The Formation of Continental Fragments in Subduction Settings: The Importance of Structural Inheritance and Subduction System Dynamics

Microcontinents and continental fragments are pieces of continental lithosphere, formed by extension and breakup, followed by plate boundary relocations. Microcontinents or continental fragments affiliated with passive margins are well documented, but those close to active margins are less studied. We use dynamic two‐ and three‐dimensional numerical experiments to investigate how preexisting weaknesses within a continental upper plate affect extension and the possible formation of continental fragments. Our parametric study of the configuration (width and viscosity) of this imposed weakness indicates that stress localization and breakup of the upper plate are most efficient for narrow weak zones and a viscosity contrast between the weak zone and the surrounding crust of at least 1 order of magnitude. Moreover, upper plate extension and breakup occurs only if extension has a rotational component, here caused by the presence of a continental indenter on the downgoing plate. The width of the indenter relative to oceanic part of the downgoing plate controls differential slab pull that triggers trench retreat and upper plate deformation. A downgoing plate with a relatively large continental indenter yields large enough slab rotation to detach a continental block from the overriding plate and form wide back‐arc basins. Variations in the weak zone angle with respect to the trench result in different basin geometries. We successfully modeled the first step in breakup of active continental margins and determined the settings that may facilitate microcontinent formation in a subduction framework.


The Formation of Microcontinents and Continental Fragments
Microcontinents are small pieces of continental lithosphere, situated above or below sea level, that are almost completely surrounded by oceanic crust. Continental fragments are similarly defined but are still attached to their parent continent via thinned continental crust (Scrutton, 1976). This continental connection distinguishes continental fragments from microcontinents. The advent of modern, high-resolution geophysical data has yielded a significant increase in the number of identified microcontinents and continental fragments in recent years (see, e.g., Tetreault & Buiter, 2014 for a review). Most in situ preserved microcontinents and continental fragments formed in divergent tectonic settings as part of continental breakup processes. In the context of this paper, we take into account both "microcontinents," which are defined as pieces of continental lithosphere completely surrounded by oceanic crust, and "continental fragments" which are not completely detached from their parent continent by oceanic crust, but may be in an incipient stage of microcontinent formation or a failed one.
Classic examples of microcontinents include the Jan-Mayen microcontinent in the north-east Atlantic Ocean (Gaina et al., 2009;Peron-Pinvidic et al., 2012a, 2012b, various microcontinents around Australia (Gaina et al., 2003), the Seychelles microcontinent in the Indian Ocean Ganerød et al., 2011;Torsvik et al., 2013;Figure 1a). A variety of mechanisms have been proposed to explain microcontinent formation in extensional settings. In a review of several cases of microcontinent formation around the globe, Müller et al. (2001) inferred that a mantle plume impinging on continental lithosphere adjacent to an active spreading ridge weakens the continental lithosphere and induces rifting followed by continental breakup. The nearby active spreading ridge is then abandoned in favor of the new mid-ocean ridge, isolating a fragment of the passive margin as a microcontinent. This scenario could apply to the Jan-Mayen microcontinent in the NE Atlantic. Peron-Pinvidic and Manatschal (2010) revised the structure and setting of continental allochthons in the Atlantic Ocean and postulated that differential thinning of preexisting structures during continental margin formation may form microcontinents and continental fragments by competing rift propagation within weak lithosphere. Examples of such continental fragments are found of the western coast of Ireland. Analogue modeling by Molnar et al. (2018) demonstrated that rotational extension applied to a continental margin in combination with inherited lithospheric weaknesses facilitates microcontinent formation. Competing strike-slip faults along transform margins have also been proposed as a mechanism to release (albeit relatively small) microcontinents (Nemcok et al., 2016). Abera et al. (2016) proposed a mechanism in which an active spreading ridge becomes magma starved, resulting in cooling and strengthening of the lithosphere. Subsequent extension could then localize afterward in a nearby continental margin, provided it is weak, due to the fact that the force required to initiate continental rifting is an order of magnitude less than breaking-up oceanic lithosphere (Abera et al., 2016).
Most research into microcontinent and continental fragment formation focuses on microcontinents formed in divergent tectonic settings and the formation of associated passive continental margins. However, some microcontinents and continental fragments may have formed in convergent tectonic settings in association with subduction. We have identified several examples where small microcontinents and continental fragments are part of a tectonic system that includes subduction. Examples include the Corsica-Sardinia block in the central Mediterranean (Advokaat et al., 2014;Faccenna et al., 2001), the Louisiade Plateau off northeastern Australia (Gaina et al., 1999;Taylor & Falvey, 1977), and the Reed and Macclesfield Banks in the South China Sea (Cullen et al., 2010;Pichot et al., 2014;Figure 1a). These microcontinents and continental fragments are formed in a complex tectonic setting where trench rotation or oblique convergence likely played an important role in their formation. For simplicity we group microcontinents and continental fragments associated with subduction systems from now on and refer to them as continental fragments.
Most of the in situ preserved continental fragments that are associated with subduction systems have formed in regions with a long and complex tectonic history. It has been shown that for passive margins, inherited structures, including but not limited to, old sutures and failed rifts, can localize the extension required for continental rifting and breakup (Brune et al., 2017;Corti, 2008;Heron et al., 2019). Inherited structures in active margins, together with subductionrelated tectonic forces, may likewise be the main ingredients for the fragmentation of continental lithosphere and formation of continental fragments in a subduction setting, but the mechanisms controlling this process are still unclear. Recently, Koptev et al. (2019) postulated that the impingement of a mantle plume on a subducting plate that carries a continental block can lead to microcontinent formation on the downgoing plate. However, we consider this scenario rather unique in the geological history. Here we aim to investigate continental fragment formation on the overriding plate focusing on inherited heterogeneities in the continental upper plate and tectonic forces involved in subduction processes.

