl, 1987).We selected two suitable areas for our comparison -the Magadi and the Bogoria basins, Kenya Rift-and we use our models to unveil some of the characteristic and anomalous fault patterns there observed.

The Magadi Basin (α = 30°)
The Magadi Basin, located in the southern Kenya Rift (Figure 10a), is a 70-km-wide asymmetric graben filled with volcanic and sedimentary sequences spanning from 23 Ma to the present (Crossley, 1979;Muirhead & Kattenhorn, 2018).The structural geometry of this basin, and of the Kenya Rift more in general, is strongly controlled by inherited pre-existing fabrics.Many of the faults in the Magadi Basin exhibit significant bending or re-orientation, generally thought to be shaped by the NW-SE trending Aswa shear zone (Le Turdu et al., 1999;Morley, 1999b;Muirhead & Kattenhorn, 2018;Smith & Mosley, 1993).Plate kinematic models by Saria et al. (2014) indicate that the extension in the Magadi region occurs in a ESE-WNW direction, approximately perpendicular to the NNE-SSW rift axis; the Kenya rift in this sector can be therefore roughly considered as an orthogonal rift.The border faults and intra-rift faults in Magadi Basin are significantly affected by two major NNW pre-existing fabrics, trending about 30° from the axis of the rift (Figure 10b; Le Turdu et al. al., 1999;Morley, 1999b;Smith & Mosley, 1993).The Nguruman Escarpment, the western border fault of the basin, shows clear trend changes along the pre-existing fabric.Some of the intra-rift faults in the central part of the basin are  Le Turdu et al., 1999;Muirhead & Kattenhorn, 2018).
basically consistent with the trend rift axis, while other segments show significant bending and reorientation, forming curvilinear and oblique arrangement of faults (i.e., "J," "S," and "Z-shaped" patterns; Figure 10b).
Our Model NPFC-4 (and subordinately Model NPFC-9) shows a high degree of similarity to the faults pattern in Magadi Basin, supporting that the pre-existing fabrics with α = 30° have a significant impact on the geometry of the rift (Figure 10c).Where fabrics and border faults intersect, the fault trends curve to parallelize the fabrics with the formation of relay structures, an architecture consistent with the geometry of border fault systems (such as the Nguruman Escarpment).Inside the rifted area, S-shaped, J-shaped, and pre-existing fabric-parallel faults are developed and form complex fault arrays (e.g., the Kordjya fault system).
Based on the results of our analog models and previous structural studies, we propose a fault evolution for the Magadi Basin (Figure 10d) envisaging the curvature of boundary faults and the formation of complex relay ramps (incipient rifting stage) followed by the formation of initially straight axial faults, subsequently developing J, S and Z-shaped patterns during rift development, as a result of pre-existing and rift-related faults interaction.

The Bogoria Basin (α = 45°)
The main rifting in the central Kenya Rift has migrated from the west to the present active axis, centered on the Baringo-Bogoria inner trough, during the past 2 Ma (Chapman et al., 1978;Le Gall et al., 2000).The Bogoria Basin is located in the southern part of the inner trough, and its current extension direction is close to E-W (Figures 10a and 11).Three NW-SE linear discontinuity structures in the basin, namely Porumbonyanza-Ol-Kokwe (POKTZ), Wasages-Marmanet (WMTZ) and Bahati (BTZ) Transverse Zones,  8a) modified after Le Turdu et al. (1999) and Morley (1999aMorley ( , 1999b)).Symbols as in Figure 10.(b) Line drawing of a zoom area of model NPFC-9 at 10 mm of extension (the model has been mirrored flipped upside-down and rotated 8° clockwise in order to fit the natural case); note the similarities in fault geometry with respect to the faults in the Bogoria Basin.(c) Evolution of faulting in the Bogoria Basin as suggested by the comparison with analog models and previous structural studies ( Le Turdu et al., 1999;Riedl et al., 2020).
have been interpreted as pre-existing fabrics laying in the deep basement, according to gravity and aeromagnetic data (Figure 11a; Le Gall et al., 2000;Le Turdu et al., 1999;Hautot et al., 2000;Smith & Mosley, 1993).The angles between discontinuities and the rift axis are about 40°-50°, so the Bogoria Basin can be regarded as a natural rift example with the pre-existing fabrics trending with α = 45°.These three inherited linear discontinuities have a significant impact on the border and intra-rift fault systems (Figure 11a).The Emsos Fault, the most prominent structure in the basin, is located east of Lake Bogoria and presents an evident S-shape.The other two faults nearby, the Solai Fault and Chui Faults, also bend at tips and connect to the NW-SE trending main faults at the north, which are apparently disturbed by the WMTZ (Grimaud et al., 1994;Le Turdu et al., 1999;Morley, 1999b).In the north, the Laikipia Escarpment, the eastern boundary of the basin, is also bent and segmented under the influence of the POKTZ.On the Maji Mota grid fault zone inside the basin, some intra-rift faults are not perpendicular to the extension direction but deflected by 10-20° toward the discontinuity trend, where they are located close to BTZ, WMTZ and Emsos Fault (Grimaud et al., 1994;Le Turdu et al., 1999).
Similar fault patterns occur in our model NPFC-5 (α = 45°), with these architectures being more evident in specific areas of the model (Figure 11b).Specifically, the existence of the pre-existing fabric with α = 45° hinders the lateral propagation of the main fault traces, and the trends of the fault segments are affected by pre-existing fabrics resulting in the S-shaped fault patterns.At the same time, the pre-existing fabric of α = 45° also causes reorientation of intra-rift faults.
We therefore suggest the following evolution scheme for the Bogoria Basin (Figure 11c).At the beginning of regional extensional stress, the rift border faults began to nucleate and propagate laterally.With ongoing extension, the trends of boundary fault segments are influenced by the inherited discontinuities and result in fault bending and the development of relay ramps.At this time, the intra-rift faults begin to develop, and the minor faults adjacent to the fabric are influenced, their trend being rotated toward pre-existing fabrics, which further complicates the intra-rift faulting system.

