A systematic comparison of experimental set-ups for ... · ies of extensional tectonics. 1 Introduction 1.1 Analogue experimental set-ups for investigating extensional tectonics Tectonic

Solid Earth 10 1063ndash1097 2019httpsdoiorg105194se-10-1063-2019copy Author(s) 2019 This work is distributed underthe Creative Commons Attribution 40 License

A systematic comparison of experimental set-ups formodelling extensional tectonicsFrank Zwaan1 Guido Schreurs1 and Susanne J H Buiter23

1Institute of Geological Sciences University of Bern Baltzerstrasse 1+3 3012 Bern Switzerland2Team for Solid Earth Geology Geological Survey of Norway (NGU) Leiv Eirikssons vei 39 7040 Trondheim Norway3The Centre for Earth Evolution and Dynamics University of Oslo Sem Saeliglands vei 2A 0371 Oslo Norway

Correspondence Frank Zwaan (frankzwaangeounibech)

Received 14 September 2018 ndash Discussion started 20 September 2018Revised 25 March 2019 ndash Accepted 27 April 2019 ndash Published 5 July 2019

Abstract Analogue modellers investigating extensional tec-tonics often use different machines set-ups and model ma-terials implying that direct comparisons of results from dif-ferent studies can be challenging Here we present a system-atic comparison of crustal-scale analogue experiments usingsimple set-ups simulating extensional tectonics involving ei-ther a foam base a rubber base rigid basal plates or a con-veyor base system to deform overlying brittle-only or brittle-viscous models We use X-ray computed tomography (CT)techniques for a detailed 3-D analysis of internal and exter-nal model evolution

We find that our brittle-only experiments are strongly af-fected by their specific set-up as the materials are directlycoupled to the model base Experiments with a foam orrubber base undergo distributed faulting whereas experi-ments with a rigid plate or conveyor base experience local-ized deformation and the development of discrete rift basinsPervasive boundary effects may occur due to extension-perpendicular contraction of a rubber base Brittle-viscousexperiments are less affected by the experimental set-up thantheir brittle-only equivalents since the viscous layer acts asa buffer that decouples the brittle layer from the base Un-der reference conditions a structural weakness at the baseof the brittle layer is required to localize deformation intoa rift basin Brittle-viscous plate and conveyor base experi-ments better localize deformation for high brittle-to-viscousthickness ratios since the thin viscous layers in these exper-iments allow deformation to transfer from the experimentalbase to the brittle cover Brittle-viscous-base coupling is fur-ther influenced by changes in strain rate which affects vis-cous strength We find however that the brittle-to-viscous

strength ratios alone do not suffice to predict the type of de-formation in a rift system and that the localized or distributedcharacter of the experimental set-up needs to be taken intoaccount as well

Our set-ups are most appropriate for investigating crustal-scale extension in continental and selected oceanic settingsSpecific combinations of set-up and model materials maybe used for studying various tectonic settings or lithosphericconditions Here natural factors such as temperature vari-ations extension rate water content and lithology shouldbe carefully considered We hope that our experimentaloverview may serve as a guide for future experimental stud-ies of extensional tectonics

1 Introduction

11 Analogue experimental set-ups for investigatingextensional tectonics

Tectonic analogue modellers have historically used differ-ent experimental apparatus and model materials to investi-gate continental extension These experiments have providedthe scientific community with highly valuable insights intothe evolution of basins and initial rift structures However arobust comparison between various experiments is challeng-ing because of the variety of experimental set-ups and modelmaterials that have been applied Experiments have for ex-ample used set-ups involving (a combination of) basal foambars basal rubber sheet rigid basal plates or conveyor-belt-style basal sheets with moving sidewalls to deform modelmaterials (eg Allemand et al 1989 Acocella et al 1999

Published by Copernicus Publications on behalf of the European Geosciences Union

1064 F Zwaan et al Comparing experimental set-ups for modelling extensional tectonics

Bahroudi et al 2003 Amilibia et al 2005 Alonso-Henaret al 2015 Philippon et al 2015) Alternatively extensioncan be achieved through gravitational gliding or spreading inwhich case no moving sidewalls or an extending base needsto be applied (eg Gartrell 1997 Fort et al 2004 Acocellaet al 2005) Analogue materials used to simulate brittle partsof the lithosphere include among others quartz or feldsparsand silica flour micro-beads and (kaolinite) clay (Hubbert1951 Elmohandes 1981 Serra and Nelson 1988 Cliftonand Schlische 2001 Autin et al 2010 Abdelmalak et al2016 Klinkmuumlller et al 2016 Fig 1) Pure silicone oils andsilicone putties are frequently used as analogues for ductileparts of the lithosphere (Weijermars and Schmeling 1986Basile and Brun 1999 Michon and Merle 2000 Sun et al2009 Rudolf et al 2015 Fig 1)

Vendeville et al (1987) present experiments that highlightseveral factors controlling the geometry of fault systems inextensional tectonics The study used rubber sheet set-upswith a brittle sand layer for homogeneous thin-skinned defor-mation brittle-viscous gravity-spreading models resting ona solid base and experiments with the whole brittle-viscouslithospheric analogue floating on a simulated asthenosphereThe results provide a first impression of the differences be-tween these set-ups revealing the correlation between faultspacing and layer thickness in brittle materials rift local-ization in brittle-viscous settings and isostatic effects suchas tilted margins due to the influence of the asthenosphereYet the many experimental parameters were widely differentfrom experiment to experiment making a quantitative com-parison difficult

Allemand and Brun (1991) test the influence of two-layerbrittle-viscous material layering but using a conveyor beltset-up to achieve both symmetric and asymmetric exten-sion with a velocity discontinuity (VD) The basal sheetsdiverge here representing a fault in the underlying (not-simulated) brittle lithospheric mantle Asymmetric extensionis shown to generate strongly asymmetric rift geometries inboth brittle and brittle-viscous models The rifts under sym-metric extension conditions also develop a degree of struc-tural asymmetry The similarities of results from four-layer(lithospheric-scale) models (Fig 1) to their two-layer modelresults support the validity of applying a VD to simulatefaults in the brittle upper mantle Model parameters such aslayer thickness material properties and extension velocitiesare however not clearly defined again making a direct com-parison of these experiments challenging

Brun (1999) summarizes extension experiments with afocus on layer rheology and extension velocity He showsthat an increase in extension velocity in crustal-scale brittle-viscous conveyor belt models leads to an increase in viscousstrength and brittle-viscous coupling favouring widespreaddeformation or wide rifting By contrast low extension ve-locities lead to localized extension or narrow rifting A simi-lar effect is obtained by changing the brittle-to-viscous thick-ness ratio a high ratio of 3 1 leads to low brittle-viscous

coupling and narrow rifting whereas a small ratio of 1 1leads to high coupling and wide rifting On a lithosphericscale however the behaviour of the upper mantle becomesimportant as well (Fig 1) a single fault in a strong uppermantle layer may induce narrow deformation in the overly-ing crustal layers whereas a weak upper mantle promotesdistributed deformation The models also suggest that withinsuch wide rifts local weaknesses can account for the devel-opment of core complexes In addition to providing a sum-marizing scheme similar to Brun (1999) Corti et al (2003)show how magma presence can control rift initiation in nar-row rifts and cause a wide rift to shift to core complex modeThe authors also describe the additional effects of oblique ex-tension and multiple extension phases on rift evolution How-ever the models presented in both review articles come fromnumerous studies and are often performed with very differenttechniques and parameters

The additional significance of VDs in the brittle uppermantle was investigated by Michon and Merle (2000 2003)by means of brittle-viscous base plate experiments where theVD is situated at the edge of the plate A single VD leads toasymmetric extension and the development of a single riftwhereas a double-VD experiment may form two or more riftbasins depending on the initial distance between the VDsThis is valid for high strain rates as low strain rates focusdeformation (narrow rifting) decreasing the number of riftbasins Apart from the varying strain rates and VDs the otherparameters such as model size materials and layer thicknessremained fixed

Schreurs et al (2006) compared results of a brittle-viscousplate base extension experiment that was run by five analoguelaboratories The overall experimental procedure was kept assimilar as possible using for example the same foil to coverthe base of the apparatus the same extension velocity andthe same viscous material (polydimethylsiloxane PDMS)But differences occurred in brittle materials (different typesof sand and a wet clay) and model dimension (width andlength) This study illustrated the overall large-scale struc-tural similarities but also showed differences in fault dip an-gle and fault spacing that were related to differences in modelmaterials andor model set-up

12 Analogue materials used in extension experiments

Brittle MohrndashCoulomb-type granular materials have verysimilar internal friction angles with respect to their naturalanalogues (ranging between ca 25 and 40 Schellart 2000Klinkmuumlller et al 2016) Granular materials such as dryquartz sand have a very low cohesion and are considered agood analogue for large-scale models aiming at the brittlecrust or the crust and lithospheric mantle (Fig 1) By con-trast high-cohesion materials such as silica flour and clay(C = 40ndash750 Pa Eisenstadt and Sims 2005 Guerit et al2016) are better suitable for modelling the uppermost kilo-metres of the crust where cohesion is an important rheolog-

Solid Earth 10 1063ndash1097 2019 wwwsolid-earthnet1010632019

F Zwaan et al Comparing experimental set-ups for modelling extensional tectonics 1065

Figure 1 Example of model layering to simulate extension in a stable four-layer lithosphere (a) Strength profile of the natural examplewith a brittle upper crust a ductile lower crust a strong brittle upper mantle and a ductile lower mantle that blends into the underlyingasthenosphere at a temperature of 1300 C (b) Model materials representing the various layers sand for the brittle parts of the lithosphereand viscous silicone (mixtures) for the ductile crust and mantle The asthenosphere is simulated with honey or viscous syrup (c) Crosssection at the end of an asymmetric extension experiment Adapted from Allemand and Brun (1991) with permission from Elsevier

ical factor Intermediate cohesion values can be obtained bymixing granular materials (Abdelmalak et al 2016 Mon-tanari et al 2017) Low-friction micro-beads with internalfriction angles of ca 20 allow for the modelling of struc-tural weaknesses or weak crustal lithologies (eg Colletta etal 1991 Panien et al 2005) The density of brittle analoguematerials depends on various factors such as its specific den-sity grain size and shape sorting and handling techniquesas well as water content (for clays) but lies generally be-tween ca 1400 and 1800 kgmminus3 (eg Krantz 1991 Eisen-stadt and Sims 2005 Klinkmuumlller et al 2016)

Pure silicone oils consist of polydimethylsiloxane(PDMS) are transparent have a density of ca 1000 kgmminus3

(Weijermars and Schmeling 1986) and a Newtonian viscos-ity between ca 103 and 105 Pa s at room temperature and attypical experimental deformation rates (Rudolf et al 2015Schellart and Strak 2016) Silicone putties are mixturesof polyborondimethylsiloxane (PBDMS) and inert fillers(Weijermars 1986) and have higher densities than puresilicone oils Examples of opaque silicone putties commonlyused in analogue modelling include Rhodorsil GommeGS1R (Cobbold and Quinquis 1980) Rhodorsil Silbione70009 (Nalpas and Brun 1993) and Dow Corning DC3179(Dixon and Summers 1985) Their density range variesbetween ca 1140 and 1420 kgmminus3 and they display New-tonian viscosities between ca 104 and 4times 105 Pa s at roomtemperature (eg Casas et al 2001 Cagnard et al 2006Konstantinovskaya et al 2007) It should be noted thatthe viscosity of silicone-based materials can in some casesstrongly depend on temperature (Cagnard et al 2006) andalso ageing processes have an effect on silicone behaviour(Rudolf et al 2015 and references therein) Pure siliconeoils and silicone putties can be mixed with for instance sandor metallic powders to modify the materialrsquos density andviscosity (eg Calignano et al 2015 Zwaan et al 2016)Other substances such as paraffin and gelatin mixtures canbe applied when power-law or temperature-dependent rheo-logical behaviour is required (eg Zulauf and Zulauf 2004

Boutelier and Oncken 2011) In lithosphere-scale modelsthe weak ductile behaviour of the asthenospheric mantleis simulated with low-viscosity materials such as honeyglucose syrup mixtures of polytungstate with glycerol oreven pure water (Mart and Dauteuil 2000 Chemenda et al2002 Schellart et al 2002 2003 Willingshofer et al 2005Molnar et al 2017) These normally exhibit Newtonianbehaviour Further details and references concerning theabovementioned and other analogue model materials can befound in a comprehensive review article by Schellart andStrak (2016)

13 Aims of this study

The analogue modelling work summarized above reveals atrend from a rather qualitative modelling approach to a morequantitative approach Older studies tend to present a rangeof models with widely different parameters (for materialsand set-up) which are often not fully described By con-trast newer studies often specify such data in much detailallowing repetition by analogue and also numerical meansYet direct comparisons between the various methods remainchallenging especially since these methods aim to simu-late different tectonic settings (see also Sect 22 and 23)In theory the scaling principles that have elevated analoguemodelling from a qualitative to a quantitative method canbe applied to compute how models should compare to eachother (eg Hubbert 1937 Ramberg 1981 Weijermars andSchmeling 1986) In practice however such calculationsremain approximate Different material handling techniques(laboratory traditions the human factor) or climatic con-ditions (room temperature humidity) may influence mate-rial behaviour and thus model results with the same set-upcan vary from laboratory to laboratory (eg Krantz 1991Schreurs et al 2006 2016 Rudolf et al 2015) Further-more our understanding of experimental material rheologymay be incomplete or poorly constrained since some param-eters are difficult to properly determine (eg Schellart 2000

wwwsolid-earthnet1010632019 Solid Earth 10 1063ndash1097 2019

Eisenstadt and Sims 2005 Schreurs et al 2006 Dooley andSchreurs 2012 and references therein Ritter et al 2016)Thus the need for reference studies of lithospheric exten-sion with standardized model parameters remains and to ourknowledge no such work is available to date