Corsica-Sardinia: A Continental Fragment in the Mediterranean Sea
Of the subduction-associated continental fragments mentioned above, the Corsica-Sardinia block in the Mediterranean (Figure 1b) is, from a geological point of view, undoubtedly the best-studied example. We have therefore chosen this region to look for potential clues on continental fragment formation mechanisms. The contemporary geological setting of the Mediterranean region is the result of a long tectonic history of oceanic basin opening and closure, from the Late Paleozoic until present (Figure 1b;Dewey & Şengör, 1979;von Raumer et al., 2003;Vissers et al., 2013). Closure of the Tethys due to Africa-Eurasia convergence Figure 1. (a) Global map with selected locations of microcontinents and continental fragments formed in divergent settings (purple) and those associated with subduction systems (red). CS = Corsica-Sardinia block, ETP = East Tasman Plateau, JM = Jan-Mayen microcontinent, LoP = Louisiade Plateau, RMB = Reed and Macclesfield Banks, Se = Seychelles. (b) Regional map of the central Mediterranean showing the first order onshore geology and era ages of the various terranes. Geological age data from UNESCO World Geological map (Bouysse, 2014). Cor = Corsica, GoL = Gulf of Lion, LP = Liguro-Provençal basin, CSZ = Calabrian Subduction Zone, NBTZ = North Balearic Transform Zone, Sar = Sardinia, Ty = Tyrrhenian Sea, RP = rotational pole of LP basin opening, COT = Continent-Ocean transition zone, COB = Continent-Ocean Boundary. dominated the Cenozoic evolution of the Mediterranean and resulted in the opening of several back-arc basins from Oligocene to Pliocene times (Advokaat et al., 2014;Faccenna et al., 2001;van Hinsbergen et al., 2014).
The various amalgamated terranes (Figure 1b) that constitute the present-day geological setting of the central Mediterranean region are likely bounded by lithospheric-scale inherited structures. Such examples can be found in the margins and the crustal structure of the Liguro-Provençal basin (Lacombe & Jolivet, 2005). The southernmost onshore areas of the Provençal margin contain thrusts that placed crystalline basement onto Permian and Mesozoic formations (Arthaud & Séguret, 1981after Lacombe & Jolivet, 2005. Crustalscale thrust faults have been interpreted on seismic reflection data from both the Gulf of Lion and the Northern Liguro-Provençal basin (De Voogd et al., 1991;Rollet et al., 2002).
At 30 Ma, south-eastward retreat of the Calabrian slab initiated rifting of the Liguro-Provençal back-arc basin (Advokaat et al., 2014;Gattacceca et al., 2007;Seranne, 1999), while at the same time the Adriatic microplate was colliding with the southern Eurasian margin (Turco et al., 2012;van Hinsbergen et al., 2014). Breakup of the Liguro-Provençal basin occurred at 21 Ma (Faccenna et al., 1997) and was followed by a 5-Myr-long ocean spreading phase during which the Corsica-Sardinia block experienced 45-50°of counterclockwise rotation (Advokaat et al., 2014;Gattacceca et al., 2007). Extension ceased in the Liguro-Provençal basin at 16 Ma, before jumping east of the Corsica-Sardinia block at 10 Ma when formation of the Tyrrhenian basin started due to the continued Calabrian slab retreat (Faccenna et al., 2001). At present, Corsica-Sardinia is surrounded by oceanic crust to the west and southeast, by a postulated transfer zone to the southwest, while connected with Italy through thinned continental crust in the northeast (Figure 1b).
From the Corsica-Sardinia example we infer that inherited tectonic structures may play an important role in subduction-associated formation of continental fragments, as they facilitate localization of deformation and continental rifting. Additionally, Wallace et al. (2005Wallace et al. ( , 2009) noted a correlation between the arrival of a buoyant indenter at the trench, observed trench rotation, and associated back-arc extension. Subduction below such a buoyant indenter will cease, while subduction of the laterally present oceanic lithosphere continues, exerting a torque on the trench resulting in trench rotation and potentially back-arc extension. This suggests a potential link between Calabrian slab rotation and the collision of the Adriatic microplate with Eurasia.
Partly based on observations made on the evolution of the Corsica-Sardinia block, we aim to investigate the role of an inherited lithospheric weakness and rotational tectonic forces in continental breakup and subsequent formation of a continental fragment on the overriding plate in a subduction system. To achieve this aim, we run two-dimensional (2-D) and 3-D experiments simulating an oceanic plate subducting under a continental plate with an imposed weak zone to simulate an inherited tectonic heterogeneity.

