Intrinsic versus extrinsic variability of analogue sand-box experiments – Insights from statistical analysis of repeated accretionary sand wedge experiments

Intrinsic versus extrinsic variability of analogue sand-box experiments – Insights from statistical analysis of repeated accretionary sand wedge experiments

Accepted Manuscript Intrinsic versus extrinsic variability of analogue sand-box experiments-insights from statistical analysis of repeated accretionar...

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Accepted Manuscript Intrinsic versus extrinsic variability of analogue sand-box experiments-insights from statistical analysis of repeated accretionary sand wedge experiments Tasca Santimano, Dr. Matthias Rosenau, Prof. Dr. Onno Oncken PII:

S0191-8141(15)00073-5

DOI:

10.1016/j.jsg.2015.03.008

Reference:

SG 3205

To appear in:

Journal of Structural Geology

Received Date: 5 November 2014 Revised Date:

5 March 2015

Accepted Date: 13 March 2015

Please cite this article as: Santimano, T., Rosenau, M., Oncken, O., Intrinsic versus extrinsic variability of analogue sand-box experiments-insights from statistical analysis of repeated accretionary sand wedge experiments, Journal of Structural Geology (2015), doi: 10.1016/j.jsg.2015.03.008. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Intrinsic versus extrinsic variability of analogue sand-box experiments- insights from statistical analysis of repeated accretionary sand wedge experiments. Tasca SANTIMANOa*, Matthias ROSENAUa, Onno ONCKENa a

German Research Center for Geosciences,

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Section 3.1 Lithosphere Dynamics Telegrafenberg C 14473, Potsdam

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*Author of Correspondence- Tasca Santimano

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Germany

Section 3.1 Lithosphere Dynamics Telegrafenberg C, Potsdam 14473, Germany

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Telephone- +49 331 288 1315

Email- [email protected]

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Dr. Matthias Rosenau

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Email- [email protected]

Prof. Dr. Onno Oncken Email- [email protected]

Keywords- analogue modelling, variability, accretionary sand wedge, statistical analysis, Chi square test, ANOVA test

ACCEPTED MANUSCRIPT Abstract

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Analogue models are not perfectly reproducible even under controlled boundary conditions

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which make their interpretation and application not always straight forward. As any scientific

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experiment they include some random component which can be influenced both by intrinsic

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(inherent processes) and extrinsic (boundary conditions, material properties) sources. In order

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to help in the assessment of analogue model results, we discriminate and quantify the intrinsic

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versus extrinsic variability of results from “sandbox” models of accretionary wedges that

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were repeated in a controlled environment. The extrinsic source of variability, i.e. the

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parameter varied is the nature of the décollement (material, friction and thickness).

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Experiment observables include geometric properties of the faults (lifetime, spacing, dip) as

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well as wedge geometry (height, slope, length).

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For each variable we calculated the coefficient of variance (CV) and quantified the variability

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as a symmetric distribution (Normal, Laplacian) or asymmetric distribution (Gamma) using a

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Chi squared test (χ2). Observables like fault dip/ back thrust dip (CV = 0.6-0.7/ 0.2 – 0.6) are

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less variable and decrease in magnitude with decreasing basal friction. Variables that are time

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dependent like fault lifetime (CV= 0.19- 0.56) and fault spacing (CV-0.12 – 0.36) have a

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higher CV consequently affecting the variability of wedge slope (CV= 0.12-0.33). These

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observables also increase in magnitude with increasing basal friction. As the mechanical

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complexity of the evolving wedge increases over time so does the CV and asymmetry of the

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distribution. In addition, we confirm the repeatability of experiments using an ANOVA test.

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Through the statistical analysis of results from repeated experiments we present a tool to

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quantify variability and an alternative method to gaining better insights into the dynamic

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mechanics of deformation in analogue sand wedges.

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ACCEPTED MANUSCRIPT 1)

Introduction

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Results from experiments can vary because of extrinsic and intrinsic controls. Generally,

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extrinsic controls are varied systematically in order to test their influence on a system in so

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called parameter studies. This approach is well suited to identify control factors which have a

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strong influence on experimental outcomes. However, if the influence is smaller it becomes

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difficult to verify that the resulting variability is attributable to extrinsic controls and not

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intrinsic variability. Experiments including parameter studies with so called analogue models,

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i.e. physical lab scale models made of weak rock analogue material (e.g. loose sand, clay,

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wax) have been created since the early nineteenth century pioneering the work of Sir Hall

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(Hall, 1815, see Graveleau et al., 2012 for a comprehensive historical review) to understand

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geological observations (e.g. the structure of a fold-and-thrust belt) by means of forward

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simulation of the underlying geodynamic processes. In contrast to numerical or analytical

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models which will always generate the same result with insignificant variability from a given

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starting configuration, experiments with analogue models never give exactly the same result

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as a consequence of inherent variability. This might be viewed as a handicap of the analogue

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modelling approach but also vice versa as a chance to simulate process variability in nature.

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The fact that variability is a matter of interest in scientific studies stems from the rising

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awareness for our limited view on geodynamic processes with single observations being only

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part of a spectrum of possible observational outcomes. If the source of variability is similar in

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the model as in nature, we argue that any physically simulated variability is preferred over

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statistically implemented noise from which variability typically arises in numerical models

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(e.g. Rosenau et al., 2010).

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Several sources of variability exist in nature (and consequently in the analogue model as well

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as in the natural prototype) both extrinsic, i.e. in the boundary conditions or material

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properties, and intrinsic due to the inherently changing physical properties of the system as it

ACCEPTED MANUSCRIPT evolves. In most parameter studies extrinsic variability is the focus, i.e. the change in

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experimental outcomes as a consequence of changes in the controlled boundary conditions or

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material properties. However, if intrinsic variability is unknown in such experiments,

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differences in the outcomes are potentially misattributed to large parts of the extrinsic

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controls. Only if intrinsic variability is significantly smaller than extrinsic variability,

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meaningful inferences from analogue models can be drawn. This indicates the importance of

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quantifying intrinsic vs. extrinsic variability in order to get an idea for the precision of

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analogue model results. However, only few studies have researched this issue so far (Cubas et

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al, 2010).

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Benchmark study by Schreurs et al. (2006) is an example of studying extrinsic variability

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related to boundary conditions. In this benchmark a simple experiment of creating a

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compressional sand wedge, was performed in six laboratories around the world without much

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prescription of the setup. Benchmark experiments showed consistently an overall cyclic

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deformation pattern of the wedge but the detailed observables and in particular the final

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geometry varied significantly. This difference was attributed to the different setup preparation

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protocols and physical differences (grain size distribution, density and frictional properties) in

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materials used. In this case, it was understood that experiments needed to have a strict setup

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protocol if they were to be compared. In a follow-up study, materials used were identical, the

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setup was constrained more heavily and consequently the variability minimized to the true

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intrinsic variability (Schreurs, pers. Comm.).

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Here we build on these findings and study intrinsic and extrinsic variability in a series of

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classical sand wedges with systematically varying basal coefficient of friction (µ basal).

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Boundary conditions and material properties were fixed and stable to a degree that is typical

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for analogue models, i.e. we used always the same experimental device and preparation

ACCEPTED MANUSCRIPT procedures and performed experiments under controlled ambient temperature and air-

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moisture. A similar approach has been undertaken by Cubas et al. (2010) studying along-

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strike variation in cross-sections of early thrusts in repeated sand wedge experiments. Here

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the cross-sections were considered independent observations. In contrast to their approach, we

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analyze variation along a single profile across many thrusts evolving during wedge evolution

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in repeated experiments. By inducing higher strain compared to Cubas et al. (2010) and

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adding variation of extrinsic parameters (basal friction) we therefore go beyond their work in

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analyzing variability related to intrinsic and extrinsic sources as well as to wedge evolution.

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Our findings show that the variability in the results are attributed to (1) variability in material

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properties and (2) the complexity of the evolving mechanics of the wedge. In our study fault

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dip is related only to the coefficient of friction of the granular material and therefore has a low

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CV. On the other hand, fault spacing is related to fault lifetime and the criticality of the wedge

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which may change over time, thus fault lifetime and spacing changes with time and can have

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a larger CV.

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2) Methodology

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2.1) Experimental setup and analysis procedure

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The analogue experiments were kept simple and consist of creating convergent accretionary

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wedges. The experimental set-up (Fig.1a) is a box with dimensions 300 cm long, 20 cm wide

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and has a horizontal base that consists of a rubber conveyor belt (coefficient of friction (µ)

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~0.68 against sand, Fig. A2) and glass sidewalls (µ ~ 0.15 against sand, Fig. A2). In the box, a

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total thickness of 3 cm layer of granular material (sand, or sand and glass beads- for frictional

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coefficient see Table 1 and Fig A2) is sieved on the conveyor belt for the entire length of the

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box. Sieving of the granular material produces a homogenous layer (Lohrmann et al., 2003;

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Maillot, 2013) which is void of any internal preexisting structures or zones of weakness that

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can be activated during the experiment. We took care that the final surface was horizontal and

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ACCEPTED MANUSCRIPT planar within the thickness of the beam of a laser level (ca. 1 mm). To create the wedge the

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layer of granular material is pushed against a stationary rigid back wall by moving the

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conveyor belt at a constant velocity of 1mm/s towards and under the back wall. The growth of

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the wedge is recorded from the side by a digital camera (CCD, 11 MPx, 16 bit) at 1 Hz. Image

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data are calibrated and cross-correlated for deriving incremental displacement (= velocity)

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fields by means of Particle Image Velocimetry (PIV) (Adam et al., 2005) (Fig.1b, 2). Further

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processing of the images and vector fields produces binary images (Fig. 1c, 2, 3a) and maps

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of the evolving geometry and displacement of the wedge (Fig. 1d, 3b,c) thus monitoring the

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formation and kinematics of faults (Fig. 3c). To visualize the evolution of the faults in time as

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the wedge grows, a horizontal profile (Fig. 3b, c) of the velocity field is created in the middle

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of the granular layer at a height of 1.5 cm from the base. These velocity profiles are then

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assembled against each other in time and displayed as a deformation map (Fig. 3d).