The aim of this study is to systematically compare a se-ries of simple crustal-scale normal-gravity laboratory exper-iments involving commonly used set-ups and to discuss thetectonic settings to which these would apply We use either afoam base a rubber base rigid base plates or conveyor-belt-style plastic sheets as a mechanism to deform the overlyingbrittle or brittle-viscous experimental materials This forms atotal of 16 reference experiments Various additional exper-iments serve to examine the effects of among others vary-ing extension velocity layer thickness and brittle-to-viscousthickness ratio We also apply X-ray computed tomography(XRCT or CT) for obtaining a highly detailed 3-D view of theinternal as well as the external evolution of our experimentsWe furthermore address the various boundary effects occur-ring in our experiments a crucial factor that may stronglyinfluence experimental results We hope that the opportuni-ties and challenges associated with our experimental set-upsand results combined with the summary of materials abovemay form an inspiration for future experimental work

2 Materials and methods

21 Material properties

We ran brittle (single-layer) and brittle-viscous (two-layer)experiments to simulate a brittle upper crust and a com-plete brittle-ductile crust respectively (Fig 2) Referencebrittle-only experiments contain a 4 cm thick layer of finequartz sand (empty= 60ndash250 microm angle of internal peak and sta-ble friction 361 and 314 respectively Zwaan et al 20162018b) The sand is sieved from ca 30 cm height into theexperimental apparatus to guarantee a sand density of ca1560 kgmminus3 The sand is flattened using a scraper at ev-ery 1 cm thickness during preparation of the experimentcausing slight density variations which subsequently ap-pear on CT images as a ldquolayeringrdquo (Fig 4f g) The refer-ence experiments with a brittle-ductile layering are built ofan additional 4 cm thick near-Newtonian viscous layer (vis-cosity η ca 15times 105 Pa s stress exponent n= 105) con-sisting of a 1 1 weight mixture of SGM-36 polydimethyl-siloxane (PDMS) silicone and corundum sand (ρspecific =

3950 kgmminus3 Panien et al 2006 Zwaan et al 2016 2018cCarlo AG 2019) The obtained density of the viscous ma-terial (ca 1600 kg mminus3) is close to that of the overlyingquartz sand layer (1560 kgmminus3) This results in a densityprofile that avoids the buoyant rise of the viscous materialthat would occur for a layering involving pure low-densityPDMS (ρ = 965 kg mminus3 Weijermars 1986) Further mate-rial properties are listed in Table 1

22 Experimental design

The experimental apparatus consists of a fixed base and twolongitudinal sidewalls which can move outward indepen-dently from each other above a fixed support table theirmotion controlled by precise computer-guided stepper mo-tors The initial width of the experiment is 30 cm in all set-ups which is considerably less than their length (as speci-fied below) This high length-to-width ratio diminishes theinfluence of boundary effects at the short sidewalls Throughmodification of the apparatus we can use four different meth-ods to transfer deformation from the base of the set-up to theoverlying experimental materials by applying either a foambase or rubber sheet base for a distributed deformation set-ting or a base of rigid plates or conveyor belt system for fo-cussed deformation (Fig 2) The confinement along the shortsidewalls varies according to the set-up as explained belowSince the various set-ups differ significantly we also specifywhich type of tectonic setting or crustal rheology is simu-lated (Fig 3) An additional overview of the similarities anddifferences between our set-ups by means of (relative) veloc-ities and shifts in reference frames is provided in AppendixA (Fig A1)

221 Distributed extension set-ups

A foam base (F series experiments) induces distributed ex-tension (eg Schreurs and Colletta 1998 Schlagenhauf etal 2008 Zwaan et al 2016 Zwaan and Schreurs 2017) An8 cm thick RG 50 polyurethane foam base is first compressedbetween the sidewalls with the experiment subsequently con-structed on top (Fig 2andashc) As the sidewalls move apart dur-ing an experiment the foam expands causing the overly-ing materials to deform (Fig 2b c) Rubber sidewalls at theshort ends of the set-up confine the materials with the dis-tributed extension of the rubber decreasing boundary effectsthere (Fig 2a) All foam base experiments have a length of79 cm for an initial length-to-width ratio of 26

For the rubber base set-up (R series experiments) a 15 mmthick Neoprene rubber sheet is spanned between the two longsidewalls (eg Vendeville et al 1987 Bahroudi et al 2003Bellahsen et al 2003 Bellahsen and Daniel 2005 Fig 2dndashf) Note that this is slightly different from set-ups applyinga narrow rubber sheet between two rigid base plates Whenthese are subsequently moved apart a limited band of dis-tributed deformation occurs above the rubber while the plateedges essentially act as VDs (eg McClay and White 1995McClay et al 2002 Corti et al 2007 Henza et al 2010)Instead we use a full rubber base for our experiments inorder to allow for a comparison with the foam base set-upand to achieve distributed extension throughout the experi-ment When the long sidewalls move apart the rubber sheetis stretched and extends uniformly along a velocity gradi-ent with a constant slope causing distributed deformation(Fig 2e f) The short sides of the experiment are free in ex-

Table 1 Material properties

Granular materials Quartz sanda Corundum sandb

Grain size range 60ndash250 microm 88ndash175 micromDensity (specific)c 2650 kgmminus3 3950 kgmminus3

Density (sieved) 1560 kgmminus3 1890 kgmminus3

Angle of internal peak friction 361 37

Angle of dynamic-stable friction 314 32

Cohesion 9plusmn 98 Pa 39plusmn 10 Pa

Viscous material PDMScorundum sand mixturea

Pure PDMS density (specific)d 0965 kgmminus3

Weight ratio PDMS corundum sand 0965 kg 100 kgMixture density ca 1600 kgmminus3

Viscositye ca 15times 105 Pa sType near-Newtonian (n= 105)f

a Quartz sand and viscous mixture characteristics after Zwaan et al (2016 2018b c) b Corundumsand characteristics after Panien et al (2006) c Specific densities of quartz and corundum sandsafter Carlo AG (2019) d PDMS specific density after Weijermars (1986) e The viscosity valueholds for model strain rates lt 10minus4 sminus1 f Stress exponent n (dimensionless) represents sensitivityto strain rate

periments with only a brittle layer that is not confined bya sidewall that may influence the experimental results Theshort sidewalls of the brittle-ductile rubber base experimentsare enclosed by a sand talus so that the viscous material can-not escape sideways (Fig 2d) Since the large forces involvedin stretching a large rubber sheet may cause damage to theexperimental apparatus the length of the rubber base experi-ments is kept to 50 cm Therefore the initial length-to-widthratio is 17

Previous authors have applied a rubber or foam base withan overlying brittle layer to simulate distributed thin-skinnedextension (eg Bahroudi et al 2003 Schlagenhauf et al2008) In nature distributed extension in the brittle crustcould develop in a setting with high brittle-ductile couplingbetween a brittle upper crust and a strong ductile lower crust(Fig 3a) either due to high strain rates or high viscosity(Brun 1999 Buiter et al 2008 Allken et al 2012 Zwaanet al 2016) Note that the sub-crustal mantle has no directinfluence in this case By contrast experiments with brittle-viscous layers on top of a rubber or foam base would sim-ulate a normal brittle-ductile crust on top of a viscously de-forming weak mantle (Fig 3b) This setting in which thestrength of the lithosphere is determined by the brittle crust(Buumlrgman and Dresen 2008) can be expected in a hot litho-sphere for instance above a mantle plume (Saunders et al1992 Burov et al 2007) or in regions subject to enhancedradiogenic heating (Mareschal and Jaupart 2013)

222 Localized extension set-ups

The plate base set-up (P series experiments) involves two2 mm thick rigid plastic plates that are fixed to the long side-walls (Fig 2gndashi) (eg Tron and Brun 1991 Brun and Tron

1993 Bonini et al 1997 Keep and McClay 1997 Michonand Merle 2000 Gabrielsen et al 2016) When these platesmove apart with the long sidewalls velocity discontinuities(VDs) develop at the basal edges of the plates The sup-port table below the plates prevents material from escaping(Fig 2h i) The short sidewalls are confined by a similarplate system that is fixed to the horizontal plates thus mov-ing in sync and creating the same boundary conditions as atthe base of the apparatus (Fig 2g) In contrast to the set-ups applying distributed extension described above the rigidbase plates allow both symmetric and asymmetric extensionIn the former case two moving VDs occur as the edges ofboth non-overlapping plates move apart whereas the lattercase results in only one VD (similar to Michon and Merle2000 see also Fig A1) The initial length of the base plateexperiments is 90 cm so that the length-to-width ratio is 3Although we did not measure the boundary friction betweenthe plastic plates and quartz sand it is likely to be close tothe values reported by Panien et al (2006) for similar quartzsand on top of either plastic or PVC ca 21

The final set-up is a modified version of the plate baseset-up involving a ldquoconveyor beltrdquo type of deformation (Cseries experiments) (eg Allemand and Brun 1991 Tronand Brun 1991 Dauteuil and Brun 1993 Keep and Mc-Clay 1997 Romaacuten-Berdiel et al 2000) Sub-millimetre-thick plastic sheets or foil (ldquoAlkorrdquo foil 120010 formerlyproduced by Alkor-Venilia and now available as ldquoGekkofix11325rdquo httpwwwgekkofixcom last access 19 May 2019Klinkmuumlller et al 2016) are fixed to the plate base set-upand are led down through a slit in the support table alongthe central axis of the experiment (Fig 2jndashl) When the longsidewalls move apart the sheets are pulled upward throughthe slit (Fig 2k l) In contrast to the plate base experiments a

Figure 2 Experimental design adopted for our reference experiments See Table 2 for a complete overview of the specific parametersapplied in this study Note that the 3-D cut-out views show examples of reference experiments with brittle-viscous layering VD velocitydiscontinuity For details on the additional experimental parameters see Table 2

single VD occurs which remains located at the centre of theexperiment Since this is true for both symmetrical and asym-metrical experiments (Fig 2k l) the plate base and conveyorbelt set-ups are different Yet the asymmetric conveyor beltmechanism is after a switch of reference frame the same asthe asymmetric plate base mechanism (Fig A1) and shouldthus produce an identical result The same sheet system isapplied on the short sidewalls in order to have a continuousconfinement (Fig 2j) These conveyor belt experiments havethe same length-to-width ratio as the plate base experimentsie 3 The angle of boundary friction of the foil with quartzsand lies between 15 and 21 (Schreurs et al 2016)

Both the plate base and conveyor base experimental de-signs involve localized deformation at VDs These VDs sim-ulate a discrete fault (or shear zone) in a strong layer under-lying the experimental materials In the case of our brittle-only experiments this would translate to a fault at the baseof the upper crust In order to have a fault in the lower crustthe latter needs to behave in a brittle fashion which in ourcase would be expected in an old cool crust (Fig 3c) Ona smaller scale one can also interpret the VD as a reac-tivated basement fault affecting overlying strata (eg Aco-cella et al 1999 Ustaszewski et al 2005) Concerning ourbrittle-viscous crustal experiments the VD translates to afault in a strong upper mantle (eg Allemand and Brun 1991Michon and Merle 2000) Such a setting can be expectedin a young stable lithosphere with a strong brittle mantle(Fig 3d) Note that VDs could be produced by differentialmotion focussed along various types of (linear) irregularitiesor inherited structures within the lithosphere but that thesemay be challenging to simulate For instance Morley (1999)points out that (1) VDs in analogue experiments cannot serveto reproduce irregularities within the overlying layers butonly structures at the base of these layers and that (2) VDsby definition represent discrete features rather than pervasivestructures (eg foliations) that may be present throughout avolume of rock

23 Additional experimental parameters and definitionof coupling

For every experimental set-up we test brittle-only materialsand brittle-viscous layering with a reference layer thicknessof 4 cm so that brittle-only and brittle-viscous experimentsare 4 and 8 cm thick respectively However for specific ex-periments we either apply a 4 cm thick brittle-viscous lay-ering or we modify the brittle-to-viscous thickness ratio bydecreasing the thickness of the viscous layer to 2 or 1 cmin order to capture the effects that a different crustal layer-ing may have on extensional structures (details in Table 2)This decrease in viscous layer thickness can be either dueto a thinner viscous lower crust assuming that the brittlecrustal thickness remains the same (Fig 3g h) or an increasein brittle crustal thickness with a constant Moho depth Inboth cases this would result in a relative strengthening of the

crust with respect to the default layering Brittle-to-viscousstrength ratios are given in Table 2 based on the calculationsin Appendix B

We also apply ldquoseedsrdquo to localize deformation in severalexperiments (Fig 2 Table 2) These seeds are 1 cm thicksemi-cylindrical viscous rods of the previously describedPDMScorundum sand mixture that are placed at the base ofthe brittle layer The seeds are continuous and stretch alongthe full axis of the experiment They form weak zones withinthe sand pack where deformation may localize since thestrong sand cover is locally thinner and thus weaker (egZwaan et al 2016) Although we acknowledge that surfaceprocesses can influence rift evolution (eg Burov and Cloet-ingh 1997 Bialas and Buck 2009 Zwaan et al 2018a) weneither apply erosion nor sedimentation in our experimentssince we aim to directly evaluate differences in experimentalresults obtained by differences in simple experimental set-ups