Conclusions
We studied the influence of inherited fabrics striking at different angles to the direction of extension on rift-related structures by means of centrifuge analog models.The modeling results indicate the following main conclusions: 1. Inherited brittle fabrics have a significant impact on the geometry of rift-related structures: this influence is evident when α ≤ 45°, where α is the angle between the trend of the inherited fabric and the rift trend, and becomes negligible α ≥ 60°. 2. In these favorable conditions, inherited fabrics induce the re-orientation of rift-related fault segments giving rise to J-shape, S-shape, and Z-shaped top-view fault geometries, as well as fabric-parallel fault branches.3. Inherited fabrics can complicate the architecture of narrow rifts, facilitating fault segmentation, the formation of relay ramps, small-scale fault steps and fault blocks, and controlling the location, pattern and segmentation of the basin depocenter.4. The results of our experiments display strong similarities and well explain the evolution and architecture of faults in portions of the East African Rift System, affected by the occurrence of pre-existing fabrics, such as the Magadi Basin and Bogoria Basin (Kenya Rift).

Appendix A
Figures A1 and A2; Tables A1 and A2.

Figure 1 .
Figure 1.Cartoon showing the modeling setup and the monitoring procedure.(a) 3D-view of the setup.UC, Upper Crust; LC, Lower Crust; WLC, Weak Lower Crust; LVL, Low-Viscosity Layer.See text for the details of the different materials used to simulate all these layers.The pre-existing fabrics (with dashed lines) are reproduced by cutting the sand composing the upper crust with a knife.The models are built on L-shaped Plexiglas walls, laterally confined by 1.5 mm-wide removable spacers on both sides.The box in the lower right corner shows the strength profiles of the model for the normal and weak crust.Here, normal crust indicates an ideal continental crust with no weak zones.(b) Deformation principle of the centrifuge models.The models are placed horizontally in the centrifuge in an internal rotor; during the centrifuge runs, the centrifugal acceleration forces the models to rotate to a vertical position.The centrifugal forces always act normally to the model surface playing the same role as gravity in nature.Before the centrifuge run, two removable spacers are removed leaving a space at both sides of the model; during the centrifuge run, the model is forced to expand to fill the lateral gaps, simulating extension.(c) Top-view geometry of the model.(d) 3D-view of the photogrammetric procedure to monitor deformation (see Maestrelli et al. (2021a), Maestrelli et al. (2021b) and the text for details).

Figure 2 .
Figure 2. Top-view photos and line-drawing of structures of models NPFC-1 and NPFC-4.α refers to the angle between the pre-existing fabric and the rift trend (see text for details).The gray dashed lines show the location of pre-existing fabrics.EXT, extension.

Figure 3 .
Figure 3. Digital Elevation Models (DEM) of the model surface and line drawing of structures of NPFC-1 to NPFC-3 at the end of deformation.The black boxes indicate the 4 cm × 4 cm zoom areas used for the statistical analysis of faults in Figures 7 and 8.Other symbols as in Figure 2.

Figure 4 .
Figure 4. Digital Elevation Models of the model surface and line drawing of structures of NPFC-4 to NPFC-6 at the end of deformation.Symbols as in Figure 3.

Figure 5 .
Figure 5. Digital Elevation Models of the model surface and line drawing of structures of NPFC-7 to NPFC-9 at the end of deformation.Symbols as in Figure 3.

Figure 6 .
Figure 6. Rose diagrams (top) and histograms (bottom) of fault orientation in the different models (see text details).The pink solid lines in the rose diagram denote the mean value of fault distribution, and the red dashed lines in both the rose diagram and histogram show the orientation of the pre-existing fabrics.The green curves in histograms are the best-fit curves generated by shape-preserving interpolation.

Figure 7 .
Figure 7. Rose diagrams and histograms of fault orientation calculated in the zoom area of the models which are highly influenced by pre-existing fabrics, illustrated in Figures 3-5.

Figure 8 .
Figure 8. Graphs of (a) average segment trend and (b) standard deviations plotted versus α in each different model.A higher average segment trend indicates stronger reorientation of fault segments, while a higher standard deviation value means a more scattered segment trend data set.The pink symbols illustrate the data of the whole model, while the blue ones illustrate those of the zoom area.The circles illustrate the models with a standard fabric width, while squares denote the model with wider fabrics.The red and blue straight lines represent the no-fabric model values of the whole model and the zoom area, respectively.The dashed curves are the tendency curves of the data of the models with normal fabrics, which are fitted by the fourth-order polynomial.The gray area denotes the peak area of the tendency curve.See TableA1for detailed data.

Figure 9 .
Figure 9. Statistical analysis of fault parameters plotted against α.The different parameters are as follows: (a) the average length of fault traces, (b) the number of fault traces, (c) the ratio of the average length of fault traces and fault segments, and (d) the ratio of the number of fault traces and fault segments.Symbols as in Figure8.The dashed curves are the tendency of the data of the models with normal fabrics, which are fitted by the fourth-order polynomial.The gray area is the peak area/ trough area of the tendency curve.See TableA2for detailed data.

Figure 10 .
Figure 10.Comparison of model NPFC-9 (α = 30°) with the fault pattern characterizing Lake Magadi, in the Kenya Rift, East African Rift System.(a) Main border faults, modified from Torres Acosta et al. (2015) and Richter et al. (2021), indicated by white lines superimposed on Digital Elevation Model (DEM) of the Kenya Rift.White arrows show present-day full-spreading rate based on plate kinematic models by Saria et al. (2014) and modified from Riedl et al. (2020).(b) Structural map of Magadi Basin.Inferred location of pre-existing fabrics is shown by gray dash lines.The border faults and intra-rift faults are drawn in white from Muirhead et al. (2015), and the faults influenced by fabrics are highlighted in yellow.Focal mechanisms of earthquakes are from Weinstein et al. (2017).(c) Line drawing of model NPFC-9 at 10 mm of extension (the model is mirror flipped upside-down and rotated 10° clockwise in order to fit the natural case); note the good consistency with the Magadi Rift fault pattern.The faults in the model influenced by pre-existing fabrics are highlighted by wider red lines.(d) Evolution of faulting in the Magadi Basin as suggested by the comparison with analog models and previous structural studies (Le Turdu et al., 1999;Muirhead & Kattenhorn, 2018).

Figure 11 .
Figure 11.(a) Structural map of the Bogoria Basin, Kenya Rift (location in Figure8a) modified after LeTurdu et al. (1999) andMorley (1999aMorley ( , 1999b)).Symbols as in Figure10.(b) Line drawing of a zoom area of model NPFC-9 at 10 mm of extension (the model has been mirrored flipped upside-down and rotated 8° clockwise in order to fit the natural case); note the similarities in fault geometry with respect to the faults in the Bogoria Basin.(c) Evolution of faulting in the Bogoria Basin as suggested by the comparison with analog models and previous structural studies (Le Turdu et al., 1999;Riedl et al., 2020).

Figure A1 .
Figure A1.The DEMs and line drawing diagrams of the 4 cm × 4 cm square target area.

Table 1
Overview of the Performed Analog Models

Table A1
Statistical Analysis Results of Fault Segment TrendNote.N t : Number of fault traces; L t max : maximum length of fault trace; L t min : minimum length of fault trace; L t a : average length of fault traces.N s : Number of fault segments; L s max : maximum length of fault segment; L s min : minimum length of fault segment; L s a : average length of fault segments.