The Development of Fault Networks at the Termination of Continental Transform Faults When Their Connecting Plate Boundary Is “Misaligned”

We report the results of a series of scaled laboratory experiments that investigate the development of fault systems in plate boundary transition zones, where deformation is distributed between a continental transform fault (e.g., Alpine Fault, New Zealand; North Anatolian Fault (NAF), Turkey; San Andreas Fault (SAF), USA) and its connecting plate boundary. In these transition zones, continental transform faults are observed to branch into multiple subsidiary faults. Here we show that large‐scale transition zone fault networks comprise crustal‐scale Riedel shears that develop sequentially outwards and away from the parent transform fault. Such fault networks form within brittle upper crust that overlies a ductile lower crust that deforms by large‐scale distributed simple shear. We argue that large‐scale distributed deformation of the lower crust occurs when continental transform faults are “misaligned” relative to their connecting plate boundaries. This misalignment may occur: (a) where a transform fault does not directly connect with a convergent or divergent plate boundary, as in the northern termination of the Alpine Fault and the western termination of the NAF; and (b) where a significant bend in the transform fault occurs in the plate boundary transition zone, as in the southern termination of the SAF. The development of such plate boundary misalignments appears to occur when a plate boundary transition zone develops as a continental transform fault propagates toward a different type of “connecting” plate boundary.

Where continental transform faults terminate and "connect" with another plate boundary type, typically hundreds of kilometers of strike-slip displacement must be accommodated across a plate boundary transition zone (Legg et al., 2004; J. T. Wilson, 1965).In some instances, this transition is "seamless" and continuous, where the deformation remains localized to the plate boundary fault as the type of plate boundary changes (when considering the plate boundaries on a tectonic scale).For example, the southern end of the transpressional Alpine Fault transitions The San Andreas Fault (SAF) (California) and its southern termination in the Salton Sea and transition to sea floor spreading in the Gulf of California.Fault traces from Legg et al. (2004).b(2) Schematic diagram illustrating the plate boundary misalignment and associated transition zone, referred to in this study, at the southern termination of the SAF.c(1) The North Anatolian Fault (NAF) has propagated progressively westward from its eastern termination against the East Anatolian Fault.At its western termination it branches in its mid section: Ez.S.F.= Ezinepazar-Sungurlu Fault, and at its western termination into northern and southern branches.Fault traces from Emre et al. (2020), Porkoláb et al. (2023), and Sunal and Korhan Erturaç (2012) c(2).Schematic diagram illustrating the misalignment and transition zone, referred to in this study, at the western termination of the NAF.(d) The Dead Sea Transform, its southern termination with pull apart basins that transition to rifting in the Red Sea (which transitions to sea floor spreading further south).Fault traces from Segev et al. (2014).
continuously from a continental transform fault to oceanic subduction of the Australian plate beneath the Pacific plate (Shuck et al., 2021;Sutherland et al., 2000) (Figure 1a(1)).Another example of a "seamless" transition is the southern termination of the transtensional DST, where an increasing number and size of pull apart basins transition to sea floor spreading in the Red Sea (Wu et al., 2012) (Figure 1d).However, there are other examples where the transition from a continental transform fault to a new plate boundary type is more complex.These examples occur where the transform fault appears "misaligned" relative to its connecting plate boundary fault.In these instances, deformation becomes distributed over a broad, intervening transition zone between the major plate boundary faults (Eberhart-Phillips & Bannister, 2010;Legg et al., 2004;Wannamaker et al., 2009;C. K. Wilson et al., 2004) (Figures 1a-1c).A number of major crustal scale faults are observed in these transition zones.Examples are the northern termination of the Alpine Fault (Figure 1a(1)), the southern termination of the SAF (Figure 1b(1)) and the western termination of the NAF (Figure 1c(1)).In regions where plate boundary deformation has become distributed across such transition zones, we refer to the two connecting plate boundaries as being "misaligned."The term "misaligned" used here reflects the relative physical positioning of two plate boundaries to generate these transition zones, as discussed in Section 5, and it should not be confused with the concept of fault misorientation used in seismological studies (e.g., Sibson, 1990).Figures 1a(2), 1b(2), and 1c(2) schematically illustrate plate boundary misalignment and associated transition zones referred to in this study.The misalignment and associated transition is shown to occur when (a) the transform fault does not directly connect to another plate boundary (Figures 1a(2) and 1c(2)) or (b) where there is a large bend in the transform fault (Figure 1b(2)).These transition zones can generate major-to-great (e.g., Magnitude ≥ 7.0) earthquakes, but unlike other major plate boundary types, how deformation localizes and migrates across them remains poorly understood (Bilich et al., 2004;Hamling et al., 2017;C. K. Wilson et al., 2004).
In this study, we simulate the boundary conditions of these broad transition zones using scaled laboratory experiments in order to determine the how faults develop and how deformation localizes and migrates in the upper crust across such transition zones.In particular, our experiment design is motivated by the boundary conditions of the transition zone in northeast South Island, New Zealand, between the Alpine Fault and the Hikurangi subduction zone (Figures 1a(1) and 1a(2)).This is because there are multiple interpretations of geophysical data across the transition zone that provide additional constraints for experiment design (Eberhart-Phillips & Bannister, 2010;Wannamaker et al., 2009;C. K. Wilson et al., 2004).Geophysical data indicates that deformation in the ductile lower crust beneath the transition zone is distributed between the two plate boundary faults, whereas deformation in the lower crust beneath the plate boundary faults is localized within large shear zones.The major faults of the Marlborough Fault System (MFS) that have developed within this transition zone (Figure 1a(1)) have an average spacing of 23 ± 10 km (Yang et al., 2019) and are shown to propagate vertically to sub-vertically from the surface to the lower crust, which is deforming by distributed deformation (Eberhart-Phillips & Bannister, 2010;Wannamaker et al., 2009;C. K. Wilson et al., 2004).
Despite appearing similar in map view, a key difference between these ∼100 km scale transition zone fault networks and smaller <10 km scale horsetail splay faults and associated flower structures is that transition zone fault networks do not join at depth (Eberhart-Phillips & Bannister, 2010;Wannamaker et al., 2009;C. K. Wilson et al., 2004).Horsetail splay faults and associated flower structures have been shown to merge to a single, localized fault at depth (Fedorik et al., 2019).Simulating large scale, distributed deformation as a basal boundary condition within an analogue experiment is therefore key to investigating fault development across plate boundary transition zones at the terminations of continental faults.
Examples of "seamless" transitions (e.g., the southern terminations of the Alpine Fault and the DST) are not discussed further in this study, as this investigation is focused on examples where the plate boundary transition zone is "misaligned."