Governing Equations and Experimental Setup
The numerical experiments are set up in a 2-D and 3-D Cartesian geometry assuming incompressible flow. We solve for the conservation of mass (equation (1)), momentum (equation (2)), energy (equation (3)), and composition (equation (4)) in a nondimensional manner, using the Boussinesq approximation (symbols defined in Table 1): The compositional (R C ) and thermal (R T ) Rayleigh numbers in equation (2) With ΔT the temperature difference between the top and the bottom of the experimental domain and Δρ c = 600 kg/m 3 the density difference between the positively buoyant felsic continental crust and the mantle. This density difference assumes a density ρ 0 of 2,700 kg/m 3 for continental crust, which represents typical values for felsic continental crust, and 3,300 kg/m 3 for the mantle (Bittner & Schmeling, 1995;Turcotte & Schubert, 2002). The governing equations are solved using the finite element code Citcom (Moresi & Gumis, 1996;Zhong et al., 2000) with an iterative conjugate gradient solver. Our mesh is fixed, but has a higher resolution in the trench region and in regions in which the viscosity contrast is high. Elements of the mesh are quadrilateral in shape and their size varies between 5 × 8 and 12 × 8 km in the 2-D experiments and between 7.5 × 10 × 8 and 17 × 20 × 8 km in all directions in the 3-D experiments.
In the 2-D and 3-D setups, the bottom of the experimental domain corresponds to the 660-km upper-lower mantle discontinuity. The 2-D experiments have an aspect ratio of 1:5 (660 × 3,300 km) while the 3-D experiments have an aspect ratio of 1:5:6 (660 × 3,300 × 3,960 km; Figure 2). On the side boundaries as well as the  top boundary we impose a free-slip boundary condition while the bottom boundary is no slip (Figure 2), simulating the viscosity contrast between the upper and lower mantle. The temperature at the top boundary is set to 0°C whereas at the bottom and right-hand side boundaries a temperature of 1,350°C is imposed, with the latter simulating an oceanic spreading ridge that allows a free right-hand boundary. All other boundaries have insulating boundary conditions ( Figure 2). In order to avoid domain induced boundary effects in 3-D, toroidal flow patterns around the subducting slab must be possible (Chen et al., 2016;Funiciello et al., 2003). We achieve this by imposing two 20-km-wide transform faults at y = 660 km and at y = 3,300 km that act as lateral boundaries to the subducting and overriding plate (orange borders in Figure 2b). These 20-km-wide boundaries have a maximum viscosity of 10 20 Pa s.
Composition is defined by a compositional tracer function C, where continental crust has the composition of C = 1 and mantle material has the composition of C = 0. Oceanic crust is not modeled as the buoyancy effect of oceanic crust in subduction dynamics is negligible at the modeled scale (Cloos, 1993) and we use an imposed weak zone at the trench to decouple the downgoing and overriding plates. The compositional tracers are advected via a particle tracing technique (Wang et al., 2015) in which the tracers are moved with the velocity field allowing discrimination between buoyant continental crust and mantle and lithospheric materials (Ballmer et al., 2007;Di Giuseppe et al., 2008). All experiments have the continental overriding plate fixed to the left-hand boundary of the model domain, simulating the presence of a large(r) continental mass ( Figure 2). Following the compilation by Christensen and Mooney (1995), the thickness of continental crust is set to 40 km. We assume a linear temperature gradient for continental crust, from 0°C at the surface to 1,350°C at 150-km depth. The initial thermal structure of the downgoing oceanic lithosphere is given by the solution of the half-space cooling model for a 50-Myr-old oceanic lithosphere (Turcotte & Schubert, 2002). In order to initiate dynamic subduction without imposing any external forces, the initial setup contains an oceanic slab already partially subducted to 260-km depth with an initial bending radius of 500 km. A 20km-wide zone with a maximum viscosity of 10 20 Pa s is imposed at the right domain boundary to 198-km depth, simulating an oceanic spreading ridge, allowing the downgoing plate to move freely during subsequent experimental evolution ( Figure 2b).
In order to decouple the subducting and overriding plates and allow subduction to occur, we impose a subduction weak zone with a maximum viscosity of 10 20 Pa s and width of 20 km which extends down to a depth of 50 km. This weak subduction interface has a fixed shape. Below this interface we impose a 200km-wide weak mantle wedge that extends to 150-km depth. This weak mantle wedge simulates the area of weakened mantle above the slab, resulting from slab dehydration and mantle melting processes and has a maximum viscosity of 10 20 Pa s. Deformation of the weak mantle wedge is allowed to accommodate changes in slab dip during the experiment (Magni et al., 2012). The initial position of the trench is imposed at x = 1,850 km ( Figure 2), but the trench is allowed to move freely along the x axis during the evolution of subduction.

Imposed Weak Zone and Initial Experiment Configuration
In order to investigate the relationship between the parameters of an inherited continental weak zone and the extension in the overriding plate, we first run 2-D experiments of oceanic subduction with an imposed lithospheric scale weak zone in the continental overriding plate ( Figure 2) followed by 3-D experiments of pure oceanic subduction. This weak zone is imposed at approximately 500 km from the trench in both 2D and in 3D ( Figure 2). Variation of the distance between the trench and the imposed weak zone between 250 and 750 km did not lead to different results. We vary the weak zone width between 60 and 260 km and its viscosity between 0.5 × 10 22 and 1.5 × 10 22 Pa s while the thickness is kept constant at 150 km. As we use a crustal viscosity of 10 23 Pa s, this implies that we impose, at the 0°C surface, a viscosity contrast of between 1.5 and 0.5 orders of magnitude.
Many contemporary microcontinents and continental fragments found close to subduction systems have formed due to extensional and, possibly, rotational tectonic processes. In order to induce such rotation in our 3-D experiments we introduce a 990-km-wide continental block into the lower plate ( Figure 2b). The collision of this block induces a torque on the trench, resulting in differential trench retreat and thus trench rotation (Magni et al., 2014;Magni et al., 2017). We vary the ratio of continental to oceanic material in the downgoing plate (as defined by their along-trench widths) to investigate potential links between this ratio and upper plate extension. This ratio (R c/oc ) is quantified by dividing the width of the continental indenter on the downgoing plate (W c ) by the width of the oceanic material on the downgoing plate (W oc ).
Due to the nature of the experimental setup the, initially straight, imposed weak zone deforms. In order to measure rotations we find the point in the imposed weak zone that has experienced no translation or rotation and utilize this as our rotation pole for measuring rotations. However, it should be noted that these experiments are fundamentally 3D and as such quantifying rotations is difficult as every part of the detaching continental fragments experiences different amounts of rotation. To take into account this complexity we measure two angles: the angle between a line running from the widest part of the newly formed back-arc basin and the original weak zone orientation at the rotation pole ( Figure 5a, dashed yellow line and angle), we call this angle the "primary rotation angle." Secondly, we measure the angle between the rotation pole and the southernmost end of the detaching continental fragment (Figure 5a, dashed orange line and angle), we call this angle the "secondary rotation angle." When these two angles have similar values, it means that the southern edge of the continental fragment experienced an amount of rotation similar to the central part and, thus, the continental fragment has rotated as one-piece with little deformation. On the other hand, when the secondary rotation angle is much lower than the primary one, it means that the southern edge did not move as much as the central part, indicting a significant curvature of the continental fragment. Therefore, the highest the difference between the primary and secondary angle is, the higher the curvature of the continental fragment is.
The initial distance between the incoming continental block and the overriding plate is 462 km ( Figure 2b); thus, the slab will reach the 660-km discontinuity before collision between the incoming continental block and the overriding plate occurs. This allows the investigated processes to occur without the complex effects of the slab interacting with the 660-km discontinuity influencing the results (Funiciello et al., 2003). Finally, the potential relationship between the angle of the weak zone (α) with respect to the initial strike of the trench and upper plate extension is also investigated (Figure 2b).

Rheology
The materials in our models can deform by viscous creep or brittle yielding. Viscous behavior is governed by both diffusion and dislocation creep (Hirth & Kohlstedt, 2004;Karato & Wu, 1993;Korenaga & Karato, 2008). Each mechanism has its effective viscosity, η (symbols in Table 1): where _ ε II is the second invariant of the strain rate, which is defined by The value of the rheological preexponent A for diffusion creep is chosen in such a way that at the mantle reference temperature (1,350°C) the effective viscosity is the reference viscosity (10 20 Pa s). For dislocation creep, the reference mantle viscosity is reached for a strain rate of 1.52 × 10 −14 s −1 , which is comparable to the strain rates in a convective upper mantle (Bercovici & Ricard, 2016). We use a value of n = 1 for diffusion creep and a value of n = 3.5 for dislocation creep (Karato & Wu, 1993). Published values of the activation energy (E) vary from 250 to 530 kJ mol −1 (Karato & Wu, 1993). We use an average of E = 360 kJ mol −1 for both diffusion and dislocation creep. Furthermore, we assume dry materials and do not consider (de-) hydration or melt processes.
A viscosity for yielding behavior is calculated using where τ y is the yield stress and τ max is the maximum yield stress. τ 0 +μ p 0 is Byerlee's law (Byerlee, 1978), where τ 0 is the yield stress (cohesion) at the surface, μ is the friction coefficient, and p 0 is the lithostatic pressure. The code calculates the viscosity for all the mechanisms described above and the effective viscosity at any point is determined by taking the minimum value of the calculated viscosities. A maximum viscosity value of 10 23 Pa s is imposed to limit lithospheric strength to realistic values. Rheology for the mantle and the crust is assumed to be the same.

Experimental Variables
We conducted 45 experiments classified into three distinct sets based on their initial geometry: 2-D oceanic subduction experiments, 3-D oceanic subduction experiments, and 3-D experiments with an incoming continental block. We run reference experiments with a homogeneous overriding plate for all three geometries.
All subsequent experiments contain an imposed weak zone. To investigate the effect of weak zone configuration on the evolution of upper plate extension, we conduct a parametric study where we vary both the width w (from 66 to 264 km), and the viscosity η w (from 0.5 to 1.5 × 10 22 Pa s) of the imposed weak zone in all three experimental setups. Using the configuration deemed most effective in terms of generated back-arc extension, we then run a set of experiments where the ratio of continental to oceanic material in the downgoing plate is varied. Finally, we run four additional experiments where we vary the angle of the imposed weak zone by ±15°. In these experiments, a counterclockwise angle is defined as negative and a clockwise angle is defined as positive (Figure 2b).

Reference Experiments
Our 2-D reference experiment considers an oceanic plate subducting below a continental overriding plate without an imposed weak zone (Figure 2a; see also Animation MS01 in the supporting information). After 2 Myr of experimental time, the subducting slab reaches the bottom of the experimental box and starts folding several times (Animation MS01). Trench retreat in this experiment is limited, with an average trench retreat velocity of 0.5 cm/year.
In order to see the difference between 2-D and 3-D setups, we add a third dimension to our 2-D models, creating a 3-D oceanic subduction experiment. The setup is otherwise the same, representing an oceanic plate subducting below a continental overriding plate without an imposed weak zone (Figure 2b). After an experimental period of 4 Myr, the subducting slab reaches the bottom and after a period of draping, it folds several times (see Animation MS02). We observe an average trench retreat velocity of 0.4 cm/year. Deformation is mostly focused above the weak mantle wedge (Animation MS02). Additionally, there was no appreciable difference in the results when we ran a 2-D experiment with the mesh resolution of our 3-D setup.
By imposing a weak zone with an initial width of 66 km and an initial viscosity of 5 × 10 21 Pa s, we test the influence of a preexisting weakness on oceanic subduction in 3D ( Figure FS01 and Animation MS03). Except for the introduction of the weak zone, the setup is the same as the 3-D oceanic experiment described above. The evolution of the experiment is similar to the 3-D oceanic experiment with no imposed weak zone (see Animation MS03). We observe an average trench retreat velocity of 0.3 cm/year and an average extension rate of 0.2 cm/year for the imposed weak zone. Thus, in these 3-D models with a purely oceanic subducting plate the overriding plate experiences very little deformation.
In our 3-D setup, trench rotation is induced by introducing a 990-km-wide continental block on the downgoing plate (Figure 2b). The rest of the downgoing plate consists of oceanic material, which subducts below a continental overriding plate that has no imposed weak zone. After 4 Myr, the subducting slab reaches the bottom of the experimental domain and folds several times. Collision between the incoming continental block and the overriding plate occurs after 9 Myr. After 35 Myr, slab breakoff initiates below the incoming continental block, but the adjacent oceanic lithosphere continues to subduct (see Animation MS04). Here trench retreat has an average velocity of 0.6 cm/year. Extension is again mainly focused above the weak mantle wedge (Animation MS04).

The Role of Continental Heterogeneities in Continental Breakup
The introduction of a weak zone in the overriding continental lithosphere of 2-D and 3-D oceanic subduction experiments yielded no significant upper plate extension. When introducing such a weak zone in a 3-D setup with an incoming continental block we do observe significant upper plate extension (Figure 3). The weak zone is imposed at 528 km from the trench in the overriding plate (Figures 2 and 3a and Animation MS05) and has an initial width of w = 66 km and a viscosity of η w = 0.5 × 10 22 Pa s. We track the evolving width of the extending zone through time by sampling a profile across the widest part of the final back-arc basin. While our experiments do not produce any volcanic arc, any extensional basin that forms in the upper plate is referred to as a "back-arc basin." In order for a direct comparison between different subsequent weak zone configurations, we nondimensionalize the width of the extended zone (w) by the initial weak zone width. North, south, east, and west are defined with respect to the top, bottom, right-, and left-hand side of the modeling domain to aid in describing the results (Figure 3a).
Collision between the incoming continental block and the overriding plate initiates at the northern end of the experimental domain after 9 Myr of model time. At this time, some early extensional structures are visible at the base of the overriding continental crust close to the trench (cross section in Figure 3a). The onset of collision results in deceleration of subduction below the incoming continental block. Slab tearing initiates at depth below the subducted continental lithosphere initiates at~22 Myr after collision initiates (Animation MS05). The slab tear starts below the northern side of the continental block, then propagates toward the center of the model. Laterally toward the south, below the downgoing oceanic lithosphere, the slab does not detach and continues to subduct. Extension then localizes in the overriding plate above the continuous oceanic subduction, as indicated by the steeper slope of the curve that describes the evolution of the extended zone through time (Figure 3b). We define breakup of the overriding plate as the moment when the percentage of continental material in the crust at 8-km depth is lower than 70%. When breakup of the overriding plate occurs, oceanic spreading starts in the back-arc basin. In nature, continental breakup is usually followed by seafloor spreading which may be preceded by subcontinental mantle exhumation. As we do not model mantle melt production, no oceanic crust forms at back-arc basins in our experiments. However, for simplicity and because in nature eventually oceanic lithosphere is always formed, we consider that after continental breakup a back-arc basin floored by oceanic lithosphere is formed.
In this case, continental breakup occurs around 21 Myr (Figure 3b), 12 Myr after the initiation of collision, and before slab break-off occurs. At this time, the rate of upper plate extension accelerates, as visible in Figure 3b. Formation of a back-arc basin is well underway after 27 Myr of experimental time (Figure 3a, middle panels), corresponding to around 1,500 km of subduction of oceanic lithosphere, which is the total amount of initially defined lithosphere. Subsequently subducted oceanic lithosphere is newer and thus younger and hotter. It thus experiences less slab pull, and a decrease in trench retreat velocity occurs around 30 Myr (Figure 3b). After 40 Myr, the rate of upper plate extension has slowed down significantly. The extended zone is now roughly 18 times wider than the original weak zone ( Figure 3b) and a continental block has partly detached from the initial overriding plate due to continental breakup and back-arc spreading. A roughly triangular shape defines the back-arc basin geometry (Figure 3a). Where trench retreat velocity is highest, we observe an extension in the overriding plate of 650 km, corresponding to an extension rate of 1.6 cm/year.
When we compare these results with the 3-D reference experiment with an incoming continental block, we observe that the presence of a weak zone plays an important role in facilitating continental breakup. Although their initial evolution is similar, once the weak zone activates and localizes deformation, extension starts and trench retreat and upper plate extension rates accelerate. We also observe that the weak zone on the overriding plate facilitates and speeds up continental extension (Figure 3c).

