Structural inheritance in amagmatic rift basins: Manifestations and mechanisms for how pre-existing structures influence rift-related faults

In the context of rift basin formation, structural inheritance describes the influence of pre-existing structures on new rift-related structures, including faults. Pre-existing structures in the crust or upper mantle can determine where rift basins form. As these basins evolve


Introduction
Continental rifts commonly form in lithosphere with a pre-existing structural framework.Given the appropriate stress orientations, stress magnitudes, fluid pressures, and thermal gradients, pre-existing structures affect the development of rifts and rift-related structures (e.g., Wilson, 1966;Morley, 1995;Krabbendam and Barr, 2000;Schumacher, 2002;Chenin and Beaumont, 2013;Fossen et al., 2016;Schiffer et al., 2018Schiffer et al., , 2020)).This structural inheritance (referred to as "rejuvenation" by Holdsworth et al., 2001a) operates at multiple scales in both frictional and viscous layers of the crust and in the lithospheric mantle (Fig. 1).
Lithospheric-scale (i.e., plate-scale) weaknesses up to thousands of kilometres in length, such as shear zones, sutures, and plumes or hot spots, span the frictional-viscous transition.These weaknesses can localise or segment entire rift systems, depending on their orientation with respect to the overall rifting direction; the influence of plumes or hot spots also depends on their location with respect to the propagating rift (McConnell, 1972;Daly et al., 1989;Versfelt and Rosendahl, 1989;Wheeler and Karson, 1989;Piqué and Laville, 1996;Doré et al., 1997;Holdsworth et al., 2001a;Miller et al., 2002;Gibson et al., 2013;Molnar et al., 2017;Peace et al., 2018b;Heron et al., 2019;Hopper et al., 2020;Amigo Marx et al., 2022).Lithospheric-scale weaknesses also modulate the evolution of the lithosphere and the magmatic budget during rifting, in some cases up to the stages of continental break-up and passive margin development (e.g., Dunbar and Sawyer, 1989;Buiter and Torsvik, 2014;Petersen and Schiffer, 2016;Gouiza and Paton, 2019;Gouiza and Naliboff, 2021;Brune et al., 2023).The most prominent present-day example of plate-scale structural inheritance is the East African Rift System.Here, south of the Main Ethiopian Rift, the rift system bifurcates into western and eastern branches, which are co-located with preexisting, relatively weak zones around Archean cratons (Fig. 2; structural inheritance in the East African Rift System is discussed in detail in Section 4.3).
At length scales of tens of kilometres or less, pre-existing structures influence the orientations, distributions and growth of basin-bounding and intra-basinal rift-related faults, as well as the geometry and internal architecture of rift basins.For example, reactivated faults or fabrics in the brittle crust may be active during the early basin-forming stage, thereby controlling the location and shape of sediment depocentres (Fig. 3) (e.g., Morley et al., 2004;Deng et al., 2020).Some rift-related faults can be misoriented with respect to inferred plate motion directions, caused by the presence of pre-existing fabrics that strike obliquely to the far-field extensional strain (e.g., Morley et al., 2004;Lyon et al., 2007;Wilson et al., 2010).Complex fault patterns can reflect the evolving interplay between faults that form within locally perturbed stress fields around pre-existing structures, and those that are not influenced by inheritance (Delvaux et al., 2012;Hodge et al., 2018;Muirhead and Kattenhorn, 2018) (Fig. 3a).
The focus on reactivation has resulted in the common synonymous use of the terms "structural inheritance" and "reactivation"; in some cases, the two terms are used interchangeably (e.g., Corti et al., 2007;Manatschal et al., 2015)."Structural inheritance" is a useful, general, and descriptive term that broadly covers all influences of pre-existing structures on younger geological features.However, reducing structural inheritance to reactivation in the context of rift basins research is problematic, as it does not acknowledge other mechanisms by which pre-existing structures influence rift-related deformation.It also suggests that there is limited or no influence of pre-existing structures in areas with no evidence of reactivation (as defined by Holdsworth et al., 1997).
A number of field and modelling studies point to the re-orientation of strain (Corti et al., 2013b;Philippon et al., 2015;Hodge et al., 2018;Samsu et al., 2021) and stress (Bell, 1996;Morley, 2010;Tingay et al., 2010a) as mechanisms of structural inheritance that are distinct from reactivation.Through strain or stress re-orientation, pre-existing structures can influence deformation localisation and distribution without exhibiting significant (i.e., observable) signs of repeated slip or displacement on the pre-existing structures themselves.These mechanisms, which are more subtle than reactivation, may be more common in rift basins than the existing body of literature on structural inheritance suggests.
By distinguishing between structural inheritance mechanisms, we can better infer the different implications that they have for the kinematics and connectivity of rift-related faults.For example, consider pre-Fig.1.Schematic strength profile of the "typical" continental lithosphere, including the frictional-viscous transition, as well as the primary rheological controls on "rejuvenation" (i.e., structural inheritance), strain distribution, and types of rocks or fabrics that act as pre-existing structures at different lithospheric depths.Modified after Sibson (1977) and Holdsworth et al. (2001aHoldsworth et al. ( , 2001b)).
A. Samsu et al. existing structures at mid-to lower-crustal depths (such as shear zones) that strike obliquely to the regional extension direction.When these preexisting structures are reactivated, they normally experience oblique slip and can be hard-linked to younger, overlying, rift-related faults that are influenced by them (Fig. 4a).However, a pre-existing mid-to lower crustal structure that does not experience significant reactivation can still re-orient the local extension direction, without necessarily being hard-linked to the younger rift-related faults (Fig. 4b).
A more complete picture of different inheritance mechanisms at the basin to sub-basin scale can help to clarify the mechanical controls on basin evolution and open opportunities to: (i) uncover the characteristics of buried structures that are commonly poorly resolved in geophysical surveys; (ii) better understand the structural evolution of basins at rifted margins; and (iii) provide additional constraints on plate reconstructions.Understanding the potential effect of pre-existing structures on younger fault networks also has implications for seismic hazards assessment (e.g., Fonseca, 1988;Wedmore et al., 2020b;Hecker et al., 2021), geothermal energy (e.g., Schumacher, 2002;Bertrand et al., 2018;Dávalos-Elizondo and Laó-Dávila, 2023), mineral exploration (e.g., Rowland and Sibson, 2004), and CO 2 and spent nuclear fuel storage (e.g., Barton and Zoback, 1994;Andrés et al., 2016).

Scope and terminology
In this review, we summarise the multifaceted ways in which preexisting structures control fault system geometry during rift basin formation in magma-poor rifts.Pre-existing structures refer to structures that already existed prior to the current rifting event.In the context of this review, we consider the crust to be rheologically layered with a thermally controlled transition that separates an upper frictional and lower viscous regime (sensu Handy et al., 2007;Fig. 1).Hence, preexisting structures will include discrete discontinuities (e.g., the contact between a dyke and surrounding host rock, Table 1a; a fault or fault zone, Table 1b; the boundary between two rheologically distinct terranes, Table 1e), pervasive strength anisotropies (e.g., penetrative metamorphic or rift fabrics from previous collisional or extensional events, Table 1c and d), and lithospheric-scale weaknesses in the viscous lower crust or lithospheric mantle (Table 1f and g).The influence of these different types and scales of pre-existing structures is discussed in Section 3.1.In a few cases, we specifically discuss the influence of preexisting "basement" structures on rift-related faults in the sedimentary "cover" (e.g., case studies on the influence of pre-existing intra-basement shear zones on rift faults; Section 3).Here we refer to basement as an assemblage of igneous or metamorphic rocks directly underlying the sedimentary cover; this terminology is commonly used in the petroleum and geothermal energy industries.The sedimentary cover is defined as basin fill related to the current rifting event (or earlier rifting events in the context of multiphase rifts).
We explore mechanisms that lead to "misorientation" of rift-related faults at the basin to sub-basin scale, which can vary depending on the characteristics of the pre-existing structures (e.g., orientation, geometry, size, and rheology).Here, the term misorientation is used to contrast the orientation of a rift-related fault to that of an "optimally oriented" normal fault formed under Andersonian fault mechanics (Anderson, 1905;Section 3.4).In the context of this contribution, an optimally oriented fault is one that strikes orthogonal to the regional extension direction and has a moderate dip.An example of a misoriented fault, which strikes obliquely to the far-field extension direction due to an underlying pre-existing weakness, is illustrated in Fig. 4.
Pre-existing structures that are moderately dipping and orthogonal to the regional extension direction (i.e., optimally oriented) can influence fault growth (Section 3.1.5).However, it is difficult to evaluate if a rift-related fault has been influenced by structural inheritance in these cases, as the fault could have formed in that orientation in the absence of a pre-existing structure (Smith and Mosley, 1993).By the same argument, structural inheritance from optimally oriented structures should not lead to marked variations in fault geometry relative to faulting of intact crust.Hence, we mainly consider pre-existing structures that are "oblique" (with respect to the far-field extension direction) and/or gently or steeply dipping.
In this review, we focus on the development of rift basins dominated by faulting rather than magmatic structures.Although spatial links between continental breakup and major flood basalt provinces have been recognised for several decades (e.g., Morgan, 1971;Courtillot et al., 1999), requiring some interplay between rifting and magmatism, it varies between case studies whether magmatism controls or is controlled by the structure of the rift.For example, some recent volcanic structures in the East African Rift System in Ethiopia are aligned with pre-existing structures that are oblique to the rift axis (Lloyd et al., 2018;Franceschini et al., 2020), implying that magma transport was controlled by inherited structures.In those examples, and in most other examples reviewed by Buiter and Torsvik (2014), rifting starts before magmatism, and magmatic activity is regionally focussed within thinned lithosphere, and locally controlled by a combination of new and inherited structures.Although we recognise that magmatism can modulate the occurrence and timing of reactivation of pre-existing structures (e.g., Muirhead and Kattenhorn, 2018), we focus here on the development of rift basins and rift structures prior to any important  (Hodge et al., 2018;Daly et al., 2020;Styron and Pagani, 2020), microplate boundaries (Stamps et al., 2021;Wedmore et al., 2021), Holocene volcanoes (Global Volcanism Project, 2013), earthquakes (M W ≥ 5, 1875-2015 from the Sub-Saharan Africa Global Earthquake Model (SSA-GEM) catalogue; Poggi et al., 2017), and the locations of Archean-Paleoproterozoic cratons (Van Hinsbergen et al., 2011).MER, Main Ethiopian Rift; TkR, Turkana Rift; KeR, Kenya Rift; AR, Albertine Rift; KvR, Kivu Rift; TR; Tanganyika Rift RR, Rukwa Rift; MR, Malawi Rift; OR, Okavango Rift; TC; Tanzanian Craton; BB, Bangweulu Block; ZC, Zimbabwe Craton; KC, Kaapvaal Craton.Underlain by GTOPO30 Digital Elevation Model (DEM).effects that may be related to magmatic activity.We speculate that the structural associations identified in this review may become conduits for future rift-related magmatism, but an in-depth discussion of this topic is beyond the scope of the present contribution.