Alpine Fault and Marlborough Fault System
The MFS comprises four major northeast-southwest striking dextral strike-slip faults that have developed within the ⁓100 km × 200 km transition zone between the dextral transpressive Alpine Fault and the Hikurangi subduction zone (Figure 1a(1)) (Wallace et al., 2007(Wallace et al., , 2012)).The MFS faults are considered to have developed sequen tially southward from 6 Ma to the present day (Hall et al., 2004;Lamb, 2011;Little & Roberts, 1997;Randall et al., 2011) and their strike is sub parallel to the obliquely convergent plate motion vector between the Pacific and Australian plates (Wallace et al., 2012).South of the MFS is the Porters Pass to Amberley Fault Zone (PPAFZ), a zone of diffuse faulting with a relatively low strain rate (Figure 1a(1)).The PPAFZ is a hypothesized location for an incipient fifth fault in the MFS (Cowan et al., 1996).
The Alpine Fault accommodates the bulk of the present day ⁓40 mm/yr oblique convergence across central South Island (Altamimi et al., 2012;Beavan et al., 2016).In northeast South Island, this plate motion is distributed across the faults of the MFS.The Wairau, Awatere and Clarence faults (Figure 1a(1)) record slip rates of 4-8 mm/yr, while the Hope Fault has a slip rate between 18-30 mm/yr (Litchfield et al., 2014;Van Dissen & Yeats, 1991).

Southern Termination of the San Andreas Fault
The SAF extends northwest-southeast for 1,200 km across California, USA, forming the plate boundary between the American and Pacific Plates (Figure 1b(1)).The SAF translates plate motion dextrally, connecting the Cascadia subduction zone in the north to sea floor spreading in the Gulf of California in the south.The relative motion between the Pacific and North American plates is estimated to be 50 mm/yr (DeMets et al., 2010).The SAF itself accommodates between 20 and 35 mm/yr of this motion along its length (Norris & Toy, 2014).This rate significantly decreases at the "Big Bend," where presently, the San Jacinto Fault splits from the SAF (Figure 1b(1)).To the south of the Big Bend, the slip rate of the San Jacinto Fault is approximately equal to the SAF (Lindsey & Fialko, 2013).To the west of the San Jacinto Fault are the Elsinore and Newport Inglewood Rose Canyon (NIRC) faults.These faults are equally spaced at ⁓30 km from each other (Scholz et al., 2010), and the net slip decreases sequentially westward across them.The San Jacinto Fault has a net slip of 20 km (Kendrick et al., 2002), the Elsinore fault 12 km (Magistrale & Rockwell, 1996) and the NIRC fault 4 km (Mills & Fisc, 1991).The San Jacinto fault developed at 1.5 Ma, at the same time the Big Bend formed in the SAF system (Bennett et al., 2004;Morton & Matti, 1993).The Elsinore Fault is slightly younger, having developed at ⁓1.2 Ma (Dorsey et al., 2012).