Our reference extension velocity is 8 mm hminus1 with bothlong sidewalls moving 4 mm hminus1 for symmetrical extensionor a single sidewall moving 8 mm hminus1 for asymmetrical ex-tension (Fig 2) Considering a reference duration of 5 h thetotal extension equals 40 mm (or ca 13 given an initialwidth of ca 30 cm) In addition we varied the extension ve-locity for selected experiments In the case of the brittle-onlyexperiments however this should not affect brittle deforma-tion structures because of the time-independent mechanicalbehaviour of the sand that directly overlies the model baseFor brittle-viscous experiments variations in extension ve-locity are equivalent to variations in viscous strength (egBrun 1999 Buiter et al 2008) and will thus affect thestrength contrast and coupling between the brittle and vis-cous materials (Fig 3e f Table 2 Appendix B) In the ex-periments with a foam or rubber base a strengthening of theviscous material due to an increase in extension rate can beseen as simulating strengthening of a hot lithosphere with in-creased brittle-ductile coupling between the upper and lowercrust but still a relatively weak mantle (compare Fig 3b withFig 3e) In the plate base or conveyor base set-up equivalenta higher extension rate would then represent a similarly hotcrust subject to increased brittle-ductile coupling overlying abrittle upper mantle (compare Fig 3d with Fig 3f) Higherextension rates may also affect the degree of coupling be-tween the analogue materials and base of the set-up whichcan have an important influence on the development of a riftsystem (eg Corti et al 2003) We therefore distinguish thefollowing types of coupling brittle-basal (between the brit-tle layer and the base of the set-up in brittle-only models)brittle-viscous (between brittle and viscous layers in brittle-viscous experiments) and viscous-basal (between a viscouslayer and the base of the set-up in brittle-viscous experi-ments) In addition we can also describe to what degree thebrittle cover is decoupled from the base of the set-up by theviscous layer in brittle-viscous experiments

Figure 3 Schematic experimental and natural strength profiles (always left and right respectively) indicating the lithospheric setting thatexperiments may represent The strength profiles of our experiments are qualitative (no scale for stress) and we have exaggerated the viscousstrength for visualization purposes Natural strength profiles can be affected by numerous factors as discussed in Sect 47 and illustratedquantitatively in Fig 12 Dotted lines in (e) and (f) indicate the schematic strength profile under reference conditions for comparison Symbollowast means the effects of these parts of the lithosphere are not simulated in the given case b d is brittleductile

Table 2 List of experimental parameters

LayeringStructuralweakness

ExtensionStrengthratio(b v)b

Shown inType

Thickness(b v)

TypeVelocity

Experiment Nature(mm hminus1) (mmyrminus1)

) F1 brittle only 40ndash mm no seed symmetric 8 ndash ndash Fig 4

F2 seed symmetric 8 ndash ndash Fig C1F3 8 ndash ndash Fig C1F4CT 8 ndash ndash Figs 4 C1

F5 brittle-viscous

4040 mm no seed symmetric 8 5 84 Fig 5

F6 seed symmetric 8 5 84 Fig C1F7CT 8 5 84 Figs 5 C1

R1cd brittle 40ndash mm no seed symmetric 1st phase 8 ndash ndash Fig 6only 2nd phase 40

R2 seed symmetric 20 ndash ndashR3 10 ndash ndashR4CT e f 20 ndash ndashR5CT d 10 ndash ndash Fig 6R6CT 20 ndash ndash

R7c d brittle- 4040 mm no seed symmetric 1st phase 8 5 84 Fig 7viscous 2nd phase 40 24 17

R8 seed symmetric 8 5 84 Fig 7

R9 no seed symmetric 80 47 84 Fig 7R10 480 280 14 Fig 7

P1 brittle only 40ndash mm no seed symmetric 8 ndash ndash Fig 8

P2 no seed asymmetric 8 ndash ndash Figs 8 C2

P3 brittle- 4040 mm no seed symmetric 8 5 84P4 viscous 2 1 337P5 40 24 17

P6 no seed asymmetric 8 5 84 Fig C1

P7 8 5 84 Figs 8 C2

P8g 2020 mm no seed symmetric 2 5 175P9g 80 190 44 Figs 8 C2

P10 4040 mm seed symmetric 8 5 84 Fig 8

C1 brittle only 40ndash mm no seed symmetric 40 ndash ndash Fig 9

C2 no seed asymmetric 40 ndash ndash Fig C2C3 40 ndash ndash Figs 9 C2

C4 brittle- 4040 mm no seed symmetric 8 5 84 Figs 9 C1C5h viscous 8 5 84 Fig C1C6h 8 5 84 Fig C1

C7 4020 mm no seed symmetric 8 5 169 Fig 9

C8 4010 mm no seed symmetric 8 5 337 Fig 9C9 80 42 34 Fig C2C10 40 24 68 Fig C2C11CT 40 24 68 Figs 9 C2

C12g 2020 mm no seed symmetric 80 190 44 Fig C2

b v Brittle-viscous CT CT-scanned models a Valid for a lower crustal viscosity (η) of 1021 Pa s b See Appendix B for calculations c Two-phase experiment with 40 mm of extension at 8 mm hminus1

followed by 20 mm of extension at 40 mm hminus1 d Total extension 60 mm e Initial experiment width 25 cm instead of 30 cm f 54 mm total extension rubber sheet ripped partly after ca 2 h (40 mmextension) g Experiments with a total 40 mm thickness (20 mm brittle 20 mm viscous) and 20 mm total extension h Attempt to reduce boundary effects (see text and Fig C2 in Appendix C for details)

Furthermore a thin (ca 05 mm thick) grid made of dark(corundum) sand with a 4times 4 spacing applied to the surfaceof each experiment allows a first-order assessment of surfacedeformation by means of top-view images without influenc-ing the experimental results Furthermore every componentof the machine around the experiment consists of X-ray-transparent materials to allow for CT scanning and variousexperiments are analysed with CT techniques to reveal their3-D internal evolution Most experiments marked in Table 2as ldquoCT-scannedrdquo were a rerun of previous tests performedwithout CT scanning Various other experiments were alsorepeated and did indicate little structural variation thus goodreproducibility is ensured (Table 2 details presented in Ap-pendix C Figs C1 C2) Moreover surface view videos and3-D CT imagery depicting the evolution of our experimentsare available as a data publication (Zwaan et al 2019)

24 Scaling

We calculate stress ratios (convention σ lowast =

σexperimentσnature) based on Hubbert (1937) and Ram-berg (1981)

σ lowast = ρlowasthlowastglowast (1)

where ρlowast hlowast and glowast represent the density length and gravityratios respectively

The strain rate ratio εlowast is derived from the stress ratio σ lowast

and the viscosity ratio ηlowast (Weijermars and Schmeling 1986)

εlowast = σ lowastηlowast (2)

Subsequently the velocity ratio vlowast and time ratio tlowast can beobtained as follows

εlowast = vlowasthlowast = 1tlowast (3)

Natural values for lower crustal viscosity may have a widerange depending on the specific tectonic setting (η = 1019ndash1023 Pa s eg Buck 1991 Brun 1999 Buumlrgman and Dresen2008) We assume an intermediate lower crustal viscosity of1021 Pa s which is in line with recent findings (Shinevar etal 2015 and references therein) An hour in our experimentsthus translates to 084 Myr in nature and our reference ve-locity (8 mm hminus1) converts to a velocity of ca 5 mm yrminus1 innature close to typical values for initial continental rifting(1ndash5 mm yrminus1 eg Saria et al 2014) The scaling parame-ters are summarized in Table 3

To ensure dynamic similarity between brittle natural andexperimental materials we calculate the ratio Rs which isa function of gravitational stress and cohesive strength (C)(Ramberg 1981 Mulugeta 1998)

Rs = (ρgh)C (4)

when adapting an intermediate cohesion of ca 8 MPa forupper crustal rocks we obtain an Rs value of 68 for both

nature and our experiments This cohesion is relatively lowcompared to the ca 20ndash40 MPa measured for continentalrocks (eg Handin 1969 Jaeger and Cook 1976 Twissand Moores 1992) but should be reasonable given that thestrength of the earthrsquos crust is generally reduced due to pre-vious phases of tectonic activity

For verifying the dynamic similarity of viscous materialsthe Ramberg number Rm applies (Weijermars and Schmel-ing 1986)

Rm = gravitational stressviscous strength

= (ρgh2)(ηv) (5)

Our experimental and the equivalent natural Rm values arethe same ca 75

The reference experiments are thus properly scaled Scal-ing the other experiments can be more challenging Whenadopting a lower crust viscosity of 1021 Pa s many experi-ments would seem to extend unrealistically fast (Table 2)However when assuming a higher lower crustal viscosity of1022 or even 1023 Pa s (eg Buck 1991) the equivalent natu-ral extension rates to those listed in Table 2 are more reason-able

3 Results

31 Foam base experiments (F series)

Figure 4 shows the results of two brittle-only foam baseexperiments (set-up in Fig 2a b) Experiment F1 (withoutseed) develops no distinct structures except for significantboundary effects along the longitudinal sidewalls towards theend of the experiment (Fig 4a) In contrast the seed in ex-periment F4 localizes deformation in the centre of the exper-iment although faulting along the long sidewalls is also visi-ble at the surface (Fig 4b) The CT data from experiment F4(with seed) reveals the evolution of these structures in moredetail (Fig 4cndashg) After ca 60 min (8 mm) of extension a riftstarts forming above the seed and becomes visible at the sur-face after 120 min (16 mm of extension Fig 4d f) This mainrift structure continues developing towards the end of the ex-periment (Fig 4e g) The CT images show how additionalfaulting occurs first along the sidewalls (Fig 4d f) later onthroughout the experiment so that at the end of the experi-ment pervasive sidewall-parallel striking normal faulting isomnipresent (Fig 4e g) Note that this distributed faulting isnot visible on the top-view images due to the low fault off-sets at the surface that do not cast shadows on the experimentsurface (Fig 4b) and may very well be present in the exper-iment without seed as well (F1 Fig 4a)

The evolution of foam base experiments with a brittle-viscous layering is summarized in Fig 5 (set-up in Fig 2ac) Experiment F5 without a seed forms no central rift basin(Fig 5a) Instead all deformation is concentrated as bound-ary effects along the long sidewalls By contrast experiment

Table 3 Scaling parameters

General parameters Brittle upper crust Ductile lower crust Dynamic scaling values

Gravitational UC Extension Density ρ Cohesion Density ρ Viscosity Ramberg Brittle stressacceleration thickness velocity (kg mminus3) C (Pa) (kg mminus3) η (Pa s) number Rm ratio Rsg (m sminus2) h (m) v (m sminus1)

Experimenta 981 4times 10minus2 22times 10minus6 1560 9 1600 15times 105 75 68Nature 981 2times 104 15times 10minus10 2800 8times 106 2870 1times 1021 75 68

UC Upper Crusta Valid for reference set-ups

Figure 4 Foam base (brittle-only) results (a b) Top views depicting the final surface structures of models F1 (no seed) and F4 (withseed) The brittle layer is 4 cm thick and the extension velocity is 8 mm hminus1 Note that the boundary effects are present on both sides of theexperiment but these are partially invisible due to shadow (cndashd) 3-D evolution of CT-scanned experiment F4 (f g) 3-D internal evolutionof CT-scanned experiment F4

Figure 5 Foam base (brittle-viscous) results (a b) Top views depicting the final surface structures of experiments F5 (no seed) and F7 (withseed) Both the brittle and viscous layers are 4 cm thick and the extension velocity is 8 mm hminus1 Note that the boundary effects are presenton both sides of the experiment but these are partially invisible due to shadow (cndashd) 3-D evolution of CT-scanned experiment F7 (f g) 3-Dinternal evolution of CT-scanned experiment F7

F7 with a seed produces a well-developed symmetric riftstructure Still this experiment also produces some minorfaulting along the long sidewalls (Fig 5b) CT images illus-trate the 3-D evolution of experiment F7 (Fig 5cndashg) Soonafter initiation (30 min 4 mm extension) a central rift struc-ture with two main boundary faults develops above the seedAs the experiment progresses this structure continues evolv-ing the rift basin grows deeper and the brittle material sit-uated between the initial boundary faults starts breaking updue to internal faulting (Fig 5d f) Some boundary effectsdevelop but are relatively minor with respect to the centralrift structure (Fig 5dndashg) Towards the end of the experimentthe brittle layer is almost breached by the upwelling viscouslayer (Fig 5e g) In this experiment deformation is strongly

focussed on the rift structure and no distributed faulting canbe distinguished

32 Rubber base experiments (R series)

The surface evolution of two selected rubber base exper-iments built of only sand is depicted in Fig 6 (set-up inFig 2d e) Experiment R1 (Fig 6a arsquo) has no seed to local-ize deformation and as a consequence deformation focusesalong the sidewalls In addition remarkable conjugate faultsdevelop within the standard experiment duration (300 min40 mm of extension) but are not well visible on our top-view images since they do not create significant topography(Fig 6a) However an additional phase of extension in exper-iment R1 (30 min at 40 mm hminus1) helps to highlight these con-

Figure 6 Rubber base (brittle-only) results (a b) Top views depicting surface structures of experiments R1 (no seed) and R5 (with seed)after 40 mm of extension Note that panel (a) represents the first phase of experiment R1 (8 mm hminus1 until 40 mm extension) and (arsquo) thesecond phase where an additional 20 mm of extension with an enhanced extension velocity of 20 mm hminus1 was applied to the same experimentto amplify fault structures Experiment R5 was run with an extension velocity of 10 mm hminus1 These deviations from the reference extensionvelocity (8 mm hminus1) are permissible since the behaviour of sand is time-independent The sand layer is 4 cm thick in both experiments Notethat the boundary effects are present on both sides of the experiment but these are partially invisible due to shadow (cndashd) 3-D evolution ofCT-scanned experiment R5 (f g) 3-D internal evolution of CT-scanned experiment R5

jugate faults (Fig 6arsquo) In contrast to experiment R1 exper-iment R5 contains a viscous seed that focuses faulting alongthe experimentrsquos central axis (Fig 6b) As a result this exper-iment develops a central rift structure Similar to experimentR1 well-defined conjugate faults occur as well