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From these deformation maps, fault spacing and lifetime for each accretionary cycle is

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measured. Specifically, fault lifetime is defined as the time between the formation of two

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consecutive faults. In this definition, fault life time only includes the time when a fault is the

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main active structure and does not include the time it is reactivated at a later stage. Fault

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spacing is the horizontal distance between the last fault and a new fault at the time of

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localization of the new fault (Fig. 3b, d). Kinematically, fault lifetime and fault spacing are

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related. Fault dip and back thrust dip are measured at the initiation of a new fault. Fault dip

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has been measured from the PIV images by visually fitting a straight line along the isolines of

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the velocity field where the gradient is highest (Fig. 3b, c).

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Binarized images of the wedge are used to derive the height, length and slope of the wedge

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for every time step automatically. The height and length are measured from the crest (highest

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point in the wedge) to the base, and from the toe of the wedge to the crest respectively (Fig.

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3a, 4). This part of the complete wedge is most representative of an active wedge (Lohrmann

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ACCEPTED MANUSCRIPT 128

et al., 2003). Wedge slope is measured as the arc tan (height of the wedge / length of the

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wedge).

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In summary, the observables measured for each experimental setup consist of fault

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characteristics i.e. fault lifetime, fault spacing (Fig. 5), dip of the fault and its respective back

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thrust as well as wedge geometry i.e. height, length, wedge slope. Estimation errors attached

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to these observables are 4mm for all lengths, 2 seconds for periods and 2o for angles.

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In this study, we tested the effect of different basal décollement layers on the intrinsic

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variability of the wedge evolution. From a sand only (no detachment layer) reference

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experiment (static/kinetic µbasal ~0.68/0.55 ) basal properties were varied by introducing a

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weak décollement layer of different thickness (0.2cm vs. 0.5 cm) and made of different sizes

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of glass beads (100-200 µm, 200-300 µm, 300-400 µm with static/kinetic µbasal increasing

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with size ~0.47-0.53/0.40-0.43, Appendix 1). The five different experimental setups that were

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realized are as follows:

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Setup 0) 3cm layer of sand (Number of experiments (N) = 7, Fig. 2a)

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Setup 3) 2.5cm layer of sand on 0.5 cm 300-400 µm glass beads (N =5, Fig. 1),

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Setup 2) 2.5cm layer of sand on 0.5 cm 200-300 glass beads (N = 5, Fig. 2b),

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Setup 1a) 2.5cm layer of sand on 0.5 cm 100-200 µm glass beads (Setup a) (N = 5, Fig. 2c)

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and

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Setup 1b) 2.8cm layer of sand on 0.2 cm 100-200 µm glass beads (Setup b) (N = 5, Fig. 2d).

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Each experiment is repeated up to 7 times for a total of 27 experiments. The internal

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coefficient of friction (µinternal) for all granular material used in this study is measured in the

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Schulze Ring shear tester (Schulze, 1994). Table 1 displays the static friction for the first or

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primary failure or fault, reactivation static friction for the reactivation of the fault as well as

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the kinetic friction.

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ACCEPTED MANUSCRIPT 2.2) Statistical analysis

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The reason to conduct a statistical analysis on a large data base from repeated experiments is

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threefold: First, to quantify intrinsic variability in the experiments, second, to detect trends

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which would be statistically irrelevant and therefore go unnoticed in a small number database

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or because they lay close to/within the error bars and thirdly, to quantify the repeatability of

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the measurements in experiments within identical setups. We grouped all the data for each

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observable (fault lifetime, fault spacing, fault dip, back thrust dip and wedge slope) of each

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setup into one population. Hence we created 5 populations for each setup and a total of 25

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populations (Table 2). For each population the basic statistical values i.e. mean, standard

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deviation and coefficient of variation (CV) were calculated (Table 2) before more advanced

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statistical treatment followed.

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Chi-square test (χ2)

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As a way to compare data populations beyond the mean and standard variation we choose to

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calculate the probability density function (pdf) for each population and compare it to

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theoretical distributions namely the Normal, Gamma and Laplacian distributions (Fig 6). To

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quantitatively determine which of the three distributions fit the best to each population, a Chi

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square test (χ2) is implemented (Table 2). The χ2 is calculated using the difference between

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the observed values from experiments and the theoretical value based on the distribution type.

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We calculated the χ2 for the observables fault lifetime, fault spacing, fault dip and wedge

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slope for all setups according to Cubas et al., 2010- Appendix A1. More information about the

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theory of the χ2 test and the probability distributions used in this paper are available in

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Appendix 2.

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In general, normal distributions characterize natural data symmetrically distributed around a

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mean. Laplacian distributions characterize symmetrically distributed data with a very narrow

ACCEPTED MANUSCRIPT peak (mode), i.e. those with low variability (low CV). However, it allows values to be further

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away from the median value at the tails (Cubas et al., 2010). In contrast the Gamma

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distribution characterizes asymmetric distributions of larger variability. Importantly,

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symmetric vs. asymmetric distributions are interpreted here in terms of observables that don’t

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vary much vs. observable that are variable especially over time. For example, a periodic

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process over time characterized by a single frequency and size plus some scatter or noise

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generates a symmetric distribution while a more complex process characterized by self-

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similar growing frequency and size generates an asymmetric distribution.

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ANOVA test

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In addition, to detect subtle differences amongst similar populations in our large database, we

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employed the analysis of variance test (ANOVA) for each population. The ANOVA test

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primarily analyses the statistical variance within a population. Specifically, since a population

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is made up of measurements from different experiments of the same setup, the test analyzes

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variance between the different experiments and within the experiments. In this manner the test

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determines whether all the measurements from the different experiments can be classified as

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originating from undistinguishable experiments or source. The test allows therefore, to detect

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statistically relevant differences between experiments that would otherwise (e.g. by the

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classical standard deviation criterion) be unnoticed. This particular test is chosen by

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examining the population in particular 1) the extent of the intrinsic variability within the

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population 2) if the distribution of the population is close to normal and 3) the independence

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of the data in a population (McKillup & Dyar, 2010). In this study the ANOVA test is used

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for each observable of each set-up 1) to analyze the variation between experiments in each

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setup and determine repeatability of the data and 2) analyze the variation between different

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setups to determine if any difference due to basal friction exists. For this test the significance

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level is set at 5% (Fisher, 1954). Therefore, with a p value more than 5%, the null hypothesis

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ACCEPTED MANUSCRIPT 206

which states that there is no difference between two or more experiments is accepted. We

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used the one – way ANOVA test since we have one parameter µbasal that is changing. This

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statistical test can be easily computed using statistical softwares or in Matlab or Excel using

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predefined functions. More details on the ANOVA are included in Appendix 2.

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As part of the ANOVA test we calculated the coefficient of determination (R2) value. R2 is a

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quantitative value of how much of the variance in a population is explained due to repeated

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experiments in contrast to intrinsic variability within experiments. A large R2 value indicates

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that the variation is due to the experimental setup or extrinsic sources in contrast to a small R2

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indicating that the variation is within the system (Zar, 2010).

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The Fisher (F) value is also calculated and compared to the critical F (Fcrit) value to determine

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if the null hypothesis should be rejected. F values lower than the Fcrit value indicates that null

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hypothesis is accepted. Fcrit can be found on a universal table based on the degrees of freedom

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and the significance level.

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In summary the p value indicates the difference in the variance between experiments and

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whether the null hypothesis should be accepted or rejected, the F value confirms this

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conclusion and the R2 value suggests whether the variance is intrinsic or extrinsic. The

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disadvantage of the ANOVA test is that if the variance of almost all measurements in a

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population is consistent but there is one measurement that is an outlier and has a differing

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variance from the rest of the population, then the p value and F value reject the null

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hypothesis. On the other hand, since the ANOVA test compares the magnitude of the

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variance, it only accepts the null hypothesis when the difference between variances of all

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measurements in a group is not significant.

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ACCEPTED MANUSCRIPT For the two statistical analyses – χ2 and ANOVA test, the first 3 faults from all experiments

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were omitted. The reason for omitting these faults is simply because faults at this stage are

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small, short lived and not representative of critical wedge evolution (Gutscher et al., 1996).

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They rather represent the initiation stage of wedge formation characterized by the dominance

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of uplift over lateral growth. This stage ends when the wedge reaches the critical taper after

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which wedge growth is quasi-stable. These faults are noticeable in the bottom right corner of

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the deformation map (Fig. 3d) and are clearly different in their size and temporal lifetime.

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Therefore when analyzing data from analogue experiments it is important to distinguish the

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parts of the experiment that are representative of the natural process studied.

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3)

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All analogue accretionary wedges regardless of µbasal evolve in a cyclic fashion. The cyclic

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evolution of a wedge involves the growth of the wedge until it reaches the critical taper it can

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sustain, at which time the formation of a new fault begins the next cycle (Chapple, 1978;

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Davis et al., 1983; Platt, 1988; Dahlen, 1990; Hoth et al., 2007)

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Experimental observations

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In this respect, wedge geometry alternates synchronizing from increasing length of the wedge

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i.e. horizontal growth by new thrust fault formation and thereby lowering the slope of the

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wedge, to increasing height of the wedge i.e. vertical growth by underthrusting thus allowing

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the slope to increase to the critical taper angle. Consequently, fault lifetime, fault spacing and

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wedge slope are interdependent. According to Dahlen (1990) (equation 99), wedge slope is

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related to the internal angle of friction of the granular material and basal friction which

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governs the fault dip angle, therefore wedge slope and fault dip are also related. However, in

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our study, since fault dip is measured only at the initiation of the fault it is dependent on the

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internal angle of friction of the granular material and independent of the other observables.