Western Termination of the North Anatolian Fault
The NAF is an east-west trending, 1,200 km long dextral strike-slip fault that forms the plate boundary between the Anatolian and Eurasian plates (Norris & Toy, 2014;Şengör et al., 2005;Sunal & Korhan Erturaç, 2012) (Figure 1c(1)).The NAF developed between 13 and 11 Ma in the east and propagated to the west, while accommodating lateral westward extrusion of the Anatolian plate away from the collision zone between the Arabian and Eurasian plates, reaching its current western termination in the Sea of Marmara at 200 ka (Norris & Toy, 2014;Provost et al., 2003;Şengör et al., 2005).The western termination of the NAF occurs northeast of the Hellenic subduction zone, which bounds the Anatolian plate to the south and west (i.e., they do not connect) (Figure 1c(1)).The shear zone associated with the NAF is narrow in the east, forming a localized, crustal scale weakness that accommodates the bulk of the plate motion.Slip rates are calculated at 22-24 mm/yr with an average total displacement of 75-85 km (Hubert-Ferrari et al., 2009;Norris & Toy, 2014;Provost et al., 2003;Şengör et al., 2005;Sunal & Korhan Erturaç, 2012).The shear zone becomes progressively wider toward the west, where the fault is younger.At the sea of Marmara, the fault splits into multiple strands, the two main structures being the Northern NAF and the Southern NAF, creating similar fault pattern to those observed in the MFS and the southern termination of the SAF.

Methods
It can be challenging to understand how strike-slip, transpressional or transtensional fault systems develop through time from field data alone.By recreating such deformation systems in simplified, scaled-down analog models, we can test hypotheses for and analyze the development of geological structures in three dimensions (3D) and through time in a controlled laboratory environment (Dooley & Schreurs, 2012).
In this study, we carried out a series of analog experiments to investigate and compare the formation of geological structures in regions of localized simple shear and regions where simple shear becomes distributed over a much larger area, as well as the transition between the two.The region of localized simple shear is analogous to a transform fault (Norris & Toy, 2014).Regions of distributed simple shear (DSS) aim to simulate transition zones at the termination of transform faults where the adjoining plate boundary does not directly connect with the transform fault (C.K. Wilson et al., 2004), as illustrated by the case studies above (Figures 1a-1c).
The sandbox consists of two halves, one that remains fixed and another which is mobile.The mobile half is pushed (dextral motion) or pulled (sinistral motion) by a linear actuator at a velocity specified by the user, allowing one side of the box to move horizontally relative to the other side, generating strike-slip motion.This motion creates a central velocity discontinuity along the base of the sandbox.This sandbox is only capable of strike-slip motion However, in each case study, the dominant mode of deformation is strike-slip, hence these faults are considered transform faults.Our analog experiments are therefore representative of this dominant strike-slip component.

Materials
The sandbox is filled with a 2.5 cm thick layer of homogeneous granular material.Our granular material has a density of 960 kg/m 3 and consists of a mixture of dry quartz sand (60%) and hollow ceramic microspheres (Envi-rospheres® 40%) (Molnar et al., 2017;Samsu et al., 2021).Both the quartz sand and the ceramic Envirospheres® have homogenous grain size distributions.Using a Hubbert-type shear box, Molnar et al. (2017) determined that this mixture has an angle of internal friction of <38° and a cohesion value of ∼9 Pa respectively, making it an appropriate analog for modeling the brittle, Mohr-Coulomb behavior of upper crustal rocks (Byerlee, 1978;Davy & Cobbold, 1991;Schellart, 2000).The material is sieved into the sandbox from a height of 10 cm, and once in place is not manipulated in any way to avoid localized compaction of grains.

Basal Boundary Conditions
Deformation of the granular material is determined by the boundary condition at the base of the box.Without modification, deformation in the granular material becomes localized over the central basal discontinuity, analogous to a transform fault.
The presence of a ductile lower crustal analog layer can be expected to result in more diffuse deformation in the brittle upper crust, with the spacing of shear zones being a function of the brittle-ductile strength ratio (Riller et al., 2012).However, test experiments showed that the addition of a viscous lower crustal analog in the sandbox, without any other modifications, was not sufficient to distribute deformation across the ⁓100 km scale that occurs in transition zones, and deformation within the lower crustal analog remained concentrated over the central discontinuity at depth.In order to be analogous to the basal boundary conditions of a transition zone in nature, we modified the sandbox to create a basal boundary condition that deformed by large scale DSS and eliminated the effects of the central discontinuity.This was achieved by taping a rectangular piece of thin, four-way stretchable elastic fabric to the base of the sandbox, over the central discontinuity (Figure 3).
Test experiments with the stretchable material overlain by sieved granular upper crustal analog material showed good consistency with previous analog experiments investigating DSS with a viscous analog lower crust (Schreurs, 2003).The size and location of the stretchable material can be varied to define several different basal boundary conditions as described in Section 3.4.
In each experiment set up, the stretchable material was taped to the base of the sandbox using two pieces of duct tape taped along the length of the material, allowing the material to freely deform into a parallelogram (Figure 3).The duct tape overlapped the stretchable material by 1 cm.Test experiments showed that the stretchable fabric folded with increased displacement of the sandbox.We found that stretching the material by 1 cm in width either side of the central discontinuity minimized the folding of the stretchable fabric within the first 40 mm of sandbox displacement (see Supporting Information S1).The stretchable fabric dimensions detailed in Figure 3, Section 3.4, and Table 1, refer to the area of exposed and stretched fabric that will deform beneath the sand during the experiment.

Experiments
The five setups used in the series of experiments reported here are illustrated in Figure 3 and characterized in Table 1.Experiment A (Figure 3a) was designed to characterize the development of a localized simple shear zone, and so involved no modification to the sandbox.Experiment B (Figures 3b and 3f) was designed to investigate the development of a DSS zone.Distributed shear was generated by taping a 14 cm × 28 cm piece of four-way stretchable fabric across the base of the box prior to adding the granular material.Experiment C (Figure 3c) was designed to model adjacent localized and DSS zones.A 14 cm × 14 cm piece of four-way stretchable fabric was taped over the base of one half of the box, while retaining the central discontinuity at the base of the other half.Experiment D (Figures 3d and 3g) tested the development of both localized and distributed shear zones in which the distributed shear zone occurs only on one side of the localized shear zone (approximating the boundary conditions of the Alpine fault and MFS).A 7 cm × 14 cm piece of four-way stretchable fabric was taped over the base of the box in the position shown in Figures 3d and 3g.Experiment E repeated Experiment D except the motion was sinistral, as shown in Figure 3e.
Each experiment was deformed at a constant velocity of 150 mm/hr.Experiments A and B were displaced dextrally by 150 mm over 60 min.Experiments C and D were displaced dextrally by 75 mm in 30 min and Experiment E was deformed sinistrally by 75 mm in 30 min.The shorter displacements in these experiments were imposed by how far the basal fabric could stretch in these different setups.The different amounts of displacement between experiments did not affect the outcomes of the investigation because mature fault systems developed in each experiment after 30 mm of displacement.Each experiment was repeated a minimum of three times to ensure reliable, repeatable results.

Experimental Analysis
A Nikon D7500 digital camera captured top view images of the experiment surface at fixed 30 s intervals during deformation of the sandbox, corresponding to 1.25 mm sandbox displacement per image.We used Digital Image Correlation (DIC) in DaVis 10.1.2to analyze the 2D surface deformation in the experiments (Adam et al., 2005).The displacement field was computed by cross correlation of the particle pattern on the surface of the experiment, which distorts and translates in each successive image due to displacement of the sandbox over the course of the experiment.For our presented results, we used a subset size of 15 pixel, a step size of 5 pixel, an increment of 2 with the calculation mode set to Accurate.To aid the DIC algorithm we randomly distributed coffee grounds onto the surface of each experiment to provide a high contrast, random pattern suitable for feature tracking.The calculated incremental displacement vector field (Adam et al., 2005) can be used to compute a range of strain quantities, including the incremental and cumulative shear strain (E xy ) (Boutelier & Cruden, 2013;Molnar et al., 2017Molnar et al., , 2018;;Riller et al., 2012;Samsu et al., 2021;Schrank et al., 2008).Incremental shear strain is the calculated "instantaneous" shear strain from the tracked changes in particle locations between two images on the XY plane where the X-axis is parallel to the direction of shear (Ramsay, 1980;Ramsay & Graham, 1970;Schrank et al., 2008).The cumulative shear strain is the sum of the incremental shear strains.Our results are presented as maps of incremental shear strain on the surface of the sandbox models.

Scaling
Since our experiments focus on modeling the brittle behavior of the upper crust, we need to scale for stress, such that the stress scale factor Σ = Pλ, where P is the density scale factor and λ is the length scale factor (Cruden et al., 2006;Schellart, 2000).Taking the density of the granular material in the laboratory ρ m = 960 kg/m 3 , to represent upper crust with a density ρ p 2,650 kg/m 3 (Molnar et al., 2017) gives P = ρ m /ρ p = 0.36, where subscripts m and p denote the model and natural prototype, respectively.Assuming, for convenience, that a 2.5 cm thick sand layer (l m ) represents a 25 km thick brittle crust (l p ) in nature gives λ = l m /l p = 1 × 10 −6 and Σ = 3.6 × 10 −7 .This means that brittle rocks with values of cohesion ∼50 MPa must be modeled by granular materials with cohesion values ∼50 × 10 −7 = 5 Pa, which is matched closely by our sand + Envirospheres® mixtures.
With the length scale factor above, the 7 cm × 14 cm piece of stretchable material at the base of the sandbox in Experiments 4 and 5 represents a 70 km × 140 km area of distributed deformation in the lower crust in nature.A displacement of 7.5 cm in the sandbox is equivalent to 75 km in nature.This area and net displacement are comparable to the MFS.The results presented only show displacement up to 3 cm, as this is the point by which a mature fault system had developed in each experiment, so there is little change to the fault system after this stage.Since the Mohr-Coulomb rheology of granular material is rate independent, we do not strictly need to consider time for scaling the deformation rates in our experiments (Fedorik et al., 2019;McClay, 1990).

Experiment A: Localized Deformation Experiment
Figure 4a1 shows that no discrete structures formed during the initial stages of deformation but a 35 mm wide zone of outwardly decreasing incremental shear strain developed over the central discontinuity.Riedel shears are visible at 5 mm displacement of the sandbox (Figure 4a2).These structures have a maximum orientation of 18° clockwise  relative to the displacement direction of the sandbox, with a spacing of 90 mm measured parallel to the central discontinuity and a perpendicular spacing of around 35 mm.At >5 mm displacement, P shears formed that link the Riedel shears and by 10 mm displacement (Figure 4a3), the Riedel shears were mostly abandoned with deformation almost entirely focussed on a single fault located over the central discontinuity.This single fault accommodated the deformation for the remainder of the experiment, although relic popup structures remained (Figures 4a3-4a7), preserved from the stage when the Riedel shears were abandoned in favor of the central through-going fault.

Experiment B: Distributed Deformation Experiment
Discrete geological structures took longer to form in Experiment B compared to Experiment A. During the initial stages of deformation (Figure 4b1), incremental shear strain is accommodated in a broad 40 mm wide zone over the center of the box, which is slightly wider than Experiment A (Figure 4a1) but with lower values.With increased displacement (Figures 4b2 and b3), this zone of incremental shear strain broadens across the width of stretchable material at the base of the box.After ∼15 mm displacement two main sets of linear structures began to form (Figure 4b4).The dominant structure is a set of equally spaced faults oriented 18° clockwise relative to the displacement direction of the sandbox, with a perpendicular spacing ranging between 10 and 20 mm, averaging around 17 mm.The orientation of these structures is consistent with them being conjugate Riedel shears.When the spacing between a pair of these faults becomes >20 mm, a smaller, parallel fault develops in-between (Figure 4b7).A second set of equally spaced linear structures is oriented around 80° relative to the displacement direction of the sandbox, with a perpendicular spacing of around 10 mm.The orientation of these structures is consistent with them being antithetic Riedel shears.

Experiments C and D: Dextral Transition Experiments
The area of localized deformation above the basal discontinuity in both Experiments C and D developed in the same manner as Experiment A (Figures 5c1,5c2,5d1,and 5d2).By the time that Riedel shears developed in the zone of localized simple shear in both experiments (∼5 mm displacement), no structures were present in the area of DSS above the stretchable material.Instead, outwards decreasing, diffuse incremental shear strain is observed over the region (Figures 5c2 and 5d2).By 10 mm of displacement in both experiments, a single fault had formed above the central discontinuity in the localized simple shear region.
Major faults began to develop in the region of DSS after ⁓15 mm of displacement in both experiments.These faults are consistent with those formed in Experiment B with an orientation ⁓18° clockwise relative to the displacement direction of the sandbox and a perpendicular spacing of ⁓20 mm.In both experiments, the first faults in the regions of DSS formed over the center of the sandbox.With increased displacement, more faults developed sequentially outwards from the center of the box, toward the edges of the stretchable material.The faults that formed closer to the center of the box eventually linked and connected with the major fault over the region of localized simple shear.However, faults developed in the region of distributed deformation but further away from the center of the box did not connect with the earlier formed faults closer to the center of the box.

Experiment E: Sinistral Transition Experiment
The faults that formed in this experiment (Figures 6e1-7) developed in the same manner as Experiment D. The fault in the zone of localized deformation formed first, followed by the faults in the region of distributed deformation.The faults in the region of distributed deformation once again nucleated within a region of diffuse strain, developing sequentially outwards from the center of the box toward the edge of the stretchable material.As in the previously described experiments, these faults are oriented 18° relative to the sinistral displacement direction of the sandbox but with the opposite polarity.

Experimental Artifacts and Limitations
A number of artifacts developed at the short ends of each experiment due to the geometry of the vertical side boundaries and corners of the sandbox (Figure 2).For example, in Experiment B regions of extension and compression are present at either end of the box, becoming more pronounced with increasing displacement (Figure 4b).Although unwanted, these boundary effects are outside the area of interest in the central region of the sandbox and therefore do not have a strong influence on the experimental results.3), determined by Digital Image Correlation.Each incremental shear strain map is given a label for reference in the results section.The location of the shear strain map within the experiments is illustrated in Figure 3.
experiment E is further away from the stretchable fabric than experiments A-D because the location of the artifact is not constrained by the edge of the sandbox.As with the artifacts related to the vertical side walls and corners, these features have no equivalent in nature.For this reason, we were careful to restrict our observations and analyses to the regions above the central part of the stretchable material, which are not obviously influenced by edge effects.
The experimental setup is also limited by the elasticity of the stretchable material, which cannot deform indefinitely.This effect is avoided by limiting the amount of displacement in experiments that used smaller pieces of stretchable material.

Fault Development in Regions of Localized Deformation
In the experiments, Riedel shears formed first followed by the development of P Shears, which linked the Riedel shears to form a single, continuous fault that localized over the central discontinuity at the base of the sandbox.The development of structures in regions of localized deformation are consistent with many similar analog modeling and field studies on the evolution of strike-slip faults (Dooley & Schreurs, 2012;Lefevre et al., 2020;Naylor et al., 1986;Riedel, 1929;Ritter et al., 2018;Schrank & Cruden, 2010;Schrank et al., 2008;Tchalenko, 1970;Venâncio & de Silva, 2023;Wilcox et al., 1973).The single faults that developed above the basal discontinuity in Experiment A, and in the localized regions of simple shear in Experiments C, D, and E (Figures 4-6), accommodated the bulk of the deformation within these regions.These faults are analogous to the Alpine, San Andreas (to the north of the big bend) and North Anatolian transform faults (Figure 1).