The CT-derived 3-D images from experiment R5 (Fig 6cndashg) reveal how deformation localizes along the seed and thesidewall in the initial stages forming a cylindrical central riftstructure (Fig 6d) However after some 20ndash25 mm of exten-sion the conjugate sets of vertical strikendashslip faults start de-veloping (Fig 6f) which become pervasive toward the end

of the experiment (Fig 6e g) This curious feature is theresult of along-strike compression as the orthogonally ex-tending rubber sheet contracts perpendicular to the extensiondirection (Fig 6arsquo) Yet the rift structure continues to evolvetoward the end of the experiment run (Fig 6e g)

Figure 7 shows results of four brittle-viscous rubber baseexperiments (set-ups in Fig 2d f) Experiment R7 with-out seed produces no clear surface structures except forstrong boundary effects along the sidewalls (Fig 7a) In con-trast experiment R8 (with seed) experiences early fault lo-calization (after 30 min a rift becomes visible at the sur-

Figure 7 Rubber base (brittle-viscous) results Top views depicting the final surface structures of (a b) experiments R7 and R8 (referenceextension velocity of 8 mm hminus1) and (c d) R9 and R10 (high extension velocity experiments 80 and 480 mm hminus1 respectively) Note thatboundary effects although partially invisible due to shadow are present on all sides of the experiment and therefore especially in the corners

face) which continues evolving towards the end of the ex-periment (Fig 7b) However this experiment also developsstrong boundary effects along the long sidewalls and at thecorners where some viscous material flows into the gap be-tween the original sand buffer and the retreating sidewallsThe rift structure is best developed in the centre of the ex-periment and dies out towards the short sidewalls involvingslight block rotation of the sand layer in the four corners ofthe experiment (Fig 7b)

Experiment R9 was run at an increased extension veloc-ity of 80 mm hminus1 (Fig 7c) and produces a central rift thatis quite similar to the rift in experiment R8 (Fig 7b) eventhough no seed is included Significantly higher extensionvelocities (480 mm hminus1 in experiment R10) result in stronglydistributed deformation with multiple rifts (Fig 7d) Thesethree experiments without a seed at different extension rates(Fig 7a c d) reveal the effect of decreasing strength con-trasts between the brittle and viscous layers (strength ratiosof 84 84 and 14 respectively Table 2) of which the impli-cations are discussed in Sect 44

33 Plate base experiments (P series)

Experiments P1 and P2 consist of a brittle sand layer on topof plastic rigid base plate(s) (Figs 2h 8a b) In experimentP1 we apply symmetric extension whereas in experiment P2extension is asymmetric Both experiments initially developa rift above the velocity discontinuity along the central axisof the experiment However with continued extension exper-iment P1 develops a rift basin with a central horst block in themiddle which does not develop in experiment P2 (Fig 8a

b) Otherwise both rift structures have the same width Noboundary effects occur along the long sidewalls

Figure 8cndashg shows the results of the plate base experi-ments with brittle-viscous layering (set-up in Fig 2g i) Ex-periments P3 and P7 are following symmetrical and asym-metrical extension respectively No seed is included Thestructural evolution is similar for both experiments Riftinginitiates at the short sidewalls where both the base plates andconfining plates are moving apart (Figs 2g i 8c d) Theserifts propagate slightly towards the centre of the experimentbut strong boundary effects along the long sidewalls take upmuch of the extension there and no continuous rift structuredevelops in the centre of the experiment (Fig 8c d) As aresult block rotation (ca 3 around a vertical axis near thetips of the propagating rifts) occurs at the short ends of theexperiments (Fig 8c d) The surface structures are largelythe same in both experiments suggesting that the applica-tion of symmetric or asymmetric extension does not have asignificant influence on this type of experiment

The application of a seed on top of the viscous layer (ExpP10 in symmetric extension) results in early localization andrift development along the central axis of the experiment(Fig 8e) This structure continues developing throughout theexperiment yet more extension is accommodated towardsthe short sidewalls than the middle section where boundaryeffects along the long sidewalls take up a larger part of thedeformation similar to experiments P3 and P7 (Fig 8c d)

The thick viscous layer in experiments P3 and P7 likelydampens the influence of the basal boundary condition onthe sand layer We therefore ran further tests (experimentsP8 and P9 both with half the reference layer thicknesses

Figure 8 Overview depicting our plate base results (a b) Top views of brittle-only experiments P1 (symmetric extension) and P2 (asymmet-ric extension) (cndashf) Brittle-viscous experiments in map view (cndashd) experiments P3 and P7 (reference extension velocity experiments withoutseed) (e) Exp P10 (reference extension velocity with seed) (f) Exp P9 (40 mm total thickness high extension velocity of 80 mm hminus1 noseed) Note that boundary effects are present on both sides of the experiment but these are partially invisible due to shadow (g) Schematicsection depicting the internal structures of experiment P9 interpreted from surface data and the topography of the stretched viscous materialas observed after removal of the sand at the end of the simulation Note the two VDs the base plates are 2 mm thick each

keeping the same brittle-to-viscous ratio ie 2 cm brittle and2 cm viscous material without seed) Both these experimentsdid not produce a continuous rift basin either However ex-periment P9 with a high 80 mm hminus1 extension velocity anda low brittle-to-viscous strength ratio of 44 (compared tothe reference ratio of 84) produces interesting basin geome-tries (Fig 8f g) Instead of developing a simple rift structurethe viscous layer at the centre of the experiment is stronglystretched creating a depression with continuous rift basins at

its margin due to what seems to be passive down-bending asthe underlying viscous layer is stretched (Fig 8g) Secondarygraben structures develop further away from the central de-pression indicating a degree of distributed deformation No-tably no boundary effects occur along the long sidewalls incontrast to the other brittle-viscous plate base experiments

Figure 9 Overview of conveyor base results (all without seed) Top views depicting the final surface structures of (a b) brittle-only experi-ments C1 and C3 (c d) brittle-viscous Exp C4 (reference layering and extension velocity) (d) experiment C7 (reference extension velocitybrittle-to-viscous ratio 2) (e) Exp C8 (reference extension velocity brittle-to-viscous ratio 4) and (f) Exp C11 (elevated extension velocity40 mm hminus1 brittle-to-viscous ratio 4) Note that the boundary effects (if present) occur on both sides of the experiment but may be partiallyinvisible due to shadow (g) CT section depicting the internal structures of Exp C11

34 Conveyor base experiments (C series)

Figure 9 shows the results of the conveyor base set-up withonly a brittle layer (experiments C1 and C3) (set-up in Fig 2jk) Both experiments develop a large rift structure along thecentral axis of the experiment (Fig 9a b) rather similar tothe plate base experiments P1 and P2 (Fig 8a b) We dohowever not directly observe a difference between resultsobtained with symmetrical and asymmetrical extension

The results of the brittle-viscous experiments show morediversity than their brittle-only counterparts (Figs 2j l 9cndashg) Experiment C4 with symmetrical extension developstwo rifts that originate from the short sidewalls and propagatetowards the experiment centre (Fig 9c) They do howevernot connect as boundary effects along the long sidewalls takeup most of the deformation in the centre similar to the struc-tures observed in the plate base equivalents (experiments P3and P7 Fig 8c d) We did not run an asymmetrical exten-

sion experiment with brittle-viscous layering since we didnot expect significant differences Instead we attempted toreduce boundary effects along the short sidewalls by apply-ing lubricants or adding a sand buffer as proposed by Tronand Brun (1991) (experiments C5 and C6 respectively) Un-fortunately the boundary effects remained or got worse (SeeAppendix C Fig C1) Furthermore we ran the conveyor baseequivalent of experiment P9 (2 cm sand 2 cm viscous mate-rial and 80 mm hminus1 extension Fig 8f g) labelled C12 withvery similar results to the plate base experiment (Fig C2)

We also tested the effect of decreasing viscous layer thick-ness in experiments C7 and C8 thus simultaneously de-creasing and increasing the brittle-to-viscous thickness andstrength ratios respectively In experiment C7 (Fig 9d) thethickness and strength ratios are 2 and 168 which does notlead to a significantly different structural evolution comparedto the reference set-up of experiment C4 (Fig 9c) How-ever decreasing the viscous layer thickness further to 1 cm(thickness and strength ratios 4 and 337) in experiment C8(Fig 9e) causes localization of faulting along the central axisof the experiment during early stages of deformation andthe development of a dual rift on both sides of the VD with ahorst in the middle This central structure subsequently re-mains in place but faulting becomes more widespread to-wards the end of the experiment (Fig 9e)

Additional tests with higher extension velocities (80 and40 mm hminus1 for experiments C9 and C10C11 respectivelysee Table 2 Fig 9f and Appendix C Fig C2) have shownto improve rift localization as faulting is less widely devel-oped than in experiment C8 (Fig 9e) Experiment C10 wassubsequently rerun in the CT scanner as experiment C11 forfurther analysis (Fig 9g) We observe that these specific ex-periments develop the same features a double-rift system oneither side of the VD of which the internal structures becomemore complex with time and a central intact but subsidedhorst in the rift centre (Fig 9g) We also observe the develop-ment of minor additional rift basins striking parallel Slightboundary effects occur along the long sidewalls in experi-ments C10 and C11 as well (Fig 9f g)

4 Discussion

41 General structures

We present a schematic overview of our experimental resultsin Fig 10 summarizing the general structures in map viewand section and Table 4 linking these observations with po-tential natural settings A clear distinction exists between thebrittle-only experiments (left-hand half of upper three rowsin Fig 10) and the brittle-viscous experiments (right-handhalf of upper three rows in Fig 10) since the viscous layeracts as a buffer between the deformation-inducing base andthe overlying sand In the brittle-only experiments no suchbuffer exists and deformation induced by the base of the set-

up is directly transmitted to the overlying sand cover lead-ing to more distinct structural differences between the experi-mental series In addition the bottom row of Fig 10 summa-rizes the structures observed in the high extension velocityexperiments and the tests with high brittle-to-viscous ratiosleading to different degrees of coupling and more complexsurface structures Our experimental results are discussed inmore detail below

42 Brittle-only reference experiments

In the foam base experiments the sand above the foam di-rectly experiences the distributed deformation induced bythe expanding foam causing fault development throughoutthe experiment but also along the long sidewalls (Figs 4a10a) Schlagenhauf et al (2008) report similar but more pro-nounced distributed rifting possibly enhanced by a higherdegree of extension of their foam base (20 vs our 13 )and a thicker sand pack (8 cm vs our 4 cm) Seeds do lo-calize rift basins in our experiments (Figs 4bndashg 10b) butthese structures only account for a minor part of the extensionas the rifts experience little subsidence with respect to mostother experiments (eg P1 and P2 in Figs 8a b 10) Thebrittle-only rubber base experiments produce similar struc-tures as the brittle-only foam base experiments distributeddeformation and a minor axial rift when a seed is applied(Figs 6 10e f) Significant faulting develops at the longsidewalls and migrates towards the centre of the experiment(Fig 6cndashg) which could be explained by stronger strain gra-dients in the rubber near the sidewalls (Ackermann 1997)A similar effect could possibly occur in the foam base ex-periments as well explaining the comparable boundary ef-fects (Fig 4) It is worth noting that the results from our ex-periments with a full rubber base (distributed faulting) differfrom those obtained with narrow rubber sheets between baseplates (localized and well-developed rift basins eg McClayand White 1995 McClay et al 2002 Schlische and With-jack 2009) This is because in the latter experiments defor-mation is strongly concentrated above the rubber sheets withthe edges of the plates acting as VDs These models producewell-developed rift structures but mix two basal boundaryconditions (distributed extension and VDs) making it moredifficult to identify equivalent natural conditions (Morley1999 see also Sect 46)

Our rubber base experiments also develop conjugatestrikendashslip faults due to the contraction of the rubber perpen-dicular to the extension direction (Poisson effect) (Smith andDurney 1992 Venkat-Ramani and Tikoff 2002 Figs 4arsquo10e f) Such structures are not always observed in othermodel studies applying a rubber base set-up (eg Vendev-ille et al 1987 Fig 11a) The Poisson effect-related struc-tures we obtain are probably due to the relatively low length-to-width ratio rubber base we use (ca 17) Narrow rubberbase models by McClay and White (1995) and McClay etal (2002) with much higher length-to-width ratios (6 and

Figure 10 Schematic summary of our experimental results (andashl) Experiments with reference brittle-to-viscous ratios (1 1) and referenceextension velocities (8 mm hminus1) (lowast means plate base experiment result only) All sections shown go through the central part of the experimentwhere boundary effects are minimal (mndashp) Additional brittle-viscous experiments with high extension velocities (80 mm hminus1) andor highbrittle-to-viscous ratios (4 1)

Figure 11 Examples of previously published analogue models of extensional tectonics (a) Cross section of a brittle-only rubber base modelas used for homogeneous thin-skinned deformation Note the conjugate fault sets Adapted from Vendeville et al (1987) with permissionfrom the Geological Society London (b) Top view and cross section of a brittle-only rubber base model similar to panel (a) althoughdeveloping the conjugate fault sets due to extension-perpendicular contraction of the rubber sheet (Poisson effect) Adapted from Bahroudi etal (2003) with permission from Elsevier (cndashd) Cross sections of brittle-only conveyor base experiments with (c) symmetric or (d) asymmetricextension both including syn-rift sedimentation Here the VD may represent a basement structure controlling deformation in the overlyingstrata Redrawn after Allemand and Brun (1991) with permission from Elsevier (endashg) Cross sections of brittle-viscous models with a platebase or conveyor belt set-up with the VD representing a fault in the strong brittle mantle affecting the overlying crustal analogues (e) Brittle-viscous plate base model with asymmetric extension illustrating the relation between the velocity discontinuity (VD) and the two rift basinsCompare with experiment C11 (Figs 9f g C2) Redrawn (with permission from Elsevier) after Michon and Merle (2003) who investigatedthe European Cenozoic Rift System and the influence of VDs in a strong upper lithospheric mantle (f) Symmetric extension model withconveyor set-up and brittle-viscous layering designed to simulate the influence of a strong mantle on a two-layer crust Adapted from Tronand Brun (1991) with permission from Elsevier (g) Brittle-viscous plate base model with asymmetric extension Note that this experimentincludes syn-rift sedimentation and aims to reproduce the North Sea Viking Graben Modified after Brun and Tron (1993) with permissionfrom Elsevier Black arrows indicate extensional motion VD velocity discontinuity