Examples and insights from nature and models
In this section, we summarise the spatial, geometric, and kinematic relationships between pre-existing structures and rift-related cover faults, based on observations from geophysical data and outcrops.Analogue and numerical models allow us to study rift and basin-forming processes over geological timescales in 2D and 3D, complementing observations from natural rifts (e.g., Allemand and Brun, 1991;Brun, 1999;Corti, 2012;Brune et al., 2017;Molnar et al., 2020;Maestrelli et al., 2022;Zwaan and Schreurs, 2022).Modelling also gives us the flexibility to examine the influence of various model parameters both separately (e.g., rheological layering, obliquity, geometry of inherited weakness) and together (Zwaan et al., 2016(Zwaan et al., , 2021a(Zwaan et al., , 2021b;;Zwaan and Schreurs, 2017).The modelling approach is especially useful for distinguishing between the relative contributions of oblique rift kinematics and inherited structures in shaping rift basins, as each on its own can create a transtensional system, resulting in rift-related faults that are oblique to the inferred paleo-extension direction.
The models we discuss here demonstrate inheritance-driven obliquity, where the model includes pre-existing weaknesses that strike obliquely to the bulk extension direction.This setup is distinct from boundary-driven obliquity, where bulk extension is oblique to the model boundaries (e.g., Tron and Brun, 1991;Keep and McClay, 1997;Autin et al., 2010).Most of the analogue models we highlight are simplified, multi-layer, crustal or lithospheric-scale experiments comprising a brittle upper crust, ductile lower crust, and in some examples a ductile lithospheric mantle.In this case, "ductile" is defined as exhibiting spatially continuous deformation at the scale of observation, and the ductile materials simulate deformation in the viscous layers of the lithosphere, although the rheology may be different (Wang, 2021).Preexisting structures in analogue models are implemented as two rheologically distinct blocks, discrete weak zones, or pervasive anisotropy (see Table 2 for an overview).Based on these models, we discuss the impact of lithospheric or crustal strength variations and inherited weaknesseswith different strike orientationson deformation localisation, deformation partitioning, and the local 3D strain field.

Map view relationships
Structural inheritance in rift basins is typically recognised through two observations in map view: "spatial co-location" and "geometric  2020), (c) modified from Morley et al. (2004).
similarity" between rift-related faults and pre-existing structures (Fig. 5) (e.g., Laó-Dávila et al., 2015;Fazlikhani et al., 2017;Dawson et al., 2018;Collanega et al., 2019;Wedmore et al., 2020b;Bosworth and Tari, 2021).Spatial co-location refers to the occurrence of rift-related faults above or in the vicinity of a pre-existing structure.Geometric similarity (sensu Holdsworth et al., 1997) is characterised, in map view or cross-section, by rift-related fault traces that trend parallel to preexisting structures; or, more rigorously in 3D, by rift-related faults that have the same strike and dip directions as pre-existing structures (Fig. 6a and b).
A growing body of work provides compelling evidence that riftrelated deformation in the active East African Rift System broadly follows Proterozoic age structures, with some younger rift basins also colocating with basins that formed during a previous Mesozoic rifting event (e.g., McConnell, 1967;Versfelt and Rosendahl, 1989;Castaing, 1991;Kolawole et al., 2021a;Wedmore et al., 2022).The multi-scale impacts of structural inheritance on rift-related structures in the East African Rift System is discussed in detail in Section 4.3.Below we highlight several other geographic areas in which structural inheritance has been recognised through the spatial co-location and geometric similarity between pre-existing structures (e.g., crustal shear zones) and rift-related faults (see Table 1 for more examples): • New Zealand: The strike of the Terrane Boundary Fault in the Great South Basin (offshore South Island), which formed during Late Cretaceous extension (i.e., Gondwana break-up), is parallel to the Devonian-Cretaceous Terrane Boundary Shear Zone (Mortimer, 2004) that separates the Median Batholith and Western Province terranes.Seismic reflection data show that the Terrane Boundary Fault links with the crustal-scale (or potentially lithospheric-scale; e. g., Muir et al., 2000;Mortimer et al., 2002) Terrane Boundary Shear Zone at depth (Phillips and McCaffrey, 2019) (Fig. 7).Farther north in the Taranaki Basin (offshore North Island), the Terrane Boundary Shear Zone and an adjacent boundary between the Median Batholith and Eastern Province terranes coincide spatially with the traces of the Cenozoic Cape Egmont and Taranaki fault systems (Muir et al., 2000).• North Atlantic: The Laerdal-Gjende fault system is co-located and hard-linked with the Devonian Hardangerfjord Shear Zone, which is associated with a major Moho offset (Faerseth et al., 1995;Fossen and Hurich, 2005;Fossen et al., 2014) (Fig. 8).Similarly, Permo-Triassic basin-bounding rift faults offshore the north coast of mainland Scotland exhibit geometric similarity with deep crustal reflectors in the underlying crystalline basement (Wilson et al., 2010 and references therein).• Northeastern Brazil, south Atlantic: From aerial imagery and in the field, Kirkpatrick et al. (2013) and Vasconcelos et al. (2019) observed km-scale traces of Mesozoic rift faults, which trend parallel to Precambrian Brasiliano shear zones and crustal-scale anomalies interpreted from magnetic and gravity data.
Plate-scale structural inheritance (also known as tectonic inheritance; Wilson, 1966;Thomas, 2006;Audet and Bürgmann, 2011;Buiter and Torsvik, 2014;Petersen and Schiffer, 2016) is demonstrated by the spatial co-location of younger rift systems with pre-existing crustal or lithospheric-scale weaknesses (Fig. 2).While not the focus of this review, tectonic inheritance exerts a first-order control on where riftsand therefore rift basins and rift-related faultsform in the first place.Rift initiation and propagation exploits pre-existing mechanical (including thermal) weaknesses, so that rifts commonly follow the trends of older rifts and/or highly deformed orogenic belts at craton boundaries (Table 1f).For example, most Phanerozoic rift basins in Africa are located within Proterozoic orogenic belts that may be linked to deep-seated weaknesses in the lithospheric mantle (Daly et al., 1989;Versfelt and Rosendahl, 1989;Tommasi and Vauchez, 2001; Table 1g).

Fig. 4.
A pre-existing weakness that strikes obliquely to the far-field extension direction can influence the orientation and kinematics of a rift-related, normal fault; as result of this interaction, the rift-related fault is "misoriented" with respect to the far-field extension direction.Different inheritance mechanisms can have different impacts on fault kinematics and linkage between the rift-related fault and pre-existing weakness, despite the two exhibiting geometric similarity in map view in both scenarios.Reactivation of the pre-existing weakness (a) is commonly associated with oblique slip along the pre-existing weakness and rift-related fault (e.g., Morley, 1995;Corti et al., 2007), in addition to hard linkage between the two structures (Phillips et al., 2016).A second mechanism through which the pre-existing weakness can influence rift-related faulting is local re-orientation of the far-field strain (b), which may result in dip-slip kinematics along the rift-related fault (Corti et al., 2013b;Philippon et al., 2015).Geometric similarity Northern Thailand (Morley et al., 2004); North Sea Rift (Faerseth et al., 1995;Phillips et al., 2016;Fazlikhani et al., 2017); offshore New Zealand (Muir et al., 2000;Collanega et al., 2019;Phillips and McCaffrey, 2019); onshore New Zealand ( Villamor et al., 2017); East African Rift System (Laó-Dávila et al., 2015;Dawson et al., 2018); East Greenland Rift System (Rotevatn et al., 2018); onshore and offshore Norway (Fossen and Hurich, 2005;Fossen et al., 2014;Fossen et

Table 2
Various ways in which natural pre-existing crustal and mantle/lithospheric heterogeneities are implemented in analogue models.Several numerical modelling studies, in which the impacts of similar types of heterogeneities were investigated, are referenced in the last column."Discrete" and "pervasive" denote the distribution of the heterogeneities at the scale of the model.

Cross sectional relationships
Geophysical data can provide insight into the geometric relationships between pre-existing structures and rift-related faults at depth, complementing map view observations.Phillips et al. ( 2016) illustrated three types of two-dimensional (2D) cross-sectional relationships between a pre-existing structure and younger, rift-related faults -"exploitative, merging, and cross-cutting" relationshipsbased on seismic reflection data from offshore southern Norway (Fig. 6).These relationships were identified from pre-existing, basement weaknesses (i.e., shear zones) and rift-related faults that have the same strike and dip direction.They used kinematic analyses of mapped faults to determine the history of fault activity and infer whether pre-existing shear zones were reactivated as the younger faults formed.Phillips et al. (2016) showed that an exploitative relationship is characterised by a throughgoing structure that links a pre-existing structure and rift-related fault.Based on the physical linkage between shear zone-internal reflectors and younger rift-related faults, they inferred that the rift-related faults initiated in relatively weak mylonitic rocks (within broader shear zones) and propagated upwards into the sedimentary cover.A similar observation of such an exploitative relationship was made by Collanega et al. (2019) in the Taranaki Basin (offshore North Island, New Zealand), except that it was the damage zone above a pre-existing fault that was reactivated.These two case studies suggest that reactivation (of a discrete, pre-existing structure) is the underlying mechanism behind an exploitative relationship between a pre-existing structure and rift-related fault (Fig. 6a).
Merging and cross-cutting relationships (Fig. 6b) differ from an exploitative relationship in that the rift-related fault nucleates above the pre-existing structure and propagates downwards until they intersect.In a merging relationship, the rift-related fault nucleates within the hanging wall of the basement structure andbecause of its steeper dipmerges at depth with the more gently dipping basement structure (Phillips et al., 2016).In a cross-cutting relationship, the rift-related fault may inherit the strike and dip direction of the basement structure but offsets it at depth.For example, the Mesozoic rift-related Dombjerg Fault (East Greenland Rift System) locally strikes parallel to the more gently dipping Caledonian Kildedalen Shear Zone but offsets it farther down-dip (Rotevatn et al., 2018).Phillips et al. (2016) attribute merging and cross-cutting relationships to strain re-orientation by a preexisting basement structure that has been reactivated (Fig. 6b).