Fault Development in Regions of Distributed Deformation
In regions that overlay a basal boundary condition of distributed deformation, the upper crustal analog developed a sub-parallel array of approximately equally spaced faults oriented ⁓18° relative to the central discontinuity, consistent with the orientation of Riedel shears.In Experiment B, antithetic Riedel shears also developed.The development of faults with this pattern is consistent with similar analog modeling studies (Schreurs, 2003).
The faults that formed over the regions of DSS (Figures 4-6) are similar to the fault patterns observed at the northern termination of the Alpine Fault (the MFS) (Figure 1a), the southern termination of the SAF (Figure 1b) and the western termination of the NAF (Figure 1c).These fault systems are oriented close to ⁓18° relative to their associated transform fault and therefore these fault systems could be considered tectonic scale Riedel shears.The southern SAF system is younger than the MFS, beginning its development at 1.5 Ma compared to 6 Ma in the MFS (Bennett et al., 2004;Morton & Matti, 1993;Wallace et al., 2012).The MFS can therefore be considered to be a more evolved system, similar to Experiment D at 30 mm displacement (Figure 5d7).In comparison to the MFS, the southern SAF pattern is similar to Experiment D at 20 mm displacement (Figure 5d5).The western termination of the NAF is even younger, having developed over the last 200 ka (Şengör et al., 2005), showing similarities to Experiment D at 15 mm displacement (Figure 5d4).

Fault Development at Transitions Between Localized and Distributed Simple Shear
Where localized deformation transitions to DSS in Experiments C, D, and E, the faults in the center of the sandbox develop first and then connect to the major transform fault in the region of localized deformation (Figures 5c,5d,and 6e).Starting as a zone of diffuse deformation (Figures 5-7), faults in the region of DSS nucleate sequentially outwards.The faults in the area of distributed shear strain therefore develop independently and are not splays from the major transform fault in the region of localized deformation (Figures 5 and 6).These faults exhibit significant slip rate reductions toward the major analog transform fault.The early forming central faults in the regions of DSS link to the main transform fault (Figure 5), and they accommodate much more displacement than the younger faults that develop subsequently (Figure 7).The displacement on these faults also decreases with age, so the youngest, peripheral faults record the least displacement (Figure 7).The connection of the central faults occurs by a series of cross-faults, which suggest participation of smaller linkage faults in allowing these spaced, major faults to "communicate" and collectively accommodate distributed shear.
These results of Experiments C, D, and E are consistent with the fault patterns and the proposed development of faults in the natural examples (Figures 1a-1c and 8).Both the Wairau Fault in the MFS (Figures 1a and 8) and the southern segment of the SAF (south of the Big Bend) (Figures 1b and 8) formed later, and accommodate less displacement than the main transform fault they join up with (Bennett et al., 2004;Morton & Matti, 1993;Wallace et al., 2012).
The MFS developed sequentially southward across the region between the Alpine Fault and Hikurangi subduction zone.The San Jacinto, Elsinore and NIRC faults associated with the southern San Andreas developed sequentially westward, away from the major transform fault (Dorsey et al., 2012).Displacement across each of these fault systems also decreases (on average) with age, consistent with fault development in Experiments C and D (Figure 5).
In the MFS (Figures 1a and 8), the Wairau Fault is the continuation of the Alpine Fault and the Awatere Fault to the south appears to either splay from or join the Alpine Fault.Both faults formed around 6 Ma (Wallace et al., 2012).Bennett et al. (2004) found that the southern San Andreas and San Jacinto faults developed at 1.5 Ma at the same time as the "Big Bend" formed on the SAF (Figure 8).This is similar to the formation of the initial faults within the regions of DSS in the transition Experiments C and D (Figures 5 and 8).
The connection of the Clarence and Hope faults in the MFS with the Alpine/Wairau Fault is poorly constrained and the slip rate of the Hope Fault decreases toward the Alpine Fault (Vermeer et al., 2021).The Hope Fault has been recently shown to have propagated from the center of the Marlborough region between the Alpine Fault and Hikurangi subduction zone, back toward the Alpine Fault (Vermeer et al., 2021).In the southern San Andreas, the San Jacinto Fault does not directly connect with the SAF.Scholz et al. (2010) also showed that the San Jacinto Fault developed at a distance away from the SAF and propagated back toward it, similar to the proposed development of the Hope Fault in the MFS.The Elsinore and NIRC faults also formed sequentially and further away from the SAF and do not connect with it.The sequential nucleation of faults in this manner starting with an initially diffuse region of deformation at a distance from the main fault branches, is consistent with the results of Experiments C and D (Figures 5, 7, and 8).
The ages of the northern and southern branches of the NAF are currently unknown but since the NAF had only propagated to the Sea of Marmara by 200 ka (Norris & Toy, 2014;Provost et al., 2003;Şengör et al., 2005) these branches must be relatively young (Figure 8).The consistency of the development of the MFS and faults associated with the southern termination of the SAF with the analog modeling results, suggest that the northern NAF and the southern NAF likely developed at the same time.Consistent with the development of the Wairau and Awatere faults in the MFS and the southern San Andreas and San Jacinto faults in California, in each case these are the first two faults to develop in the transition zone.