Table 4 Overview of links between our experimental set-ups and initial conditions the resulting structures observed in our experiments andtheir potential natural analogues

Set-up Layering Extensionvelocity

Thicknessratio(b v)

Strength ratio(b v)

Couplinga observed inexperiments

Potential naturalanalogue

Structural style observedin experiments

brittle slow ndash ndash Very high coupling ofbrittle layer with substratum

Strong ductile lowercrust (Fig 3a)

No seed distributedrifting (Fig 10a arsquo)

Seed distributed riftingwith small localized riftbasin (Fig 10b brsquo)

NB Rubber base con-jugate faults may occur(Fig 10e ersquo f frsquo)

brittle-viscous

slow 1 1 84 (highstrength contrast lowb v coupling)

Low coupling betweenall componentsa brittle coverdecoupled from base of set-up

Weak hot litho-sphere (strongmantle absent)(Fig 3b)

No seed only boundaryeffects (Fig 10c crsquo)

Seed localized rifting(Fig 10d drsquo)

fast 1 1 14ndash84(low strength contrasthigh b v coupling)

High coupling betweenall componentsa brittle coverpotentially coupled to base ofset-up but brittle-viscouscoupling dominant

Strong ductile lowercrust but weak duc-tile upper mantle(Fig 3e)

No seed distributedrifting (Fig 10m mrsquo)

Seed distributed riftingwith a localized riftbasin(eg Zwaan et al 2016)

Cold lithosphereFault in (thick)brittle crust or brittlemantle (Fig 3c)

Strongly localized rifting(Fig 10i irsquo j jrsquo)

brittle-viscous

slow 1 1 84 (high strengthcontrast low b vcoupling)

Low coupling betweenall componentsa brittlecover decoupled frombase of set-up

Hot lithospherewith thick ductilelower crust abovebrittle upper mantle(Fig 3d)

No seed only boundaryeffects (Fig 10k k)

Seed localizedrifting (Fig 10l lrsquo)

fast 4 1 337 (very highstrength contrast verylow b v coupling)

Low b v coupling butsoft linkage betweenbase of set-up and brittle cover

Cold lithospherewith thin ductilelower crust abovebrittle upper mantle(Fig 3h)

No seed distributed(double) rifting(Fig 10o orsquo)

Seed Not known

fast 1 1 44 (low strengthcontrast high b vcoupling)

Very high coupling between allcomponentsa brittle cover poten-tially coupled to base of set-upbut viscous-base couplingdominant

Hot lithospherewith thick ductilelower crust abovebrittle upper mantle(Fig 3f)

No seed localizedstretching and down-bending basin(Fig 10m mrsquo)

Seed not known

fast 4 1 68 (intermediatestrength contrastintermediate b vcoupling)

Low brittle-base decouplingbrittle cover stronglyinfluenced by base of set-up

Localized (double)rifting (Fig 10p prsquo)

Seed not known

b v brittle-viscous a We distinguish four types of coupling and decoupling brittle-basal brittle-viscous and viscous-basal coupling as well as cover-basal decoupling due to thepresence of a viscous layer (see Sect 23) b All components all parts of the experiment ie the sand layer viscous layer and substratum (base of the set-up)

4 respectively) do not undergo any visible contraction per-pendicular to the extension direction whereas an experimentby Bahroudi et al (2003) with a length-to-width ratio of 08develops strong conjugate faulting (Fig 11b) The faults inBahroudi et al (2003) have a normal fault component aswell possibly because the rubber was stretched from one sideonly It is furthermore interesting to note that the Poisson ef-fect may occur in very different types of models or materi-als Chemenda et al (2002) for instance applying an elasto-plastic mixture of various components floating on water tosimulate the lithosphere and asthenosphere also obtain per-

vasive conjugate faults due to extension-perpendicular con-traction

Contrary to their rubber and foam base equivalents astrong localization of faulting above the velocity discontinu-ity (VD) occurs in the brittle-only plate base and conveyorbase experiments (Figs 8a b 9a b 10i j) The plates andsheets translate overlying materials except at the velocitydiscontinuity where extension localizes and deep rift basinsform The centre of the rift basins in both the asymmetricand symmetric experiments lies practically at the same levelas the experimental base at the end of the experiment (4 cm

depth scaling to a 20 km deep basin in nature) (Figs 8a b9a b 10i j) In nature isostatic compensation would havereduced basin depth but this effect is absent here Such ex-periments may therefore best be used for investigating ini-tial (small) amounts of extension (eg maximum of half thethickness of the brittle crust) Larger amounts of extensioncould be simulated when significant sedimentation is ap-plied preserving a more realistic topography by filling in thegenerated ldquoaccommodation spacerdquo and providing additionalmaterial for the formation of new structures (eg Allemandand Brun 1991 Brun and Tron 1993 Keep and McClay1997 Gabrielsen et al 2016 Fig 11c d) The small horststructure along the axis of the symmetric extension plate baseexperiment (Figs 8a 10i) is likely formed when both platesmove away leaving a small quantity of material behind in themiddle Previous authors have shown the impact extensionasymmetry can have on rift geometry by creating stronglyasymmetric rift basins (Allemand et al 1989 Allemand andBrun 1991 Panien et al 2005 Fig 11c d) Yet these effectsare not directly observed in our experiments possibly due tothe relatively minor total extension the absence of syn-riftsedimentation or because we lack the necessary cross sec-tions as these models were not CT scanned

43 Brittle-viscous reference experiments

The presence of a viscous layer in our experiments leads toquite different structures with respect to those observed intheir brittle-only counterparts (Fig 10) The brittle-viscousfoam and rubber base cases produce basically the same struc-tures when no seed is present faulting only occurs along thesidewalls whereas a seed strongly concentrates deformationas well resulting in a central rift structure (Figs 5 7a b 10cd g h) The decoupling of the sand from the foam or rubberbase allows the brittle cover to behave as rigid blocks moreor less passively floating on the viscous layer (Zwaan et al2018a) By contrast the sand in the brittle-only experimentsis directly coupled to the base forcing a pervasive type offaulting (Fig 10a b e f) Due to this decoupling effect ofthe viscous layer no conjugate strikendashslip fault sets occur inour brittle-viscous rubber base experiments nor in those ex-periments performed by Bellahsen et al (2003) or Bellahsenand Daniel (2005) The fact that the rifts in our rubber baseexperiments are less developed towards the short ends of theset-up is most likely caused by the use of a sand talus to con-tain the viscous material there (Figs 2d 7bndashd) This creates adeformation contrast between the immobile talus and the de-forming material above the rubber sheet an effect that couldpotentially be reduced by using a rubber sidewall as in thefoam set-up (Figs 2a 5)

In contrast to the results of the brittle-only experimentsthat show strong differences depending on the set-up thoseof the brittle-viscous plate base and conveyor base experi-ments are quite similar to their foam and rubber base equiv-alents (Fig 10) most likely due to the tendency of the vis-

cous material to easily spread out when subject to relativelyslow extension rates All of these experiments however seeminor rifting initiating at the short sides of the set-up be-cause there the materials are confined by sidewalls or sheetsthat move in sync with the long sidewalls imposing the sameboundary conditions there as at the base of the set-up The re-sulting additional drag enhances the extensional deformationat these short edges forcing the development of rifts whichpropagate toward the centre of the experiment (Figs 8cndashe9c d 10k l) In the centre however the viscous spreadingmechanism is dominant so that we observe the same struc-tures as in the other brittle-viscous experiments (Fig 10)This ldquoshort sidewall effectrdquo is also present when applyinga seed (Figs 8e 10l) causing the rifts to be more developedat the short ends of the experiment and may also have oc-curred in a model by Mart and Dauteuil (2000) Their exper-iment involves a curious propagating rift system initiating atthe short edge of the set-up which has a similar plate con-finement as in our experiments We see similar rift initiationfrom the sides of the model in the work by Autin et al (20102013) as well In order to reduce this type of boundary ef-fect higher strain rates can be applied (Fig 9endashf) Howeverthe use of a sand talus to confine the short ends of the experi-ment as suggested by Tron and Brun (1991) does not reducethese boundary effects in our experiments as the sand is evenmore strongly coupled to the experimental materials the sideplates or sheets causing more friction (experiment C5 Ap-pendix C2 Fig C2) This is expressed by the internal frictionangle of our quartz sand being higher than that of quartz sandwith respect to the plastic plates or sheets used at the shortsidewalls (361 versus ca 20)

As with the reference brittle-only experiments we do notobserve a clear difference between symmetric and asymmet-ric extension Yet previous authors have shown that asym-metric extension may affect brittle-viscous experiments aswell This is however mostly in combination with a rela-tively thin viscous layer that allows for a more direct transferof deformation from the set-up base to the sand cover (egAllemand et al 1989) By contrast the relatively thick vis-cous layer in our reference experiments acts as a buffer de-coupling the sand from the extending plates or sheets at thebase of the experiments (see also Sect 45)

44 Velocity effects distributed extension versuspassive down-bending and marginal grabenformation

As discussed in Sect 43 the reference brittle-viscous foamand rubber base experiments without a seed see the brittlecover decoupled from the set-up base Increasing the exten-sion rate as in experiments R9 and R10 (Fig 7c d Table 2)seems to increase the influence of the set-up distributed ex-tension is induced at the base and observed at the surface ofthe experiments Yet the lower strength ratios (84 and 14for experiments R9 and R10 compared to the reference ra-

tio of 84 see Table 2) also indicate higher brittle-viscouscoupling which is known to cause distributed or wide rift-ing (eg Brun 1999 Buiter et al 2008 Zwaan et al 2016Figs 7c d 10m) Since both the enhanced cover-basal andhigh brittle-viscous coupling should lead to similar resultsit is challenging to determine which factor is dominant Stillthe type of deformation in these experiments is not as evenlydistributed as in their brittle-only equivalents (Figs 4 10ab e f) suggesting that the influence of the base is secondarycompared to the effects of brittle-viscous coupling We canalso infer that the central rift in experiment R9 (Fig 7c) prob-ably forms due to some wide rifting effect the higher theextension rate (while keeping all other parameters constant)the higher the brittle-viscous coupling and the more rifts de-velop as illustrated by experiment R10 (Fig 7d)

Yet considering the results from the high-velocity rubber-base experiments R9 and R10 (Figs 7c d 10m) those ofthe high-velocity brittle-viscous plate or conveyor base ex-periments P9 (Figs 8f g 10n) and C12 (Fig C2) may seemsomewhat remarkable instead of developing distributed rift-ing these experiments generate a ldquodown-bentrdquo depressionbordered by marginal grabens (Figs 8f g 10n C2) that mayalso be present in the models by Gabrielsen et al (2016) Thehigh extension velocity in P9 and C12 (80 mm hminus1) causeshigh coupling between the viscous layer and the brittle cover(strength ratio 44) as well as between the viscous layerand the base This basal coupling leads to intense stretch-ing (necking) above the VD(s) and subsequent downwardldquobendingrdquo of the sand cover (Fig 8g) High coupling be-tween the viscous layer and the base also explains why noapparent boundary effects are visible along the longitudinalsidewalls The bending of the brittle layer at the edge of thesystem causes local extension in the sand and the formationof marginal grabens which seems to resemble the structuresalong the Western Escarpment of the Afar (northernmost sec-tor of the East African Rift System) in Ethiopia (eg Abbateand Sagri 1969 Chorowicz et al 1999) However interest-ing as these structures may be the high extension velocitiesmay approach unrealistic values (see Sect 24) highlightingthe importance of careful model scaling

As previous studies have shown increasing brittle-viscouscoupling can be linked to more distributed faulting styles(eg Davy et al 1995 Schueller et al 2005 2010 Dyk-sterhuis et al 2007 Moresi et al 2007 Buiter et al 2008Zwaan et al 2016) which is seen in our rubber base exper-iments as well (experiments R9 and R10 Figs 7c d 10m)However the experiments in these previous studies generallyuse a very weak or free-slip base allowing their models to be(fully) controlled by the rheology of the brittle-viscous lay-ers When such basal boundary conditions are not met cou-pling between the viscous layer and the substratum is also animportant factor as illustrated by our plate and conveyor baseexperiments (experiments P9 and C12) (Figs 8f g 10n C2)We thus identify a competition between brittle-viscous cou-pling and viscous-basal coupling in such systems depending

on which the resulting structures may vary widely Withinthe context of extensional tectonics this is in line with theconcept that the strength of the uppermost mantle can havea significant influence on the deformation of the overlyingcrustal layers (eg Brun 1999 Corti et al 2003)

45 Effects of different brittle-to-viscous thicknessratios

Our brittle-viscous plate and conveyor base experiments withthe reference parameters but no seed (P3 P7 C4 Figs 8cndashd 9c 10k) fail to produce proper rift basins in contrast totheir brittle-only equivalents (experiments P1 P2 C1 andC3 Figs 8a b 9a b 10i j) Instead we either need a seedas in the foam and rubber base experiments (experiment P10Figs 8e 10l) or a high brittle-to-viscous thickness ratio (gt 2)to localize deformation (experiments C8 and C11 Fig 9endashg) The decrease in viscous layer thickness in experimentsC7 and C8 causes increasing strength contrasts from the ref-erence value of 84 to 169 and 337 respectively (Table 2)corresponding to a trend towards localized (narrow) rifting(Fig 9cndashe) This is in line with the model results presented byBrun (1999) for example However increasing the extensionrate in experiment C11 (resulting in a lower strength con-trast) does not lead to distributed deformation but to more lo-calized faulting Similar to the high extension rate examplesdiscussed in Sect 44 our results thus suggest that brittle-to-viscous strength ratios alone are not sufficient to properlyinfer a specific rifting mode but that additional factors suchas viscous-basal coupling need to be considered as well

Furthermore in the experiments with high brittle-to-viscous ratios (ie C8 and C11) we obtain double-rift struc-tures rather than the single-rift basins seen in our brittle-onlyexperiments and previous publications (Figs 8a b 9a b 10ij 9endashg) For instance Brun and Tron (1993) apply a rela-tively thin viscous layer (brittle-to-viscous ratio of ca 2) andobtain well-developed rift structures in symmetric extension(Fig 11g) The relatively thin viscous layer probably allowsfor a shift to a brittle-dominated system leading to rift lo-calization near the VD similar to our brittle-only plate andconveyor base experiments (Fig 8a b 9a b) However theextension model by Tron and Brun (1991 Fig 11f) producesthe same double rift structure including the additional faultsaway from the central rifts as our experiment C11 (Fig 9fg) Also Keep and McClay (1997) and Schreurs et al (2006)obtained two rifts with symmetrical extension experimentsinvolving a conveyor or plate base and a brittle-to-viscousratio of 4 and 6 respectively A lateral transfer of deforma-tion through the viscous layer away from the VD (ie ldquosoftlinkagerdquo eg Stewart et al 1996) is the probable cause ofthis dual rift arrangement (Michon and Merle 2000 2003Fig 11e) This feature seems to occur in lithospheric-scalemodels involving the asthenosphere as well (Allemand andBrun 1991 Brun and Beslier 1996 Cappelletti et al 2013Nestola et al 2015 Fig 1) A single-rift structure may form

Figure 12 Strength profiles calculated for our reference experiments (a) and various natural cases (bndashf) Reference values for the naturalexample are Tmoho = 600 C and v = 05 mm yrminus1 (b) Extension velocity variations are shown in (c) and (d) and variations due to differentMoho temperatures are depicted in (e) and (f) The crust and mantle flow laws used here are anorthosite dislocation creep (Rybacki et al2006) and olivine dislocation creep (Hirth and Kohlstedt 2003) Note that the filled-in profile represents a wet lithosphere whereas the dottedprofiles delineate a dry lithosphere scenario The horizontal lines indicate various brittle-to viscous ratios (see discussion in text)

due to factors as higher strain rates (Keep and McClay 1997Michon and Merle 2000) asymmetric extension or possiblysyn-rift sedimentation (eg Brun and Tron 1993 Fig 11g)The formation of a single- or dual-rift structure is most likelyinfluenced by the viscosity of the viscous layer as well Ex-periments with high brittle-to-viscous thickness ratios thusseem to be highly sensitive to various parameters Whetherthe various thickness ratios mentioned above are realistic de-pends on the specific tectonic setting that is simulated aslithospheric rheological profiles are known to vary consid-erably in extensional settings (eg Brun 1999 Burov 2011Tetreault and Buiter 2018 see also Sect 47)

46 Boundary effects and experimental confinement

Most of our reference experiments except for the brittle-onlyplate and conveyor base experiments develop some degreeof normal faulting along the long sidewalls (Fig 10) In thebrittle-only experiments this may be due to enhanced localstretching of the rubber base (Ackermann 1997) an effectquite possibly present in the foam base equivalents as wellThe rigid sand layer in the brittle-viscous experiments on theother hand is subject to ldquoinertiardquo ie an inability to moveand extend as easily as the viscous materials leaving ldquogapsrdquoalong the sidewalls that take up significant amounts of defor-mation in the experiment (Zwaan et al 2018a)

This ldquoinertiardquo effect occurs in various model studies andmay significantly affect the quality of the experimental re-sult Some authors seem to avoid these problems by simplyignoring them and focussing on the structures in the centreof the experiment Others attempt to reduce faulting by ap-plying a viscous layer that does not reach the model side-walls (Tron and Brun 1991 Schreurs et al 2006 Gabrielsenet al 2016) However by narrowing the viscous layer the

boundaries of the viscous material become rheological con-trasts that may trigger faulting themselves thus causing anew type of boundary effect (eg Bonini et al 1997) Thisalso raises the question of what the viscous layer representsin nature if not a continuous viscous lower crust Even nar-rower patches of viscous material for instance simulating aweak zone in the crust due to magmatism may lead to nar-rower rift structures (eg Brun and Nalpas 1996 Dauteuilet al 2002) and the seeds in our experiments can be seen asthe most extreme exponent of this trend The inferred widthof the structural weakness is also relevant for set-ups involv-ing a narrow rubber base fixed between two base plates (egMcClay and White 1995 McClay et al 2002 Corti et al2007 Henza et al 2010) In such experiments all deforma-tion tends to focus above the rubber sheet with its edges act-ing as VDs imposing the boundaries of the rift system (seealso Sect 42)

Our results show that the type of confinement along theshort edges of the brittle-viscous experiment forms anotherimportant factor generating boundary effects which is sim-ilar to the findings by Schreurs et al (2006) In the foambase experiments the rubber sheet sidewalls cause little tono additional deformation yet the sand talus confinementin the rubber base experiments generates significant bound-ary effects and enhanced rifting is associated with the platebase and conveyor base confinements However the similar-ity of the structures in the centre of all our reference brittle-viscous experiments (due to the likely dominance of the vis-cous spreading mechanism under low brittle-viscous cou-pling conditions) may suggest that if the short edge bound-ary effects can be reduced the type of extension mechanismwould be of little influence under our standardized condi-tions Therefore we could perhaps have obtained compa-rable results for brittle-viscous experiments even without a

method to induce deformation directly at the base of the ex-perimental materials only moving apart the two longitudinalsidewalls may suffice to cause uniform spreading of the vis-cous layer (eg Le Calvez and Vendeville 2002 Marques2012) However the results of such experiments may againvary with different strain rates layering and layer thicknessmaterials application of sedimentation etc highlighting thechallenges of directly comparing the results from differentmodelling studies and the need to specify all relevant pa-rameters and boundary conditions as well as any resultingboundary effects

47 Recommendations for further extensionexperiments

Our extension experiments represent different rheologicalstratifications and extension conditions and may serve asa guide for future modelling studies aiming at investigat-ing extension in specific tectonic settings (Fig 3) Since theoverview presented in Fig 3 remains schematic we calcu-lated a series of rheological profiles for natural cases to al-low for a direct rheological comparison to the experimentalstrength profiles (Fig 12) We used the rheological values ofTable 3 with laboratory flow laws often adopted for the lowercrust and lithospheric mantle (Hirth and Kohlstedt 2003 Ry-backi et al 2006) and we varied both extension velocity (05to 10 mm yrminus1) and Moho temperature (550 and 650 C) Thecalculations show that extension velocity has a relatively mi-nor influence on the rheological profile with respect to tem-perature and dry or wet versions of the flow laws The plotsalso indicate that our reference brittle-to-viscous thicknessratio of 1 1 although often used in analogue models (Cortiet al 2003 and references therein) is quite low (compareFig 12a with Fig 12b) and may only occur in a relativelywet and hot lithosphere (Figs 3b 12f) This may for instancebe in accordance with the situation in the East African RiftSystem (Fadaie and Ranalli 1990 Corti 2009) but a 2 1 or3 1 ratio would fit better with the calculations for a normal-temperature lithosphere (Fig 12bndashd) A strong upper man-tle as inferred for (brittle-viscous) plate and conveyor baseset-ups only occurs in a wet cold lithosphere (Fig 12e) orin a completely dry lithosphere (dotted lines in Fig 12) yetthe complete absence of hydrous minerals may be unrealistic(Xia and Hao 2010) Furthermore our strength profile cal-culations are based on monomineralic flow laws (anorthositeand olivine Hirth and Kohlstedt 2003 Rybacki et al 2006)whereas continental rocks are of course polymineralic Dif-ferent rheological profiles for natural settings can be obtainedby not only varying the thermal gradient but also by varia-tions in water content temperature or by simply using otherflow laws We choose lower crust and mantle flow laws (Ry-backi et al 2006 Hirth and Kohlstedt 2003 respectively)that are fairly recent and neither overly weak nor strong incomparison with other flow laws

The rheological calculations highlight that one shouldcarefully consider the various factors that may influence thestrength of the lithosphere in a given tectonic setting be-fore selecting a specific experimental set-up It is also im-portant to stress that although the materials involved mayonly represent the upper parts of the crust deeper parts ofthe lithosphere (basement or mantle) are simulated via thechosen experimental extension mechanism (Fig 3) This ismost evident for brittle-only experiments that are directlycoupled to the set-up (Fig 10) However we have shown thatfor low extension velocity brittle-viscous experiments whichaim at representing a hot lithosphere any extension mech-anism should suffice due to the high degree of decoupling(Fig 10) This decoupling effect could also allow for a sim-ple way to model an oceanic lithosphere which is generallyconsidered to comprise a brittle oceanic crust and a viscouslithospheric mantle (eg Benes and Scott 1996) Note how-ever that in such experiments an imposed weakness seems tobe necessary to create any rift structure at all (Fig 10) Sinceefforts should be made to keep boundary effects to a mini-mum we recommend using the foam base method for suchbrittle-viscous models (see also Sect 46)

Our experiments could be extended to include more lay-ers (three- or four-layer lithospheres) (eg Corti et al 2003and references therein) and an underlying asthenosphere thatwould allow for an assessment of the effect of isostatic com-pensation on a stretching lithosphere In such cases a stronglithosphere would strongly affect rifting processes (Brun1999 Corti et al 2003) whereas in the case of a weak litho-sphere (Figs 3b e 12f) the (rising) asthenosphere may havean important impact The presence of an asthenosphere ana-logue would also allow the vertical motions associated witha major fault or shear zone in the strong upper mantle (egVendeville et al 1987 Allemand and Brun 1991 Fig 1)In the commonly used plate and conveyor base set-ups sucha fault is represented by the VD yet any associated verticalmotions are not simulated The symmetric conveyor belt ex-tension mechanism may not be well suited to crustal-scalemodels as the continuous ldquoupwellingrdquo of the plastic sheetsresembles a convection cell system which could be taken tosimulate sub-lithospheric mantle behaviour and would there-fore be more appropriate for lithospheric-scale models drivenby mantle convection For crustal-scale wide rift experimentswe recommend using an asymmetric plate base or conveyorbelt mechanism instead which are the same after a shift ofreference frame (Appendix A)

It could also be worthwhile to repeat our experiments withother brittle materials and viscous analogues which maybetter capture the behaviour of the lithosphere (overviewin Schellart and Strak 2016) The use of temperature-dependent materials would allow for the inclusion of temper-ature effects (eg Boutelier and Oncken 2011) which canstrongly control rifting as shown by numerical simulations(Tetreault and Buiter 2018) Also the feedbacks betweenmagmatism and rifting need to be further explored (eg Corti

et al 2003 2015) A next necessary step in modelling large-scale rift structures is to include surface processes as well(eg Burov and Cloetingh 1997 Bialas and Buck 2009Zwaan et al 2018a)

We would like to stress the importance of standardizedmodelling methods and strict laboratory procedures (egKlinkmuumlller et al 2016) Different handling techniques lab-oratory conditions and personal preferences may cause varia-tions in for instance sand density (eg Krantz 1991) or rhe-ology of viscous materials (Rudolf et al 2016) and can havesignificant effects on model results (Schreurs et al 20062016) By means of standardized procedures within a mod-elling group these variations can be reduced Yet reproduc-ing the same model results in different laboratories will prob-ably always remain a challenge (see efforts by Schreurs et al2006 2016)

5 Conclusions

We present a systematic comparison of four set-ups com-monly used for analogue modelling of crustal-scale exten-sion We examine distributed extension obtained by a foamor rubber base and localized extension by rigid basal platesor conveyor-belt basal sheets We find the following points

ndash Brittle-only experiments are strongly affected by the ex-perimental set-up as the materials are directly coupledto the base of the set-up Foam base or rubber baseexperiments therefore undergo distributed deformationand wide rifting whereas plate base or conveyor baseexperiments experience localized deformation and nar-row rifting

ndash Strong boundary effects may occur due to extension-perpendicular contraction effects during stretching ofa rubber base (Poisson effect eg Smith and Durney1992) This may be mitigated by using a high length-to-width ratio for rubber base set-ups

ndash Brittle-viscous experiments are less affected by the ex-perimental set-up than brittle-only equivalents as theviscous layer acts as a buffer that decouples the brit-tle layer from the base of the set-up In our referenceexperiments this decoupling implies that a seed must beinserted in order to produce a rift basin

ndash Brittle-viscous experiments with low brittle-viscousstrength contrasts and a rubber base set-up show dis-tributed rifting as expected based on previous studiesYet plate and conveyor base experiments (expected lo-calized extension) with high strain rates (expected dis-tributed extension) develop intense localized stretchingof the viscous layer leading to the formation of a down-bent basin with marginal grabens This suggests that thebrittle-viscous strength ratio on its own does not deter-mine the style of deformation in a rift system but that

the nature of the underlying substratum is important aswell

ndash Brittle-viscous plate and conveyor base experimentswith higher brittle-to-viscous thickness ratios (thus de-creasing brittle-viscous coupling) achieve better faultlocalization which is in line with previous work How-ever higher strain rates in these experiments (whichincrease brittle-viscous coupling) improve localizationhighlighting once again that brittle-viscous coupling isnot the only parameter influencing the fault style of riftsystems

ndash Of the brittle-viscous experiments we tested the leastboundary effects occur for a set-up involving a foambase and a stretchable rubber sidewall This sidewallmethod could also be applied to a rubber base set-upto minimize boundary effects In contrast the plate baseand conveyor base set-ups can experience major bound-ary effects along their short sidewalls that may proofdifficult to reduce

The significant differences between experimental results ob-tained with the different set-ups ndash sometimes due to seem-ingly small differences in for instance extension velocityor layer thicknesses ndash indicate the need to accurately spec-ify model parameters and boundary conditions in order toallow for meaningful comparisons between (analogue) mod-elling studies The combination of rheological stratificationand experimental set-up defines the tectonic setting that is in-vestigated Our set-ups can be applied to study extension ofcrustal materials in various tectonic settings or lithosphericconditions with different levels of basement control Herefactors as temperature extension rate water content andlithology should be taken into account (Fig 12) We advise toavoid the symmetric conveyor belt method for crustal-scalemodels

Finally we recommend that every laboratory standardizeits procedures and methods as much as possible in order tominimize variations due to different handling techniques andpersonal preferences

Data availability The underlying research data in the form of sur-face view time-lapse videos as well as 3D CT imagery are madeavailable as a data publication via GFZ Data Services (Zwaan et al2019 httpsdoiorg105880fidgeo2019018)

Appendix A Schematic overview of relations betweenexperimental set-ups

Figure A1 provides an overview of the various set-ups andhow these compare to each other by means of extension ve-locities and shifts of reference frames All symmetric ex-tension set-ups are different foamrubber base experiments(Fig A1a b) develop an extension gradient whereas theplate and conveyor base experiments develop velocity dis-continuities (Fig A1d e and i j respectively) Also the plateand conveyor set-ups are different from each other (eg mov-ing and fixed VDs occur in plate base and conveyor base con-figurations respectively as is revealed after applying a shiftof reference frame Fig A1e j) Asymmetric extension set-ups differ from their symmetric equivalents as well but arebetween themselves after a shift of reference frame basi-cally the same (Fig A1f g k l)

Figure A1 Schematic overview of relations between experimental set-ups illustrated with shifts of reference frame (v = velocity VD= ve-locity discontinuity) Compare with Fig 2 (andashb) Foam and rubber base set-ups in which the base induces an extension gradient (cndashg) Platebase set-ups (hndashl) Conveyor base set-ups Shifts of reference frame are used to highlight the direct differences between set-ups Note thatmost set-ups fundamentally differ as indicated by the ldquo 6=rdquo sign except for the asymmetric plate base and conveyor base set-ups (fndashg kndashl)which are fundamentally the same The latter are indicated by the ldquo=rdquo sign Darker colours indicate mobile parts of the set-ups whereasbrighter colours indicate static parts

Appendix B Brittle and viscous strength calculations

B1 Brittle domain

For calculating brittle strength in our experiments we use theMohrndashCoulomb yield criterion written in terms of principalstresses σ1 and σ3

12(σ1minus σ3)= 12(σ1+ σ3)sin(ϕ)+C cos(ϕ) (B1)

where σ1 is the maximum compressive stress ϕ the angle ofinternal friction and C the cohesion

12(σ1+ σ3) represents the mean stress which we equateto lithostatic pressure ρgz Brittle layer strength is then ob-tained by integrating over the thickness of the brittle layerhb

hbinto

(σ1minus σ3)dz=

hbinto

(2ρgz sin(ϕ)+ 2C cos(ϕ))dz

= ρgh2b sin(ϕ)+ 2Chb cos(ϕ) (B2)

B2 Viscous domain

Strength profiles for viscous layers depend on the viscosityof the material η and the principal strain rates ε1 and ε3

(σ1minus σ3)= 2ηε1minus 2ηε3 (B3)

We simply assume pure shear for the initial stages of theexperiment and thus ε1 = 2V2W = VW and ε3 =minusε1(where V and Ware half the extension velocity and half thewidth of the experiment respectively) so that

(σ1minus σ3)= 4ηVW (B4)

Viscous layer strength then becomes

hvinto

(σ1minus σ3)dz=

hvinto

(4ηVW)dz= 4ηV hvW (B5)

where hv represents viscous layer thickness

Appendix C Experimental reproducibility

Figures C1 and C2 show the surface results of repeated ex-periments in order to evaluate their reproducibility In mostcases the structures are very similar Although the bound-ary effects in P6 and P7 (Fig C1) do show some variationthe structures in the centre are the same in both cases (norift) Experiments C4ndashC6 seem quite different (Fig C1) butC5 and C6 are tests to reduce boundary effects As pro-posed by Tron and Brun (1991) we added sand to con-fine the short ends of the experiment but instead of im-proving the situation this measure increases boundary ef-fects most likely due to the higher friction of sand In C6(Fig C1) we added a lubricant (hand soap) between thesides and the model Since there was no improvement weaborted the experiment after 120 min Note that asymmet-ric brittle-viscous plate base experiment P6 and symmetricbrittle-viscous conveyor belt experiment C4 are quite similardue to viscous decoupling effects Also asymmetric brittle-only plateconveyor base experiments P2 C2 and C3 producethe same structures (Fig C2) since both the plate base andconveyor base set-ups are after a shift of reference frameidentical in asymmetric extension conditions The double riftstructure in conveyor base experiment C10 is almost identi-cal to the version generated in C11 (Fig C2) although thecurving nature of the normal faults does provide local varia-tions in rift width High-velocity models P9 and C12 developvery similar structures although those in the conveyor beltset-up (C12) are better developed than in plate base experi-ment P9 (Fig C2) Note that the additional rift basins in C12are also present in P10 but not very visible due to their lessevolved state and the unfavourable lighting conditions

Figure C1 Reproducibility tests Final top views of experiments F2ndashF4 (brittle-only foam base with seed) F6 and F7 (brittle-viscous foambase with seed) P6 and P7 (brittle-viscous plate base experiments no seed) and C4ndashC6 (brittle-viscous conveyor base no seed) Note thatC5 and C6 were attempts to decrease boundary effects by replacing part of the basal viscous layer with sand (transparent overlay) oradding a lubricant (hand soap) along the short ends of the set-up respectively The former however increased boundary effects whereas thelatter did not significantly change surface structures and was therefore halted after 2 h Extension velocities are 8 mm hminus1 in all cases Notethat boundary effects are present on both sides of the experiment but these are partially invisible due to shadow

Figure C2 Reproducibility tests Final top views of experiments P2 C2 and C3 (brittle-only asymmetric plate base P and conveyor base C)C9ndashC11 (brittle-viscous conveyor base experiments 4 1 brittle-viscous thickness ratio high velocity 40 mm hminus1 for experiments C10 andC11 and 80 mm hminus1 for experiment C9) and experiments P9 and C12 (brittle-viscous plate base P and conveyor base C half layer thicknesshigh extension velocity 80 mm hminus1)

Author contributions The first author FZ performed the analoguemodels and composed the first version of the manuscript Secondauthor and project supervisor GS assisted with the model inter-pretation and the finalizing of the manuscript This study was in-spired by a collaboration on numerical-analogue comparisons withthird author SB who helped planning and discussing the modelseries provided strength calculations and helped in finalizing themanuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We would like to express our gratitude toNicole Schwendener for assisting us with the CT scanning and theengineers from IPEK Rapperswil (Theodor Wuumlst Reto GwerderRudolf Kamber Michael Ziltener and Christoph Zolliker) for up-grading the experimental apparatus We thank John Naliboff andJuumlrgen Adam for fruitful discussions and for the testing of analysistechniques as well as Ernst Willingshofer and an anonymous re-viewer for their helpful and constructive feedback We are gratefulto Matthias Rosenau and Kirsten Elger for archiving the underly-ing data associated with this paper in the form of a data publication(Zwaan et al 2019)

Financial support This project was funded by the Swiss NationalScience Foundation (grant no 200021_1470461) The Universityof Bern provided additional resources to upgrade the experimentalapparatus Susanne J H Buiter received financial support from theNorwegian Research Council (grant no 213399F20)

Review statement This paper was edited by Ylona van Dinther andreviewed by Ernst Willingshofer and one anonymous referee

References

Abbate E and Sagri M Dati e considerazioni sul margine orien-tale dellrsquoaltopiano etiopico nelle province del Tigrai e del WolloBollettino della Societagrave geologica italiana 88 489ndash497 1969

Abdelmalak M M Bulois C Mourgues R Galland O Leg-land J-B and Gruber C Description of new dry granular ma-terials of variable cohesion and friction coefficient Implicationsfor laboratory modeling of the brittle crust Tectonophysics 68439ndash51 httpsdoiorg101016jtecto201603003 2016

Ackermann R V Spatial distribution of rift related fractures fieldobservations experimental modelling and influence on drainagenetworks Unpublished PhD thesis Rutgers University USA1997

Acocella V Faccenna C Funiciello R and RossettiF Sand-box modelling of basement-controlled transferzones in extensional domains Terra Nova 11 149ndash156httpsdoiorg101046j1365-3121199900238x 1999

Acocella V Morvillo P and Funiciello R What con-trols relay ramps and transfer faults within rift zones In-

sights from analogue models J Struct Geol 27 397ndash408httpsdoiorg101016jjsg200411006 2005

Allemand P and Brun J-P Width of continental rifts and rheo-logical layering of the lithosphere Tectonophysics 188 63ndash69httpsdoiorg1010160040-1951(91)90314-I 1991

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Keep M and McClay K R Analogue modelling ofmultiphase rift systems Tectonophysics 273 239ndash270httpsdoiorg101016S0040-1951(96)00272-7 1997

Klinkmuumlller M Schreurs G Rosenau M and KemnitzH Properties of granular analogue model materialsA community wide survey Tectonophysics 684 23ndash38httpsdoiorg101016jtecto201601017 2016

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Le Calvez J H and Vendeville B C Experimental designsto model along-strike fault interaction Journal of the VirtualExplorer 7 1ndash17 httpsdoiorg103809jvirtex2002000432002

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Mart Y and Dauteuil O Analogue experiments of prop-agation of oblique rifts Tectonophysics 316 121ndash132httpsdoiorg101016S0040-1951(99)00231-0 2000

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Michon L and Merle O Mode of lithospheric extension Con-ceptual models from analogue modeling Tectonics 22 1028httpsdoiorg1010292002TC001435 2003

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Moresi L Quenette S Lemiale V Meacuteriaux C Appelbe B andMuumlhlhaus H-B Computational approaches to studying non-linear dynamics of the crust and mantle Phys Earth Planet Int163 69ndash82 httpsdoiorg101016jpepi200706009 2007

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Panien M Schreurs G and Pfiffner A Sandbox experi-ments on basin inversion testing the influence of basinorientation and basin fill J Struct Geol 27 433ndash445httpsdoiorg101016jjsg200411001 2005

Panien M Schreurs G and Pfiffner A Mechanical be-haviour of granular materials used in analogue modellinginsights from grain characterisation ring-shear tests andanalogue experiments J Struct Geol 28 1710ndash1724httpsdoiorg101016jjsg200605004 2006

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Ramberg H Gravity Deformation and the Earthrsquos Crust Aca-demic Press London 1981

Ritter M C Leever K Rosenau M and Oncken O Scalingthe sandbox ndash Mechanical (dis) similarities of granular materi-als and brittle rock J Geophys Res-Sol Ea 121 6863ndash6879httpsdoiorg1010022016JB012915 2016

Romaacuten-Berdiel T Aranguren A Cuevas J Tubiacutea J MGaipas D and Brun J-P Experiments on granite intru-sion in transtension in Salt Shale and Igneous Diapirsin and around Europe edited by Vendeville B Mart Yand Vigneresse J-L Geol Soc Spec Publ 174 21ndash42httpsdoiorg101144GSLSP19991740102 2000

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Schellart W P and Strak V A review of analogue modelling ofgeodynamic processes Approaches scaling materials and quan-tification with an application to subduction experiments J Geo-dyn 100 7ndash32 httpsdoiorg101016jjog201603009 2016

Schellart W P Lister G S and Jessell M W Analogue mod-elling of asymmetrical back-arc extension in Analogue mod-elling of large-scale tectonic processes edited by Schellart WP and Passchier C Journal of the Virtual Explorer 7 25ndash42httpsdoiorg103809jvirtex200200046 2002

Schellart W P Jessell M W and Lister G S Asymmetricdeformation in the backarc region of the Kuril arc northwestPacific New insights from analogue modelling Tectonics 221047 httpsdoiorg1010292002TC001473 2003

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Schueller S Gueydan F and Davy P Mechanics of thetransition from localized to distributed fracturing in lay-ered brittle-ductile systems Tectonophysics 484 48ndash59httpsdoiorg101016jtecto200909008 2010

Schlagenhauf A Manighetti I Malavieille J and DominguezS Incremental growth of normal faults Insights from a laser-equipped analog experiment Earth Planet Sc Lett 273 299ndash311 httpsdoiorg101016jepsl200806042 2008

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Schreurs G and Colletta B Analogue modelling of fault-ing in zones of continental transpression and transten-sion in Continental Transpressional and Transtensional Tec-tonics edited by Holdsworth R E Strachan R Aand Dewey J F Geol Soc Spec Publ 135 59ndash79httpsdoiorg101144GSLSP19981350105 1998

Schreurs G Buiter S J H Boutelier D Corti G CostaE Cruden A R Daniel J-M Hoth S Koyi H AKukowski N Lohrmann J Ravaglia A Schlische R WWithjack M O Yamada Y Cavozzi C Delventisette CBrady J A E Hoffmann-Rothe A Mengus J-M Monta-nari D and Nilforushan F Analogue benchmarks of short-ening and extension experiments in Analogue and Numeri-cal Modelling of Crustal-Scale Processes edited by BuiterS J H and Schreurs G Geol Soc Spec Publ 253 1ndash27httpsdoiorg101144GSLSP20062530101 2006

Schreurs G Buiter S J H Boutelier J Burberry C Callot J-P Cavozzi C Cerca M Chen J-H Cristallini E Cruden AR Cruz L Daniel J-M Da Poian G Garcia V H GomesC J S Grall C Guillot Y Guzmaacuten C Hidayah T N Hil-ley G Klinkmuumlller M Koyi H A Lu C-Y Maillot BMeriaux C Nilfouroushan F Pan C-C Pillot D PortilloR Rosenau M Schellart W P Schlische R W Take AVendeville B Vergnaud M Vettori M Wang S-H With-jack M O Yagupsky D and Yamada Y Benchmarking ana-logue models of brittle thrust wedges J Struct Geol 92 116ndash139 httpsdoiorg101016jjsg201603005 2016