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This independence of the fault dip from other observables is also evident in a cross-

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ACCEPTED MANUSCRIPT correlation of observables from this study (Fig. A2.1) and in the study by Cubas et al. (2010).

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On a smaller time scale, the geometric change shows systematic cyclicity between

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accretionary cycles. At the formation of a new fault, the pop-up of the fault at the toe of the

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wedge provides a linear increase in length of the wedge. At this point the height of the wedge

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is stationary. The height increases at the end of an accretionary cycle thus steepening the

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slope of the wedge. On a larger time scale, over multiple accretionary cycles, wedge growth

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according to critical wedge theory with a roughly constant slope results in an increase in

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height and width over time according to power law functions (Dahlen, 1990).

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In a self-similar like wedge, which grows ideally by “regular” accretion (i.e. adding material

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in a fashion optimized to maintaining the critical taper throughout wedge evolution) fault

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lifetime and fault spacing are related and they evolve systematically throughout the evolution

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of the wedge: For high µbasal wedges fault lifetime and spacing increases over time. As a result

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of the underthrusting mode both are limited by the length of the wedge (Gutscher et al.,

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1996). For low µbasal wedges which grow rather by frontal than basal accretion fault lifetime

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and spacing stabilizes towards a value which is consistent in maintaining the critical taper

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(Fig. 5). In terms of intrinsic variability, fluctuations around these consistent trends become

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important. Noticeably fluctuations are minimized in wedges with a thin or absent décollement

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layer (setup 1b and 0). In wedges with a thick décollement layer (setup 3, 2, 1a), distinct

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faults can be extra-long lived (i.e. they are apparently longer active than necessary to maintain

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the critical taper) and thus increase the spacing between two adjacent faults (Fig. 5). Such

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extra-long lived faults occur when the fault that underthrusts the wedge is occasionally

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weakened due to the entrainment of low friction material along the fault plane (glass beads

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from the thick décollement layer). On the other hand, lack of such a weakening mechanism

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can cause older faults to be reactivated in order to heighten the wedge to the taper angle (Platt,

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1988).

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ACCEPTED MANUSCRIPT 284

The reactivation of internal pre-existing faults can be classified as second order deformation

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and formation of new faults at the tip of the wedge as first order deformation. In both styles

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of deformation the height of the wedge is increased to conform to the critical taper. The two

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varying styles of deformation are observed in setup 1a and 1b which demonstrate

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underthrusting style of deformation (Fig. 2) and fault reactivation (distributed strain)

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respectively. Difference in the two setups is observed in the fault lifetime and spacing (Fig.

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5). Underthrusting produces long-lived faults followed by short lived faults, whereas wedges

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with uniformed spaced first order faults may consist of fault reactivation.

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4)

Statistical results

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Histograms of the observables for each setup are represented by one of the three distribution

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types, Normal, Gamma and Laplacian. The best fitting type of distribution for each population

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is calculated by the Chi square test (χ2) (Table 2). The main goal of representing the

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populations with distribution curves is to describe the symmetry and variability of the

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populations. For many of the populations, the difference between χ2 calculated for each

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distribution type is very small (Table 2), therefore, all three distribution curves have been

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displayed in Fig. 6. The majority of the observables are best represented by a Gamma or

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Laplacian distribution (Table 2). Histograms of the fault dip for the setup 3 and 1b represent a

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Normal distribution. Fault spacing for setup 0 is best represented by a Normal distribution but

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can also be described as a Gamma or Laplacian distribution since the χ2 test for all three

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distributions is very similar. Fault dip for many setups could be represented as a bimodal

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distribution, however the difference in dip between each peak and mean value is

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approximately 2o which is within the error bars of the estimation. Observable back thrust dip

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between different setups is indistinguishable within the standard deviation (approximately 3°)

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and is not further considered in this analysis. The maximum CV for all setups is for the

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ACCEPTED MANUSCRIPT observable fault lifetime followed by the related observable fault spacing that has the second

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highest CV. The minimum CV for all setup is for the populations related to dip (Table 2,

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Fig.7a). Fault dips also have mean values that decreases with increasing µbasal (Fig. 6). Wedge

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slope has a lower variability (CV ranges from 0.12-0.33 for all setups) compared to fault

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lifetime (CV- 0.19-0.56) and spacing (CV- 0.12-0.36), however the mean value for all three

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observables are linked and show a decreasing trend with decreasing µbasal in this probabilistic

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approach (Table 2, Fig. 6). Overall the observables from the reference setup (setup 0)

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experiments are more symmetrical than of lower µbasal where many of the distribution curves

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of the observables are right skewed. The distribution for fault lifetime-setup 3 and 2 can also

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be considered bi-modal. However, the second mode is not well developed and not present for

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the related observable fault spacing of the same setups. Aside from setup 0 and the

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experiment with a thinner décollement layer (setup 1b), the trend of the CV for the

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observables fault lifetime and spacing increase as µbasal decreases for the other three setups

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(setup 3, 2, 1a) (Fig. 7a).

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The ANOVA test is used primarily to quantify the variation in the results within a population

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and determines whether results in the population come from the same system. Fault spacing

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and lifetime are two observables that have the highest CV especially for setups with glass

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beads (except setup 1b) due to the co-existence of large and short lived faults. Despite this

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observation the ANOVA test concludes that all results for the population fault spacing and

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lifetime come from alike experiments. Therefore the ANOVA test also recognizes that the

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magnitude of the variation in the observables is also repeatable between the experiments. For

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the observable fault lifetime in all the setups, the p- value supports the hypothesis that there is

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no difference between experiments within the setups. On the contrary, results show that there

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is a difference (p-value below 5%) between experiments for the population fault dip for the

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setup 1a , fault spacing for the setup 0 and 1b and back thrust dip for the setup 2 (Table 3). In

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ACCEPTED MANUSCRIPT these populations, an outlier in any one of the experiments causes a different magnitude of

337

variability than the other experiments and thus the results of the ANOVA test reject the null

338

hypothesis. If there realistically is a difference between experiments in a population then the

339

ANOVA test would show a rejection of the null hypothesis for all the observables in that

340

setup, which is not the case.

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341

F values clearly support the hypothesis that there is a difference between experiments of

343

different µbasal. From the ANOVA, the three experimental setups with the same décollement

344

thickness - setup 3, 2, 1a show an overall decreasing trend in the p value for the observables

345

fault lifetime and spacing, indicating that the difference in the variance between experiments

346

increases as µ basal decreases (Fig. 7b). However the p values are not below the 5%

347

significance level and the null hypothesis that all measurements in the populations come from

348

similar sources is accepted. In contrast the R2 value for the above mentioned observables and

349

setups increases with decreasing µ basal indicating that the statistical variance due to variations

350

between experiments in a population (Fig. 7c) also increases. Compared to the other setups

351

the same observables - fault lifetime and spacing - of setup 0 and 1b have lower p values (the

352

null hypothesis for fault spacing of setup 0 and 1a are rejected) and higher R2 values. Also

353

indicating that the difference between the variances of different experiments is high but this

354

variation is not within the experiments but due to extrinsic sources. However the difference

355

between the variances for these two setups is not higher than that for setup 3, 2, 1a since the

356

CV for fault lifetime and spacing for setup 0 and 1a is still lower than that for setup 3, 2, 1a

357

(Table 2, Fig. 7a).

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Although majority of the p values (Table 3) for all observables and all setups support the

360

hypothesis that there is no difference in measurements between experiments, there are some

361

exceptions. These exceptions can be explained by outliers in the data. An outlier or value

ACCEPTED MANUSCRIPT 362

significantly larger or smaller than the mean value in an experiment causes a different

363

variance for that experiment. When this experiment is compared to other experiments of the

364

same setup but with a significantly different variance, the calculated p value appears to be less

365

than the 5% significance level.

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5)

368

Here we discuss the range of variability between different fault observables (i.e. fault lifetime,

369

fault spacing, fault dip) and wedge observables (i.e. wedge slope) and the difference in the

370

variability between different setups. We demonstrate that the mechanics of deformation

371

controls the intrinsic variability in observables and that regardless of the varying intrinsic

372

variability in the populations, the mechanical relationship between fault, wedge observables

373

and µ basal is apparent. Since our experiments consist of large amounts of shortening and

374

formation of many faults we also examine the time evolution of the wedge and it’s reflection

375

on the statistical data.

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Discussion

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5.1) Intrinsic variability in fault observables

378

We observe that fault observables of the same setup have different magnitudes of variability.

379

For example fault lifetime and spacing have a higher variability and asymmetry than fault dip.

380

Since faults are first order structures that change the geometry of the wedge, they also

381

influence any variability in the wedge slope. As a feedback fault lifetime is determined by

382

wedge criticality. Any changes in the physical properties of the wedge changes the frequency

383

of fault formation therefore making the observables fault lifetime, fault spacing and wedge

384

slope dependent on each other. Since wedge slope is also dependent on the µ basal and µ internal

385

(Davis, et al., 1983; Dahlen, 1990) which determines the fault dip, all observables are related

386

to each other. However, fault lifetime and fault spacing show a significantly higher CV than

387

fault dip and back thrust dip (Table 2). A comparison of the CV for all the fault observables

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ACCEPTED MANUSCRIPT reveals that the CV for fault lifetime and fault spacing range from 0.12-0.56. The CV for fault

389

dip is significantly lower and ranges from 0.06-0.07. This observation for fault dip is also

390

evident in the study by Cubas et al. (2010). The main difference between the observables is

391

that fault lifetime and spacing are time dependent. As the wedge grows the mechanical

392

process related to fault frequency may change with the evolution of the wedge (Platt, 1988).

