Superimposed folding and thrusting by two phases of mutually orthogonal or oblique shortening in analogue models

Hongling Deng*, Hemin A Koyi, Faramarz Nilfouroushan

Hans Ramberg Tectonic Laboratory, Department of Earth Sciences, Uppsala

University, Villavagen 16, SE-752 36 Uppsala, Sweden

*Corresponding author. Fax: +46 (0) 18 471 25 91. E-mail addresses: hongling.deng@geo.uu.se

Abstract Orogens may suffer more than one phase shortening resulting in superposition of structures of different generations. Superimposition of orthogonal or oblique shortening is studied using sandbox and centrifuge modelling. Results of sand models show that in orthogonal superimposition, the two resulting structural trends are approximately orthogonal to each other. In oblique superimposition, structures trend obliquely to each other in the relatively thin areas of the model (foreland), and mutually orthogonal in areas where the model is thickened during the first phase of shortening (i.e. the hinterland). Thrusts formed during the first shortening phase may be reactivated during the later shortening phase. Spacing of the later phase structures is not as wide as expected, considering they across the pre-existing thickened wedge. Superposition of structures results in formation of type 1 fold interference pattern. Bedding is curved outwards both in the dome and basin structures. Folded layers are dipping and plunging outwards in a dome, while they are dipping and plunging inwards in a basin. In the areas between two adjacent domes or basins (i.e. where an anticline is superimposed by a syncline or a syncline is superimposed by an anticline), bedding is curved inwards, and the anticlines plunge inwards and the synclines outwards. The latter feature could be helpful to determine the age relationship for type 2 fold interference pattern. In tectonic regions where multiple phases of shortening have occurred, the orogenic-scale dome-and basin and arrowhead-shaped interference patterns are commonly formed, as in the models. However, in some areas, the fold interference pattern might be modified by a later phase of thrusting. Similar to models results, superimposition of two and/or even more deformation phases may not be recorded by structures all over the tectonic area. Keywords: multiple orthogonal/oblique shortening, superimposed deformation, structure spacing, fold interference patterns Citaion: Deng H. et al., 2015; Superimposed folding and thrusting by two phases of mutually orthogonal or oblique shortening in analogue models, Journal of Structural Geology, in press.

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1. Introduction 37

Multiple phases of deformations are reported from different parts of the world where 38

early phase structures are modified by a later phase shortening (Steiger, 1964; Roy, 39

1995; Saha, 2002; Maxelon and Mancktelow, 2005; Roca et al., 2006; Weinberger et 40

al., 2009; Abdelsalam, 2010; Dario et al., 2010; Derryberry, 2011; Cashman et al., 41

2011; Li et al., 2012; Mescua and Giambiagi, 2012; Shah, 2012; Sen, 2013). For 42

example, Lim and Cho (2012) reported that two mutually orthogonal shortening 43

phases have occurred during the Daebo Orogeny in Chungnam Basin, Korea. In the 44

Mount Isa Inlier, Australia, four mutually oblique shortening phases have been 45

documented (Abu Sharib and Bell, 2011). Deng et al. (2005) suggested five 46

shortening phases to have occurred in the Yanshan Orogenic Belt, North China, 47

where both mutually parallel and oblique superimpositions are shown. 48

Experimental and case studies on multiple phases of shortening have mainly focused 49

on reactivation of pre-existing faults (Corredor, 2003; Ramon and Rosero, 2006; 50

Deng et al, 2014), and refolding of early phase folds (Derryberry, 2011). On outcrop- 51

and regional-scale, when a later phase of deformation overprints pre-existing 52

structures in an orthogonal or oblique way, fold interference pattern may form by 53

folding superimposition (Ramsey, 1962; Ghosh, 1992; Maloof, 2000; 54

Jayangondaperumal and Dubey, 2001; Grimes and Mosher, 2003; Lim et al., 2012; 55

Sen, et al., 2012). Transpressive deformation in a strike-slip fault zone and oblique 56

ramps of a thrusts system may be reactivated by oblique-slip movements during later 57

phase of shortening that is perpendicular to the trend of previous structures 58

(Jayangondaperumal and Dubey, 2001; Soto et al., 2007). 59

A number of analytical and experimental investigations have been conducted on fold 60

interference patterns that are resulted from superimposition of two phases of folds 61

trending mutually perpendicular. For example, four classical types of interference 62

patterns, type 0 to type 3 proposed by Ramsay (1962, 1967) based on shear folding 63

are widely known and referenced. Grasemann et al. (2004) have extended this 64

nomenclature to six types (type 1-3 and type 01-03). In order to investigate the 65

effects of early folded layers on formation of the later phase folds during buckling 66

superimposition, a number of experimental and natural case studies have been 67

conducted (e.g. Ghosh and Ramberg, 1968; Skjernaa, 1975; Watkinson, 1981; 68

Ghosh et al., 1992, 1993, 1995, 1996; Grujic, 1993; Aller and Gallastegui, 1995; 69

Grujic et al., 2002; Simon, 2004; Sengupta et al., 2005; Pastor-Galan et al., 2012; 70

Tian et al., 2013; Bose et al., 2014). Ghosh et al. (1992) proposed four modes of 71

interference pattern for buckling superimposition based on a series of experiments 72

with increase in tightness of the early phase of folding. However, superimposition of 73

thrust-related folding is also documented by some authors (e.g., Crespo-Blanc, 2007; 74

Abu Sharib and Bell, 2011; Lim and Cho, 2012; Shah, 2012). 75

In this study, a series of sandbox models were conducted to simulate superimposition 76

of folding and thrusting resulted from two phases of mutually orthogonal and oblique 77

shortening. Horizontal sections were taken at different levels in each model to follow 78

the 3D geometry of the superimposed structures. Based on model results, we 79

discuss several problems related to these structures: general characteristics of 80

superimposed folds and thrusts in map-view; features of superimposed structures 81

shown in different levels; comparison of superimposed folds and thrusts between 82

orthogonal and oblique superimposed shortening and effect of superimposition on 83

spacing of the phase-2 structures. In addition to sandbox model results, two 84

centrifuge models which examined the buckling superimposition formed by two 85

phases of orthogonal shortening are shown in this study. The reason for conducting 86

centrifuge models and illustrating the results here is to help investigating fold 87

interference patterns by excluding the effect of thrusting, which is not possible in 88

sandbox models where both fold and thrust develop. Three natural examples are 89

shown and compared with the model results. They are from the Chungnam Basin, 90

Korea, Mount Isa Inlier, Australia, and the central part of the Yanshan Orogenic Belt, 91

North China, where multiple mutually orthogonal or oblique shortening phases have 92

occurred. 93

94

2. Model setup and procedure 95

The sandbox models were built up with a uniform initial dimension, length of 52 cm, 96

width of 48 cm and thickness of 1.5 cm. In these models, dry loose quartz sand with 97

grain size of 80-120 µm, density of 1.53 g/cm3, and internal friction angle of 30-33° 98

(Maillot and Koyi, 2006) was used to simulate the brittle deformation in the upper 99

crustal rocks. Sand layers were about 2 mm thick and interstratified by thin marker 100

horizons of coloured sand (less than 1 mm) that acted as passive makers. A length 101

ratio of 10-5 was applied to scale the models to natural prototype, i.e. 1 cm in the 102

models represents 1 km in nature. All the models were shortened above an 103

aluminium plate with a relatively low basal friction coefficient of µ = 0.23 (Liu et al., 104