The Role of the Weak Zone Configuration
The experiment described above (Figure 3) shows that the presence of an initially imposed weak zone facilitates extension and breakup of the upper plate. We investigate the influence of weak zone configuration by varying its width (w) from 66 to 264 km, and its viscosity (η w ) from 0.5 to1.5 × 10 22 Pa s. After we implement these new parameters, we run all previously presented experiments in 2D, in 3-D oceanic subduction, and in 3D with an incoming continental block on the lower plate (Figures 2 and 4). Our expectations are that weak zones with a lower viscosity will yield wider back-arc basins as they allow for more efficient extension localization.
We compare the results of different 2-D experiments after roughly 1,500 km of subduction was completed (Figure 4a). Both narrow and wide weak zones experience some extension (up to 110-170%), but the weak zone with the lowest viscosity (η w = 0.5 × 10 22 Pa s) enables the highest amount of upper plate extension (125-170%). In 2-D models, wider weak zones facilitate more extension; thus, it follows that wider backarc basins will form if the initial weak zone is wider and weaker. However, Figure 4a shows that initially narrower weak zones with lower viscosities extend more than wider weak zones with slightly higher viscosity. This implies that, in our 2-D experiments, viscosity is the dominant factor controlling the amount of extension facilitated by weak regions on the upper continental plate. Therefore, although widest initially imposed weak zone results in the most extension in 2D, the viscosity appears to be more dominant.
Three-dimensional experiments with oceanic subduction, visualized after 1,500 km of subduction, show a different pattern compared to the 2-D cases (Figure 4b). Firstly, the amount of stretching of the extended zone increases significantly (140-280% depending on the configuration) for all tested width and viscosity configurations. Secondly, the trend of the experiments with the lowest viscosity weak zone (η w = 0.5 × 10 22 Pa s) differs significantly. The widest imposed weak zone (w = 264 km) experiences less extension than the two narrower imposed weak zones (w = 99 and 132 km) with the same viscosity ( Figure 4b).
Experiments with the same weak zone parameters, but also containing a continental block on the lower plate, yield the highest amount of upper plate extension after 1,500 km of subduction ( Figure 4c). The two narrowest weak zones (w = 66 and 99 km) with the lowest viscosity (η w = 0.5 × 10 22 Pa s) have extended approximately 1,000-1,200% with respect to their original width. As in the 3-D experiment with a purely oceanic lower plate, the weak zones with the lowest viscosity (η w = 0.5 × 10 22 Pa s) stretch around 3 times more than those with a higher viscosity (Figure 4c). Stretching of the weakest and narrowest weak zone increases dramatically after 1,500 km of subduction (Figure 4c). Toward the end of the experiments, after 40 Myr and subduction of a minimum of 1,800 km of oceanic material, the back-arc basin has experienced approximately 1,800% extension with respect to its initial width (Figure 4c). Thus, we conclude that, with this setup, the narrowest and weakest weak zone allows the highest amount of extension, which is opposite to the results obtained in 2D. Furthermore, for a given viscosity, the width of the weak zone seems to be the most important factor that controls back-arc basin extension in the 3-D experiments we conducted.

The Role of the Continental/Oceanic Area Distribution on the Subducting Plate
Results from Magni et al. (2017) suggest that there is a potential link between the ratio of continental to oceanic material in the downgoing plate and kinematics of upper plate extension. Following this line of investigation, we performed an additional set of experiments, in which we vary the ratio R c/oc on the downgoing plate ( Figure 2). We tested ratios R c/oc of 1.0, 0.78, 0.6, and 0.45 (Figure 5a). In these experiments, we impose a 66-km-wide weak zone (w) with a viscosity of (η w ) 0.5 × 10 22 Pa s in the overriding plate. The width of the upper plate extended zone through time is tracked along a profile that crosses the widest part of the final back-arc basin. As different ratios result in different final geometries, the location of this section varies for each experiment. Figure 5a shows top views of the four experiments with different continent/ocean ratio at 40 Myr, which is 31 Myr after the initiation of collision of the incoming continental block. The results display a trend: the highest R c/oc ratio (1.0) results in the widest back-arc basin, the rotation angles (primary rotation: 52°; secondary rotation: 34°) and lateral detachment of the rifted continental crust from the overriding plate at the southern boundary of the modeling domain ( Figure 5 and Animation MS06). When the ratio decreases (R c/oc = 0.78), the rifted continental lithosphere still separates laterally from the overriding plate, but less than in the previous experiment while the rotation angles are lower (primary rotation: 48°; secondary rotation: 23°; Figure 5 and Animation MS07). With a further decrease of the R c/oc ratio (0.6), the rotation decreases to 47°( primary rotation) and 10°(secondary rotation), and no lateral detachment of the rifted continental fragment from the southern side of the overriding plate is observed, a trend which is also observed for lower values of R c/oc (0.45; Figure 5a and Animations MS05 and MS08, respectively). Moreover, the difference between the primary and secondary rotation angles increases, indicating a larger curvature of the continental fragment. All experiments yield back-arc basins with breakup as defined above (less than 70% continental material in the crust at 8-km depth).
In all four experiments, continental breakup initiates in the back-arc domain at roughly 20 Myr of experimental time, approximately 11 Myr after the initiation of continental collision. We measure the rift evolution by tracking the width of the newly forming oceanic domain along a profile that crosses the widest part of the final back-arc basin (the green lines in Figure 5a). The trend of decreasing back-arc basin width with decreasing R c/oc ratios observed in the top views is also present in the plots of the rift evolution ( Figure 5b). The highest ratio of continental to oceanic material produces the widest back-arc basin and thus has the fastest back-arc extension. For each successive experiment where the ratio of continental to oceanic material decreases, the final rifted width of the back-arc basin decreases. The evolution of this extension through time is similar for the different experiments with the main difference being the final rifted width and the extension rate (Figure 5b).