393

Wedge slope in the experiments is also time dependent and changes both within an

394

accretionary cycle and as the wedge grows toward criticality over multiple cycles. Effectively

395

criticality in “real” wedges might vary over time because of the weakening of the wedge due

396

to incorporation of weak faults. The skew in fault lifetime and spacing populations (Fig. 6) or

397

possible development of a second mode in the fault lifetime distribution (setup 3 and 2) may

398

reflect evolving wedge dynamics. This explains why fault lifetime, fault spacing and wedge

399

slope have a higher CV than fault dip. Fault dip and back thrust dip in this study are not time

400

dependent since they are measured only at the instance when a new fault is formed and not

401

throughout the lifetime of the fault. Since these two observables only depend on the µ of the

402

granular material, there is little possibility for variation thus generating a smaller CV than the

403

other observables.

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5.1.1) Low variability of fault dip

406

The low variability in fault dip is represented by a CV = 0.06-0.07, and mostly symmetrical

407

type of distribution. Since the dip is measured at the initial formation of the fault, the change

408

in dip i.e. rotation of the fault during the rest of the accretionary cycle is not recorded.

409

Therefore the measurement is not time dependent. Fault dip initiates at the velocity

410

discontinuity between the conveyor belt and the overlying granular layer. After initiation it

411

propagates into the overlying sand layer (Suppe and Medwedeff, 1990). The relationship

412

between fault dip and µ is defined as

413

δ = 45-  -ψ

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(1)

ACCEPTED MANUSCRIPT where δ is the angle of the fault, ϕ is the angle of internal friction of the sediment (in this case

415

the sand) and ψ is the angle between the maximum compressive stress and the x axis

416

(Coulomb, 1773; Hafner, 1951; Lallemand et al, 1994). Therefore fault dip is related only to ϕ

417

and ψ at any point in time.

418

A range in the µ basal or a measuring error may explain the small variations in fault dip. In our

419

experiments we use granular material with a particular range in grain size to control the µbasal.

420

Since there is a range in the grain size, this also produces a range in the µbasal and may produce

421

the small range in fault dip measurements. On the other hand, the highest standard deviation

422

for the fault dip is ±1.92o (Table 2). The estimated measuring error is 2o and the highest

423

standard deviation for frictional coefficients measured in the Ring shear tester is ±0.047 for

424

sand on a conveyor belt (Fig A2-E). This would produce a deviation of ±2.67o (ϕ = tan-1 µ).

425

Therefore the variation in fault dip could come from the variation in the size of the granular

426

material or measuring error.

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5.1.2) Variability in fault lifetime and spacing

429

The µinternal and µbasal of the wedge controls the slope or critical taper of the wedge (Davis et

430

al, 1983; Dahlen, 1984; Dahlen, 1990; Suppe, 2007). The critical taper is directly related to

431

the fault strength, in particular to the properties of the décollement, and inversely related to

432

the wedge strength or cohesion and internal angle of friction of the wedge (Dahlen, 1990;

433

Suppe, 2007). Since faults are the first order structures that aid in changing the geometry of

434

the wedge and hence the taper, the lifetime and accordingly the spacing of the fault is such

435

that it is able to bring the wedge slope to the preferred taper. Therefore, the lifetime of a fault

436

is dependent on wedge slope (Chapple, 1978).

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437 438

In setup 0, the experiments have the highest µbasal and since there is a strong basal coupling,

439

the resulting wedge is steeper than the wedges from the other setups (Table 2, Fig. 6)

ACCEPTED MANUSCRIPT (Gutscher et al, 1996; Saha et al., 2013). In this setup thrust sheets continue to underthrust the

441

wedge to raise the height of the wedge. Compared to setup 1b where the µbasal is lowest, the

442

resulting wedge is shallower (Fig. 6) and the wedge deforms by frontal accretion. In both

443

these setups the fault lifetime and spacing have trends that are similar over time (Fig. 5).

444

However the slight skewness in the distributions (Fig. 6) is mainly because the two

445

observables are time dependent. At the beginning of the wedge formation, faults are short

446

lived and closely spaced. As the wedge is established and due to self-similar like growth of

447

the wedge the fault properties also grow creating a skew in the distribution (Saha et al., 2013).

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448

In a system (setup 3, 2, 1a) with altering internal properties due to the entrainment of glass

450

beads, the fault properties also change. Lowering of the fault plane friction can lengthen the

451

fault lifetime as a result, making deformation easier to continue along the fault for a longer

452

time (Platt, 1988; Cubas et al, 2008). To compensate for the long duration of these faults, long

453

lived faults are always followed by short lived faults. Perhaps, this is the wedges way to

454

return back to a state of criticality. In these setups, the long-lived faults produce a skew

455

towards larger faults or even the formation of a second peak in the histograms (Fig. 6). The

456

skewness or asymmetry in the histograms represents the evolution of the wedge over time in

457

particular the change in fault properties. As a result of the large difference in fault length, the

458

distributions for both fault lifetime and fault spacing are further skewed for these setups

459

compared to setup 0 and 1b.

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461

5.1.3) Influence of thickness on granular basal décollement

462

The evolution of the wedge is affected by the physical properties of the initial sand layer and

463

décollement layer. Our study demonstrates that the thickness of the granular décollement

464

layer also influences the style of deformation that the wedge employs to reach its critical

465

taper. The influence of the thickness of the décollement layer can be seen in the experiment

ACCEPTED MANUSCRIPT with setup 1a and 1b. The only difference between the two setups is the thickness of the basal

467

décollement layer. Setup 1a has a décollement layer of ~ 0.5 cm and setup 1b has décollement

468

layer of ~ 0.2cm. When a new fault is formed in the wedge with a thick décollement layer, the

469

glass beads from the décollement layer get entrained onto the fault plane lowering the

470

frictional coefficient along the fault plane. This allows the wedge to continue deforming along

471

the weak fault plane and to continue underthrusting the wedge allowing it to grow in height.

472

In this manner, a thick décollement layer weakens the fault plane by the entrainment of low

473

friction material changing the style of deformation from frontal accretion to underthrusting

474

(Platt, 1988). This interaction between materials of differing friction also affects the wedge

475

making it heterogeneous and changing the overall strength of the wedge. Since the critical

476

taper is dependent on a force balance that includes the cohesion and internal friction (Davis et

477

al., 1983), the taper changes and the wedge must adjust accordingly. The adjustment of the

478

wedge over time as a response to changing parameters and an evolving taper is represented by

479

an asymmetric distribution or possible second peak that represents the change in fault

480

behavior.

481

A thinner basal décollement layer allows the frictional properties of the fault and

482

consequently the physical properties of the wedge to remain more consistent throughout the

483

growth of the wedge. Therefore there is no change in the force balance or the preferred

484

critical taper angle. In comparison to the wedges with altering fault plane friction, the wedges

485

with thin décollement layer (setup 1b) or décollement layer with granular material that is the

486

same as the rest of the wedge (setup 0), have a very periodic and predictable fault lifetime and

487

spacing. This observation is strongly supported by the lower CV for observables fault lifetime

488

and spacing in setup 1b and 0 compared to the CV of the same observables in setup 1a (Table

489

2, Fig 7). Since our experiments with wedges of thin décollement layer (setup 1b) show little

490

or no evidence of underthrusting, deformation moves to older faults and reactivates these

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ACCEPTED MANUSCRIPT 491

older faults to raise the height of the hinterland part of the wedge in order to reach the

492

preferred taper angle (Platt, 1988).

493

5.2) Mechanical causes for the differences between setups

495

Fault dip, fault lifetime and spacing and consequently wedge slope are all related to the µ of

496

the entire wedge i.e. µ internal and µ basal of the wedge. In our study a difference as low as 0.03 in

497

the µbasal shows a systematic change in fault and wedge observables. The relationship shows

498

that as µbasal increases, fault lifetime and spacing also increase but fault dip decreases (Davis

499

et al., 1983, Dahlen, 1984; Konstantinovskaia and Malavieille, 2005). In addition, the

500

thickness of the décollement layer between setups causes a significant difference in the

501

mechanical evolution of the wedge for the different setups.

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502

5.2.1) Relationship between basal friction and fault lifetime and spacing

504

Fault lifetime and spacing decreases for decreasing µ basal primarily because of the frictional

505

properties of the décollement granular material and its relationship to the critical taper angle.

506

For low µ basal the critical taper angle is low therefore a deforming wedge of certain length

507

does not have to grow as much in height compared to a wedge with the same length but

508

higher µ basal. Thus, fault structures that are essential in changing the geometry of the wedge

509

are driven by the µ basal of the wedge. The lifetime of the fault is directly related to the height

510

of the critical wedge and how much the wedge must be underthrusted for the wedge to reach

511

the critical height (Davis et al., 1983; Cubas et al., 2008).

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512 513

In the wedges (setup 3, 2, 1a) with the thick (~0.5 cm) décollement layer the entrainment of

514

low friction material along the fault plane changes the style of deformation of the wedge.

515

These wedges with a thick décollement layer produce long faults followed by short lived

516

faults therefore producing a skewed distribution of fault lifetime and spacing (Fig. 6).