Subtle indicators of inheritance impacting fault orientation
The influence of basement heterogeneities has also been invoked in areas where geometric similarity is not observed, but instead: (i) the strikes of coeval normal faults vary within a relatively small area (on the order of several km) (e.g., Morley, 2010;Reeve et al., 2015) (Fig. 9), (ii) normal fault strikes are oblique to the strikes of basement structures and not perpendicular to the inferred regional extension direction (Fig. 6c and Fig. 10) (Samsu et al., 2019), and/or (iii) fault strikes vary across areas that overlie different basement terranes (see Fig. 2 in Wilson et al., 2010).In the absence of evidence of reactivation, which is normally inferred from geometric similarity and other kinematic or chronostratigraphic indicators (Holdsworth et al., 1997), variable rift fault strikes that are oblique to pre-existing structures may indicate the subtle influence of basement rocks with fabrics that are oblique to far-field rifting directions.
In the brittle part of the crust, local perturbations of the regional stress field can be attributed to lateral variations in the elastic properties of rocks (Bell, 1996 and references therein).Deviation from the far-field or regional stress trajectories occurs because the principal stresses are deflected when they cross an interface between two materials with contrasting elastic properties (e.g., Zhang et al., 1994;Morley, 2010;Zang and Stephansson, 2010) (Fig. 11).Stress perturbations around a pre-existing weakness or discontinuity (e.g., a fault or damage zone) have been observed in photoelastic, numerical, and rock deformation experiments.In the field, they are reflected by curving of joints near a pre-existing fault (Cruikshank and Aydin, 1995;Muirhead and Kattenhorn, 2018;Samsu et al., 2020) or variable strain axes and kinematics of secondary, smaller-scale fault populations around a larger fault (Riller et al., 2017;Maerten et al., 2002).
We can invoke basement influence on rift-related faults in the overlying cover by considering stress coupling between the two units.Bell (1993Bell ( , 1996) ) proposed that stress orientations in a sedimentary unit can "exhibit the signature" of underlying rocks, if there is no intervening weak unit that acts as a mechanical detachment.He refers to this coupled system as an "attached stress regime" (Fig. 11c) and draws on an example from the Labrador Shelf (offshore eastern Canada), where the in-situ maximum horizontal stress measured from borehole breakouts is similarly oriented to the focal mechanism P-axis of a 1971 earthquake with an epicentre located in the basement.In an attached stress regime, we can infer that any deflection or deviation of the far-field stress within the basement rocks would be transferred onto the directly overlying sedimentary unit(s) and accommodated by new brittle structures (i.e., faults and other fractures) during rifting.Such mediation of stresses from basement to cover is apparent in the Lake Rukwa area of the East African Rift System.Here, Morley (2010) suggested that the NW-SE trending Precambrian basement foliation has locally rotated the regionally dominant N-S maximum horizontal stress, resulting in similar NW-SE trends for the present-day maximum horizontal stress direction (Delvaux and Barth, 2010;Delvaux et al., 2012) and Cenozoic riftrelated faults.In contrast, where a mechanically weak unit (e.g., shale-dominated unit, salt, or low-angle fault) is present between basement and cover rocks, the in-situ maximum horizontal stresses tend to show more variable orientations ("detached stress regime" in  (2009).A similar zigzag fault pattern has been observed in other parts of the EARS (e.g., Lake Tanganyika, Lezzar et al., 2002;Malawi Rift, Hodge et al., 2018).Fig. 11c).

Basement strength variations impacting fault propagation and distribution
Lateral variations in the strength of basement rocks control the propagation and distribution of rift-related normal faults.For example, the NW-trending Southern Sudan Rift terminates abruptly against the NE-trending Central African fault zone, which follows the trace of the steep Late Proterozoic Foumban Shear Zone (Daly et al., 1989).Farther south, the northern tip of the western branch of the East African Rift   At the basin scale, the propagation of a normal fault can be inhibited by a relatively strong basement block when the lateral boundary between the weak and strong units is at a high angle to the fault strike.In the Great South Basin (offshore South Island, New Zealand), Phillips and McCaffrey (2019) documented two styles of normal faulting near the Terrane Boundary Fault, which separates the dominantly sedimentary Western Province from the dominantly plutonic Median Batholith.Within the hanging wall of the Terrane Boundary Fault, a largedisplacement normal fault within an Upper Cretaceous sedimentary unit splays into a system of low-displacement segments as it approaches a structural high in the mainly granitic basement.
Analogue and numerical models similarly demonstrate strain partitioning in heterogeneous lithosphere during rifting.In a multi-layer model, strain distribution during extension is attributed to the coupling between the brittle and ductile model layers, which depends on the applied strain rate and mechanical layering (i.e., thermal structure) of the model lithosphere (Kusznir and Park, 1986;Cowie et al., 2005;Wijns et al., 2005;Sokoutis et al., 2007;Zwaan et al., 2021b).This strain distribution determines where basin-bounding faults and accommodation space are created during rifting.Extension of two laterally juxtaposed crustal domains of different integrated strengths (i.e., a weaker basement next to a stronger basement) results in earlier strain localisation and more widely spaced and higher displacement faults in the weaker domain (Phillips et al., 2023;Samsu et al., 2021).When the domain boundary strikes perpendicular to the extension direction, greater strain localisation above the weaker domain leads to rift margin asymmetry (Corti et al., 2013a;Beniest et al., 2018).

Pre-existing weaknesses impacting fault growth
It is now generally observed that the growth of individual normal faults follows a two-to three-stage process: (1) the full fault length is established relatively early in an individual fault's history; (2) after the full length is established, displacement accrual occurs with no further fault lengthening; and (3) possible lateral tip retreat (e.g., Walsh et al., 2002;Jackson and Rotevatn, 2013;Nicol et al., 2017;Rotevatn et al., 2018;Lathrop et al., 2021Lathrop et al., , 2022)).During the first stage of fault growth, lateral propagation of normal faults may be restricted by pre-existing structures that are oriented at a high angle to the fault propagation direction (Tranos et al., 2019;Kolawole et al., 2022).Faults that acquire their full length at low displacement (i.e., constant fault length growth model) have been linked to the exploitation of geometrically similar, pre-existing crustal weaknesses (i.e., reactivation; Nicol et al., 2005;Vétel et al., 2005;Paton, 2006;Whipp et al., 2014;Rotevatn et al., 2018;Williams et al., 2022), with foliation-parallel normal faults reaching lengths >40 km within a few earthquake cycles (Hecker et al., 2021).However, rapid normal fault lengthening is also observed where there is no evidence for faults following pre-existing weaknesses, and so structural inheritance is not necessarily a prerequisite for this growth mechanism (Rotevatn et al., 2019;Lathrop et al., 2022).Hence, rapid lengthening of optimally oriented normal faults is only equivocal evidence for structural inheritance, as these faults may have grown this way without the influence of a geometrically similar pre-existing structures.

The scale of observation determines how we recognise inheritance
When structural inheritance occurs, its expression may not be recognisable at all scales.The activation of >1 km-long or km-wide weaknesses in lower levels of the crust can result in rift-related faults that are spatially co-located and geometrically similar with the reactivated weaknesses (Fig. 13a and b).However, rift-related faults show a more complex geometry at the sub-km scale (Fig. 13c and d).Outcrop observations suggest that the influence of crustal-scale basement weaknesses is less prominent at the meters scale, which has been attributed to the increasing complexity of fault zone architecture as faults accommodates greater amounts of strain (Kirkpatrick et al., 2013).While fault initiation is controlled by grain-scale anisotropy, the coalescence of fault segments and the development of fault core rock (i.e., cataclasite and fault gouge) with increasing displacement results in complex networks of subsidiary brittle structures (Childs et al., 2009;Kirkpatrick et al., 2013;Deng et al., 2017b;Williams et al., 2022).The main fault zone therefore maintains an orientation that is parallel to the pre-existing weakness, while secondary faults deviate from the main fault trend, cross-cutting local foliation in some places (Fig. 19c; also see Figs. 3 and 4 in Hodge et al., 2018).These scale-dependent manifestations of basement-involved inheritance can only be recognised using a multi-scale approach.

Factors modulating the orientations of rift-related faults and their linkage with pre-existing structures
There are a number of factors that determine the degree and mechanism of structural inheritance, which in turn determine the geometric relationship between rift-related faults and the pre-existing structure (Section 3.1).Based on analogue and numerical experiments, these factors are: (i) the obliquity of the pre-existing structure with respect to the bulk extension direction, which is defined as the angle α measured between the strike of the weakness and the orthogonal to the extension direction (e.g., Agostini et al., 2009), (ii) the geometry and size of the pre-existing structure, and (iii) its strength relative to surrounding rocks, which may depend on depth (i.e., the rheology of the host layer).Further, the influence of penetrative anisotropies (Section 3.2.2) can be distinct from that of discrete structures.
The depth of a pre-existing weakness controls the amount of strain localisation in the brittle upper crust.A weakness in the lithospheric mantle will distribute strain over a wider area than a shallower weakness in the lower crust (Sokoutis et al., 2007).Further, an oblique weakness situated in a deeper level of the lower crust results in distributed, en échelon shearing, while a shallower weakness of the same orientation results in more localised faults that are geometrically similar to the weakness (Osagiede et al., 2021).
A hierarchy of inheritance is apparent in models where discrete weaknesses of variable orientations are present in more than one layer and compete to localise strain.Weaknesses in the strong upper crust and lithospheric mantle layers are preferentially (re)activated over a weakness in the lower crust, if the lower crust is relatively weak (Chenin and Beaumont, 2013;Molnar et al., 2020).When weaknesses are present in both the upper crust and lithospheric mantle, their relative contributions to strain localisation are determined by the degree of mechanical coupling between the two layers.This coupling depends on kinematic boundary conditions (e.g., rate of divergence) and the thickness and strength of the intervening, potentially weak, lower crust (Zwaan et al.,

Obliquity of discrete pre-existing weaknesses
Discrete, pre-existing weaknesses in the brittle upper crust influence the orientations, kinematics, growth, and linkage of rift-related faults in different ways, depending on their strike (Brun and Tron, 1993;Bellahsen and Daniel, 2005;Corti et al., 2007;Chattopadhyay and Chakra, 2013;Ghosh et al., 2020;Maestrelli et al., 2020;Zwaan and Schreurs, 2020;Zwaan et al., 2021aZwaan et al., , 2021b) (also see Table 2).Weaknesses that are at a high angle to the bulk extension direction (α < 30 • ) are reactivated in a normal sense, exhibiting mainly dip-slip kinematics and accommodating most of the extensional strain.Weaknesses that are  Bell, 1996).S Hmax trajectories are perpendicular to the trend of a strong zone and parallel to the trend of a weak zone.(c) Stress coupling between basement and cover rocks occurs in an "attached stress regime" (sensu Bell, 1996).Stress decoupling occurs when there is an intervening, mechanically weak layer (e.g., evaporites, overpressured shales, and low-angle faults).All panels modified after Bell (1996).(Sandwell et al., 2011).at a lower angle to the bulk extension direction are reactivated with a greater strike-slip component of movement; these typically give rise to secondary, extension-oblique faults that link the primary, extensionperpendicular faults (Bellahsen and Daniel, 2005;Osagiede et al., 2021).In general, the reactivation of discrete, pre-existing weaknesses that are hosted in the brittle upper crust results in geometric similarity between some of the rift-related faults and the pre-existing weaknesses.
Pre-existing weaknesses in the ductile parts of the lithosphere also influence the orientations and arrangement of rifts and rift-related faults.When the ductile weakness is oriented at a high angle to the extension direction (α < 45 • ), it guides the map-view strike of rift segments (Corti, 2008;Agostini et al., 2009;Tommasi et al., 2009;Tommasi and Vauchez, 2015;Petersen and Schiffer, 2016;Molnar et al., 2020).In contrast, a ductile weaknesses that is oriented at a low angle to the extension direction (α > 45 • ) determines where rifts are segmented and transfer zones form.In the brittle upper crust, faults form en échelon patterns of faults at the lateral boundary between the underlying ductile weakness and normal-strength lithosphere (see border faults in Fig. 14).For both low-and high-obliquity rifts, the strike of these faults is between the main rift trend (i.e., the trend of the linear weakness) and the bulk extension direction (Agostini et al., 2009;Corti et al., 2013b).The obliquity of these faults with respect to the far-field extension reflects the relative contributions of extension perpendicular to the rift trend and shear parallel to the rift trend (Withjack and Jamison, 1986).Early interpretations based on fault orientations alone suggested that these faults have oblique-slip kinematics (Agostini et al., 2009), which is a response to transtension under the imposed bulk extension boundary condition.Similar studies later showed that the extension-oblique faults actually display dip-slip kinematics (Corti et al., 2013b;Philippon et al., 2015), highlighting local slip re-orientation that is associated with the underlying ductile weakness.These insights from modelling support the interpretation of extension-oblique faults with dip-slip kinematics in some natural settings, including in the Main Ethiopian Rift (Philippon et al., 2015 and references therein), the Baikal Rift (Petit et al., 1996), and the Rukwa Basin in the East African Rift System (Delvaux et al., 2012).They also imply that strain re-orientationan inheritance mechanism that is different to reactivationcan occur when a preexisting ductile weakness is oblique to the far-field extension direction.