2013; Deng et al., 2014) in order to form a wide wedge. Models shortened above a 105

high-friction (µ= 0.55) produce narrower wedges (Koyi and Vendeville, 2003). 106

Superimposed shortening on a regional scale has been reported from some fold-107

thrust belts, for example the Chungnam Basin, Korea (Lim and Cho, 2012), Mount 108

Isa Inlier, Australia (Abu Sharib and Bell, 2011), and the central part of the Yanshan 109

Orogenic Belt, North China (Deng and Koyi, 2015). The shortening phases producing 110

the superimposed structures can be orthogonal or oblique to each other. In order to 111

recognize differences and similarities between structures developed during 112

orthogonal and oblique shortening scenarios, three kinds of set-up were used in the 113

modelling strategy (Table 1). One set-up was used to run two models (S1 and S2). In 114

model S1, two motors that were perpendicular to each other, separately pushed a 115

backstop forward during each phase to shorten the sand layers orthogonally (Fig. 1a). 116

In model S2, the same procedure was conducted as in model S1. However, after the 117

phase-1 shortening, the top of structural wedge was eroded by 6-8 mm and new 118

layers (6 mm) were sedimented. The second set-up was used in model S3, where 119

shortening directions in two phases were still mutually perpendicular. However, a 120

wooden right triangle with the interior angles of 45° was inbuilt to act as the backstop 121

during the phase-1 (Fig. 1b). This triangle backstop provided a compressive 122

component perpendicular to its hypotenuse, which formed a series of structures 123

trending parallel to the hypotenuse. During the phase-2, shortening direction was 45° 124

oblique to the strikes of the phase-1 structures. As such, a strict oblique 125

superimposed shortening could be achieved with this set-up. In the third set-up, an 126

aluminium plate was placed under the sand package in model S4. The model was 127

firstly shortened by a backstop and several structures were formed (Fig. 2a). After 128

that, a wooden wall has been placed in the model, which made an angle of 60° to the 129

trend of the phase-1 structures. Part of the model corner was removed to allow for an 130

oblique shortening, and the rest of the model was shortened against the wooden wall 131

during the second deformation phase. The shortening was achieved by pulling the 132

underlying metal plate at 60° angle (Fig. 2b). Consequently, with this set-up, the two 133

shortening directions were 60° oblique to each other in two sequential phases. 134

In addition to sandbox experiments, two centrifuge models were also run. The first 135

model (C1) consisted of 7 plasticine layers, with a dimension of 15 ×15 ×1 cm. The 136

second model (C2) consisted of 10 layers, 5 of plasticine and 5 of weaker material 137

(plasticine mixed with silicone putty and barite powder). Both the plasticine and the 138

mixture behave in non-Newtonian way where their effective viscosity is dependent on 139

the strain rate (Fig. 3). The two different types of layers were placed alternatively, 140

simulating a sequence with competence contrast. The model was initially 18 cm long, 141

16 cm wide and 1 cm thick. The plasticine material used in our models has a density 142

of 1.64-1.65 g/cm3, and the viscosities ranging from 2×108 to 7×108 Pa·s at strain 143

rates between 2×10-6 s-1 and 2×10-5 s-1. The mixture material has the density of 1.66-144

1.67 g/cm3, and the viscosity is 2×107 to 2×108 Pa·s at strain rates of 1-8×10-6 s-1. At 145

model strain rate of 10-6 to 10-5 s-1, the viscosity ratio between the plasticine and the 146

mixture layers was about one and half order of magnitude (Fig. 3). The dimension of 147

the models may be scaled to a natural prototype where 1 cm represents 1 km. The 148

models were initially shortened in one direction during spinning in the centrifuge at 149

700 G. After that, the models were shortened in the centrifuge in a direction 150

orthogonal to the first shortening direction. For each deformation phase, the models 151

were spun in the centrifuge for about 30 minutes. 152

Top surface of each model was scanned by a high-resolution Laser scanner at 153

regular interval during model deformation to monitor the change in topography. 154

Structure spacing was measured from the surface of the models using the method 155

introduced by Koyi et al. (2000). Structure spacing is the distance between the middle 156

lines of two sequential box folds in the sandbox models (Deng et al., 2014). Change 157

of the structure spacing was recorded at every 1 cm shortening. Lateral- and dip-slip 158

were monitored for the phase-1 thrusts during the second shortening phase, in order 159

to investigate their reactivation. In model S3, because the inbuilt triangle backstop 160

produces both compression and dextral shearing (Fig. 1b), we also measured 161

displacement along the phase-1 thrusts as they developed during the first shortening 162

phase. During the phase-1, four reference point-pairs were placed on either side of 163

thrusts traces on the top surface of model S3, in order to monitor movement along 164

the thrusts. Dip-slip was monitored by measuring the distance between the two points 165

along a line perpendicular to the trend of the thrust, whereas strike-slip was 166

monitored by measuring any lateral deviation of the points from this line. The 167

horizontal distance between two points of each pair was decreased with shortening. 168

We recorded the decrease of the horizontal distance which was converted them to 169

displacement along the thrust. During the second shortening phase, more reference 170

point-pairs were added on either side of the phase-1 thrusts traces on the top surface 171

of each model. The relative displacement of two points in each pair, either along 172

strike or in dip direction, was measured during the shortening phase-2 in order to 173

monitor any reactivation of the phase-1 structures. 174

175

3. Sandbox model results 176

3.1 Superimposition of folding and thrusting (models S1-S4) 177

After the first shortening phase a sand wedge formed close to the backstop, which is 178

the hinterland of the models (Figs. 4a, c and e). In the foreland, the sand layers 179

remain undeformed. Thickness of the model decreases from the hinterland towards 180

the foreland, reflected in surface topography (Figs. 4a, c and e). During the phase-2, 181

the shortening direction was either orthogonal or oblique to the trends of the phase-1 182

structures. Due to thickness change, deformation front did not propagate throughout 183

the entire model at the same time. The undeformed foreland of the phase-1 was 184

shortened to form a series of structures, which propagated laterally to the pre-existing 185

wedge, overprinting the phase-1 structures. As a result, highest topography was 186

shown in the superimposed hinterlands (Figs. 4b, d and f). 187

After shortening of the models in two directions, horizontal slices were taken and 188

analysed. The structural complexity of the models was described in two horizontal 189

sections for each model (Figs. 5-8). One slice is taken at a relatively shallow level (for 190

example in model S1, the shallow-level section was 3.4 cm above the basal plate), 191

and another slice at a deeper level (2.2 cm above the basal plate in model S1). 192