ACCEPTED MANUSCRIPT Accordingly, the CV for fault spacing and fault lifetime for setup 3, 2, 1a are higher than that

518

for setup 0 and 1b.The experiments with setup 0, 1a and 1b has the highest and lowest µbasal

519

respectively in this study. Setups 0 and 1b have little change to the physical properties of the

520

fault plane thus producing a more symmetric distribution of fault lifetime and spacing (Fig.

521

6).

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522

Although the experiments have a systematic change in the µ basal, the statistical results i.e. CV,

524

p value and R2 value show that the experiments can be further divided into two categories

525

based on the thickness of the décollement layer and the resulting style of deformation.

526

Accordingly the CV is lower for the experiments with evenly spaced faults (setup 0 and 1b)

527

and higher for experiments with underthrusting due to weakened faults (setup 3, 2, 1a) (Fig.

528

7a). In addition for the latter experiments the CV increases as µ basal decreases. The p value

529

shows a decreasing trend and R2 an increasing trend (Fig. 7b, c), indicating that as µ basal

530

decreases the repeatability value of experiments decreases. This observation could imply that

531

wedges with lower µ basal become more susceptible to extrinsic changes if all other

532

components within the system are the same for each setup. It is known that experimental

533

artifacts become significant when basal friction is very low in comparison to lateral friction

534

(Vendeville, 2007), and this would also produce very low p values.

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5.2.2) Increase in fault dip due to decreasing basal friction.

537

For all the setups the fault dip for the fore thrusts ranges from 26o +/- 1.82 to 30o +/- 1.92, and

538

increases with decreasing µbasal. As µ basal decreases by an average of 0.07 fault dip increases

539

by a minimum of 0.6o. In our experiments the décollement layer is sand (setup 0) or glass

540

beads (setup 3, 2, 1a and b). Fault dip is controlled primarily by the mechanics of faulting, in

541

particular the internal angle of friction (Hafner, 1951). Since the fault propagates from the

542

velocity discontinuity between the conveyor belt and the décollement layer, fault dip is related

ACCEPTED MANUSCRIPT to the internal angle of friction for sand (setup 0) and glass beads (setup 3, 2, 1a, b).

544

Mechanically, the dip of a fault is also related to the orientation of the maximum component

545

of stress (σ1). In a completely Andersonian setting i.e. where shear stress at the base is zero, ψ

546

(equation 1) is also zero. In this case, the orientation of the maximum stress component is

547

parallel to the convergence direction in a uniform thickness of incoming granular material.

548

However, in our experimental settings, we have the formation of shear zone between the

549

conveyor belt and the granular material. Here the magnitude of the shear stress is proportional

550

to the µbasal. As shear stress at the base increases due to increasing µbasal so does the rotation of

551

the maximum stress component and increase in ψ. Therefore, according to equation 1, the

552

consistent decrease in fault dip with increasing µbasal is an effect of the rotation of the

553

maximum stress component from the horizontal. This is also consistent with the findings of

554

Davis and Engelder (1985) studying salt detachments. Statistically fault dip demonstrates a

555

consistently low CV for all the setups regardless of µ basal, style of deformation and in

556

comparison to the other observables (Fig. 7a). This supports the idea that in each setup fault

557

dip is dependent only on the internal angle of friction of the granular material and

558

independent of other observables. For the three setups that demonstrate underthrusting (setup

559

3, 2, 1a), p values for fault dip tend to decrease and R2 show a shallow but increasing trend,

560

also indicating an increase in intrinsic variability possibly due lower stability in the system

561

when µ basal is lowered. This observation is similar to the other observables of the same setups.

563 564

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5.3) Relating interpretations of the statistical analysis to geodynamic natural observations.

565

The statistical trends produced from this study are more beneficial if they can be related to

566

observations in nature. It is important to note the mechanical interaction of parameters (i.e.

567

coefficient of friction, basal friction) when interpreting data from nature or creating models.

568

In particular, for observables (fault lifetime, spacing or wedge slope) that may have a high

ACCEPTED MANUSCRIPT variability, a distinctive solution may not be apparent (for example, in our study, the change

570

in fault lifetime and spacing is due to the change in fault plane friction). Therefore to make

571

reliable interpretations a larger data set is preferred. In addition if the probability distribution

572

curve is known for that observable then this may also aid in the strength of the interpretations.

573

On the other hand, if the observable is highly variable, it presents a clue that there are other

574

controlling factors involved and that need to be investigated. Ideally, when creating a model

575

(analogue or numerical) of a natural system, quantitative values of the physical parameter

576

(µ internal, µ basal, fault plane friction) of the system are taken from nature. However, if the

577

parameter is known to vary especially over time, then it is also important to test a range of

578

values in the model.

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579

It is also important to know the evolutionary stage of deformation. For example one system

581

can have two styles of deformation over time - frontal accretion at earlier stages of the

582

evolution of the wedge and subsequent predominance of underthrusting. Statistically they

583

may originate from the same system. However measurement taken from one or the other stage

584

or at the transition between stages can result in varying interpretations about the initial setting.

585

Furthermore, a change in the fault behavior observed in the field may not necessary mean a

586

different system but only a change in the deformation style due to internal or external

587

influences on the system. Our study is an example of this case and shows that this change in

588

the style of deformation can be initiated by a small change in the thickness of the décollement

589

layer.

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6)

Conclusion

592

Observables related to faults show different magnitudes of variability although they are from

593

the same experimental setup. For example fault dip (CV- 0.06-0.07) shows a lower variability

594

than fault lifetime (CV- 0.19-56), spacing (CV- 0.12-0.36) and wedge slope (CV- 0.12-0.33).

ACCEPTED MANUSCRIPT The difference in variability is related to the dependency of the observable on the interaction

596

of different components of the wedge as it evolves. Fault dip is only dependent on the internal

597

angle of friction of the basal and overlying granular material and measured at the initial stage

598

of formation of the fault, therefore the CV for fault dip is low. In contrast fault lifetime,

599

spacing and subsequently wedge slope varies with changes in the growth of the wedge. Other

600

dynamic changes in the wedge that affect fault lifetime and spacing is the change in fault

601

plane friction due to entrainment of low friction material from a thick décollement layer.

602

A difference in µ basal between 0.03 and 0.15 among the varying setups is statistically

603

distinguishable for all observables. Fault lifetime, fault spacing and related wedge slope

604

decrease with decreasing µ basal. Fault dip increases with decreasing µ basal. These observations

605

are consistent with the mechanics of faulting and deformation of the wedge defined by the

606

critical taper theory (Davis et al., 1983). The setups can be further categorized based on the

607

style of deformation resulting from the difference in initial setup design. The statistical test

608

ANOVA confirms that data from experiments within each setup are repeatable to a high

609

degree (low R2 values – Table 3). Moreover, the statistical results (p value and R2 from the

610

ANOVA test) show that repeatability decreases in setups with high CV and decreasing µ basal.

611

Overall, results signify that the variability of the observables is related to its dependency on

612

the complexity of the system. Therefore, when applying a theoretical analysis, for example,

613

wedge mechanical analysis to natural systems one needs to take into consideration the

614

possible range of values for each observable from natural observations (Maillot et al., 2007;

615

Cubas et al., 2013).

616

Repeating experiments presents the opportunity to quantify the intrinsic variability that is due

617

to geodynamic processes in the experimental system. It allows one to identify the robustness

618

of the results. A single result from one experiment could be near or far from the precise mean

619

value and this uncertainty can be minimized by the repetition of experiments. Thus adding a

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ACCEPTED MANUSCRIPT higher degree of precision to the interpretations. This does not imply that data from previous

621

analogue modelling studies that lack repetition are incorrect. Our study also shows that

622

despite the higher variability in some observables, the relationship between µ basal and mean

623

values for fault and wedge observables is evident. Many observables from previous

624

experiments that are quantitatively measured like fault dips have a low variability, therefore

625

interpretations are credible. Repeating experiments also allows the experimenter to assess

626

whether the variability of the results is due to the experimental setup or due to the processes

627

involved in the system and accordingly improve the design. Thus, we advise experimenters to

628

repeat experiments especially those created to study complex tectonic processes, if the

629

technical possibility exist.

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630 631

Below is a summary of the statistical tools that can be used to analyze data from repeated

632

experiments for better interpretation of the results.

1) Represent the results or observables with distribution curves to qualitatively describe

634

the variability. Determine which distribution best fits the population by calculating the

635

χ2 for each distribution. We advise to use the statistical analysis by Cubas et al. (2010)

636

- Appendix 1.

638 639 640

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2) The type of distribution that represents a population indicates the variability and also

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the sensitivity of the observable. An observable that is more sensitive to changes in the system or dependent on other observables will have a population with a large statistical variation (fault lifetime, fault spacing and wedge slope). On the contrary,

641

populations with small statistical variations are from independent observables like

642

fault dip.

643

3) Use the variability between experiments to determine how reproducible data from

644

experiments are with the help of the ANOVA test. The p value and R2 value indicate

645

not only whether the experiments are repeatable but also to what extent. In our study it

ACCEPTED MANUSCRIPT is observed that experiments with low µ basal are less repeatable. This observation could

647

imply that wedges with lower µ basal become more susceptible to extrinsic changes if all

648

other components within the system are the same.

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ACCEPTED MANUSCRIPT Acknowledgements

650

We would like to thank Marina Morlock for her help in conducting the first analogue

651

experiments for this study and processing the data. TS would like to thank Nadaya Cubas for

652

initial discussions on the critical taper theory. Technical support from Fang-Lin Wang,

653

Thomas Ziegenhagen and Frank Neuman was greatly appreciated in the analogue lab. We

654

would also like to thank Nadaya Cubas and Bertrand Maillot for their constructive criticism

655

on this paper. Tasca Santimano is supported by the European Union FP7 Marie Curie ITN

656

project TOPOMOD (project # 264517).