The Role the Imposed Continental Weak Zone Angle
In previous experiments we imposed the weak zone parallel to the trench to limit model complexity. However, as this geometry is seldom found in nature, we perform an additional set of experiments to test the influence of the initial angle of the weak zone with respect to the trench. Taking the experiments with R c/oc ratios of 0.6 and 1.0, an imposed weak zone width (w) of 66 km and a viscosity (η w ) of 0.5 × 10 22 Pa s, we vary the angle of the weak zone with respect to the trench with 15°in both clockwise (positive) and counterclockwise (negative) directions. Top views depicting the log 10 (second invariant of the strain rate) with continental crust contours, after 40 Myr of experimental time, are displayed in Figure 6a. Rotation angles are measured in the same manner as in section 3.4. Different geometries are observed for different initial weak zone orientations. For α = −15°counterclockwise angle on the experiment with R c/oc = 0.6, we observe lateral detachment of the continental crust from the southern lateral domain boundary and a 29°primary (yellow) and 21°secondary (orange) angle (Figure 6a (top right panel) and Animation MS09). This is different from the experiment with the same setup (w = 66 km, η w = 0.5 × 10 22 Pa s, R c/oc = 0.6), but with a different weak zone angle α (0°) in which there is no lateral detachment of continental crust from the rest of the continental overriding plate (Figure 6a (top middle panel) and Animation MS05). The geometry of the newly formed back-arc basin has a wedge shape, whereas the basin in the 0°experiment is triangular. When we impose a weak zone with an angle α = +15°clockwise in an otherwise similar setup, the detached continental block is around 2 times wider when compared to the experiment with a α = 0°weak zone, but back-arc basin width is much narrower and more elongated (Figure 6a (top right panel) and Animation MS10). The rotation angles are also lower, with a 27°p rimary angle (yellow) and 8°secondary angle (orange). Compared to the α = 0°experiment, the shape of the back-arc basin is narrower and more elongated.
The experiment with w = 66 km, η w = 0.5 × 10 22 Pa s, and R c/oc = 1.0 showed significant lateral detachment of continental crust from the southern lateral domain boundary, as well as a wide back-arc basin 10.1029/2019JB018370

Journal of Geophysical Research: Solid Earth
VAN DEN BROEK ET AL.
( Figure 6a, middle bottom panel). A counterclockwise angle α of −15°in this setup (w = 66 km, η w = 0.5 × 10 22 Pa s, R c/oc = 1.0) results in a relatively narrow sliver of continental material that detaches laterally from the southern side of the continental overriding plate behind a large v-shaped back-arc basin (Figure 6a and Animation MS11). Rotation angles have very similar values 39°(primary rotation) and 36°(secondary rotation), indicating a large rotation of the entire block of the continental fragment. Imposing an angle of α = +15°clockwise on the weak zone yields similar results to those obtained for the R c/oc = 0.6, α = +15°e xperiment. The geometry of the back-arc basin in this experiment (R c/oc = 1.0, α = +15°) is more vshaped and somewhat wider when compared to the one describe in the previous paragraph (R c/oc = 0.6, α = −15°; Figure 6a (bottom right panel) and Animation MS12). Rotation angles are also similar to the R c/ oc = 0.6, α = +15°experiment with a 29°primary rotation and 18°secondary rotation angle. In order to quantify the effect of the initial weak zone angle, we calculate the area of the new back-arc basin.
Using the position of the trench to delineate the overriding plate, the back-arc basin area is calculated by summing the area of all cells in the overriding plate where continental material is <70%. Experiments where the weak zone is imposed under a negative angle (α = −15°counterclockwise) angle yield a higher area (29% and 5% more for R c/oc = 1.0 and R c/oc = 0.6, respectively) of newly formed oceanic back-arc lithosphere when compared to the experiment with no angle on the imposed weak zone (α = 0°; Figure 6b).
Conversely, experiments where the weak zone is imposed under a positive angle (α = +15°clockwise) yield a lower area (26% and 6% less for R c/oc = 1.0 and R c/oc = 0.6, respectively) of newly formed oceanic back-arc lithosphere when compared to the experiment with no angle on the imposed weak zone (α = 0°; Figure 6b).

Conditions Enabling the Formation of Continental Fragments in Subduction Settings
We find that extension in the overriding plate does not always result in continental breakup. In order to induce extension and trigger breakup of the overriding plate in our relatively unconfined setup, the presence of a preexisting weak zone is required. While experiments without such an imposed weak zone do experience limited trench retreat (Animation MS04), extensional stress in the overriding plate does not localize sufficiently considering our current rheology, and breakup does not occur (Animations MS02 and MS04).
In the 2-D cases, this is consistent with previous 2-D numerical models that showed that extension is not achieved in strong overriding plates (Garel et al., 2014) and, in some cases, a weak back-arc lithosphere is needed to create a back-arc basin (Wolf & Huismans, 2019). For the 3-D cases, this differs from previous models, in which back-arc basins can form without a preexisting weak zone in the overriding plate (e.g., Magni et al., 2014). However, these back-arc basins formed in a very confined setup where two separate continental blocks on the downgoing plate collide with a continental overriding plate. Subsequent back-arc basin formation is then due to the continued subduction of oceanic material between the two continental blocks and associated trench retreat.
Deformation of the lithosphere, whether it is brittle or ductile, can result in permanent damage of the rocks and thus in inheritance. Brittle failure usually occurs in (semi)discrete planes when the surrounding stress exceeds the yield stress of the material (Byerlee, 1978). Due to strain(-rate) weakening processes, the resulting structure can be weaker than the surrounding material and will thus be preferentially activated during subsequent application of stress. Localization of ductile deformation is usually associated with the switch to grain size sensitive deformation mechanisms (Drury, 2005). However, in polycrystalline mixtures the presence of more than a single phase inhibits grain growth and healing of damaged material due to grain boundary pinning (Manohar et al., 1998). This results in slow grain growth and long healing times, providing damage memory and tectonic inheritance (Bercovici & Ricard, 2014. Inherited structures can thus be the result of numerous tectonic processes and therefore have different geometries, extent, and rheological properties. They include, but are not limited to, old failed rifts (El Harfi et al., 2006;Ziegler et al., 2001), old orogenic sutures, and subduction zones (Morgan et al., 1994;Schiffer et al., 2015). These previously deformed regions can contain faults, (ductile) shear zones and deformed mantle material, all of which can locally influence the strength of the lithosphere (Mazzotti & Gueydan, 2018). Subsequent deformation can localize along these inherited, weaker structures (Balázs et al., 2017;Bercovici & Ricard, 2014;Heron et al., 2016), facilitating further rift development within the tectonic system. Due to the inherent complexities of nature, quantifying the strength of inherited structures is difficult. However, numerical and rock deformation experiments indicate that inherited rheological weaknesses can be 1-2 orders of magnitude weaker than the surrounding lithosphere (Mazzotti & Gueydan, 2018).
Our variation of weak zone configurations implies that the viscosity contrast at the surface between the imposed weak zone and its surroundings must be of a certain magnitude, before sufficient localization of extension and breakup occurs. We find that in our setup this viscosity contrast must be at least 1 order of magnitude, implying that, in nature, lower magnitude viscosity variations might be negligible for the larger-scale evolution of the subduction system. Indeed, in our experiments, the most efficient back-arc rifting and separation of a continental block from its parent continent occurs when the initial imposed weak zone has a viscosity that is 1.5 times lower at the surface than the surrounding crust (Figures 4 and 5).
Results from 3-D experiments also indicate that narrow weak zones within the overriding continental plate facilitate relatively more extension than wider weak zones (Figure 4). This is most likely because higher stresses are localizing in a smaller unit area, resulting in higher strain rates. The final shape of the continental fragment and the back-arc basin is controlled by the orientation of the initially imposed weak zone in the overriding plate relative to the trench ( Figure 6). While we did not test variations in the convergence direction relative to the trench, such variations could potentially impose additional differential stress on the upper plate. This can result in further variations in the evolution and final geometry of the continental fragment and back-arc basin.
The initial geometry of the subducting plate can be important for the dynamics of subduction and its influence on overriding plate extension. By introducing a continental block on the downgoing plate, we induce lateral variation in the upper plate stress that causes trench rotation and a more pronounced, local, extensional regime in the overall convergent setting (Figure 3). Trench rotation by an indenter has been previously proposed based on observations of contemporary convergent plate boundaries (Wallace et al., 2009). A torque that acts on the trench results from the opposing forces created by the subducting continental part of the subducting plate and the slab pull force of the laterally ongoing oceanic subduction (Wallace et al., 2005). Together with upper plate heterogeneities, lateral along trench stress gradients in the upper plate caused by slab rotation are the second necessary requirement for separation of continental crustal material from active continental margins and formation of continental fragments. Previous 3-D experiments with a similar rotational setup (e.g., Magni et al., 2017) obtained back-arc basin formation and very narrow continental fragments without introducing a weak zone in the overriding plate. However, in these models, the rifting starts very close to the trench and yields fragments of around 150 km wide, whereas our experiments produce fragments with a minimum width of 200 km yielding more substantial continental fragments. Additionally, analogue modeling of a divergent tectonic setting has also found that rotational opening kinematics and preexisting weak zones are required for continental fragment formation in such a setting (Molnar et al., 2018).
Our results also indicate that relatively high ratios of along-strike width of continental to oceanic material (high R c/oc ) result in wider back-arc basins, (single-sided) lateral detachment of the rifted continental lithosphere from its parent continent along the southern lateral domain boundary, and larger rotation angles (primary and secondary; Figure 5). Such a high R c/oc ratio implies a relatively narrow subducting oceanic slab after the initiation of collision between the incoming continental block and the overriding plate (Figures 2 and 5). This observation fits with previously proposed hypotheses that narrow subducting plates have a lower viscous resistance in the mantle and that narrow slabs as well as slab edges experience more trench retreat and rotation (Schellart et al., 2007;Wallace et al., 2009). Such increased rates imply a higher differential stress in the overriding plate resulting in more efficient back-arc basin formation. Additionally, this effect is also seen in the measured rotation angles. When we define a "residual rotation angle" as the difference between the primary and secondary rotation angles, results indicate that a higher R c/oc ratios (and weak zone angles) result in a lower residual angle of the continental fragment. Comparing Figures 5 and 6, this residual angle can be considered as a proxy for the bulk rotation of the continental fragment; that is, a high residual angle implies a curved continental fragment, while a low residual angle implies a relatively straight continental fragment that is laterally detached from its parent continent.

Model Limitations
As all modeling studies, our models required several simplifications of complex natural features and properties in order to be able to run the experiments. The rotation of the oceanic slab is favored by the presence of transform faults that we impose as weak regions adjacent to the subducting and overriding plate. This is a simplified model representation of transform faults in nature that accommodates the migration of the trench (i.e., STEP faults; Govers & Wortel, 2005). Moreover, this setup allows for toroidal mantle flow around the subducting slab, which is crucial to avoid domain induced boundary effects (Chen et al., 2016;Funiciello et al., 2003). A free surface, instead of free slip, boundary condition might affect the stresses at the surface. This is relevant for the evolution of topography in subduction settings (Quinquis et al., 2011), but we do not expect the overall dynamics to change significantly for our scale of interest. We neglected an oceanic crust, but as we include yielding, the strength of the oceanic plate at Earth's surface is sufficiently low to allow the downgoing plate to decouple from the surface free-slip boundary and subduct (Quinquis et al., 2011).
Our setup imposes a weak mantle wedge between the subducting and overriding plate to facilitate decoupling between the two plates and to simulate the weak mantle wedge present in nature. By imposing, rather than dynamically calculating this weak mantle wedge, we potentially influence the effects of the toroidal mantle flow on the base of the overriding plate lithosphere, something that has been suggested to play an important role in upper plate back-arc extension (Chen et al., 2016). However, other authors argue for a more dominant role of shallow crustal forces related to the collision of a positively buoyant indenter at the trench in the nucleation and evolution of back-arc rifting (Wallace et al., 2009).
Although the composition and structure of the continental crust can vary widely, we have used an initial homogeneous crust. We use an average density of ρ c = 2,700 kg m 3 , which is a commonly used value for the upper crust (Bittner & Schmeling, 1995;Turcotte & Schubert, 2002). Changes to the crustal density result in changes to the buoyancy of the continental material, which controls the occurrence and timing of slab break-off (Magni et al., 2017;van Hunen & Allen, 2011). For our study it is relevant that slab break-off occurs, but the exact timing and depth is of lesser importance. In general, a denser continental crust would delay the time of slab break-off, but would not change the model evolution (van Hunen & Allen, 2011).
Potential geometrical variations, such as variable lithospheric thicknesses of an inherited weak zone, are not taken into account in our setup. However, as we are mainly interested in the first-order processes controlling activation of our imposed weak zone and its subsequent evolution in a subduction setting, we feel that these limitations do not significantly influence the dynamics of the system.

Model Comparison With the Central Mediterranean Sea
Our results have first-order geometric and kinematic similarities with the evolution and present-day architecture of the Corsica-Sardinia block in the central Mediterranean. The model with R c/oc = 1.0 and α = −15°i s probably the closest to this natural example (Figures 6 and 7), although our experiments aimed to investigate basic ingredients for the formation of continental fragments in subduction systems, not this particular setting.
It has been postulated that the initial African slab that subducted below Eurasia was initially very wide, stretching from, at least, the western side of the Balearic islands to southern part of the Alps (Figure 7a; Advokaat et al., 2014 ;van Hinsbergen et al., 2014). However, upon the initiation of trench retreat, the slab segmented into two distinct slabs: the Calabrian and Balearic (Figure 7a), formed along the then forming North Balearic Transfer Zone. This North Balearic Transfer Zone is a postulated lithospheric STEP fault whose existence is inferred in many reconstructions (Rosenbaum et al., 2002;van Hinsbergen et al., 2014). This proposed segmentation evolved in a much narrower Calabrian slab, which allowed for more trench retreat and slab rotation, which it experienced during its subsequent evolution (Advokaat et al., 2014;Gattacceca et al., 2007). This rotation was likely caused by the collision of an incoming continental block (Adriatic microplate) with the overriding plate (Eurasia). The Ligurian margin from which the Corsica-Sardinia detached, also experienced a long tectonic history and its structure is rather heterogeneous, as it contains Pyrenean, basement involved thrust structures (Lacombe & Jolivet, 2005), as well as various geological boundaries (Figure 1b). While there are no evidences that these structures affected the entire lithosphere, we infer that prior to breakup (Advokaat et al., 2014;van Hinsbergen et al., 2014), the Ligurian-Corsican region had a composite continental crust (or lithosphere); therefore, we postulated that the presence of a preexisting weak zone was very likely. Furthermore, the geometry of the back-arc basin in our R c/oc = 1.0, α = +15°experiment and that of the Liguro-Provençal basin are similar. Both in nature and in our models, separated continental blocks rotated around a nearby pole and experienced rotational basin opening that resulted in a v-shaped back-arc basin (Figure 7).
In the case of the central Mediterranean, the locus of extension relocated from the Liguro-Provençal basin to the Tyrrhenian basin around 10 Ma (Faccenna et al., 2001). The mechanisms that control this plate boundary relocation are still debated. Using results obtained from analogue modeling, Faccenna et al. (2001) postulated that, when the subducting slab reaches the 660-km transition zone, the combination of a reduced subduction velocity and the weight of the slab itself results in bending of the slab and curving of the trench. Consequently, trenchward relocation of extensional stress at the surface occurred, and caused the extension to relocate to the Tyrrhenian basin. Other authors suggest that the collision of the Calabrian trench with the African continent and Adriatic microplate caused lateral cessation of subduction and slab tearing along the margins. This potentially caused acceleration of the trench retreat velocity, strong toroidal mantle flow around the slab, and changes in the stresses in the back-arc (Faccenna et al., 2005(Faccenna et al., , 2007Magni et al., 2014). Our experiment only captured the first step in continental fragment formation, but failed to reproduce the plate boundary relocation. Further experiments investigating more ad hoc geometries, as well as the mechanisms controlling relocation of extension, may provide additional insight into the interplay between subduction mechanisms and formation and complete isolation of a microcontinent or continental fragment.

Conclusions
We used 2-D and 3-D numerical experiments to investigate the conditions required for localizing extension and to breakup a continental overriding plate that leads to the separation of a continental block from the active plate margin. Our results indicate that formation of a continental fragment or microcontinent from the overriding plate requires a preexisting, inherited weak zone with a viscosity that is, at minimum, 1 order of magnitude lower than the surrounding lithosphere at the surface. Furthermore, the presence of alongtrench stress gradients in the upper plate due to slab rotation is a second requirement to attain sufficiently high stress values able to localize and initiate upper plate extension (Figures 3 and 5). This localization is most efficient in narrower (66 km wide) weak zones where stress is higher over a smaller unit area. Single-sided detachment of the rifted block from its parent continent occurs for systems with relatively narrow subducting oceanic plates, as these narrow slabs result in the highest differential stress in the upper plate ( Figure 5). Our results shed some light on the processes that controlled the separation of the Corsica-Sardinia block from Eurasia by highlighting the roles of tectonic inheritance and the Adriatic indenter in the formation of the Liguro-Provençal basin.