During both phases of shortening, all the models are characterized by a series of 193

box-folds bounded by fore-and back-thrusts formed in the limbs of folds. The models 194

were shortened above a metal base plate with low basal friction (µ = 0.23), which 195

formed a low angle taper wedge (ca. 8-10°). 196

In general, two structural areas are shown in map-view of each model. The first area 197

is located far away from the pushing walls, where the model experienced only one 198

shortening phase, either in the phase-1 or phase-2. In these areas the box-folds in 199

map-view are displayed by parallel bedding on either sides of the structures and 200

repetition of bedding across the structures (e.g. Figs. 5b and 6b). In the rest of the 201

model, superimposition of two phases’ box-folds commonly displays a rectangular 202

geometry. Generally, this rectangular geometry is characterized by bedding curved 203

outwards, which indicates the superimposition of a phase-2 anticline on a phase-1 204

anticline, or a phase-2 syncline on a phase-1 syncline (e.g. Figs. 5c and 7c). The 205

resulted interference pattern belongs to type 1 dome-and-basin structure (Ramsay, 206

1962, 1967). In the same horizontal section, the dome formed by an anticline 207

overprinting an anticline uplifts relatively deep structural level layers, compared with 208

its adjacent basins where the relatively shallow structural level is exposed (e.g. Figs. 209

5c and 7c). For each model, in the shallow horizontal section, a dome structure is 210

relatively wide. However, when the section is cut deeper, the same dome becomes 211

narrower (e.g. Figs. 6c and d). An opposite situation is observed in the basin formed 212

by a syncline on a syncline, where the area of the basin also becomes larger with 213

depth (e.g. Figs. 5 and 6). These changes are strongly controlled by the geometry of 214

box-folds. In other words, in a vertical section the hinge zone of the anticline is 215

narrowing with depth, whereas the syncline becomes wider. 216

This relationship is different when synclines and anticlines superimpose. When a 217

phase-2 anticline overprints a phase-1 syncline and/or a phase-2 syncline overprints 218

a phase-1 anticline, an axial depression forms in the anticline and an axial 219

culmination forms in the syncline (Ramsay, 1962). In such superimposition cases, the 220

resulting geometry displays bedding commonly curved inwards shown by closures of 221

anticlines and synclines (e.g. Figs. 5c, 6c, and 8c). Closures of the anticlines plunge 222

inwards, whereas closures of the synclines plunge outwards. 223

In map-view, the traces of fore-and back-thrusts are located in the limbs of kink folds, 224

and sub-parallel to their axes (Figs. 5-8). Both phase-1 and phase-2 thrusts cut 225

across the rectangular domes and basins (e.g. Figs. 5c and 8c). Since the box-folds 226

(pop-ups) are bounded by conjugate fore-and-back-thrusts in the models, the two 227

superimposed box-folds form a dome structure which is the shared pop-up structures 228

of both phases of folding. In contrast, the basin is the product of the shared pop-229

down structures. The superimposition of these pop-up and pop-down structures 230

dissects the surface of the model into rectangular blocks (Figs. 5-8). However, some 231

of these blocks are the surface expression of superimposition of an anticline 232

overprinting a syncline and/or syncline overprinting an anticline. In these cases, the 233

block is defined by superimposition of a pop-up on a pop-down, or a pop-down on a 234

pop-up (e.g. Figs. 5c and 7c). Several features shown by the models indicate the 235

sequence of two thrusting phases. The traces of the phase-2 thrusts are relatively 236

continuous, and some of them are branching in the superimposed areas (e.g. Figs. 237

5a and 8b). In contrast, the phase-1 thrusts are segmented by the phase-2 structures. 238

Most of these segments are displaced and bent during further shortening. 239

Dimensions of the phase-1 structures (folds and thrusts) change across the phase-2 240

structures. For example, in the eroded hanging wall of a phase-2 thrust, a narrow 241

hinge zone of the phase-1 anticline is shown, and its bounded thrusts in the two 242

limbs are close to each other (e.g. Fig. 5d). However, in the eroded footwall of this 243

phase-2 thrust, the exposed hinge zone of this anticline and the distance between 244

the bounded thrusts are wide. The situation is opposite in the phase-1 syncline 245

overprinted by a phase-2 thrust. A wide hinge zone (trough) of the phase-1 syncline 246

is exposed in the hanging wall of the phase-2 thrust, whereas in the footwall a 247

narrower hinge zone is shown and the bounded thrusts are closer. This situation is 248

governed by the geometry of box-folds and the bounding conjugate fore- and back-249

thrusts, where the hinge zone of the anticline is narrowing with depth, whereas the 250

syncline becomes wider. As such, displacement along the phase-2 thrust uplifts the 251

narrow hinge zones of the phase-1 anticline and relatively wide phase-1 synclines 252

from the originally deep level to the currently shallow level in the hanging wall. After 253

erosion, the phase-1 thrust is apparently offset along the strike of the phase-2 thrust 254

in map-view (e.g. Fig. 5d). 255

3.2 Superimposition with erosion and sedimentation after the phase-1 (model S2) 256

When erosion and sedimentation are included in the model after the first shortening 257

phase, i.e. forming an unconformity, structures display some characteristic 258

differences between shallow and deep horizontal sections (Fig. 6). At very shallow 259

levels, where the unconformity is not exposed yet, only the phase-2 folds and thrusts 260

are shown by the post-erosional sediments. When intermediate levels are exposed, 261

the unconformity boundary clearly separates two structural levels (Fig. 6a). Post-262

erosional sediments which have experienced only the second shortening phase are 263

folded to large synclines bounded by the phase-2 fore-and-back thrusts. In the 264

adjacent areas, structural levels below the unconformity are uplifted by the phase-2 265

of anticlines and their bounded thrusts. Therefore, the superimposed structures are 266

exposed. In these areas, the general trend of the phase-1 folds is easily recognized, 267

which is almost perpendicular to the trend of the phase-2 folds (Fig. 6c). 268

In the much deeper levels, where both the deformed and undeformed post-erosional 269

sediments are not seen anymore, the superimposed structures and the structures 270

from only the phase-1 are shown (Fig. 6b). In this deep level, superimposed folds 271

display map-view geometries similar to those shown in model S1, where orthogonal 272

superimposed shortening occurs without erosion and sedimentation (Fig. 5). The 273

rectangular dome-and-basin structures are shown. The phase-2 thrusts clearly cut 274

and displaced the phase-1 structures. 275

276

4. Centrifuge models (C1 and C2) 277

In the centrifuge models of two mutually orthogonal shortening phases, fold 278

superimposition produces type 1 dome-and-basin interference patterns, and type 2 279

mushroom-shape or arrowhead structure (Figs. 9 and 10) described by Ramsay 280

(1962, 1967). 281

In the centrifuge models, the two phases of shortening produce dome-and-basin 282

structures where folds have rounded hinge zone devoid of thrusts (Figs. 9 and 10). In 283

general, the domes and basins are outlined by outwards curved bedding. The deeper 284

layers are exposed within a dome, while the basins show the relatively shallower 285

layers. In some places, the domes and basins show crescent geometries, which 286

indicate a transition from type 1 to type 2 interference patterns, where the phase-1 287

and phase-2 folds can be distinguished (e.g. Figs. 9c and 10c). 288

In the areas where a phase-2 anticline overprints a phase-1 syncline and/or a phase-289

2 syncline overprints a phase-1 anticline, beddings are commonly curved inwards, 290

and closures of the anticlines plunge inwards while the synclines plunge outwards. 291

This feature is better observed in the phase-1 folds in the centrifuge models. For 292

example, after a phase-1 anticline is overprinted by a phase-2 syncline, the hinge of 293

the anticline is bent by the syncline. Therefore, two closures of the phase-1 anticline 294

are symmetric to the axis of the phase-2 syncline and plunge towards each other (Fig. 295

9c). In the case of the phase-2 anticline overprinting the phase-1 syncline, the two 296

closures of the syncline plunge away from each other (Fig. 10c). 297

298

5. Discussions 299

5.1. Comparison between orthogonal and oblique superimposition 300

Two types of superimpositions were experimented in this study, orthogonal (sandbox 301

models S1 and S2, and centrifuge models C1 and C2) and oblique (sandbox models 302

S3 and S4), respectively (Table 1). Basically, fold interference patterns formed by the 303

orthogonal and oblique superimposition do not have obvious differences. Dome-and-304

basin interference pattern (type1) is characterized by roughly rectangular geometry in 305

sandbox models, and more irregular shapes in the centrifuge models. The 306

rectangular geometry is distorted or apparently sheared in the models with oblique 307

superimposition. However, two phases of orthogonal shortening produce structures 308

trending orthogonally, both fold axial traces and thrusts (Figs. 5-6, and 9-10). This is 309

because the structures tend to be parallel to the mutually perpendicular pushing walls 310

during each phase, even though some curved traces are seen. For example, the 311

phase-1 fold axes are refolded and bent by the phase-2 folding (Fig. 10); trends of 312

the phase-2 structures are curved due to the lateral thickness variation (Figs. 5, for 313

more discussion about lateral thickness variation see later). In contrast, structures 314

formed by oblique superimposition may trend oblique to each other, but in some 315

areas of the model, they still could be approximately mutually perpendicular (Figs. 7-316

8). The latter situation can be clearly observed in model S4, where the phase-2 317

structural traces are parallel to the oblique pushing wall on the right side, thinner part 318

of the model, but gradually change trend to the direction perpendicular to the phase-1 319

structural traces on the left, thicker side and in the frontal part of the model away from 320

the pushing wall (Fig. 8). The reasons for this change in trend of structural traces is 321

possibly that the phase-2 structures advance more forwards on the left side of the 322

model where the sand package is thickened during the phase-1 shortening (Fig. 2). 323

5.2 Reactivation of the phase-1 structure during the oblique phase-2 shortening 324

In this study, oblique superimposition was conducted for two models (S3 and S4), in 325

which the phase-2 shortening was oblique to the trend of the phase-1 structures. As 326

such, reactivation of the phase-1 thrusts is expected to observe during the phase-2. 327

Reactivation of pre-existing structures during subsequential shortening phase has 328

been reported by Soto et al., (2007) who experimented an initial pure strike-slip 329

phase subsequently overprinted by shortening phase that is perpendicular to 330

shearing direction. They documented that a series of Riedel faults from the early pure 331

strike-slip were reactivated as oblique thrusts during the later shortening. 332

In model S3, both lateral- and dip-slip occurred along the thrusts during the first 333

shortening phase, due to the present of the inbuilt triangle backstop (Figs. 1b, 11 a 334

and b). Monitoring of the reference point-pairs show that both dextral- and dip-335

displacement along the thrusts increase with shortening, which indicates 336

transpression of the thrusts during the phase-1. The right triangle backstop makes a 337

45° with the direction of shortening, and results in similar amount of dip- and strike-338

slip movement along the thrusts (Figs. 11 a and b). During the phase-2, the fourteen 339

reference point-pairs that were monitored along the phase-1 structures (comparing 340

initial and final stages) showed relative sinistral- and dip-displacements. In other 341

words, a reversal in strike-slip has occurred from dextral during the phase-1 342

shortening to sinistral during the phase-2 (Figs. 11 c and d). During the second 343

shortening phase, displacement along strike of the thrusts is slightly larger than dip-344

displacement, along either the No.1 or the No.2 phase-1 thrusts. More amount of 345

displacement were measured along the segment of the No.1 phase-1 thrust that is 346

close to the phase-2 backstop (Figs. 4c and d; 11 c and d). However, along the No.2 347

phase-1 thrust, both sinistral- and dip-displacement do not show significant difference 348

along the whole thrust trace. We interpret that the segment of the No.1 phase-1 349

thrust had both large dip- and strike-slip because it is located in the area close to the 350

fixed and pushing boundaries (Figs. 4c and d, the backstops of the phase-1 and 351

phase-2). When the backstop pushed the sand layers forwards during the phase-2, 352

one side of the segment had less space to move forwards. Consequently, more 353

relative displacement has occurred between the two sides of the thrust during its 354

reactivation. 355

A slightly different scenario was observed in model S4 which also had an oblique 356

superimposition. During the second shortening phase, along the structure closest to 357

the deformable boundary, sinistral-slip and extension are observed (Figs. 3e and f; 358

11e). It is noticed that even though extension was measured by monitoring the 359

position of the reference point-pairs, it is not possible to determine whether extension 360

actually occurred along fault surface of the phase-1 structure or that the whole 361

imbricate underwent penetrative extension. Lateral escape towards the deformable 362

boundary during phase-2 deformation resulted in penetrative extension of the 363

imbricate that was close to the deformable boundary (Fig. 2b). The sinistral-slip 364

observed in this part is thus interpreted to be due to this lateral escape. Additionally, 365

the sinistral-slip can be due to the differential propagation of the phase-2 deformation 366

front, further in the thickened hinterland relative to the thinner foreland. In contrast, 367

towards the foreland of the phase-2, where oblique superimposition has occurred, 368

the phase-1 thrusts were reactivated by dextral-slip during the phase-2 shortening 369

(Fig. 11e). 370

Observations of models S3 and S4 indicate that pre-existing structures can be 371

reactivated either in dip direction or along strike during the later phase where 372

shortening direction is oblique to their trend. However, the amount of slip is different 373

in different segments of the thrusts. Along the segments that are relatively close to 374

the fixed boundary, more slip may occur during the reactivation of the thrusts. 375

5.3 Effect of superimposition on structure spacing 376

Experimental investigations indicate that structure spacing mainly depend on the 377

entire thickness of the deformed sand package (Ramsay and Huber, 1987; Marshak 378

and Wilkerson, 1992; Massoli et al., 2006), material properties (Jeng and Huang, 379

2008; Hudleston and Treagus; 2010), and friction along the basement above which 380

the sand package is shortened (Mulugeta, 1988; Liu et al., 1992). In general, 381

structure spacing increases with increasing the bulk thickness of sand package, 382

when deformation occurs above a low basal-friction. 383

In the sandbox models presented here, after the first shortening phase, formation of 384

a sand wedge produces a lateral thickness change (Figs. 4a, c and e). This thickened 385

sand wedge goes under the phase-2 shortening either perpendicular or oblique to the 386

strikes of the phase-1 structures (Figs. 4b, d and f). Therefore, in order to investigate 387

the effect of superimposition on the spacing of the phase-2 structures, the effect of 388

lateral thickness variation on the structure needs to be taken into account. As such, a 389

test model with lateral thickness tapering was run (Fig. 12). In this test model, initial 390

thickness of the sand package changes gradually from 3.5 to 1.3 cm parallel to the 391

pushing wall. This thickness change is comparable to the models, which have 392

undergone one shortening phase and have developed a wedge. These phase-1 393

wedges are usually around 3 cm thick in the hinterland and about 1.5 cm thick in the 394

undeformed foreland. 395

In the test model, thrusts generate from the thinner part, and then propagate laterally 396

into the thicker part with shortening. Traces of the thrusts are roughly continuous 397

from the thinner to the thicker part, which is not the same as the model results by 398