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tectonic faulting- new insights from granular-flow experiments and high-resolution optical

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Dahlen, F.A., 1984. Noncohesive Critical Coulomb Wedges: An Exact Solution. Journal of

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Dahlen, F.A., 1990. Critical Taper model of fold-and-thrust belts and accretionary wedges.

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Davis, D., Engelder, T., 1985. The role of salt in fold-and-thrust belts. Tectonophysics 119(1),

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Davis, D., Suppe, J., Dahlen, F.A., 1983. Mechanics of Fold and Thrust Belts and

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Fisher, R.A., 1954. Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh.

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Graveleau, F., Malavieille, J., Dominguez, S., 2012. Experimental modelling of orogenic

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Gutscher, M-A., Kukowski, N., Malavieille, J., Lallemand, S., 1996. Cyclical behavior of

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Hafner, W., 1951. Stress distributions and faulting. Bulletin of the Geological Society of

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America 62, 373-398.

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Hall, J., 1815. On the Vertical Position and Convolutions of certain Strata and their relation

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with Granite. Transactions of the Royal Society of Edinburgh 7,79-108.

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Hoth, S., 2005. Deformation, erosion and natural resources in continental collision zones:

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insight from scaled sandbox simulations. Ph.D. Thesis, Freie University, Berlin.

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Hoth, S., Hoffmann-Rothe, A., Kukowski, N., 2007. Frontal accretion: An internal clock for

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bivergent wedge deformation and surface uplift. Journal of Geophysical Research 112,

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DOI: 10.1029/2006JB004357.

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Lallemand, S., Schnürle, P., Malavieille, J., 1994. Coulomb theory applied to accretionary and

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nonaccretionary wedges: Possible causes for tectonic erosion and/or frontal accretion. Journal

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of Geophysical Research 99(B6), 12,033-12,055.

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Lohrmann, J., Kukowski, N., Adam, J., Oncken, O., 2003. The impact of analogue material

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properties on the geometry, kinematics, and dynamics of convergent sand wedges. Journal of

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Structural Geology 25, 1691-1711.

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Maillot, B., 2013. A sedimentation device to produce uniform sand packs. Tectonophysics

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593, 85-94.

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McKillup, S., Dyar, M.D., 2010. Geostatistics Explained: an Introductory Guide for Earth

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Scientists. Cambridge University Press, Cambridge.

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Platt, J.P., 1988. The mechanics of frontal imbrication: a first-order analysis. Geologische

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Rundschau 77/2, 577-589.

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Rosenau, M., Nerlich, R., Brune, S., Onken, O., 2010. Experimental insights into the scaling

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and variability of local tsunamis triggered by giant subduction megathrust earthquakes.

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Journal of Geophysical Research 115, B09314, doi:10.1029/2009JB007100.

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Saha, P., Bose, S., Mandal, N., 2013. Varying frontal thrust spacing in mono-vergent wedges:

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An insight from analogue models. Journal of Earth System Science 122 (3), 699-714.

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Schreurs, G., Buiter S.J.H., Boutelier, D., Corti, G., Costa, E., Cruden, A. R., Daniel, J-M.,

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Hoth, S., Koyi, H.A., Kokowski, N., Lohrmann, J., Ravaglia, A., Schlische, R.W., Withjack,

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M.O., Yamada, Y., Cavozzi, C., Delventisette, C., Elder Brandy, J. A., Hoffmann-Rothe, A.,

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Mengus, J-M., Montanari, D., Nilforoushan, F., 2006. Analogue benchmarks of shortening

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and extension experiments. In: Buiter, S.J.H., & Schreurs, G. (Eds.), Analogue and Numerical

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Modelling of Crustal-Scale Processes. Geological Society of London, 1-27.

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Schulze, D.,1994. Entwicklung und Anwendung eines neuartigen Ringschergerätes.

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Aufbereitungstechnick 35(10), 524-535

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Suppe, J., and Medwedeff, D.A., 1990. Geometry and kinematics of fault-propagation

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folding. Eclogae Geol. Helv. 83, 409-454

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Suppe, J., 2007. Absolute fault and crustal strength from wedge tapers. Geology 35, 1127-

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Twiss, R.J., Moores, E.M., 1992. Structural Geology. W.H. Freeman and Company, New York

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Vendeville, B.C., 2007. The 3-D Nature of stress Fields in Physical Experiments and Its

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Impact on Models Overall Evolution. Solicited Oral Contribution. In: EGU General

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Assembly, Vienna, 15-20 April, 2007

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Zar, J.H., 2010. Biostatistical Analysis, Fifth Edition. Pearson Prentice-Hall, New Jersey.

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ACCEPTED MANUSCRIPT Figure captions

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Figure 1 – Experimental box for all the experimental setups. Data and processed images

762

obtained from the PIV system include a) calibrated image of the wedge, b) binarized image of

763

the wedge and c) processed images of the wedge showing the horizontal velocity field (Vx)

764

along the wedge. The experiment shown in this figure is from setup 3- sand +0.5cm layer of

765

300-400µm glass beads.

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Figure 2- Examples of calibrated images, binarized images and processed images of the

768

wedge showing the horizontal velocity field (Vx) for a) sand (setup 0), b) sand +0.5cm layer

769

of 200-300µm glass beads (setup 2), c) sand +0.5cm layer of 100-200µm glass beads (setup

770

1a) and d) sand +0.2cm layer of 100-200µm glass beads (setup 1b). All images display 160

771

cm of shortening. The processed images show the difference in deformation style in particular

772

underthrusting in setup 0 and frontal accretion in setup 1b.

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Figure 3 – Method of how the observables are measured using the data collected by the PIV

775

cameras a) Binarized images of the wedge are used to calculate the height and length of the

776

wedge for each time step. The incoming layer is not included in the length or height of the

777

wedge. b) Fault spacing is measured as the horizontal distance, along the profile line, between

778

two consecutive faults, when the former fault is at the end of its activity as a first order fault

779

and a new fault is formed. The velocity along the profile line for each time step is plotted in d.

780

The fault spacing is accurately measured from this plot. c) Fault dip and back thrust dip are

781

measured after strain is completely localized and at the initiation of a new fault plane and

782

back thrust plane. d) Deformation map displaying the velocity for each profile line from c).

783

Therefore the x axis is the length of the wedge and the y axis is the time step. Pink area

784

represents the velocity of the incoming layer. The transition between pink to black in the x

785

axis is the location of the fault plane on the profile line. From this map the fault lifetime and

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fault spacing can be measured. Fault lifetime is the time (or number of time steps) the fault is

787

active as a first order structure.

788

Figure 4 – Wedge height and length for all experiments within a) sand (setup 0), b) sand

790

+0.5cm layer of 300-400µm glass beads (setup 3), c) sand +0.5cm layer of 200-300µm glass

791

beads (setup 2), d) sand +0.5cm layer of 100-200µm glass beads (setup 1a) and e) sand

792

+0.2cm layer of 100-200µm glass beads (setup 1b). Dashed black line represents the power

793

law trendline for both height and length of the wedge.

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Figure 5- Fault lifetime and fault spacing for all experiments within a) sand (setup 0), b) sand

796

+300-400µm glass beads (setup 3) , c) sand +200-300µm glass beads (setup 2), d) sand +100-

797

200µm glass beads (setup1a), e) sand +100-200µm glass beads (setup 1b). b) c) and d) show

798

the occurrence of long lived and widely spaced faults followed by short lived and closely

799

spaced faults, thus producing a zig-zag trend.

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Figure 6 – Histograms for each observables- fault lifetime, fault spacing, fault dip and wedge

802

slope for each experimental setup. Normal, Gamma and Laplacian probability distributions

803

are represented in green, red and blue curves respectively. Q value is for the best fit

804

distribution curve based on the Chi square test (Table 2) and N indicates the number of

805

samples.

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Figure 7- Plots showing the comparison of a) CV b) p value (ANOVA test) and c) R2

808

(ANOVA test) for each observable in the different setups. Linear trendlines are only shown

809

for setups 3, 2, 1a since they differ from the other setups (0 and 1b) in the style of

810

deformation and the thickness of the décollement layer.

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ACCEPTED MANUSCRIPT Table captions

813

Table 1 – Material physical properties for the grains used in the experiments include grain

814

size, density, static friction, static reactivation friction and kinetic friction. The coefficient of

815

frictions for all materials were measured in a Ring-shear tester and the data can be found in

816

Fig. A2

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Table 2 – Statistics for all the observables for each experimental setup. For each observable,

819

the number of samples (n), mean, standard deviation, coefficient of variation (CV), median

820

and median deviation are presented. The Chi-square test (χ2) is calculated between the

821

observed values and the expected values based on the Normal model, the Gamma model and

822

the Laplacian model. The best fit distribution according to the χ2 test is presented in bold. For

823

the Gamma model the shape parameter (a) and scale parameter (b) are also indicated.

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Table 3- ANOVA test results for each observable for each experimental setup. The calculated

826

p-value, R2, Fisher value and critical Fisher value are shown in the table.

827

indicate a rejection of the null hypothesis.