Oblique penetrative anisotropies
Penetrative anisotropies can be considered as an area comprising alternating strong and weak zones (e.g., a pre-existing metamorphic fabric or a system of parallel rift-related faults from a previous rift phase).Penetrative anisotropies (oblique to the far-field extension direction) in the ductile layer can re-orient the far-field strain over a wide area, creating a complex pattern of extension-oblique faults in the brittle upper crust over the entire anisotropic domain.This form of inheritance was demonstrated in a crustal-scale analogue experiment by Samsu et al. (2021), in which the orthorhombic fault pattern above an anisotropic ductile lower crust (with the anisotropy oriented 45 • to the imposed extension) is distinct from normal faults that developed above a homogeneous ductile lower crust in the adjacent domain.The anisotropic lower crust contains strength contrasts between the strong and weak zones that make up the anisotropy.The strong and weak zones resist extension to different degrees, so that the difference in the rate of thinning between these zones results in shearing at the strong-weak interfaces.This process results in localised re-orientation of the 3D strain field (i.e., non-coaxial deformation, where the strain ellipses are rotated) and therefore non-Andersonian faulting above the anisotropic domain.
At the basin scale, strain re-orientation is evidenced by laterally variable fault patterns above different blocks that contain different variably-oriented pre-existing fabrics (e.g., North Coast Transfer Zone, Scotland; Wilson et al., 2010).At the outcrop scale, strain can also be partitioned due to mechanical heterogeneities in faulted rocks.For example, in the Carboniferous Northumberland Basin (northeast England), minor faulting in the hanging wall of the reactivated 90-Fathom Fault is partitioned into an extension-dominated regime in dolostones and wrench-dominated transtension in quartz-rich sandstones (De Paola et al., 2005).This lithological control on fault kinematics has been Fig. 13.A pre-existing crustal weakness can influence rift-related cover faults at a range of scales.Tectonic or plate-scale inheritance contributes to rift localisation (a), while basin to sub-basin scale inheritance results in spatial co-location and geometric similarity between pre-existing structures (e.g., basement shear zones and foliation) and rift-related normal faults (b).At the outcrop scale, some minor faults can deviate from the main fault and crosscut pre-existing foliation, reflecting the complex architecture of a fault zone (c) or reactivation of other pre-existing structures, such as dykes (d).Thick arrows indicate the inferred regional extension direction during rifting.attributed to differences in the Poisson's ratio of different rock types.This idea suggests that contrasts in the mechanical (in this case, elastic) properties of rocks contribute to strain re-orientation.
Both crustal-scale models and basin to outcrop-scale field observations suggest that during rifting, strain re-orientation operates at a range of length scales in response to sufficient contrast in the mechanical properties of the extended heterogeneous medium.Future experiments involving anisotropies with various orientations, different widths/ thicknesses and strength ratios of the alternating strong-weak zones, and different kinematic boundary conditions, will increase our understanding of the influence of ductile and brittle fabrics on rift-related faulting.

Depth and size dependence
The depth dependence of inheritance influences the type of linkage between pre-existing structures and younger rift-related faults in the overlying units.Rift-related faults in deeper sedimentary units, for example, are hard-linked with and geometrically similar to reactivated structures in the underlying basement (Fig. 15).In contrast, shallower faults are perpendicular to the regional extension direction but form an en échelon arrangement parallel to the pre-existing structures (Fig. 3b) (Collanega et al., 2019;Deng et al., 2020;Phillips et al., 2022); these shallow faults are soft-linked by relay zones in map view (Giba et al., 2012).As faulting progresses, the shallow faults may become laterally linked at the surface (Deng and McClay, 2021).Vertical linkage between deep and shallow fault segments creates an up-sequence rotation of fault strike to define a sigmoidal fault geometry in 2D (cross section) and a twisted fault surface in 3D (Fig. 15b).An intervening, mechanically weak unit would in theory decouple stress and strain between the basement and cover units (Section 3.1.3).However, when this intervening weak unit is relatively thin, vertical linkage between pre-existing and new faults may mainly be controlled by the displacement and geometry of the pre-existing structures (e.g., the presence of relay ramps between same-generation, pre-existing faults) (Phillips et al., 2022).Collanega et al. (2019) documented the depth-dependent upward propagation of rift-related faults, observed from seismic reflection data from the Taranaki Basin.Here, Plio-Pleistocene rift-related faults nucleated either from intrabasement shear zones (possibly Mesozoic in age; Muir et al., 2000) or within damage zones above Late Miocene reverse faults.Collanega et al. (2019) suggested that the upward propagation of these faults into the overlying cover during rifting was controlled by the obliquity of the shear zone with respect to the regional extension direction.Shear zones that strike perpendicular to the extension direction are hard-linked to rift-related faults that extend into the upper levels of the cover.In contrast, shear zones that strike more obliquely to the extension direction are hard-linked to rift-related faults that are restricted to the lower levels of the cover.Another component that modulates the influence of an oblique preexisting weakness is its size (e.g., its thickness measured normal to the margin of the structure).Collanega et al. (2019) inferred that rift-related faults nucleating at a thick, pre-existing shear zone (with a map-view width of ~1 km and 15-20 • dip) propagated further upwards to shallower depths compared to rift-related faults that nucleated at a thinner shear zone (with a map-view width of 100 m and 20-30 • dip).Analogue experiments also show that the dimensions and orientations of a preexisting weakness variably influence fault localisation and kinematics (Osagiede et al., 2021).A thick oblique weakness may be more influential than a thin one due to the larger volume of reduced integrated strength near and within the weakness.

Multiphase rifting: The influence of first-phase faults on second-phase faults
In multiphase rifting, the extension direction in the second rift phase can be different to that of the first rift phase.Analogue models show that where the strike of first-phase normal faults is optimal for reactivation, these "pre-existing" faults can influence the fault system geometry of the second rift phase (e.g., Keep and McClay, 1997;Bellahsen and Daniel, 2005;Henza et al., 2010;Chattopadhyay and Chakra, 2013;Ghosh et al., 2020).It has also been observed in natural multiphase rifts that faults from the first rift phase can undergo oblique reactivation, while new faults also form with strikes perpendicular to the new extension direction.Second-phase faults may abut first-phase faults, transferring strain to a locally reactivated segment of the first-phase fault (i.e., "trailing fault"; Nixon et al., 2014).The first-and second-phase fault sets form a zigzag geometry in map view (Wang et al., 2021a).Analogue experiments by Henza et al. (2011) suggest that the amount of displacement on first-phase faults influences the lengths of second-phase faults and their connectivity with the first-phase faults (Fig. 16).In addition, the size and distribution of first-phase faults appears to control strain localisation during second-phase faulting (Bailey et al., 2005).
Natural examples serve to highlight the nuances of structural inheritance in multiphase rifts, where factors other than fault geometry, such as thermal weakening, may influence whether faults are reactivated during subsequent rifting phases.During multiphase rifting in the northern North Sea, N-S striking faults that formed during the Permo-Triassic phase of rifting on the Horda Platform are co-located with regions affected by previous Devonian extension, with the faults possibly soling out into Devonian shear zones (Bell et al., 2014).However, these Permo-Triassic faults were not subsequently reactivated during later Middle Jurassic rifting, even though their N-S strike would have been favourable for reactivation during E-W to NW-SE extension (Bell et al., 2014;Fazlikhani et al., 2021).Instead, early Jurassic thermal doming of the North Sea resulted in lithospheric thermal weakening, which favoured the nucleation of new faults in the North Viking Graben to the west of the Horda Platform.However, subsequent rifting in the Late Jurassic-Early Cretaceous reactivated faults that formed during the first Permo-Triassic rifting phase.Here, reactivation was diachronous, with faults closest to the North Viking Graben reactivating first (Bell et al., 2014).

Geomechanical considerations on the reactivation of non-optimally oriented faults
One of the mechanisms of structural inheritance that we discuss in this reviewreactivationrequires some degree of movement on preexisting planes of weakness (e.g., pre-existing faults, shear zones, pervasive fabrics, or lithological contacts).For strain re-orientation, it is less clear whether such movement is required and in which situations; nevertheless, strain re-orientation has been observed to occur in conjunction with reactivation.In this section we review the wide range  2019).Numbers 1-3 indicate the progression of rifting and increasing thickness of cover rocks.Faults near the basement-cover interface are geometrically similar with and rooted in the reactivated basement weaknesses (e.g., shear zone, metamorphic foliation).Shallower faults are perpendicular to the regional extension (black arrows), suggesting that they are influenced to a lesser degree by the pre-existing weaknesses.
of conditions under which pre-existing planes of weakness are expected to undergo frictional failure and potentially contribute to inheritance.
The tendency for frictional slip to reactivate planes of weakness (as opposed to the nucleation of new faults in intact rock; Byerlee, 1978;Butler et al., 1997;Holdsworth et al., 1997Holdsworth et al., , 2001b) is governed by the local stress state, the orientation of the planes of weakness (Jaeger and Cook, 1979;Morris et al., 1996;Lisle and Srivastava, 2004), and the effective frictional strength of these weaknesses relative to that of surrounding intact rock (Section 3.4.1).Reduced effective frictional strength in pre-existing planes of weakness has been attributed to both pore fluid pressures in excess of hydrostatic fluid pressure, and lower cohesion or frictional coefficient due to grain-scale features such as: (a) interconnected zones of phyllosilicates or clays that provide low-friction sliding surfaces (Byerlee, 1978;Holdsworth, 2004;Collettini et al., 2009bCollettini et al., , 2019)); (b) grain boundary alignment and compositional banding (e.g., in gneisses; Shea and Kronenberg, 1993;Kirkpatrick et al., 2013); and (c) high grain boundary porosity and/or low intergranular cohesion in non-foliated rocks (e.g., non-cohesive cataclasites; Sibson, 1977).
For a rift basin forming in an idealised Andersonian normal fault stress regime (Anderson, 1905) with a vertical maximum principal compressive stress (σ 1 ), the fault population will be dominated by normal faults that strike perpendicular to the horizontal minimum principal compressive stress (σ 3 ) and dip 58-68 • (Collettini and Sibson, 2001).Much of our understanding of the geomechanics of inheritance in rift settings relates to deviations from this idealised scenario, in which pre-existing structures either strike obliquely to σ 3 and/or have a dip ∕ = 58-68 • (e.g., Etheridge, 1986;Ranalli and Yin, 1990;Massironi et al., 2011;Williams et al., 2019).Here, we examine 2D and 3D approaches (Sections 3.4.1 and 3.4.2,respectively) to understand how slip occurs along pre-existing planes of weakness that are not optimally oriented for frictional reactivation.

Influence of frictional strength and fluid pressure on basement structures
In the case of a pre-existing plane of weakness that strikes orthogonal to σ 3 , the plane of weakness contains the intermediate principal compressive stress (σ 2 ).Therefore, assuming pure dip-slip, a 2D analysis can provide insights into the conditions required for reactivation, depending on the dip of the plane of the weakness.This analysis follows Sibson (1985), who defined an effective stress ratio required for slip to occur: where μ s is the static coefficient of friction, which is a measure of the friction between two cohesionless stationary surfaces that are in contact (Byerlee, 1978), and σ 1 ′ and σ 3 ′ are the maximum and minimum effective principal stresses (σ 1 ′ = σ 1 -P f and σ 3 ′ = σ 3 -P f ; where P f is the pore fluid pressure).θ is the angle between the plane of weakness and σ 1 .
A second outcome of Eq. 1 is the significant influence of friction on the reactivation potential of pre-existing planes of weakness in basement rocks.Laboratory measurements have yielded static friction coefficients as low as 0.2 for wet phyllosilicate and clay-rich fault gouges (Moore and Lockner, 2004;Numelin et al., 2007), compared to 0.5-0.85 for most other Earth materials tested in wet and dry conditions (e.g., Byerlee, 1978;Jaeger et al., 2007).This means that for structures rich in graphite, phyllosilicates, or clays (especially illite-smectite, chlorite, talc, biotite, and pyrophyllite), such as pre-existing faults, the range of dips that are optimally or favourably oriented for failure expands considerably.Pre-existing faults with coefficients of friction as low as 0.3 are therefore able to reactivate, even if their dips are as low as 25 • (e. g., low angle normal faults; e.g., Collettini et al., 2009aCollettini et al., , 2009b;;Healy, 2009;Massironi et al., 2011;Demurtas et al., 2016;Singleton et al., 2018) or nearly subvertical, without requiring elevated fluid pressure (Fig. 18b).
Pore fluid factor diagrams (Fig. 18c; Cox, 2010) are a useful alternative graphical method and can be used to assess the role of friction, fluid pressure, and stress on the potential for frictional sliding of basement structures at a given depth.Based on this approach, Cox (2010) suggested that for the more unfavourably oriented normal faults (e.g.~30 • dip) with a typical frictional strength (μ = 0.75), there is only a narrow range of differential stress in which it is possible for slip to occur, and that elevated pore fluid pressures are a pre-requisite.However, using the same approach, Fig. 18c shows that when basement structures with low frictional strength are present, there is a wider range of stress conditions under which they are capable of sliding, with or without the presence of elevated fluid pressures.Fig. 18b also implies that sliding on these lower friction structures can occur over a range of fault dip angles.These pre-existing weaknesses are likely to be the first structures to begin sliding at the inception of rifting and therefore have the potential to become important controls on subsequent basin geometry.

Extension of geomechanical analyses to 3D and implications for sedimentary basins
A 3D approach is required to examine the mechanics of structural inheritance when pre-existing basement structures strike obliquely to σ 3 (i.e., the plane of weakness does not contain σ 2 ) (Williams et al., 2019).
For example, "slip tendency analysis" (Morris et al., 1996;Lisle and Srivastava, 2004) provides a method to estimate the potential of a cohesionless plane of weakness to activate under any stress state (Fig. 17).More recently, Leclère and Fabbri (2013) introduced a 3D solution for the effective stress ratio, R, for reactivation that accounts for cohesion and does not assume an Andersonian stress regime.Relatively few studies have used this 3D approach to investigate the reactivation potential of pre-existing structures that strike obliquely to the regional extension direction.Williams et al. (2019) applied the 3D solution of Leclère and Fabbri (2013) to the southern Malawi Rift to show that weaknesses with a non-optimal strike (>50 • to the trend of σ 3 ) can still reactivate.In their example, pre-existing faults with a favourable dip of ~50-60 • can be reactivated if they are slightly weaker than intact rock (μ ~ 0.55-0.65 vs. μ ~ 0.7), or have an elevated but small pore fluid factor (pore pressure over normal stress ~0.1-0.3)compared to dry intact rock.Hence, a wide range of orientations and fluid pressure conditions are likely under which relatively weak basement surfaces can be reactivated.The geomechanical considerations above enable us to be more specific about the conditions in which inheritance is likely to occur.Basement rocks comprising metamorphosed and deformed carbonaceous shales have the potential to contain graphite-rich planes of weakness (implying low μ s = 0.2-0.4).Likewise, crystalline basement subjected to hydrothermal alteration or containing hydrated ultramafic rocks (ophiolites or Archean greenstone) may host phyllosilicate-and talc-rich zones of weakness.The 3D reactivation analysis could also be used in multiphase rifts to test whether faults that formed in the initial phase of rifting are reactivated in subsequent rifting phases with different extension directions.However, caution should be applied in this case, as local changes in stress and crustal rheology may mean that a fault's orientation relative to far-field stresses is not the only indicator for whether it will reactivate in later rifting events (Bell et al., 2014).
It is also well established that many sedimentary basins develop elevated pore fluid pressures below a critical depth due to compaction disequilibrium and other mechanisms (Suppe, 2014;Zhang, 2019).Given that basinal fluids are known to infiltrate into the basement (Yardley et al., 2000;Gleeson et al., 2003), there are situations in which basement rocks may be saturated in hydrothermal fluids at elevated pressure.As such, elevated fluid pressures and low friction planes of weakness are common in basement rocks, implying that structural inheritance during basin formation should be the norm rather than the exception.

Reactivation and strain re-orientation are the two distinct structural inheritance mechanisms that influence rift-related faulting
2D and 3D observations from outcrops, geophysical data, and analogue and numerical models provide insight into the interactions between pre-existing and younger rift-related structures, as summarised in Section 3. From this synthesis, we suggest that two mechanisms underpin the control of pre-existing structures on rift-related fault orientations and geometries: reactivation and strain re-orientation (Fig. 19).Notably, both mechanisms can be active during the same rift phase, either along different pre-existing structures (with different orientations) within the same basin, or along the same pre-existing structure at different depths.
In the context of this discussion, (frictional) reactivation implies slip along a pre-existing weak surface in the brittle crust.During rifting, a pre-existing basement weakness can be a nucleation site from which a new fault propagates into the overlying cover (e.g., Phillips et al., 2016;Collanega et al., 2019) (Fig. 6a).Strain re-orientation refers to non-  (Cox, 2010), for normal dip-slip faults (10 km depth) that are optimally oriented for each value of static friction coefficient.Basement stress states increasing from near hydrostatic fluid pressure and low differential stress have the potential to reactivate pre-existing structures with lower coefficients of static friction, relative to intact rock, over a wide range of stress and fluid pressure conditions.coaxial deformation patterns, which result from partitioning of the farfield extensional strain at the interface between two mechanically distinct rock units (e.g., adjacent blocks of metamorphic or igneous basement domains).For example, bulk stretching of anisotropic blockwhere the anisotropy is oblique to the far-field extension directionis accommodated by different rates of extension in the strong and weak rocks, resulting in shearing along the strong-weak boundary (e.g., Samsu et al., 2021).Strain re-orientation can also occur in conjunction with movement along a pre-existing structure (i.e., reactivation) (Phillips et al., 2016).
Both reactivation and strain re-orientation may be associated with local perturbations of the far-field stress around a pre-existing structure (i.e., local stress re-orientation) (Section 3.1.3).Stress re-orientation has been observed and modelled in three scenarios: (i) dynamic stress changes due to movement along a fault or shear zone (Barton and Zoback, 1994); (ii) deflection of stress trajectories due to elastic contrasts in the brittle crust (Fig. 11a and b) between a pre-existing structure and its host rock or between two adjacent basement domains (Bell, 1996;de Joussineau et al., 2003;Morley, 2010); and (iii) strength contrasts in the viscous crust that results in strain re-orientations (Samsu et al., 2021) which alters the stress field in an overlying mechanically coupled brittle crust.We therefore suggest that rheological contrast is a prerequisite for inheritance, which must be present for reactivation and/ or strain re-orientation to occur.In sedimentary basins, a locally rotated stress field within the basement can be transferred to the overlying basin fill when the two units are mechanically coupled.If, however, an intervening weak layer separates basement and cover, then stress coupling between the basement and cover rocks is limited (Fig. 11c).This variable decoupling by an intervening weak layer (Phillips et al., 2022) has implications for hard and soft-linkage between pre-existing basement structures and rift-related faults in the overlying cover (see Section 4.2).
Reactivation and strain re-orientation can occur concurrently during a single rift episode but result in different spatial and geometric relationships between the pre-existing basement structures and rift-related faults (Fig. 19).Applied to the offshore southern Norway study area of Phillips et al. (2016), the distinction between these mechanisms and the extent of their influence may explain why rift-related faults exploit, merge with, or cross-cut different basement shear zones within the same basin (Section 3.1.2).Strain re-orientation can also explain the occurrence of rift-related faults that form abovebut do not exhibit geometric similarity witha pre-existing basement weakness or anisotropy.The range of geometric relationships associated with strain re-orientation emphasises that reactivation is not synonymous with structural inheritance, of which strain re-orientation is a common and important mechanism.
Whether reactivation or strain re-orientation occurs may depend on whether a pre-existing structure behaves in a frictional or viscous manner.Discrete, pre-existing weaknesses in the brittle upper crust undergo frictional reactivation when they are appropriately oriented relative to the far-field stress (Section 3.4).On the other hand, weak zones with relatively low viscosity in the viscous lower crust or lithospheric mantle influence deformation by localising and/or re-orienting strain, as demonstrated by brittle-ductile analogue models (Section 3.2).In natural rifts, this distinction may be used to determine whether the inherited weakness lies in the frictional or viscous crustal regimes (cf.Holdsworth et al., 2001a; Fig. 1).

Hard and soft-linkage classification
The natural examples presented in Section 3.1 demonstrate an array of geometric relationships between pre-existing structures and younger rift-related faults (Fig. 6).We suggest that these relationships can be classified into hard-and soft-linked inheritance, to denote whether a riftrelated fault is physically connected to a deeper pre-existing structure (Fig. 19c and d): Hard-linked inheritance is characterised by a physical link between a deeper pre-existing structure and a younger, rift-related fault in the overlying sedimentary cover.Soft-linked inheritance is defined as the apparent influence of a deeper pre-existing structure on a rift-related fault, where a physical link between the two is not observed.We note that this classification does not describe the genetic relationship between the pre-existing and rift-related structures or the inheritance mechanism (Fig. 19a and b).