Soto et al, (2003), where much more closely spaced thrusts develop in the thinner 399

model part. Controlled by the thickness tapering, thrusts advance more forwards in 400

the thicker part of the model, and thus strikes of the thrusts are not parallel to the 401

pushing wall, but make an angle to it (Fig. 12). Older thrusts make a smaller angle 402

with the wall (ca. 5°) than the younger thrusts which make a larger angle (ca. 15°) 403

with the wall. Structure spacing also changes along strike from 6 cm where the initial 404

thickness is 1.5 cm, to 13 cm where the initial thickness is 3 cm (Fig. 13a). 405

In the models with two phases of shortening (e.g. model S1), when the initially 1.5 cm 406

thick sand package was shortened during the phase-1, structure spacing in the 407

beginning is similar to that measured in the thin part of the test model and decreased 408

by about 1.0 cm at the final stage (Fig. 13b). During the phase-2 shortening (e.g. 409

models S1 or S3) which is orthogonal or oblique to the direction of the phase-1 410

shortening, thrusts generate with different structural spacing in the thinner and thicker 411

parts. Spacing is larger in areas thickened during the phase-1 shortening, and 412

becomes smaller where such thickening is limited (Figs. 13c, e and f). However, 413

structure spacing in the thickened areas of these superimposed models is less 414

increasing than in the thick part of the test model where no earlier shortening had 415

taken place. In model S2, after eroding the upper part of the phase-1 wedge and 416

depositing new sediments, a uniform thick sand package (3.0 cm) was prepared to 417

be shortened during the phase-2. Structure spacing in this model is slightly smaller 418

than that taken in the test model within the 3.0 cm thick sand (Fig. 13d). 419

Structure spacing also changes with the amount of bulk shortening. In the test model 420

(in the thickest, intermediate and thinnest parts) structure spacing decreases by 1.1-421

1.4 cm from the initial to the final stage of shortening. However, in the superimposed 422

models, the change in structure spacing with shortening is different in the thinner and 423

thicker parts. Generally, the decrease in spacing with shortening is larger in the 424

thinner part than in the thicker part (Figs. 13c, e and f). 425

These analyses show that during two phases of shortening (models S1, S3 and S4), 426

spacing of the phase-2 structures is much less than structure spacing in the test 427

model whose initial thickness was similar to that of the models after the phase-1 428

shortening. This difference may be due to the fact that in the test model, thickness is 429

gradually tapering, whereas in the superimposed models thickness of the model 430

changed laterally in steps due to the formation of the phase-1 imbricates. In the latter 431

case, the thickness changes abruptly across each imbricate. During the second 432

shortening phase, the phase-2 thrusts propagate along strike from the thinner part 433

(phase-1 foreland) into the thicker part (phase-1 hinterland) of the model. The phase-434

2 thrusts are expected to advance more forwards and thus showing increasing 435

structure spacing, as they propagate into thickened hinterland areas. However, due 436

to the presence of the stepped imbricates, there seems to be a mechanical difficulty 437

for the phase-2 thrusts to either gradually propagate across or make a big jump cross 438

the steps of the phase-1 thrusts. As such, the thrusts advance closely to their trace in 439

the thinner parts when they propagate over the steps. Consequently, structure 440

spacing taken in the thicker part of each model is shorter than that in the model 441

where thickness changes gradually along strike than in steps. In model S2, after the 442

phase-1, erosion and sedimentation remove part of the wedge (i.e. topography) and 443

create a flat surface. During the second orthogonal shortening phase, the structure 444

spacing is significantly larger than in the other superimposed models with the phase-445

1 stepped imbricates. Difference of spacing between model S2 and the other models 446

imply that thickness changing in steps across the phase-1 imbricates has a 447

significant effect on spacing of the phase-2 structures. 448

5.4 Type 1 and modified Type 2 interference patterns 449

Fold interference patterns formed in the sandbox models are characterized by 450

rectangular dome-and-basin structures in map-view, i.e. type 1 interference pattern, 451

during orthogonal and/or oblique superimposition of box folds (Figs. 5-8). In theory, 452

each dome is surrounded by four basins, and each basin is surrounded by four 453

domes (Ramsay, 1962; Ramsay and Huber, 1987). The trend of the two phases of 454

folds can be found by joining the culminations of adjacent domes or the depressions 455

of adjacent basins (Ramsay, 1967; Ghosh, et al. 1992). However, Ghosh et al. (1992) 456

also suggested that when the two phases of folds have similar tightness and 457

curvature, the hinge lines of folds of both phases are not easy to recognize over the 458

domes and basins. As shown by model results, in the relatively deep sections fewer 459

layers are visible to display the rectangular geometry of the dome structure (e.g. Figs. 460

6a and d). Consequently, the ‘dome’ structure may disappear, and thus a basin is not 461

always surrounded by four domes (e.g. Figs. 9c and d). In this case, if part of the 462

superimposed structure has been eroded or been overlain by later sedimentation in 463

natural cases, it is more difficult to determine the original fold interference patterns 464

and the trend of each folding phase. 465

Several features for fold superimposition are shown by model results. These might 466

not be diagnostic, but could be helpful to recognize where dome-and-basin 467

interference pattern occurred. Generally, a dome structure that is formed by an 468

anticline superimposed on an existing anticline is characterized by bedding being 469

curved outwards in map-view, and outwards dip directions. Closures of anticlines 470

also plunge outwards (e.g. Figs. 7c, 8c, and 14a). In deep structural levels, this 471

outward curvature of bedding is not so obvious because beds are connected. At 472

these deeper levels the dome is recognized by to the dip directions outwards and 473

closures of the adjacent synclines plunging outwards in all directions (e.g. Fig. 9d). 474

Similarly, where a syncline overprints a syncline to form a basin, bedding is curved 475

outwards in map-view, but dip directions and plunges are inwards (e.g. Figs. 5c and 476

9d). In areas where an anticline overprints a syncline and/or a syncline overprints an 477

anticline, bedding is commonly curved inwards, and the anticline plunges inwards, 478

whereas the syncline plunges outwards. Dip directions are not all inwards or 479

outwards, but indicate two anticline closures in one direction and two syncline 480

closures in another direction (e.g. Figs. 5c, 9c, 10c and 14a). 481

Based on Ramsay’s model (1967), to form the type 2 interference pattern, the early 482

phase of folds usually has an overturned limb before superimposed by the 483

subsequential folding phase. However, some researchers (Watkinson, 1981; Ghosh 484

et al., 1992; Grujic, 1993; Sengupta et al., 2005) have suggested that when the early 485

phase of folds have an initial interlimb angle of less than 90° but are with no 486

overturned limb, type 2 interference pattern could still be formed during buckling 487

superimposition (Fig. 14b). In the centrifuge models, some phase-1 folds have 488

narrow hinge zones, relatively small interlimb angle and steep inclined axial plane but 489

no overturned limb. During the second orthogonal shortening phase, mushroom- or 490

arrowhead-shaped interference pattern was developed in map-view (Figs. 9 and 10). 491

In order to interpret the arrowhead-shaped structures and distinguish this interference 492

pattern from Ramsay’s model (1967), we introduce the modified type 2 interference 493

pattern here (Fig. 14b). In the modified type 2, the phase-1 folds have steeply 494

inclined axial plane and no overturned limb. After phase-2 orthogonal shortening, the 495

phase-1 anticlines and synclines still can be recognized. The arrowhead-shaped 496

structures represent either the superposition of a later anticline on an early anticline 497

or a syncline on an earlier syncline, whereas the neck of the arrow represents that an 498

anticline overprints an earlier syncline or a syncline overprinting an earlier anticline 499

(Figs. 9d, 10c and 14b). For clarifying the modified type 2 interference pattern, we 500

use the case of a later anticline overprinting an earlier anticline-syncline pair as an 501

example (Fig. 14b). The phase-2 anticline overprints the phase-1 anticline to form an 502

asymmetric dome in the shape of an arrowhead. In this arrowhead, in map-view, 503

bedding is curved outwards in faces of the arrowhead and inwards towards the neck 504

of the arrow, where the phase-2 syncline forms. The deformed layers are dipping 505

outwards, and the closures are also plunging outwards in different directions. In 506

contrast, in the neck of the arrow, where the phase-2 anticline overprints a phase-1 507

syncline, bedding is curved inwards in three directions and outwards in the forth 508

direction towards the arrowhead. In this zone, the phase-1 synclines plunge away 509

from each other and are generally mirror symmetric to the phase-2 anticline traces, 510

whereas, the phase-2 anticline and syncline plunge inwards. 511

As Ramsay and Huber (1987) had pointed out, in the typical dome-and-basin 512

interference pattern, the relative timing of the two folding phases is not easy to 513

deduce from geometric criteria alone, i.e. the relatively symmetric dome and basin 514

geometry. However, in many cases the superimposed structures formed by two 515

folding phases display intermediate situation between type 1and type 2 interference 516

patterns in map-view, i.e. more similar to modified type 2. In this case, the relative 517

timing of superimposition could be determined according to the map-view geometry 518

and the characteristics of layer dip and fold plunge. 519

5.5 Superimposition of two hinterlands and forelands 520

During the first shortening phase, the model was thickened by imbrication in the 521

hinterland and its thickness decreased towards the undeformed foreland (Figs. 4a, c 522

and e). The second shortening phase was orthogonal or oblique to the phase-1 and 523

formed its own hinterland and foreland which were superimposed on the phase-1 524

hinterland and foreland (Figs. 4b, d and f). Consequently, different structural regimes 525

were formed and show in map-view. In the area of the phase-2 hinterland 526

overprinting the phase-1 hinterland, highest topography was created and hence, 527

once eroded, the deepest lithologies in the core of the domes were exposed (Figs. 5, 528

6 and 8). On the contrary, the area where the forelands of the two shortening phases 529

superimpose remains undeformed as they are not affected by either of the shortening 530

phases (e.g. Fig. 5b). As a result, the lowest topography is formed in the area, where 531

the forelands of the two shortening phases were superimposed. In some parts of the 532

model, the phase-1 hinterland was not affected by the phase-2 shortening, or the 533

phase-2 structures were formed in the phase-1 foreland. In these two areas, either 534

the phase-1 or the phase-2 structures are seen (Figs. 5, 6 and 8). 535

As such, in a tectonic region with multiple phases of shortening, the relatively deep 536

lithologies and the multidirectional structure trends are exposed in some areas. In 537

contrast, in other places the relatively shallow lithologies can be seen, where 538

probably only one phase of structures is recorded. According to this, the hinterland 539

and foreland of each shortening phase might be determined. 540

541

5.6 Natural examples 542

5.6.1 The Chungnam Basin, Korea 543

Lim and Cho (2012) investigated the Early to Middle Jurassic low-grade metamorphic 544

strata (Nampo Group) in the Chungnam Basin, Korea (Fig. 15). They documented 545

two phases of shortening, roughly orthogonal to each other. In the first shortening 546

phase (Middle Jurassic to early Late Jurassic) the Nampo Group and the 547

Precambrian basement were folded and thrusted towards WNW. Reverse faults and 548

gentle folds, roughly trending E-W, were formed during the second phase which was 549

almost in an N-S direction. The phase-2 folds are north-verging. Lim and Cho (2012) 550

reported dome-and-basin interference pattern to have formed by the superimposed 551

two phases of shortening. 552

Deformation of the Chungnam Basin displays many map-view characteristics 553

(superimposition of folding and thrusting) similar to our model results which have 554

undergone two phases of orthogonal shortening (Figs. 5 and 15). The dome-and-555

basin structures are formed by the phase-2 anticlines overprinting phase-1 anticlines, 556

and phase-2 synclines overprinting phase-1 synclines. In the core of the dome, the 557

older and deeper strata are exposed, whereas the younger and shallower strata are 558

shown in the core of the basins (Figs. 5c vs. 15). Superimposed structures are mainly 559

observed in the central and southern part of the Chungnam Basin. However, the 560

northern part of the area is dominated by the phase-1 structures, even though some 561

effects from the phase-2 are observed (Lim and Cho, 2012). Distribution of different 562

phases of structures may indicate that the central and southern area of the 563

Chungnam Basin experienced superimposition of two hinterlands, which is coincident 564

to the transporting directions in each phase, i.e. WNW towards in the phase-1, and 565

north verging in the phase-2. Strike-slip during the phase-2 was observed in some 566

segments of the phase-1 thrusts, which imply these segments experienced 567

reactivation during the phase-2. In general, the reactivated segments are striking 568

slightly oblique to the shortening direction of the phase-2 (N-S direction). As such, 569

even though the two phases of shortening directions were orthogonal, some 570

segments of the phase-1 thrusts actually have undergone oblique superimposition. 571

This situation is similar to our observations from model S3, where during the phase-2 572

the model was shortened in a direction 45° oblique to the trend of the phase-1 573

structures. These pre-existing structures were reactivated during the second phase of 574

shortening (Figs. 7 and 11a-d). 575

5.6.2 The Central part of the Yanshan Orogenic Belt, North China 576

Another natural example of superposition of shortening is the central part of the 577

Yanshan Orogenic Belt (YOB), North China (Fig. 16). Investigations from many 578

researchers documented that the YOB has been shortened in multiple phases during 579

the Mesozoic (e.g. Davis et al., 2001; Deng et al., 2005; Cope et al., 2007). In the 580

geological map two kilometer-scale superimposed folds are shown in the central part 581

of the YOB, which are called Daheishan and Pingquan superimposed folds, 582

respectively. Our previous studies indicate that these two superimposed folds were 583

formed by two phases of orthogonal shortening, which were inferred to have occurred 584

earlier than Early Jurassic (Deng and Koyi, 2015). The early phase folds are roughly 585

trending NW-SE. They are refolded by later ENE-WSW folding. As a result, 586

arrowhead interference pattern can be seen in map-view (Fig. 16). Several thrusts 587

striking NE to ENE and NW to NNE cut the superimposed folds, which are interpreted 588

to postdate the folding phases. 589

The arrowhead-shaped map-view geometries of the Daheishan and Pingquan 590

superimposed folds are similar to the results of the centrifuge models (Figs. 9c, 10c 591

and 14b). These are interpreted to be modified type 2 interference patern (Ramsay, 592

1962, 1967; Deng and Koyi, 2015). Early NW-SE trending anticlines were overprinted 593

by a later NE-SW trending anticline, forming asymmetric domes. In the dome, 594

bedding is curved outwards, and the folds plunge outwards. The relatively deep and 595

old units are exposed in the core of the domes. In the Pingquan superimposed folds, 596

part of the early phase syncline can still be seen, which is shown by the inwards 597

(northwards) curved bedding and the outwards (southwards) plunging fold axis. This 598

feature indicates the superimposition of an early syncline by a later anticline (Figs. 9c 599

and 14b). In the Daheishan and Pingquan superimposed folds, thrusts were 600

developed later than the two folding phases, which differs from the sandbox models 601

where the box-folds and their bounded thrusts formed together during each 602

shortening phase. However, there are still some lessons we could learn by 603

comparing model results to the map-views of Daheishan and Pingquan 604

superimposed folds. In the sandbox models, because folds and thrusts were formed 605

simultaneously, the thrusts do not cut through the fold interference pattern. For 606

example, the phase-1 thrusts cut the limbs of the phase-1 folds, while the phase-2 607

thrusts cut the limbs of the phase-2 folds and all the early phase structures (e.g. Figs, 608

5c and 8c). However, none of the phase-2 thrusts cut across the hinge zone of the 609

phase-2 folds, and thus the dome-and-basin structures remain intact. In contrast, in 610

the Daheishan superimposed folds, a NE striking thrust (SPF) cuts the hinge zone of 611

the later phase NE-SW trending fold (Fig. 16). In both the Daheishan and Pingquan 612

superimposed folds, the NW striking faults (YSF and LLF) cut through the hinge zone 613

of the early NW-SE trending folds and trace from one limb of the structure to another 614

(Fig. 16). As such, the arrowhead interference patterns are modified by the thrusting. 615

This might be a hint that thrusting is later than formation of fold superimposition. 616

5.6.3 The Mount Isa Inlier, Australia 617

Abu Sharib and Bell (2011) recognized four distinct orogenic phases in the eastern 618

Mount Isa Inlier, Australia. Shortening direction changed from one phase to the next, 619

resulting in formation of folds with different trends (Fig. 17). As such, both orthogonal 620

and oblique superimposition can be seen in this area. In the phase-1, NW-SE 621

trending tight macroscopic folds were formed by NE-SW shortening. In general, the 622

folds are gently southeast plunging. Thrusts formed in the phase-1 were moving 623

towards SW. The phase-2 N-S shortening resulted in a series of micro to 624

macroscopic, E-W trending folds and thrusts verging towards north. This shortening 625

phase caused the pre-existing NW-SE trending phase-1 folds to rotate to E-W trends. 626

The subsequent phase-3 E-W shortening dominated the entire Mount Isa Inlier where 627

foliations are well developed. However, N-S trending regional folds were mainly 628

shown in the southern part of the area. During the phase-4, shortening direction was 629

NW-SE, which locally induced NE-SW trending folds (Abu Sharib and Bell, 2011). 630

As in the models, each phase of shortening did not overprint throughout the entire 631

Mount Isa Inlier area, i.e. folds of each phase formed only in some areas (Figs. 5b, 632

6b and 17). In the southern part, the N-S trending phase-3 folds are dominant, 633

whereas folds from other phases are not observed. As such, folding superimposition 634

between the phase-3 folds and the other phase folds is not seen. In the northern part, 635

three phases of folds are shown. The phase-1 folds are obliquely overprinted and 636

rotated by the second folding phase. They were subsequently refolded by the fourth 637

folding phase, where the first and forth shortening directions were mutually 638

orthogonal. The bent axial traces of the phase-1 folds have similar geometry as that 639

shown by the centrifuge model results (Figs. 9c and 17). Axial traces of the E-W 640

trending phase-2 folds were displaced by an N-S striking fault that has the same 641

trend as the phase-3 folds. It is also shown that the phase-2 folds were overprinted 642

by a later NNE-SSW trending fold that was probably formed during the fourth 643

shortening phase. This oblique superimposition is also responsible for the curved 644

map-view axial traces of the phase-2 folds. 645

646

6. Conclusions 647

Analogue models of two phases of mutually orthogonal or oblique shortening, 648

produce superimposed folding and thrusting. Model results show that in the 649

orthogonal superimposition trends of the later phase structures are roughly 650

orthogonal to those of the pre-existing structures. In the oblique superimposition, the 651

later phase structures may trend oblique to the pre-existing ones in the early phase 652

foreland area, while turn to orthogonally across the pre-existing structures in the 653

thickened hinterland of the first shortening phase. During the later shortening phase, 654

pre-existing phase-1 thrusts are reactivated in dip direction and along strike. Model 655

results show that spacing of the later phase structures is variable: spacing is larger in 656

the phase-1 hinterland (thickened area) and smaller where such thickening is limited 657

(in the foreland). However, the increase in spacing in the hinterland is less than in 658

thick models where no earlier shortening has taken place. 659

Dome-and-basin (type 1) and arrowhead-shaped (modified type 2 here) interference 660

patterns structures are observed in the models. Both in the dome and in the basin 661

structures, bedding is curved outwards in map-view. Layers are dipping and 662

anticlines are plunging outwards in the dome, whereas in the basin bed dip and fold 663

plunge are inwards. In the areas between two adjacent domes or basins, bedding is 664

curved inwards in map-view, while the anticlines plunge inwards and the synclines 665

outwards. Model results show that in the arrowhead-shaped interference pattern, the 666

relative timing of folding superimposition could be determined according to the map-667

view geometry. Early phase folds show the inward curved bedding and outward 668

plunging closures for an early syncline and inward plunging for an early anticline. 669

Model results show that superimposed structures are not necessarily observed 670

everywhere within an area that has suffered two phases of shortening. 671

Superimposition of two hinterlands produces highest topography and shows the 672

superimposed structures and deepest units after erosion. Model results also show 673

that an unconformity between two shortening phases in an area separates different 674

structures. Superimposition is only seen in the layers below the unconformity, 675

whereas in the layers above the unconformity only the later deformation phase 676

structures show. 677

Comparison between model results and natural examples shows that orogenic-scale 678

dome-and-basin, and arrowhead-shaped interference patterns are commonly formed 679

in area undergoing two phases of orthogonal shortening. In natural examples, similar 680

to model results, reactivation of the pre-existing early phase thrusts can be observed. 681

Map-view geometry of fold interference pattern might be modified by later phase 682

thrusting. In a tectonic region, structures might not be developed everywhere during 683

each deformation phase. As such, superimposition of two and/or even more 684

deformation phases may not be seen all over the area. 685

686

Acknowledgements: 687

Hongling Deng is funded by China Scholarship Council (Grant 2010640002) and 688

Swedish Research Council (VR) through Hemin Koyi, and Department of Earth 689

Sciences at Uppsala University for partial salary compensation. Hemin Koyi is funded 690

by the Swedish Research Council (VR). Faramarz Nilfouroushan is funded by 691

Swedish Research Council (VR) through Hemin Koyi. The authors thank Elena 692

Druguet and Marco Bonini for their constructive reviews, comments and suggestions, 693

which helped improving this manuscript, and also thank the editor Ian Alsop for his 694

suggestions and handling the manuscript. 695

696

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851

Figure captions: 852

Table 1. Model summary. Sandbox models S1, S2 and centrifuge models C1 and C2 853

experienced two phases of mutually orthogonal shortening. Sandbox models S3 and 854

S4 simulate two phases of oblique superimposed shortening. 855

Figure 1. a) Schematic drawing of the experimental setup for orthogonal model S1 856

and S2. b) Schematic drawing of the experimental setup for oblique model S3. 857

Figure 2. b) Schematic drawing of the experimental setup for model S4 after the 858

phase-1 shortening. A series of folds and thrusts are formed. b) Schematic drawing 859

of the experimental setup for model S4 during the phase-2 shortening. The inserted 860

wooden backstop is fixed on table and allows the pulled metal plate moving under it. 861

Figure 3. Viscosity vs. strain rate plot for the plasticine and the mixture materials. 862

Measurements were taken under room temparature, T=22℃. 863

Figure 4. Laser scanned images of the topography of the sandbox models. a), c) and 864

e) Topographies of the models after the phase-1 shortening. b), d) and f) 865

Topographies of the models after the phase-2 shortening. 866

Figure 5. Horizontal section of model S1 cut at the shallow a) and deep b) levels, 867

respectively. Two phases of fold and thrust traces are shown. The filled rhombus and 868

triangles represent the phase-1 folds and thrusts, respectively, and the open ones 869

represent the phase-2 structures. The same symbol system is applied to Figures 6-870

10 for distinguishing the phase-1 and phase-2 structures. Two marker layers are 871

highlighted to display the map-view geometry of superimposed structures (the same 872

in Figures 6-8). c) Line drawing showing close-up of details of fold and thrust 873

interference patterns. d) Line drawing showing phase-2 thrusts displacing phase-1 874

structures. 875

Figure 6. Horizontal section of model S2 cut at the shallow a) and deep b) levels, 876

respectively. Orthogonal superimposition occurs with the processes of erosion and 877

sedimentation after the phase-1. Fold and thrust traces are shown. The dashed line 878

shows the unconformity boundary. The dot line indicates the bottom layer of the post-879

erosional deposit. c) and d) Line drawings showing detailed close-up of fold 880

interference patterns and thrusts at the shallow and deep levels, respectively. The 881

insets are turned 90° clockwise. 882

Figure 7. Horizontal section of model S3 cut at the shallow a) and deep b) levels, 883

respectively. Two phases of fold and thrust traces are shown. The inbuilt triangle 884

backstop produces compression and dextral shearing during the phase-1. c) Line 885

drawing showing the detailed close-up of superimposed structures. The inset is 886

turned 45° anticlockwise. 887

Figure 8. Horizontal section of model S4 cut at the shallow a) and deep b) levels, 888

respectively. Two phases of fold and thrust traces are shown. c) Line drawing 889

showing close-up of superimposed structures in detailed. 890

Figure 9. Horizontal sections of the centrifuge model C1 cut at the shallow a) and 891

deep b) levels, respectively. The model was orthogonally shortened in two phases. c) 892

and d) Line drawings showing details of fold interference patterns at the shallow and 893

deep levels, respectively. 894

Figure 10. Horizontal sections of the centrifuge model C2 cut at the shallow a) and 895

deep b) levels, respectively. The model was orthogonally shortened in two phases. c) 896

Line drawings showing details of fold interference patterns. 897

Figure 11. a) and b) Dextral-slip and dip-slip along the phase-1 thrusts increases with 898

shortening in model S3 during the phase-1, respectively. c) Sinistral-slip and dip-slip 899

along the phase-1 thrusts during the phase-2 in model S3, respectively. e) From 900

hinterland to foreland, strike-slip changes from sinistral to dextral direction, extension 901

changes to shortening, which is observed along the phase-1 thrusts in model S4, 902

during the phase-2. 903

Figure 12. a) Laser scanned image of the topography of the test model, showing the 904

thickness tapering along strike. b) Line drawing (from map-view) of the test model. 905

After 29% bulk shortening, three structures were formed. 906

Figure 13. Structure spacing plotted against bulk shortening. Measurements were 907

taken from the topography reference points. a) Structure spacing was measured in 908

the test model with lateral thickness tapering, along the sand thickness of 1.5, 2, 2.5, 909

and 3 cm, respectively. b) Structure spacing was measured in model S1 during the 910

phase-1, along the middle line of the model. c)-f) Structure spacing of the phase-2 911

structures in models S1-S4 during the phase-2. Measurements were taken in 912

different part of the model with different thicknesses. 913

Figure 14. a) Fold interference patterns type 1 proposed by Ramsay (Ramsay, 1962, 914

1967; Ramsay and Huber, 1987). b) Suggested modified type 2, where the early 915

phase of folds have an asymmetric profile with a steeply inclined axial plane, but no 916

overturned limb. Arrows in the map-view sections show the plunges of fold closures. 917

Figure 15. A simplified geological map showing the main trends of structures in the 918

Chungnam Basin, Korea. Inset shows the location of the Chungnam Basin. Two 919

phases of orthogonal shortening induce dome-and-basin fold interference pattern, 920

which is highlighted by dotted-lines (after Lim and Cho, 2012, figures 2 and 9d). 921

Figure 16. Geological map of the central part of the Yanshan Orogenic Belt showing 922

the Daheishan folds and Pingquan folds. Proterozoic strata are shown as 923

stratigarphic Formations. The abbreviations, e.g. Chc, represent the name of the 924

Formation. NC-North China; CDF-Caoniangou-Dajikou fault; LLF-Lijialiangzi fault; 925

SPF- Sangyuan-Pingquan fault; WZF- Wanzhangzi fault; YSF-Yuzhangzi-Shangyuan 926

fault; XSF-Xiadianzi-Shangyuan fault (after HBG-SGSG, 1976). Inset shows the 927

location where the Daheishan folds and Pingquan folds exposed. 928

Figure 17. A simplified geological map showing the main trends of folds in the 929

eastern Mount Isa Inlier. The folding phases are labelled by the letters e.g. F1, F2 etc. 930

Inset shows the location of the eastern Mount Isa Inlier (after Abu Sharib and Bell, 931

2011, figure 1). 932

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Table 1. Model summary

Models Model

numbers Analogue material

Angle between two phases of shortening

direction (°)

Angle between ph2 shortening and trend of

ph1 structure (°)

Bulk shortening in

ph1 (%)

Bulk shortening in

ph2 (%)

Additional information

sandbox

S1 Pure sand 90 90 19 31

S2 Pure sand 90 90 43 20 Erosion and

sedimentation after ph1

S3 Pure sand 90 45 45 19 Inbuilt triangle

backstop in ph1

S4 Pure sand 60 60 45 29 Deformable

sidewalls in ph2

centrifuge

C1 Pure plasticine 90 90 39 30

C2 Mixture (plasticine + silicone putty + barite powder)

90 90 42 39

Table