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Bold values

ACCEPTED MANUSCRIPT Appendix A1

829

Methods: Derivation of material properties using a ring-shear tester

830

Material properties were derived using a Schulze Ring shear tester specially designed to

831

measure friction coefficients in loose granular material accurately at low confining pressures

832

and shear velocities similar to sandbox experiments (Lohrmann et al., 2003; Schulze 1994). In

833

this tester, a sand layer is sheared either against a base or internally at constant normal load

834

and velocity while the shear stress is measured continuously. The resulting stress curve

835

(example shown in Appendix Fig. A1) typically rises from zero to a peak level (= static

836

friction) within the first few millimetres of shear before it drops and stabilizes after formation

837

of a shear zone in the material or at the interface (= kinetic friction). Stopping the shearing

838

and resetting the shear stress followed by a renewed shearing (re-shear) results in a second,

839

similar shear curve whose peak (= reactivation static friction) is somewhat lower than the first

840

peak. From these curves, the strengths at first and second peak as well as on the plateau are

841

picked manually and assigned static, reactivated static and kinetic frictional strength for the

842

applied normal load, respectively. Density of material is calculated based on the weight of the

843

material sieved into the shear cell and the volume which is monitored accurately throughout

844

the shear test.

845

Two analysis methods are applied to derive friction coefficients and a realistic variability

846

from that data: First, linear regression of the normal load vs. shear strength data pairs, i.e. by

847

fitting a linear failure envelope to the data in the Mohr space. The slope of the line and the y-

848

axis intercept are accordingly the friction coefficient and cohesion, respectively. However,

849

because this method overestimates real precision and may be biased by a curved failure

850

envelope we performed a second analysis which relies on calculating all possible two point

851

slopes and intercepts for mutually combined data pairs. These data are then evaluated by

852

means of univariate statistics by means of calculating mean and standard deviation and

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ACCEPTED MANUSCRIPT comparing the probability density function (pdf) to that of a normal distribution. Usually it is

854

found that the peaks of the experimental pdf are much narrower than a normal distribution pdf

855

suggesting that the calculated standard deviation is a conservative value which tends to

856

underestimates real precision. The standard deviations reported in Table 1 represent a trade-

857

off between the mean and standard deviations derived by the two methods described above.

858

Because inferred cohesion values are low (in the order of view tens of Pa) and show a large

859

scatter (tens to hundreds of Pa) we do not rely on the cohesion values but conclude cohesion

860

is neglectable in our material.

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Figure A1.1: Example of stress curve raw data as derived from Ring shear testing. See text

863

for explanation.

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Figure A1.2: Friction data set. In Each panel A-F the static, reactivated static and kinetic

866

friction data are plotted in Mohrspace (with a linear fit indicated) and as histograms of fiction

867

coefficients and cohesion as derived from mutual two-point regression analysis. See text for

868

explanation.

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ACCEPTED MANUSCRIPT Appendix A2

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Method: Statistical tests used in this study

871

1) Chi square test (χ2 test)

872

The theoretical formula for this test is similar to that in Cubas et al. (2010) and calculated as

873

follows

874

  = ∑ 

875

Where O= observed values, E = expected values based on the distribution and m= number of

876

intervals from the histograms. χ2 test as shown in Table 2 is calculated as follows

877

   = 1 − 

878

Therefore a high   test value indicates the least difference between the theoretical values and

879

the dataset.

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880

The theoretical distribution functions for the different distribution types are as follows

882

Normal distribution 

  !

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(3)

 = √ 

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where ̅ = mean, σ2 = variance

(4)

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Gamma distribution

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(2)

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# $% & '

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  =

888

where a = shape factor, b = scale factor and Γ is the Gamma function

( $ )*

(5)

889 890

Laplacian distribution

891

  = (  +

892

where / = median, 2b2 = variance



-| | . '

(6)

ACCEPTED MANUSCRIPT 893

2) ANOVA test

895

For a population consisting of measurements from several experiments, N is the number of

896

experiments and 01 is the total number of measurements in all experiments. The sum, mean

897

(̅ , and variance (2  is calculated for each experiment in the population. The degree of

898

freedom (3 , Sum of squares (SS) and Mean of squares (MS) are calculated between

899

experiments (B) and also within each experiment (W) as follows

900

34 = 5 − 1

901

36 = 01 − 5

902

 774 = ∑8  0 ̅ − ̅ 1

903

where 0 , ̅  is the number of measurements and mean respectively for the 9 :; experiment,

904

and ̅ 1 is the mean of all measurements.

905

776 = ∑8 <= − ̅  >

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=

(7) (8) (9)

(10)

906

where = is the ? :; measurement in experiment 9

907

@7 = BC

908

771D:*E = 774 + 776

909

@71D:*E = @74 + @76

910

As part of the ANOVA test we calculated the coefficient of determination (R2) value. R2 is a

911

quantitative value of how much of the variance of an observable is explained due to variation

912

between the experiments in contrast to within experiments.

913

G  = AA

914

A large R2 value indicates that the variation is due to the experimental setup or extrinsic

915

sources in contrast to a small R2 indicating that the variation is within the system (Zar, 2010).

916

(11) (12) (13)

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AA H IJI$K

(14)

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The Fisher (F) value is calculated to determine if the null hypothesis can be rejected.

918

L=

MA H

MAN

=

O*P*QR& H

(15)

O*P*QR&N

919

3) Cross-correlation of fault observables.

921

Figure A2.1- Graphs showing the correlation between the fault observables- fault lifetime,

922

fault spacing and fault dip for all setups. There is a clear correlation between fault lifetime and

923

fault spacing showing their interdependence. There is a very low correlation between fault dip

924

and fault lifetime or spacing indicating that fault dip is independent of the latter observables.

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Glass beads Glass beads Glass beads Sand Sand on rubber conveyor belt Sand on glass

Internal Internal Internal Internal Basal

Density (g/m3)

Grain size (µm)

Static friction

Standard deviation

1.59 1.60 1.64 1.72

100-200 200-300 300-400 > 630

0.47 0.50 0.53 0.68 0.62

0.03 0.04 0.04 0.04 0.05

0.15

0.09

0.12

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Stable reactivation friction 0.46 0.47 0.51 0.63 0.60

Standard deviation

Kinetic friction

Standard deviation

0.01 0.02 0.02 0.02 0.02

0.40 0.42 0.43 0.55 0.56

0.02 0.02 0.01 0.01 0.02

0.07

0.12

0.06

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Type

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Material

Table 1 – Santimano et al.

b 20 20 0.12 0.12 0.26

N.A. 0.04 0.22 N.A. 0.73

0.47 0.27 0.06 0.02 0.26

6.34 16 286 2883 14

24 14 0.09 0.02 0.85

0.39 0.46 0.20 N.A. 0.76

129 227 26 45 12

50 43 1.14 0.41 2.49

0.57 0.80 0.19 0.48 0.78

106 93 1.59 2.16 3.04

0.65 0.86 0.36 N.A. 0.77

0.56 0.36 0.06 0.05 0.19

3.47 8.35 327 395 28

54 30 0.09 0.11 0.55

0.81 0.91 0.36 N.A. 0.86

176 237 29 45 15

85 76 1.41 1.33 2.43

0.59 0.78 0.23 0.67 0.77

84 71 1.79 2.74 4.14

N.A. 0.11 0.21 N.A. N.A.

0.54 0.33 0.06 0.06 0.33

5.33 12 268 235 10

29 16 0.11 0.19 1.23

0.17 0.42 0.21 N.A. 0.69

129 193 29 45 11

55 48 1.13 1.78 3.34

0.40 0.38 0.50 0.08 0.41

20 16 1.92 0.80 2.54

0.91 0.94 0.30 N.A. N.A.

0.19 0.12 0.06 0.02 0.26

26 75 255 3019 17

4.04 1.94 0.12 0.01 0.56

0.92 0.94 0.28 N.A. N.A.

105 148 30 45 9.10

17 13 1.66 0.31 1.86

0.87 0.98 0.16 0.47 0.78

n 58 58 64 64 1297

Sand + 300-400 µm GB setup 3

Fault Lifetime Fault Spacing Fault dip Back thrust dip Wedge slope

48 48 53 52 853

153 241 26 44 12

71 65 1.59 0.82 3.23

Sand +200-300 µm GB setup 2

Fault Lifetime Fault Spacing Fault dip Back thrust dip Wedge slope

39 39 43 43 896

189 258 28 44 15

Sand +100-200 µm GB setup 1a

Fault Lifetime Fault Spacing Fault dip Back thrust dip Wedge slope

40 40 45 45 938

155 217 29 44 12

Sand +100-200 µm GB setup 1b

Fault Lifetime Fault Spacing Fault dip Back thrust dip Wedge slope

63 63 68 67 764

106 146 30 44 9.69

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Population Fault Lifetime Fault Spacing Fault dip Back thrust dip Wedge slope

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a 9.51 14 217 390 65

Setup Sand only setup 0

Gamma model

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CV 0.33 0.26 0.07 0.06 0.12

Laplacian model χ2 Median test Median deviation 0.76 188 48 0.95 298 62 0.63 26 1.32 N.A. 45 0.92 17 1.68 0.96

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χ2 test 0.89 0.94 0.67 N.A. 0.91

Table 2- Santimano et al.

ACCEPTED MANUSCRIPT Fault lifetime

Setup

Fault spacing

Fault dip

Back thrust dip

between experiments of each setup p value R2 F value F crit

0.10 0.17 1.85 2.28

0.02 0.24 2.74 2.28

0.06 0.18 2.08 2.26

0.91 0.03 0.33 2.26

Sand +300-400 µm GB setup 3

p value R2 F value F crit

0.92 0.02 0.22 2.58

0.90 0.02 0.26 2.58

0.08 0.15 2.15 2.56

0.66 0.04 0.60 2.57

Sand +200-300 µm GB setup 2

p value R2 F value F crit

0.94 0.02 0.19 2.65

0.85 0.03 0.33 2.65

0.08 0.19 2.25 2.61

0.03 0.23 2.92 2.61

Sand +100-200 µm GB setup 1a

p value R2 F value F crit

0.53 0.08 0.79 2.64

0.16 0.16 1.71 2.64

0.03 0.22 2.85 2.60

0.46 0.08 0.92 2.60

Sand +100-200 µm GB setup 1b

p value R2 F value F crit

8.36E-07 0.43 11.20 2.53

0.16 0.09 1.69 2.51

0.07 0.12 2.24 2.52

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Sand setup 0

between different basal frictions or setups

1.42E-08 0.59 16.85 2.57

2.94E-14 0.77 39.12 2.57

4.54E-13 0.62 26.54 2.51

0.03 0.17 2.73 2.55

Table 3- Santimano et al.