Hard-linked inheritance
A shallow, rift-related fault and a deeper, pre-existing structure are classified as hard-linked if they have identical strike and dip direction and an exploitative, merging, or cross-cutting relationship (sensu Phillips et al., 2016; Section 3.1.2)(Fig. 19).We established that an exploitative relationship between a rift-related fault and pre-existing weakness (Fig. 6a) relies on reactivation of the pre-existing weakness.The relative contributions of strain re-orientation and reactivation mechanisms to the merging and cross-cutting relationships are exemplified by riftrelated normal faults that inherit the strike of a nearby, pre-existing Rheological contrast is a pre-requisite for both mechanisms of structural inheritance (i.e., reactivation and strain re-orientation), with which local perturbations of the far-field stress are associated.Such stress perturbations can be driven by dynamic stress changes due to movement along a pre-existing weakness or by elastic and strength contrasts in the brittle and viscously deforming crust, respectively.The two inheritance mechanisms can be inferred based on the 2D and 3D geometric relationships between pre-existing structures and rift-related faults.These geometric relationships which have been further classified into hard and soft linkage (referred to as hard-linked and soft-linked inheritance, respectively, in the text).
shear zone with a gentler dip than the rift-related normal faults (e.g., Fazlikhani et al., 2017;Rotevatn et al., 2018;Osagiede et al., 2020).Geometric similarity between the rift-related faults and the pre-existing shear zone may be initiated by strain re-orientation, for example caused by a pervasive grain-scale fabric that formed in the same deformation event as the shear zone (Kirkpatrick et al., 2013).In this case, movement along the weak layers within the fabric enables strain re-orientation.Evidence from in-situ stress measurements and earthquake focal mechanisms suggest that such strain re-orientation is associated with local reorientation of the far-field maximum (and minimum) horizontal stress trajectories by the mechanically weak zones (Bell, 1996;Morley, 2010).
The combination of geometric similarity with hard-linked inheritance may be limited to deeper rift-related faults which are closer to the pre-existing structure in terms of vertical distance (Section 3.2.3).This depth dependence is demonstrated by rift-related faults that are segmented and oblique to a pre-existing structure in the upper part of the cover but appear to merge into a continuous structure striking parallel to the pre-existing structure at depth, where the weak (relative to the surrounding rock) pre-existing structure has re-oriented the local stress field (Tingay et al., 2010b;Deng et al., 2017b;Collanega et al., 2019).The influence of this pre-existing weakness decreases with increasing vertical distance from the basement structure.Near the surface, the far-field stresses have a greater influence on fault orientation (Yale, 2003), so that the shallow faults exhibit an en échelon arrangement that strikes parallel to the basement structure and perpendicular to the far-field extension direction (i.e., the minimum horizontal far-field stress) (Fig. 3).

Soft-linked inheritance
The soft-linked inheritance classification applies when rift-related faults are spatially co-located with a deep pre-existing structure, but the fault strikes are oblique to both the pre-existing structure and inferred regional extension direction (e.g., Samsu et al., 2019) and/or we cannot observe hard linkage between the pre-existing structure and rift-related fault in cross section (e.g., Phillips et al., 2022).Analogue experiments suggest that such "misoriented" faults form when the preexisting structures behave in a viscous as opposed to frictional manner during rifting, regardless of whether they are discrete or pervasive (Section 3.2).Models with a discrete weakness in the ductile lower crust, which strikes ≤45 • relative to the extension direction, demonstrate the formation of extension-oblique faults in the overlying crust (Agostini et al., 2009;Corti et al., 2013b) (Fig. 14).Dip-slip kinematics and slip reorientation along the extension-oblique faults (Philippon et al., 2015) reflect strain re-orientation near the boundary between the weaker and stronger lower crust domains and in the overlying upper crust.Strain reorientation can also occur across a wider area when the ductile layer is mechanically anisotropic, with pervasive, closely spaced weaknesses that are oblique to the far-field extension direction (Samsu et al., 2021).The anisotropy gives rise to transtensional strain, even under boundary conditions that simulate orthogonal rifting, resulting in sets of non-Andersonian faults with strikes that are oblique to the anisotropy in map view (cf.Fig. 16).
The presence of a relatively weak, ductile layer (e.g., clay, salt) can decouple the basement from cover units, as observed in seismic reflection data and through in-situ stress measurements (Bell, 1996) (Fig. 11, Fig. 10).Where an intervening weak layer is present between two cover units, this decoupling effect can result in a combination of soft-linked and hard-linked inheritance.In this case, the pre-existing basement weakness is geometrically similar to rift-related faults below the mechanically weak layer but geometrically dissimilar to an en échelon fault array above the weak layer (e.g., Jackson and Rotevatn, 2013;Roche et al., 2020;Phillips et al., 2022).
The spatial co-location of inferred, deep-seated basement structures with transfer zones (also known as accommodation zones) that separate distinct rift segments and basins (e.g., Rowland and Sibson, 2004;Fossen et al., 2016) can also be described as soft-linked inheritance.The absence of cover faults parallel to the inferred pre-existing structures imply that the pre-existing structures were not directly reactivated and are not hard-linked to any of the rift-related faults.Therefore, we can infer that the pre-existing structure, which strikes at a high angle to the main rift trend, is not favourably oriented for reactivation but locally reorients the far-field extension direction.While it is widely acknowledged that such pre-existing structures contribute to continental-scale rift segmentation, there is scope for further exploring the relationship between soft-linked inheritance and the formation of sub-basin-scale relay structures (cf.Fossen and Rotevatn, 2016).

Applying the structural inheritance framework to the East African Rift System
In the following section, we use the East African Rift System (EARS) to consider how the structural inheritance framework presented above (Sections 4.1 and 4.2) can be applied to a continental rift.We have chosen an active rift as multi-disciplinary and multi-scale datasets are readily available to constrain rift extension directions (e.g., geodesy, earthquake focal mechanisms, fault slickensides) and hence to investigate the occurrence of reactivation and strain re-orientation inheritance mechanisms.Furthermore, as the pre-eminent example of an active continental rift, the EARS allows us to investigate inheritance at all stages of continental rift evolution from nascent seafloor spreading in Afar to incipient faulting in the Okavango Rift of Botswana (Fig. 2; McConnell, 1972;Chorowicz, 2005;Ebinger, 2005;Macgregor, 2015;Daly et al., 2020).
Hard-and soft-linked structural inheritance has influenced the evolution of the EARS at many spatial scales (and also magma emplacement mechanisms and volcanic activity; see Corti et al., 2022 for examples from the Main Ethiopian Rift).A famous example of plate-scale inheritance is present south of the Main Ethiopian Rift, where the Eastern and Western Branches of the EARS wrap around the relatively rigid Archean Tanzanian craton and spatially co-locate with orogenic belts that formed during the progressive Proterozoic amalgamation of the African Continent (Fig. 2; Daly et al., 1989;Versfelt and Rosendahl, 1989;Nyblade and Brazier, 2002;Corti et al., 2007).New geodetic and geologic evidence indicates that this is just one of several cases of plate-scale structural inheritance where the EARS bifurcates to co-locate with preexisting weak zones around Archean cratons; in this context, the initiation and propagation of EARS rifting appears to be faciliated by relatively weak, previously deformed Proterozoic lithosphere that bound more rigid blocks (Fig. 2; Daly et al., 2020;Stamps et al., 2021;Wedmore et al., 2021).However, these pre-existing structures alone may not be sufficient for the extension of thick, cold, continental lithosphere in the magma-poor western branch of the EARS to proceed to full continental break-up (Muirhead et al., 2019;Brune et al., 2023).
The 3D geometric relationship between faults and fabrics in the EARS at depth is uncertain.However, it is likely that where fabrics are moderately dipping (e.g., southern Malawi Rift, Fig. 21a; Wedmore et al., 2020b), relationships are exploitative (sensu Phillips et al., 2016).Merging or cross-cutting relationships are present in regions where the fabrics are subvertical (e.g., northern Malawi Rift; Dawson et al., 2018;Kolawole et al., 2018).Geometric similarity is not ubiquitous within the EARS.For example, some faults in the Tanganyika Rift and central Malawi Rift are not parallel to surrounding crustal fabrics (Muirhead et al., 2019;Scholz et al., 2020), and the degree to which metamorphic fabrics influence fault orientations can change as rift extension progresses (Muirhead and Kattenhorn, 2018;Nutz et al., 2022).Furthermore, local variations in fabric orientation may disrupt geometric similarity at the scale of an individual fault, resulting in faults that locally cross-cut fabrics, along-strike fault segmentation, and/or faults that are Z-shaped in plan-view due to scarps that are continuous across perpendicular bends (Fig. 21b; Hodge et al., 2018;Corti et al., 2022).
When invoking a mechanism for the geometric similarity in the EARS it is not always clear if: (1) fabrics are non-optimally oriented to the regional extensional direction, but reactivate because they are (3) Eocene-Miocene faults that formed in response to magmatism and thermal doming, and that uplifted and tilted the KSFB block (Vétel et al., 2005).Landsat 8 image provided from USGS Earth Explorer.NTFZ = N'Doto Transverse Fault Zone; S 1 = extension direction.frictionally weak and/or incohesive (i.e., hard-linked exploitative reactivation, Fig. 6a; (Dawson et al., 2018;Wedmore et al., 2020b), (2) fabrics are optimally oriented to the regional extension direction and so geometric similarity is a coincidence (Baker et al., 1972;Smith and Mosley, 1993), or (3) non-optimally oriented fabrics are actively rotating the local (i.e., at the scale of the fault; Twiss and Unruh, 1998) extension direction, so that foliation-parallel faults exhibit dip-slip displacement despite striking oblique to the regional extension direction (Fig. 21b) (Tingay et al., 2010b;Corti et al., 2013bCorti et al., , 2022;;Muirhead and Kattenhorn, 2018;Williams et al., 2019).Analogue models imply that the latter is an example of soft-linked structural inheritance, as these local extension directions reflect deep-seated (not surface or shallow) weaknesses in the crust (Corti et al., 2013b;Philippon et al., 2015).Therefore, mechanisms (1) and ( 3) could apply at different depths to the same fault (Hodge et al., 2018;Wedmore et al., 2020b).
Structural inheritance in the EARS is not limited to geometric similarity.For example, as rift extension proceeds in the EARS, it is typically observed that strain migrates from large basin-bounding faults to a network of smaller intrabasin faults in the rift valley (Ebinger, 2005).Early localisation of rift-related strain onto a border fault may be facilitated by the exploitation of a discrete pre-existing weakness (e.g., a terrane boundary or viscous shear zone; Wheeler and Karson, 1989;Katumwehe et al., 2015;Scholz et al., 2020;Wedmore et al., 2020b;Kolawole et al., 2021b).Alternatively, pervasive lateral heterogeneities  (Jackson and Blenkinsop, 1997;Hodge et al., 2018).(a) Surface traces of faults and foliation in southern Malawi (Williams et al., 2019(Williams et al., , 2021;;Kolawole et al., 2021a).Trend of the minimum principal compressive stress (σ 3 ), foliation trend lines and strike and dip measurements from (Williams et al., 2019 and references therein).(b) Map of the BMF and surrounding surface foliation orientations (Hodge et al., 2018 and references therein).The relative orientation of the fault, surrounding foliation, and along strike minima in fault scarp height have been used to divide it into the seectionss illustrated by thick, coloured lines (Hodge et al., 2018).Field examples of where the BMF is (c) parallel and (d) oblique to the surrounding foliation (Williams et al., 2022) in the crust (e.g., a wide anastomosing shear zone) can promote distributed deformation involving migration of extensional strain from the basin boundary to intrabasin faults (Kolawole et al., 2018(Kolawole et al., , 2021b;;Wedmore et al., 2020a).Normal fault lengthening by exploitation of preexisting fabrics (Section 3.1.5;Walsh et al., 2002) may account for why faults in the EARS achieved their full length at an early stage of their displacement accumulation (Fig. 20) (Vétel et al., 2005;Accardo et al., 2018;Corti et al., 2019;Ojo et al., 2022) and exhibit narrow fault damage zones (Fig. 21c) (Hodge et al., 2020;Carpenter et al., 2022;Williams et al., 2022).Therefore, an important observation at the <100 km scale is that although the EARS is a classic example of plate-scale structural inheritance and co-location with relatively weak lithosphere (e.g., Versfelt and Rosendahl, 1989), this inheritance is not synonymous with reactivation.Instead, reactivation is limited to where discrete, relatively weak structures are available in an orientation that is favourable for reactivation as the dominant (frictional or viscous) deformation mechanism (Wheeler and Karson, 1989;Kolawole et al., 2018;Heilman et al., 2019).However, at depths or locations where such structures are not available, the orientations and dimensions of new structures are locally variable and likely related to underlying basement anisotropy (Hodge et al., 2018;Williams et al., 2019;Wedmore et al., 2020b;Carpenter et al., 2022).

Implications of structural inheritance for natural hazards and resources
Conceptual understanding of tectonic inheritance and fault/fabric reactivation has been integrated into previous studies on rift evolution and basin formation in the context of paleotectonic reconstructions (e.g., Gouiza and Paton, 2019;Heron et al., 2019) and hydrocarbon exploration (e.g., Morley, 1995;Lyon et al., 2007;Whipp et al., 2014;Wang et al., 2021b).However, there is still scope for investigating the wideranging implications of structural inheritance from a hazards and risk, geo-energy, and minerals exploration perspective.
Seismic hazard investigation is a practical application for the study of structural inheritance in rift basins.For example, since there is spatial co-location between rift basins and Proterozoic orogenic belts in the EARS (Section 4.3), historical seismicity in East Africa is broadly colocated with these pre-existing structures (Fairhead and Henderson, 1977;Sykes, 1978;Craig et al., 2011).Indeed, it has been demonstrated that individual earthquakes in the EARS can have slip surfaces subparallel to pre-existing metamorphic fabrics (Kolawole et al., 2018).Further, the influence of structural inheritance on the distribution of extensional strain between border and intra-rift faults will dictate whether regions of high seismic hazard are in the basin interior or along the margin(s) (Dawson et al., 2018;Wedmore et al., 2020a;Williams et al., 2021).Pre-existing crustal fabrics also modulate the along-strike segmentation of faults, and this can affect whether faults rupture in relatively frequent, moderate-magnitude segmented fault ruptures, or more uncommon whole-fault, large magnitude ruptures (Biasi and Wesnousky, 2016;Hodge et al., 2015Hodge et al., , 2018;;Wedmore et al., 2020b).There is also increasing evidence that the dynamics of individual earthquake ruptures (e.g., stress drop, fracture energy, ground motions, slip distributions) will be influenced by pre-existing structures (Heermance, 2003;Williams et al., 2022;Nevitt et al., 2023;Mo and Attanayake, 2023).These implications of structural inheritance for earthquake modelling and hazards assessment are worthy of further study, including in "stable" continental regions, where earthquakes are often observed to follow pre-existing structures (e.g., Calais et al., 2016;Yang et al., 2021;Rimando and Peace, 2021;Muir et al., 2023).
From a geo-energy perspective, inherited structures can impact the architecture of fluid flow pathways, including connectivity between deep and shallow units.The extraction of geothermal energy and the formation of hydrothermal mineral systems rely on hydrothermal fluid circulation, which is affected by the spatiotemporal pattern of deformation.For example, heat and mass transfer from deep sources to shallower depths are facilitated by convection through networks of open fractures (e.g., Rowland and Simmons, 2012).These fractures are especially important in rocks with low primary porosity and permeability, such as crystalline basement.At the plate scale, tectonic inheritance controls the location and lithology of sedimentary basins as well as the preservation of fluid pathways between deep heat and metal sources and shallow reservoirs (e.g., Hoggard et al., 2020).At the basin scale, rifting can bring about favourable stress conditions for reactivating pre-existing faults as permeable fractures.
The Upper Rhine Graben is an example of a deep geothermal system where the most permeable reservoir is located at the top of the granitic basement (e.g., Vidal and Genter, 2018;Glaas et al., 2021).NNW-SSE to N-E striking Variscan faults and fabrics in the basement may have been reactivated in a normal sense during the basin's multiphase history of Cenozoic regional shortening and extension (e.g., Schumacher, 2002), contributing to thick (i.e., wide-aperture) fractures with enhanced permeability (Glaas et al., 2021).Bertrand et al. (2018) show that preexisting faults, fabrics, and lithologies in the Upper Rhine Graben can impact fracture patterns at some scales but not others, demonstrating that the impact of inheritance on flow modelling is scale dependent.Structural mapping, with an aim to understand the multi-scale controls of inheritance on fractures, has been applied to other geothermal systems, including in France (Dezayes et al., 2010), Mexico (Norini et al., 2019), and the UK (Yeomans et al., 2020).
In the Taupō Volcanic Zone (New Zealand), structural inheritance appears to control shallow geothermal systems and the formation of hydrothermal gold and silver deposits at <2000 m depths (i.e., epithermal ore deposits).Upwelling of hot water plumes is enhanced at the intersections of mapped or inferred structures, including faults, basement-controlled transfer zones, and caldera boundaries (Rowland and Sibson, 2004;Rowland and Simmons, 2012;Villamor et al., 2017;Milicich et al., 2021).Rowland and Sibson (2004) associated the segmentation of the NNE-SSW trending rift system, via so-called accommodation zones, with WNW-ESE trending basement structures interpreted from geophysics.The same geometric relationship has also been inferred for the similarly NNE-SSW trending Coromandel Volcanic Zone farther north (Bahiru et al., 2019).Rowland and Simmons (2012) suggested that such basement structures may be physically linked with potentially permeable shear zones in the lower crust, enabling fluid transport across the frictional-viscous transition zone (Cox et al., 2001), though at present there is no evidence of hard linkage between the basement structures and shallower rift-related structures.
Inheritance of lithospheric boundaries and crustal-scale weaknesses during rifting contributes to the formation of world-class sediment-hosted base metal deposits (i.e., copper, lead, zinc, and nickel) near craton edges (e.g., Mount Isa, Australia; Gibson et al., 2016;Hoggard et al., 2020).Here, the long-lived nature of the craton edge is attributed to focusing of deformation over multiple extensional and contractional events.Rifting of thick cratonic lithosphere facilitates the formation of deep, widely spaced faults that remain active (through reactivation) for up to 100 Ma, extending the time window for mineralisation (Allen and Armitage, 2012) and the distribution of basin fill lithologies that are conducive to mineralisation (Hoggard et al., 2020 and references therein).In addition, reactivation of crustal structures maintains focused fluid flow between the deep and shallow levels of basins (Gibson et al., 2016).
The examples we discuss here suggest that there is scope for applying our knowledge of lithospheric and crustal-scale controls of inheritance to geothermal and mineral systems, which can contribute to successful exploration and development of geothermal energy, base metals, and critical metals.Characterising pre-existing structures in detail and quantifying their reactivation potential under in-situ stresses are essential for geothermal drilling projects (Deichmann and Giardini, 2009;Diehl et al., 2017), in addition to exploring the feasibility of geological storage of both CO 2 (e.g., Andrés et al., 2016) and disposal of spent nuclear fuel (e.g., Barton and Zoback, 1994) to support the current energy transition.

Concluding remarks
Compositional heterogeneities and mechanical discontinuities in pre-deformed lithosphere can locally alter the local stress and/or strain field.This structural inheritance, which has been observed from the plate scale down to the outcrop scale, is probably the norm rather than exception, and it influences the location and geometry of entire rift systems, basins, and faults during rifting.Lithospheric and crustal-scale zones of weakness facilitate localised thinning, that contributes to the formation and propagation of rifts along inherited higher strain belts, and guides potential magmatism.At the same scale, accommodation zones are spatially co-located with inferred deep-seated structures that strike at high angles to the main rift.The boundaries and evolution of rift basins are controlled by boundary faults that, if inconsistent with the farfield strain, may indicate exploitation of a reactivated basement weakness and/or reflect a locally re-oriented strain field above a deep, potentially viscously deforming structure.Individual faults at the subbasin scale may also exploit weak surfaces in the basement or a preexisting rift fabric.Some faults may appear to be unaffected by inheritance and reflect the far-field regional extension, suggesting that the vertical and lateral extents of stress and strain re-orientation are limited by the depth, size, orientation, and relative strength of the pre-existing structure.Additionally, the influence of the pre-existing structure over time is modulated by weakening or strengthening (e.g., healing), as well as the evolving thermal and rheological structure of the lithosphere during rifting (e.g., Bell et al., 2014;Claringbould et al., 2017).
We have distilled observations of structural inheritance into two key mechanisms: reactivation and strain re-orientation.One or both of these mechanisms are activated when extension affects two mechanically distinct terranes or occurs in the presence of a pre-existing, anomalously weak (or strong) structure within relatively homogeneous-strength rock.Reactivation is generally associated with geometric similarity and hard linkage between a pre-existing structure and younger, rift-related faults.These observations are consistent with many of the expressions of inheritance found around the world, most notably around the Atlantic passive margins and in the East African Rift System (Table 1).However, strain re-orientation is invoked for observations of soft linkage, particularly where a rift-related fault is oblique to both the far-field extension direction and pre-existing structures (e.g., Tingay et al., 2010b;Giba et al., 2012;Collanega et al., 2019;Phillips et al., 2022).While strain reorientation is not as readily recognisable as reactivation, further understanding of the conditions under which strain re-orientation applies can help us explain the presence of complex fault patterns in rift basins, better constrain the far-field paleostrain in ancient rifts, and more confidently map basement structures under cover.The conclusion that structural inheritance in rift settings is the norm, not the exception, implies that inheritance mechanisms are also important in other tectonic settings (e.g., strike-slip and orogenic systems); examining whether or not this is true could be a fruitful avenue for future research.
In this review, we offer ideas on how our collective knowledge of structural inheritance in rift basins (summarised in Section 3) can be organised into a loose framework for: (i) identifying natural examples of structural inheritance, (ii) considering possible mechanisms for this inheritance and the conditions that promote them, and (iii) evaluating how structural inheritance can impact projects related to geological hazards and natural resources.We acknowledge fully that the framework presented here can be expanded upon as new insights emerge.Recognising the various expressions and drivers of structural inheritance is a necessary step in broadening and deepening our understanding of this phenomenon.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 3 .
Fig. 3. Basin to sub-basin scale examples of pre-existing faults influencing rift-related faulting and the formation of sediment depocentres.(a) In the Dampier Subbasin (NW Shelf of Australia), reactivation of a pre-existing basement fault (F1a) led to the formation of rift-related faults in the overlying cover, with an en échelon arrangement in map view.As rifting progressed, reactivation of the pre-existing fault continued, but a new set of faults formed in the cover, with strikes that are orthogonal to the regional extension direction.(b) 3D visualization of faults in (a) at the Middle Jurassic level, interpreted from seismic reflection data.Faults F1b-f may be linked to the reactivated basement fault F1a at depth.(c) Schematic illustration of penetrative basement fabrics that are reactivated at the early stage of rifting and later become less active, based on observations from Suphan Buri and South Pattani basins (Thailand).(a-b) modified from Deng et al. (2020), (c) modified from Morley et al. (2004).

Fig. 5 .
Fig. 5. Example of map-view spatial co-location and geometric similarity between pre-existing fabrics and basin-bounding, rift-related faults in the Chew Bahir Basin, southern Ethiopia.This interaction resulted in an angular or zigzag fault pattern.(a) Satellite image and (b) traces of faults and basement fabrics from Corti(2009).A similar zigzag fault pattern has been observed in other parts of the EARS (e.g., Lake Tanganyika,Lezzar et al., 2002; Malawi Rift, Hodge et al., 2018).

Fig. 6 .
Fig.6.Geometric relationships between pre-existing structures and overlying rift-related normal faults in map view and cross section (exploitative, merging, and cross-cutting relationships afterPhillips et al., 2016).The inferred inheritance mechanisms behind these relationships are reactivation (a) and strain re-orientation (b and c).Thick arrows indicate the inferred regional extension direction during rifting.

Fig. 7 .
Fig. 7. Interpreted seismic reflection profile across the Great South Basin, offshore South Island of New Zealand (from Phillips and McCaffrey, 2019), showing hard linkage between the pre-existing, Devonian-Cretaceous Terrane Boundary Shear Zone and the Late Cretaceous, basin-bounding Terrane Boundary Fault.

Fig. 9 .
Fig. 9. Example of roughly coeval (i.e., within 10 Ma time window) N-S and NE-SW striking normal fault faults, which were active during Jurassic-Cretaceous E-W directed extension in the Måløy Slope, northern North Sea.NE-SW faults are interpreted to have formed under the influence of the underlying NE-SW striking fabric during an early phase of E-W extension.(a) Top basement depth below sea level in the study area of Reeve et al. (2015).Red dashed line indicates the areal extent of a pre-existing, NE-SW striking, intrabasement fabric interpreted by Reeve et al. (2013).(b) Simplified map of the main N-S striking fault set and smaller N-S and NE-SW trending faults (modified fromReeve et al., 2015).Numbered white lines in (a) are Bouguer gravity anomaly contours (in mGal) (fromSmethurst, 2000).White crosses and circles indicate borehole locations and numbers inReeve et al. (2015).GFS = Gjøa Fault System; MFS = Måløy Fault System; OFS = Øygarden Fault System.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 10 .
Fig. 10.(a) Cretaceous faults (in red) in the Gippsland Basin (Australian Southern Margin), with rose diagrams showing that faults strike NE-SW in the western onshore portion and WNW-ESE in the eastern offshore portion.These rift-related faults are interpreted to have formed during broadly N-S extension (Samsu et al., 2019 and references therein; map from Samsu et al., 2021).The western onshore part of the basin is underlain by the Paleozoic Melbourne Zone, which is characterised by folded turbidites with a NNE-SSW striking fabric in the study area, and the Neoproterozoic-Cambrian Selwyn Block (Cayley et al., 2002; McLean et al., 2010).(b) Photograph of folded turbidites of the Melbourne Zone.Equal area stereonets show poles to bedding and the fold axis (b) and fold hinges (c).(b-d) are modified from Samsu et al. (2020).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 11 .
Fig. 11.Map view illustration of the re-orientation of maximum horizontal stress (S Hmax ) near a mechanically strong (a) and weak (b) zone (modified afterBell, 1996).S Hmax trajectories are perpendicular to the trend of a strong zone and parallel to the trend of a weak zone.(c) Stress coupling between basement and cover rocks occurs in an "attached stress regime" (sensuBell, 1996).Stress decoupling occurs when there is an intervening, mechanically weak layer (e.g., evaporites, overpressured shales, and low-angle faults).All panels modified afterBell (1996).

Fig. 14 .
Fig. 14.Map-view summary of analogue experiments showing differences in the evolution and pattern of rift-related faults above a ductile weak zone (WZ) that is oblique to the imposed extension direction (modified after Agostini et al., 2009).Thick black arrows indicate the extension direction.Major faults are oblique to the extension direction and weak zone irrespective of weak zone obliquity.

Fig. 15 .
Fig. 15.Conceptual illustration of the depth-dependent influence of pre-existing weaknesses in metamorphic basement rocks, based on observations by Collanega et al. (2019).Numbers 1-3 indicate the progression of rifting and increasing thickness of cover rocks.Faults near the basement-cover interface are geometrically similar with and rooted in the reactivated basement weaknesses (e.g., shear zone, metamorphic foliation).Shallower faults are perpendicular to the regional extension (black arrows), suggesting that they are influenced to a lesser degree by the pre-existing weaknesses.

Fig. 16 .
Fig. 16.Analogue experiments of multiphase rifting in wet clay, showing the influence of fault displacement during the first and second rift phases on fault length and connectivity(Henza et al., 2011).

Fig. 17 .
Fig. 17.Mohr diagram plots of shear stress (τ) versus normal stress (σ n ) for reactivation analysis of cohesionless faults that contain σ 2 .(a) The orientation of four faults with different reactivation potential as quantified by their stress ratio (R = σ 1 ′/σ 3 ′) and normalized slip tendency (T' s ; Lisle and Srivastava, 2004).For the case of the optimally oriented fault (θ = 30 • ), R is denoted R* and T' s = 1.In (b)-(d), R and T' s are schematically depicted for the reactivation of (b) favourably oriented, (c) unfavourably oriented, and (d) severely misoriented fault.In cases (b)-(d) a reduction in frictional strength (μ s ) and/or increase in pore fluid pressure (P f ) is required for fault reactivation.Modified after Williams et al. (2019).

Fig. 18 .
Fig. 18.(a) Stress ratio (R) required for frictional reactivation vs. fault dip for a cohesionless normal dip-slip fault (μ s = 0.7) in an Andersonian stress regime.Shown are the dip angles for the optimal fault orientation for (re)activation and the range of fault dips that are favourably oriented for failure.Also shown is the range of unfavourably oriented fault dips that require elevated fluid pressures to fail.(b) Reactivation potential for faults with low coefficients of static friction.The potential for failure of favourably oriented faults extends over a much wider range of dips.(c) Pore fluid factor-stress diagram(Cox, 2010), for normal dip-slip faults (10 km depth) that are optimally oriented for each value of static friction coefficient.Basement stress states increasing from near hydrostatic fluid pressure and low differential stress have the potential to reactivate pre-existing structures with lower coefficients of static friction, relative to intact rock, over a wide range of stress and fluid pressure conditions.

Fig. 19 .
Fig. 19.Classification of the drivers (a), mechanisms (b), and expressions of structural inheritance (c and d) in rift-related faulting. of structural inheritance.Rheological contrast is a pre-requisite for both mechanisms of structural inheritance (i.e., reactivation and strain re-orientation), with which local perturbations of the far-field stress are associated.Such stress perturbations can be driven by dynamic stress changes due to movement along a pre-existing weakness or by elastic and strength contrasts in the brittle and viscously deforming crust, respectively.The two inheritance mechanisms can be inferred based on the 2D and 3D geometric relationships between pre-existing structures and rift-related faults.These geometric relationships which have been further classified into hard and soft linkage (referred to as hard-linked and soft-linked inheritance, respectively, in the text).

Fig. 20 .
Fig. 20.Basin-scale structural inheritance in the Turkana Rift.(a) Landsat 8 natural colour image and (b) simplified geological map (after Vétel et al., 2005, and references therein).We highlight in (b) the influence of structural inheritance on the post-Pliocene Kino Sogo Fault Belt (KSFB) from: (1) an arcuate belt of Proterozoic metamorphic fabrics that are inferred to occur from the Hammer Range in the north, below faulted Pliocene-age lavas within the KSFB, to the N'Doto massif in the south; (2) NW-SE striking structures from Cretaceous-Paleogene Anza Rift; and(3) Eocene-Miocene faults that formed in response to magmatism and thermal doming, and that uplifted and tilted the KSFB block(Vétel et al., 2005).Landsat 8 image provided from USGS Earth Explorer.NTFZ = N'Doto Transverse Fault Zone; S 1 = extension direction.

Fig. 21 .
Fig. 21.(a) Basin and (b-d) fault-scale structural inheritance in the EARS using the example of southern Malawi Rift and the Bilila-Mtakataka Fault (BMF)(Jackson and Blenkinsop, 1997;Hodge et al., 2018).(a) Surface traces of faults and foliation in southern Malawi(Williams et al., 2019(Williams et al., , 2021;;Kolawole et al., 2021a).Trend of the minimum principal compressive stress (σ 3 ), foliation trend lines and strike and dip measurements from(Williams et al., 2019 and references therein).(b) Map of the BMF and surrounding surface foliation orientations (Hodge et al., 2018 and references therein).The relative orientation of the fault, surrounding foliation, and along strike minima in fault scarp height have been used to divide it into the seectionss illustrated by thick, coloured lines (Hodge et al., 2018).Field examples of where the BMF is (c) parallel and (d) oblique to the surrounding foliation (Williams et al., 2022).Equal area, lower hemisphere stereonets indicate relative orientations of foliation planes and joints in damage zones surrounding faults, shaded great circle region indicates local trend of BMF scarp and a range of plausible fault dips (40-65 • ; Hodge et al., 2018; Stevens et al., 2021; Williams et al., 2022).Maps in (a) & (b) are underlain by SRTM 30 m DEM and TanDEM-X 12 m DEM respectively.
Fig. 21.(a) Basin and (b-d) fault-scale structural inheritance in the EARS using the example of southern Malawi Rift and the Bilila-Mtakataka Fault (BMF)(Jackson and Blenkinsop, 1997;Hodge et al., 2018).(a) Surface traces of faults and foliation in southern Malawi(Williams et al., 2019(Williams et al., , 2021;;Kolawole et al., 2021a).Trend of the minimum principal compressive stress (σ 3 ), foliation trend lines and strike and dip measurements from(Williams et al., 2019 and references therein).(b) Map of the BMF and surrounding surface foliation orientations (Hodge et al., 2018 and references therein).The relative orientation of the fault, surrounding foliation, and along strike minima in fault scarp height have been used to divide it into the seectionss illustrated by thick, coloured lines (Hodge et al., 2018).Field examples of where the BMF is (c) parallel and (d) oblique to the surrounding foliation (Williams et al., 2022).Equal area, lower hemisphere stereonets indicate relative orientations of foliation planes and joints in damage zones surrounding faults, shaded great circle region indicates local trend of BMF scarp and a range of plausible fault dips (40-65 • ; Hodge et al., 2018; Stevens et al., 2021; Williams et al., 2022).Maps in (a) & (b) are underlain by SRTM 30 m DEM and TanDEM-X 12 m DEM respectively.

Table 1
Various types and scales of pre-existing structures, their influence on younger rifts and rift structures, and examples of where such interactions occur.