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Stewart S A Harvey M J Otto S C and Weston P J In-fluence of salt on fault geometry examples from the UK salt

basins in Salt Tectonics edited by Alsop G I BlundellD J and Davison I Geol Soc Spec Publ 100 175ndash202httpsdoiorg101144GSLSP19961000112 1996

Sun Z Zhong Z Keep M Zhou D Cai D Li X Wu Sand Jiang J 3-D analogue modelling of the South China Sea Adiscussion on breakup pattern J Asian Earth Sci 34 544ndash556httpsdoiorg101016jjseaes200809002 2009

Tetreault J L and Buiter S J H The influence of extensionrate and crustal rheology on the evolution of passive mar-gins from rifting to break-up Tectonophysics 746 155ndash172httpsdoiorg101016jtecto201708029 2018

Tron V and Brun J-P Experiments on oblique riftingin brittle-ductile systems Tectonophysics 188 71ndash88httpsdoiorg1010160040-1951(91)90315-J 1991

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Ustaszewski K Schumacher M E Schmid S M and Nieuw-land D Fault reactivation in brittle-viscous wrench systemsndashdynamically scaled analogue models and application to theRhine-Bresse transfer zone Quaternary Sci Rev 24 365ndash382httpsdoiorg101016jquascirev200403015 2005

Vendeville B Cobbold P R Davy P Brun J-P andChoukroune P Physical models of extensional tecton-ics at various scales in Continental Extensional Tec-tonics edited by Coward M P Dewey J F andHancock P L Geol Soc Spec Publ 28 95ndash107httpsdoiorg101144GSLSP19870280108 1987

Venkat-Ramani M and Tikoff B Physi-cal models of transtensional folding Geol-ogy 30 523ndash526 httpsdoiorg1011300091-7613(2002)030lt0523PMOTFgt20CO2 2002

Weijermars R Flow behaviour and physical chemistry ofbouncing putties and related polymers in view of tec-tonic laboratory applications Tectonophysics 124 325ndash358httpsdoiorg1010160040-1951(86)90208-8 1986

Weijermars R and Schmeling H Scaling of Newtonian and non-Newtonian fluid dynamics without inertia for quantitative mod-elling of rock flow due to gravity (including the concept ofrheological similarity) Phys Earth Planet In 43 316ndash330httpsdoiorg1010160031-9201(86)90021-X 1986

Willingshofer E Sokoutis D and Burg J-P Lithospheric-scaleanalogue modelling of collision zones with a pre-existing weakzone in Deformation Mechanisms Rheology and Tectonicsfrom Minerals to the Lithosphere edited by Gapais D BrunJ-P and Cobbold P R Geol Soc Spec Publ 243 277ndash294httpsdoiorg101144GSLSP20052430118 2005

Xia Q K and Hao Y T The distribution of water in thecontinental lithospheric mantle and its implications for thestability of continents Chinese Sci Bull 58 3897ndash3889httpsdoiorg101007s11434-013-5949-1 2010

Zulauf J and Zulauf G Rheology of plasticine usedas rock analogue the impact of temperature com-position and strain J Struct Geol 26 725ndash737httpsdoiorg101016jjsg200307005 2004

Zwaan F and Schreurs G How oblique extension and struc-tural inheritance influence rift segment interaction Insightsfrom 4D analog models Interpretation 5 SD119ndashSD138httpsdoiorg101190INT-2016-00631 2017

Zwaan F Schreurs G Naliboff J and Buiter S J H Insightsinto the effects of oblique extension on continental rift interactionfrom 3-D analogue and numerical models Tectonophysics 693239ndash260 httpsdoiorg101016jtecto201602036 2016

Zwaan F Schreurs G and Adam J Effects of sedimenta-tion on rift segment evolution and rift interaction in orthogonaland oblique extensional settings Insights from analogue modelsanalysed with 4D X-ray computed tomography and digital vol-ume correlation techniques Global Planet Change 171 110ndash133 httpsdoiorg101016jgloplacha201711002 2018a

Zwaan F Schreurs G Gentzmann R Warsitzka M and Rose-nau M Ring-shear test data of quartz sand from the TectonicModelling Lab of the University of Bern (CH) V 1 GFZ DataServices httpsdoiorg105880fidgeo2018028 2018b

Zwaan F Schreurs G Ritter M Santimano T and Rosenau MRheology of PDMS-corundum sand mixtures from the TectonicModelling Lab of the University of Bern (CH) V 1 GFZ DataServices httpsdoiorg105880fidgeo2018023 2018c

Zwaan F Schreurs G and Buiter S J H 4D X-Ray CT data andsurface view videos of a systematic comparison of experimentalset-ups for modelling extensional tectonics GFZ Data Serviceshttpsdoiorg105880fidgeo2019018 2019

Abstract

Introduction

Analogue experimental set-ups for investigating extensional tectonics

Analogue materials used in extension experiments

Aims of this study

Materials and methods

Material properties

Experimental design

Distributed extension set-ups

Localized extension set-ups

Additional experimental parameters and definition of coupling

Scaling

Results

Foam base experiments (F series)

Rubber base experiments (R series)

Plate base experiments (P series)

Conveyor base experiments (C series)

Discussion

General structures

Brittle-only reference experiments

Brittle-viscous reference experiments

Velocity effects distributed extension versus passive down-bending and marginal graben formation

Effects of different brittle-to-viscous thickness ratios

Boundary effects and experimental confinement

Recommendations for further extension experiments

Conclusions

Data availability

Appendix A Schematic overview of relations between experimental set-ups


Appendix B1 Brittle domain

Appendix B2 Viscous domain


Author contributions

Competing interests

Acknowledgements

Financial support

Review statement

References

Bahroudi et al 2003 Amilibia et al 2005 Alonso-Henaret al 2015 Philippon et al 2015) Alternatively extensioncan be achieved through gravitational gliding or spreading inwhich case no moving sidewalls or an extending base needsto be applied (eg Gartrell 1997 Fort et al 2004 Acocellaet al 2005) Analogue materials used to simulate brittle partsof the lithosphere include among others quartz or feldsparsand silica flour micro-beads and (kaolinite) clay (Hubbert1951 Elmohandes 1981 Serra and Nelson 1988 Cliftonand Schlische 2001 Autin et al 2010 Abdelmalak et al2016 Klinkmuumlller et al 2016 Fig 1) Pure silicone oils andsilicone putties are frequently used as analogues for ductileparts of the lithosphere (Weijermars and Schmeling 1986Basile and Brun 1999 Michon and Merle 2000 Sun et al2009 Rudolf et al 2015 Fig 1)

Vendeville et al (1987) present experiments that highlightseveral factors controlling the geometry of fault systems inextensional tectonics The study used rubber sheet set-upswith a brittle sand layer for homogeneous thin-skinned defor-mation brittle-viscous gravity-spreading models resting ona solid base and experiments with the whole brittle-viscouslithospheric analogue floating on a simulated asthenosphereThe results provide a first impression of the differences be-tween these set-ups revealing the correlation between faultspacing and layer thickness in brittle materials rift local-ization in brittle-viscous settings and isostatic effects suchas tilted margins due to the influence of the asthenosphereYet the many experimental parameters were widely differentfrom experiment to experiment making a quantitative com-parison difficult

Allemand and Brun (1991) test the influence of two-layerbrittle-viscous material layering but using a conveyor beltset-up to achieve both symmetric and asymmetric exten-sion with a velocity discontinuity (VD) The basal sheetsdiverge here representing a fault in the underlying (not-simulated) brittle lithospheric mantle Asymmetric extensionis shown to generate strongly asymmetric rift geometries inboth brittle and brittle-viscous models The rifts under sym-metric extension conditions also develop a degree of struc-tural asymmetry The similarities of results from four-layer(lithospheric-scale) models (Fig 1) to their two-layer modelresults support the validity of applying a VD to simulatefaults in the brittle upper mantle Model parameters such aslayer thickness material properties and extension velocitiesare however not clearly defined again making a direct com-parison of these experiments challenging

Brun (1999) summarizes extension experiments with afocus on layer rheology and extension velocity He showsthat an increase in extension velocity in crustal-scale brittle-viscous conveyor belt models leads to an increase in viscousstrength and brittle-viscous coupling favouring widespreaddeformation or wide rifting By contrast low extension ve-locities lead to localized extension or narrow rifting A simi-lar effect is obtained by changing the brittle-to-viscous thick-ness ratio a high ratio of 3 1 leads to low brittle-viscous

coupling and narrow rifting whereas a small ratio of 1 1leads to high coupling and wide rifting On a lithosphericscale however the behaviour of the upper mantle becomesimportant as well (Fig 1) a single fault in a strong uppermantle layer may induce narrow deformation in the overly-ing crustal layers whereas a weak upper mantle promotesdistributed deformation The models also suggest that withinsuch wide rifts local weaknesses can account for the devel-opment of core complexes In addition to providing a sum-marizing scheme similar to Brun (1999) Corti et al (2003)show how magma presence can control rift initiation in nar-row rifts and cause a wide rift to shift to core complex modeThe authors also describe the additional effects of oblique ex-tension and multiple extension phases on rift evolution How-ever the models presented in both review articles come fromnumerous studies and are often performed with very differenttechniques and parameters

The additional significance of VDs in the brittle uppermantle was investigated by Michon and Merle (2000 2003)by means of brittle-viscous base plate experiments where theVD is situated at the edge of the plate A single VD leads toasymmetric extension and the development of a single riftwhereas a double-VD experiment may form two or more riftbasins depending on the initial distance between the VDsThis is valid for high strain rates as low strain rates focusdeformation (narrow rifting) decreasing the number of riftbasins Apart from the varying strain rates and VDs the otherparameters such as model size materials and layer thicknessremained fixed

Schreurs et al (2006) compared results of a brittle-viscousplate base extension experiment that was run by five analoguelaboratories The overall experimental procedure was kept assimilar as possible using for example the same foil to coverthe base of the apparatus the same extension velocity andthe same viscous material (polydimethylsiloxane PDMS)But differences occurred in brittle materials (different typesof sand and a wet clay) and model dimension (width andlength) This study illustrated the overall large-scale struc-tural similarities but also showed differences in fault dip an-gle and fault spacing that were related to differences in modelmaterials andor model set-up

12 Analogue materials used in extension experiments

Brittle MohrndashCoulomb-type granular materials have verysimilar internal friction angles with respect to their naturalanalogues (ranging between ca 25 and 40 Schellart 2000Klinkmuumlller et al 2016) Granular materials such as dryquartz sand have a very low cohesion and are considered agood analogue for large-scale models aiming at the brittlecrust or the crust and lithospheric mantle (Fig 1) By con-trast high-cohesion materials such as silica flour and clay(C = 40ndash750 Pa Eisenstadt and Sims 2005 Guerit et al2016) are better suitable for modelling the uppermost kilo-metres of the crust where cohesion is an important rheolog-

Shown inType

Thickness(b v)

TypeVelocity

F5 brittle-viscous

P7 8 5 84 Figs 8 C2

24 Scaling

Rs = (ρgh)C (4)

= (ρgh2)(ηv) (5)

3 Results

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Shown inType

Thickness(b v)

TypeVelocity

F5 brittle-viscous

P7 8 5 84 Figs 8 C2

24 Scaling

Rs = (ρgh)C (4)

= (ρgh2)(ηv) (5)

3 Results

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Shown inType

Thickness(b v)

TypeVelocity

F5 brittle-viscous

P7 8 5 84 Figs 8 C2

24 Scaling

Rs = (ρgh)C (4)

= (ρgh2)(ηv) (5)

3 Results

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Shown inType

Thickness(b v)

TypeVelocity

F5 brittle-viscous

P7 8 5 84 Figs 8 C2

24 Scaling

Rs = (ρgh)C (4)

= (ρgh2)(ηv) (5)

3 Results

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Shown inType

Thickness(b v)

TypeVelocity

F5 brittle-viscous

P7 8 5 84 Figs 8 C2

24 Scaling

Rs = (ρgh)C (4)

= (ρgh2)(ηv) (5)

3 Results

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Shown inType

Thickness(b v)

TypeVelocity

F5 brittle-viscous

P7 8 5 84 Figs 8 C2

24 Scaling

Rs = (ρgh)C (4)

= (ρgh2)(ηv) (5)

3 Results

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Shown inType

Thickness(b v)

TypeVelocity

F5 brittle-viscous

P7 8 5 84 Figs 8 C2

24 Scaling

Rs = (ρgh)C (4)

= (ρgh2)(ηv) (5)

3 Results

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Shown inType

Thickness(b v)

TypeVelocity

F5 brittle-viscous

P7 8 5 84 Figs 8 C2

24 Scaling

Rs = (ρgh)C (4)

= (ρgh2)(ηv) (5)

3 Results

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

24 Scaling

Rs = (ρgh)C (4)

= (ρgh2)(ηv) (5)

3 Results

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

4 Discussion

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Thicknessratio(b v)

Strength ratio(b v)

brittle-viscous

Seed Not known

Seed not known

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

5 Conclusions

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

B1 Brittle domain

hbinto

(σ1minus σ3)dz=

hbinto

B2 Viscous domain

hvinto

(σ1minus σ3)dz=

hvinto

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Abstract

Introduction



Aims of this study


Material properties

Experimental design




Scaling

Results





Discussion

General structures







Conclusions

Data availability







Competing interests

Acknowledgements

Financial support

Review statement

References

Documents

A systematic comparison of experimental set-ups for ... · ies of extensional tectonics. 1 Introduction 1.1 Analogue experimental set-ups for investigating extensional tectonics Tectonic