What Causes Deformation to Become Distributed?
Although the fault pattern evolution in Experiments C and D (Figures 5 and 7) helps to explain key features of the MFS, southern SAF and western NAF, similar fault patterns do not occur at the terminations and plate boundary transitions of all continental transform faults.In many examples, such as the southern Alpine Fault and the southern DST (Figures 1a and 1d), the transition between plate boundary types is localized and continuous.In these examples, the plate boundaries directly connect and deformation of the lower crust remains localized within the plate boundary.Here we discuss the possible causes of distributed deformation at plate boundary transitions.
How zones of distributed deformation develop where continental transform faults transition to a new plate boundary type, appears to depend on the tectonic history of the transform fault itself.Where the transition between the transform fault and the connecting plate boundary remains localized on a continuous plate boundary fault, the tectonic development of the adjoining plate boundaries is coeval (Shuck et al., 2021;Sutherland et al., 2000).Conversely, the northern Alpine Fault, southern SAF and western NAF all evolved independently from their "connecting" plate boundary.In each case, the transition zone between the continental transform fault and its connecting plate boundary developed by propagation of the transform fault toward the connecting plate boundary, resulting in a "misalignment" of the plate boundaries and the generation of a region of distributed deformation.
In New Zealand, the Alpine Fault propagated northeast while the Hikurangi subduction zone migrated southwest, leading to a transition zone of distributed deformation marked by the MFS (Figure 8b) (Lamb et al., 2016;Randall et al., 2011;Wallace et al., 2012; C. K. Wilson et al., 2004).The SAF began to develop at 28 Ma, when a spreading ridge entered a subduction zone, halting subduction and causing a transition to transform plate motion which propagated southwards (Dickinson & Snyder, 1979a, 1979b;Mckenzie & Morgan, 1969).This southward propagation resulted in the development of the Big Bend (Bennett et al., 2004) and the associated misalignment was sufficient to cause distributed deformation (Figure 8c.) In Turkey, the NAF formed in response to the westward escape of the Anatolian plate due to the collision between the Arabian and Eurasian plates.The NAF is still propagating westward toward the Hellenic subduction zone but is yet to connect with it, causing deformation to become distributed toward the fault tip (Norris & Toy, 2014;Provost et al., 2003;Şengör et al., 2005).The fault is only 200 ka old at its western end where it reaches the Sea of Marmara (Şengör et al., 2005) (Figure 8d).

Conclusion
The analog experiments presented here (Figures 4-6) contain boundary conditions analogous to tectonic scale transition zones where plate boundaries are "misaligned."These experiments show the development of fault patterns in a brittle upper crustal analog, overlying a region of DSS.The resulting fault pattern forms as a series of equally spaced, crustal-scale Riedel shear faults that develop sequentially away from the major transform fault, outwards across the region of distributed deformation.These faults occur away from the major transform fault and nucleate within a zone of initially diffuse deformation (Figure 7).Once formed these faults propagate back toward the major transform fault and for the most part do not connect with it, except for the first formed fault in the region of distributed deformation that eventually becomes a continuation of the major transform.
The consistency of the fault patterns that develop in the analog experiments  with those observed in nature in the MFS (the northern termination of the Alpine Fault), the southern termination of the SAF, and the western termination of the NAF (Figure 8), suggest that fault development in the experiments is a good analog for fault development across transition zones.We conclude these fault patterns likely develop from deformation of the brittle upper crust overlying ductile lower crust undergoing DSS.
DSS deformation of the lower and upper crust can occur when transitions between continental transform faults and adjoining plate boundaries become misaligned.We propose that this is likely to occur when two plate boundaries form at different times, and where the transition zone between them develops where a continental transform fault propagates toward its connecting plate boundary.We propose that such zones of distributed deformation essentially represent "young" plate boundary transitions, and with time the associated crustal scale Riedel shear faults may be abandoned to form a continuous transition from one plate boundary to another.Anindita Samsu is thanked for teaching and guidance in the Monash University Geodynamics laboratory.Lachlan Grose for constructive discussions during preparation of the manuscript and for assistance in generating the image stacks used in Figure 7. Mike Hall, for constructive feedback on the manuscript.Jan Oliver Eisermann for guidance on DIC analysis.Michelle L. Cooke and Andrew Nicol for constructive feedback on the thesis chapter from which this manuscript is based.Thanks go to Anonymous Reviewer 1, Tim Dooley (Reviewer 2) and Associate Editor Ernst Willingshofer for constructuve feedback on the manuscript.Open access publishing facilitated by Monash University, as part of the Wiley -Monash University agreement via the Council of Australian University Librarians.

Figure 1 .
Figure 1.Four fault maps showing examples of continental transform faults from across the globe, and their termination and transition to a new plate boundary type.a(1).The oblique dextral Alpine Fault in South Island, New Zealand.To the south its termination and transition to subduction along the Puysegur subduction zone.To the north the transition to subduction along the Hikurangi subduction zone with accommodation of deformation through the Marlborough Fault System.Fault traces © GNS Science 2016.a(2).Schematic diagram illustrating the plate boundary misalignment and associated transition zone, referred to in this study, between the Alpine Fault and the Hikurangi subduction zone.b(1) The San Andreas Fault (SAF) (California) and its southern termination in the Salton Sea and transition to sea floor spreading in the Gulf of California.Fault traces from Legg et al. (2004).b(2) Schematic diagram illustrating the plate boundary misalignment and associated transition zone, referred to in this study, at the southern termination of the SAF.c(1) The North Anatolian Fault (NAF) has propagated progressively westward from its eastern termination against the East Anatolian Fault.At its western termination it branches in its mid section: Ez.S.F.= Ezinepazar-Sungurlu Fault, and at its western termination into northern and southern branches.Fault traces from Emre et al. (2020), Porkoláb et al. (2023), and Sunal and Korhan Erturaç (2012) c(2).Schematic diagram illustrating the misalignment and transition zone, referred to in this study, at the western termination of the NAF.(d) The Dead Sea Transform, its southern termination with pull apart basins that transition to rifting in the Red Sea (which transitions to sea floor spreading further south).Fault traces from Segev et al. (2014).

Figure 2 .
Figure 2. Analog modeling apparatus aka "the sandbox" used to conduct experiments for this investigation.(a) Schematic diagram of the Sandbox.(b) Photograph of the sandbox after the moving side has pushed 6 cm by the linear actuator.

Figure 3 .
Figure 3.The basal boundary conditions of the "sandbox" for each experiment in this investigation.(a)-(e) show schematic diagrams of the starting and finishing position of each experiment.The black dashed line shows the position of the stretchable material taped to the base of the sandbox in each experiment.The blue dotted line shows the position of the shear strain maps in Figures 4-7.(a) Experiment A, Localized simple shear experiment, sandbox is unmodified.(b) Experiment B, Distributed Simple Shear (DSS) experiment, stretchable material taped across the base of the sandbox.(c) Experiment C, the stretchable material is taped across half of the sandbox, so half deforms by localized and half by DSS.(d) Experiment D, the stretchable material is taped so that DSS occurs on one side of the localized shear zone, analogous to the boundary conditions of the Alpine Fault and Marlborough Fault System.(e) Experiment E, a replica of experiment C except the box is pulled sinistrally by the linear actuator.(f) A photograph of the experimental setup of the basal boundary conditions for Experiment B (b). (g) A photograph of the experimental setup of the basal boundary conditions for experiment D (d).

Figure 4 .
Figure 4. Exy incremental shear strain maps at 5 mm displacement intervals (from 1.25 to 30 mm) of the surface of Experiments A and B (as detailed in Figure3), determined by Digital Image Correlation.Each incremental shear strain map is given a label for reference in the results section.The location of the shear strain map within the experiments is illustrated in Figure3.
Other artifacts are related to the stretchable material used to create the DSS basal boundary condition.Pop-up structures and pull apart basins formed above the untaped edges of the stretchable material (perpendicular to the 10.1029/2023TC007823 11 of 19 central discontinuity) (Figures 4-6).The pop-up structures develop from thrust faults in the sand associated with the forward propagation of the basal material during sandbox displacement.Pull apart basins form where the material has been pulled away from its original position.The pop-up artifact associated with the stretchable fabric in

Figure 5 .
Figure5.Exy incremental shear strain maps at 5 mm displacement intervals (from 1.25 to 30 mm) of the surface of Experiments C and D (as detailed in Figure3), determined by Digital Image Correlation.Each incremental shear strain map is given a label for reference in the results section.The location of the shear strain map within the experiments is illustrated in Figure3.

Figure 6 .
Figure6.Exy incremental shear strain maps at 5 mm displacement intervals (from 1.25 to 30 mm) of the surface of Experiments E (as detailed in Figure3), determined by Digital Image Correlation (DIC).Each incremental shear strain map is given a label for reference in the results section.The location of the DIC mask (each result image) is illustrated in Figure3.

Figure 7 .
Figure 7. Image stacks of Digital Image Correlation (DIC) incremental shear strain maps from Experiments C and D (dextral transition experiments) from 0 to 30 mm displacement.The image stacks show changes in incremental shear with increased displacement, and therefore illustrate fault development at the surface of the model along the chosen line.The DIC shear strain maps for experiments C and D are shown at 30 mm displacement, detailing the line chosen for the image stack.For each experiment there is an image stack in the region of localized simple shear: line c1-c2 and d1-d2, and an image stack in the region of distributed simple shear: line c3-c4 and d3-d4.

Figure 8 .
Figure 8. Fault outlines of the case studies compared to the fault outline of experiment D at 30 mm displacement (Figure 5d7).The case studies have been rotated for comparison with the analog experiment.The region of proposed distributed shear is highlighted in orange each for each example.Red arrows indicate direction of plate motion.DSS = Distributed Simple Shear.TZ = Transition Zone.SZ = Subduction Zone.TF = Transform Fault (a) analog model (Experiment D at 30 mm displacement).(b) The northern termination of the Alpine Fault and the Marlborough Fault System.(c) The southern termination of the San Andreas Fault.(d) The western termination of the North Anatolian Fault (NAF).
Where the term "Transition" is used in the column Basal Boundary Condition, it implies a region of localised and distributed deformation within the same experiment.Details of the Five Analog Experiments Conducted for This Investigation