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ACCEPTED MANUSCRIPT Intrinsic versus extrinsic variability of analogue sand-box experiments- insights from statistical analysis of repeated accretionary sand wedge experiments Tasca SANTIMANO, Matthias ROSENAU, Onno ONCKEN

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Highlights

We statistically quantify variability in repeated analogue experiments.

-

Extrinsic source of variability is due to varying basal friction.

-

A probability based comparison between the different observables is presented.

-

The ANOVA test is used to confirm the repeatability of results.

-

We show that the mechanics of deformation control the variability.

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static friction peak

kinetic friction level

20

5

10

15 shear [mm]

20

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shear load [kg]

reactivation static friction peak

25

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ACCEPTED MANUSCRIPT

Sand (G23) internal 0.68529 (95%: 0.68183<>0.68875) (54 measurements)

0.62777 (95%: 0.62428<>0.63127) (54 measurements)

0 0.5

0.9

100 0 -1000

-500 0 500 cohesion (Pa)

0 0.55

1000

Glass beads (300-400) internal 0.53131 (95%: 0.52525<>0.53737) (54 measurements)

0.75

100

0 -200

0 200 cohesion (Pa)

2000 2000

8000

4000

4000 2000

0

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.53039+/-0.03972 (1215 data) -24.3646+/-162.6242 Pa (1215 data) 200 400 300

counts

150 100 50 0

0.4 0.5 0.6 friction coefficient

0.7

200 100 0 -2000

-1000 0 cohesion (Pa)

1000

static reactivation friction

6000

counts

0

2000

4000

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.5481+/-0.012659 (1215 data) 83.6748+/-41.1281 Pa (1215 data) 200 300

200

100 50

0.55 0.6 0.65 friction coefficient

0.7

100

0 -100

0

100 200 cohesion (Pa)

300

0.42893 (95%: 0.42743<>0.43043) (54 measurements)

0

2000

4000

kinetic friction

6000 4000 2000 0

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.50879+/-0.0159 (1214 data) 20.7723+/-68.224 Pa (1214 data) 150 600

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.43114+/-0.0082835 (1213 data) 4.281+/-37.3185 Pa (1213 data) 150 600

100

100

400

50

0 0.45

0.5 0.55 0.6 friction coefficient

0.65

counts

4000

0

8000

counts

6000

0

0 0.5

400

shear strength (Pa)

shear strength (Pa)

static friction

8000

2000

150

10000

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shear strength (Pa)

0.6 0.65 0.7 friction coefficient

4000

0.50314 (95%: 0.50073<>0.50555) (54 measurements)

10000

counts

50

EP

B

0.6 0.7 0.8 friction coefficient

200

200

6000

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50

4000

100

counts

100

shear strength (Pa)

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.62698+/-0.017266 (1215 data) 109.2084+/-55.9641 Pa (1215 data) 150 300

300

counts

counts

150

2000

counts

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.67555+/-0.035547 (1214 data) 28.5609+/-114.4291 Pa (1214 data) 200 400

kinetic friction

8000

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4000

counts

2000

5000

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10000

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5000

10000

static reactivation friction

shear strength (Pa)

shear strength (Pa)

static friction 10000

0

0.55032 (95%: 0.54768<>0.55296) (54 measurements)

15000

counts

15000

200

0 -500

0 500 cohesion (Pa)

1000

0

2000

4000

400

counts

A

50

0 0.4

0.45 friction coefficient

0.5

200

0 -400

-200 0 200 cohesion (Pa)

400

ACCEPTED MANUSCRIPT

Glass beads (200-300) internal 0.50221 (95%: 0.49782<>0.5066) (72 measurements)

0.47007 (95%: 0.46696<>0.47319) (70 measurements)

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.50011+/-0.035773 (2160 data) 23.13+/-127.9183 Pa (2160 data) 400 800

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.47237+/-0.020338 (2038 data) 41.4431+/-91.2477 Pa (2038 data) 300 800

600

100 0

D

0.4 0.5 0.6 friction coefficient

0.7

400 200 0 -1000

-500 0 500 cohesion (Pa)

100

0

1000

0.46663 (95%: 0.46184<>0.47141) (54 measurements)

0.4 0.5 0.6 friction coefficient

0.7

200

0 -500

0 500 cohesion (Pa)

2000

4000

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.46853+/-0.029369 (1214 data) -10.092+/-114.9539 Pa (1214 data) 200 400 300

counts

150 100 50 0

0.4 0.5 0.6 friction coefficient

0.7

counts

0

200 100 0 -1000

-500 0 500 cohesion (Pa)

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.41931+/-0.019954 (2158 data) 18.8197+/-94.0515 Pa (2158 data) 300 800

1000

static reactivation friction

4000 2000

0

0

2000

4000

100

0.4 0.45 friction coefficient

0.5

400 200 0 -1000

-500 0 500 cohesion (Pa)

1000

0.40278 (95%: 0.40043<>0.40513) (54 measurements)

shear strength (Pa)

6000

2000

600

0 0.35

1000

4000

kinetic friction

6000 4000 2000 0

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.46173+/-0.013418 (1214 data) 1.237+/-49.6772 Pa (1214 data) 300 600

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.40274+/-0.018254 (1215 data) -8.1448+/-64.4635 Pa (1215 data) 300 400

200

200

400

100

0 0.35

0.4 0.45 0.5 friction coefficient

0.55

counts

2000

0

8000

counts

4000

EP

shear strength (Pa)

static friction

6000

0

200

8000

AC C

shear strength (Pa)

400

2000

0.45969 (95%: 0.45836<>0.46102) (54 measurements)

8000

counts

4000

600

Glass beads (100-200) internal

0

2000

4000

TE D

200

0

200

counts

counts

counts

300

0

kinetic friction

6000

counts

4000

counts

2000

2000

M AN U

0

shear strength (Pa)

2000

4000

counts

4000

static reactivation friction

6000

RI PT

6000

8000

SC

static friction

8000

0

0.41889 (95%: 0.41569<>0.4221) (72 measurements)

8000

shear strength (Pa)

shear strength (Pa)

10000

200

0 -500

0 cohesion (Pa)

500

0

2000

4000

300

counts

C

100

0

0.35 0.4 0.45 friction coefficient

0.5

200 100 0 -400

-200 0 200 cohesion (Pa)

400

ACCEPTED MANUSCRIPT

Sand (G23) basal on black rubber belt 0.62128 (95%: 0.61663<>0.62594) (72 measurements)

0.58446 (95%: 0.58225<>0.58667) (72 measurements)

4000 2000 0

4000

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.62227+/-0.046799 (2159 data) -20.1912+/-147.8079 Pa (2159 data) 600 1000

0 -1000

0 1000 cohesion (Pa)

counts

100 0 0.5

2000

0.13938 (95%: 0.13259<>0.14617) (72 measurements)

3000

0 -200

0

200 400 cohesion (Pa)

0

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.56223+/-0.022762 (2158 data) 36.5417+/-72.0611 Pa (2158 data) 300 400

100

0.8

100 0 -200

0

200 400 cohesion (Pa)

600

0.11847 (95%: 0.11142<>0.12552) (72 measurements)

static reactivation friction

1000

0

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.12026+/-0.061432 (2095 data) 54.2483+/-211.629 Pa (2095 data) 600 800

400

400

400

0 -0.5

0 0.5 friction coefficient

1

0 -2000 -1000 0 1000 cohesion (Pa)

2000

200

0 -0.5

0 0.5 friction coefficient

1

200

0 -2000 -1000 0 1000 cohesion (Pa)

2000

0

2000

4000

600

counts

400

counts

counts

200

4000

kinetic friction 2000

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.12125+/-0.070649 (2080 data) 57.6545+/-224.6019 Pa (2080 data) 600 600

200

2000

0.5 0.6 0.7 friction coefficient

200

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.14826+/-0.08989 (2051 data) 74.4117+/-232.3463 Pa (2051 data) 600 600

400

0

4000

300

0 0.4

600

1000

0

2000

3000

counts

4000

0.9

2000

AC C

2000

EP

shear strength (Pa)

static friction 2000

counts

shear strength (Pa) counts

4000

0

0.6 0.7 0.8 friction coefficient

0

0.11615 (95%: 0.1084<>0.1239) (72 measurements)

3000

1000

100

M AN U

1

200

2000

200

TE D

0.5 friction coefficient

counts

counts

counts 0

500

200

Sand (G23) basal on glass

0

4000

300

200

F

2000

4000

6000 8000 10000 12000 14000 16000 normal load (Pa) 0.59118+/-0.02397 (2157 data) 52.4794+/-71.7629 Pa (2157 data) 400 300

400

0

0

6000

counts

2000

6000

kinetic friction

8000

shear strength (Pa)

0

static reactivation friction

8000

RI PT

5000

10000

counts

shear strength (Pa)

shear strength (Pa)

static friction 10000

0

0.55444 (95%: 0.55241<>0.55647) (72 measurements)

10000

shear strength (Pa)

15000

SC

E

200

0 -0.2

0 0.2 0.4 friction coefficient

0.6

400 200 0 -2000 -1000 0 1000 cohesion (Pa)

2000

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT