Analog Models of Fold-and-Thrust Wedges in Progressive Arcs: A Comparison With the Gibraltar Arc External Wedge

Abstract

The timing and kinematics of the different types of structures and the associated vertical-axis rotations that permit an arcuate external wedge to acquire progressively its curved shape throughout its deformation history—known as progressive arcs—are key questions in natural cases of arcuate fold-and-thrust belts that we want to address through analog modeling. We present laboratory models of fold-and-thrust belts formed with a backstop that deforms in map view to simulate progressive arcs in a thin-skinned tectonic regime. Our setup makes use of a deformable backstop rigid enough to push from behind the initial parallelepiped but deformable in map view. This innovative design permits us to increase the amplitude of the arc indenting in the model as its radius of curvature decreases, that is, it simulates a progressive arc. Taking the Gibraltar Arc external wedge situated in the western Mediterranean to scale our models in terms of rheology, velocities, and sizes, four types of experiments were made. We varied the type of substratum (sand or silicone), the silicone thickness, and the width and length of the initial analog pack in order to test the influence of each of these parameters on the resulting fold-and-thrust belts. All experiments led to the formation of arcuate wedges where strain was partitioned into: (a) arc-perpendicular shortening, accommodated by thrusts which main structural trend is broadly subparallel to the indenter shape and with divergent transport directions, and (b) arc-parallel stretching, accommodated by normal and conjugate strike-slip faults. The normal and strike-slip faults contributed to the fold-and-thrust belt segmentation and the formation of independent blocks that rotated clockwise and counterclockwise depending on their position within the progressive arc. Our experiments allow to simulate and understand the finite deformation mode of the external wedge of the Gibraltar Arc. Accordingly, they shed light on how an arcuate fold-and-thrust belt can develop progressively in terms of structural trend and transport directions, types and distribution of the structures accommodating strain partition, and timing of vertical-axis rotations.

Full text

ORIGINAL RESEARCH
published: 31 March 2020
doi: 10.3389/feart.2020.00072
Frontiers in Earth Science | www.frontiersin.org 1March 2020 | Volume 8 | Article 72
Edited by:
Valerio Acocella,
Roma Tre University, Italy
Reviewed by:
Marco Bonini,
Italian National Research Council, Italy
Antonio Casas,
University of Zaragoza, Spain
*Correspondence:
Alejandro Jiménez-Bonilla
ajimbon@upo.es
Specialty section:
This article was submitted to
Structural Geology and Tectonics,
a section of the journal
Frontiers in Earth Science
Received: 10 December 2019
Accepted: 26 February 2020
Published: 31 March 2020
Citation:
Jiménez-Bonilla A, Crespo-Blanc A,
Balanyá JC, Expósito I and
Díaz-Azpiroz M (2020) Analog Models
of Fold-and-Thrust Wedges in
Progressive Arcs: A Comparison With
the Gibraltar Arc External Wedge.
Front. Earth Sci. 8:72.
doi: 10.3389/feart.2020.00072
Analog Models of Fold-and-Thrust
Wedges in Progressive Arcs: A
Comparison With the Gibraltar Arc
External Wedge
Alejandro Jiménez-Bonilla 1
*, Ana Crespo-Blanc 1, Juan C. Balanyá 2,
Inmaculada Expósito 2and Manuel Díaz-Azpiroz 2
1Departamento de Geodinámica-Instituto Andaluz Ciencias de la Tierra, Universidad de Granada-CSIC, Granada, Spain,
2Departamento de Sistemas Físicos, Químicos y Naturales, Universidad Pablo de Olavide, Seville, Spain
The timing and kinematics of the different types of structures and the associated
vertical-axis rotations that permit an arcuate external wedge to acquire progressively
its curved shape throughout its deformation history—known as progressive arcs—are
key questions in natural cases of arcuate fold-and-thrust belts that we want to address
through analog modeling. We present laboratory models of fold-and-thrust belts formed
with a backstop that deforms in map view to simulate progressive arcs in a thin-skinned
tectonic regime. Our setup makes use of a deformable backstop rigid enough to push
from behind the initial parallelepiped but deformable in map view. This innovative design
permits us to increase the amplitude of the arc indenting in the model as its radius
of curvature decreases, that is, it simulates a progressive arc. Taking the Gibraltar Arc
external wedge situated in the western Mediterranean to scale our models in terms of
rheology, velocities, and sizes, four types of experiments were made. We varied the type
of substratum (sand or silicone), the silicone thickness, and the width and length of the
initial analog pack in order to test the influence of each of these parameters on the
resulting fold-and-thrust belts. All experiments led to the formation of arcuate wedges
where strain was partitioned into: (a) arc-perpendicular shortening, accommodated by
thrusts which main structural trend is broadly subparallel to the indenter shape and
with divergent transport directions, and (b) arc-parallel stretching, accommodated by
normal and conjugate strike-slip faults. The normal and strike-slip faults contributed to the
fold-and-thrust belt segmentation and the formation of independent blocks that rotated
clockwise and counterclockwise depending on their position within the progressive arc.
Our experiments allow to simulate and understand the finite deformation mode of the
external wedge of the Gibraltar Arc. Accordingly, they shed light on how an arcuate
fold-and-thrust belt can develop progressively in terms of structural trend and transport
directions, types and distribution of the structures accommodating strain partition, and
timing of vertical-axis rotations.
Keywords: analog model, progressive arc, thin-skinned tectonics, strain partitioning, block rotation, Gibraltar Arc
external wedge

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
INTRODUCTION
The fold-and-thrust belts of orogenic systems that exhibit
map-scale curves are puzzling structures that frequently
generate debate. Among others, key questions are the type
of structures that permit an arcuate fold-and-thrust belt to
acquire progressively its curved shape and the relationships
of these structures—in terms of timing and kinematics—with
the vertical-axis rotations in the different parts of the arcuate
belt (e.g., Marshak, 2004; Weil and Sussman, 2004). Regarding
this question, while primary arcs are characterized by uniform
displacement directions and do not involve significant late
stage vertical-axis rotations, secondary arcs (or oroclines) are
formed by pure bending of an initially straight fold-and-thrust
belt (Eldredge et al., 1985; Hindle and Burkhard, 1999; Weil
et al., 2010). Nevertheless, primary and secondary arcs are
only two end-members of an oversimplified classification. In
fact, most arcuate external fold-and-thrust belts of orogenic
systems acquired their curvature progressively throughout their
deformation history. These are known as progressive arcs, in
which differential vertical-axis rotations along the arc limbs
occur during folding and thrusting (Weil and Sussman, 2004;
Musgrave, 2015).
The best way to quantify vertical-axis rotation in arcuate
fold-and-thrust belts goes hand in hand with paleomagnetic
analysis (e.g., Schwartz and Van der Voo, 1983; Weil et al.,
2012; Johnston et al., 2013; and references therein), but a full
understanding of arc kinematic evolution must be complemented
with other approaches. Among a wide range of methods, analog
modeling is a powerful tool that permits not only to compare
the finite deformation in both natural cases and models but also
to investigate the strain field associated with variations of the
indenter geometry.
Such methodology permits to test the influence of some of
the parameters that control the development of arcuate structural
patterns in external zones. Some of these parameters are: (a) the
variations in thickness of the deforming layers (e.g., Marshak and
Wilkerson, 1992; Calassou et al., 1993; Mitra, 1997; Corrado et al.,
1998; Soto et al., 2002; Storti et al., 2007); (b) the lateral variations
in the rheology of the detachment and/or that of the deforming
layers (Mitra, 1997; Macedo and Marshak, 1999; Cotton and
Koyi, 2000; Schreurs et al., 2001; Bahroudi and Koyi, 2003; Luján
et al., 2003, 2006b; Reiter et al., 2011); (c) the topography of
the foreland (Marques and Cobbold, 2002); (d) the syn-tectonic
sedimentation and/or erosion (Wu et al., 2015); (e) the presence
of obstacles of different shapes and strength and/or previous
structures (Marshak et al., 1992; Dominguez et al., 2000; Duarte
et al., 2011; Ter Borgh et al., 2011); and (f) the shape, velocity,
and motion direction of the indenter (Lu and Malavieille, 1994;
Zweigel, 1998; Macedo and Marshak, 1999; Lickorish et al.,
2002; Marshak, 2004; Crespo-Blanc and González-Sánchez, 2005;
Crespo-Blanc, 2007, 2008; Reiter et al., 2011; Crespo-Blanc et al.,
2012, 2018; Rauch, 2013).
In all these models, the indenter used to generate thin-
skinned, curved fold-and-thrust belts was rigid and maintained
shape and size during the whole experiment. These rigid indenter
models failed to reproduce some conspicuous features observed
in many arcuate fold-and-thrust belts, such as widespread
arc-parallel stretching, thicker wedges in the lateral branches,
or strong vertical rotations, as observed, for example, in the
western Mediterranean arcs (Figure 1A; e.g., Balanyá et al.,
2007 and Crespo-Blanc et al., 2016 for the Gibraltar Arc
and Cifelli et al., 2016 for the Calabrian Arc). So, we
modified the experimental setup by using a backstop that can
progressively deform during the experiment as observed in
western Mediterranean arcs.
As a natural case, we take the Gibraltar Arc external wedge
situated in the westernmost Mediterranean (Figure 1A) in order
to scale the materials, setup, and convergence velocities of
our analog models. We present the results of experiments
with a flexible backstop that deformed in map view while the
experiment progressed. Meanwhile, the deformable backstop
pushed from behind the parallelepiped of analog materials;
the backstop geometry varied from straight to arcuate. The
arc amplitude and length increased, whereas its curvature
ratio diminished. So, these are the first models of progressive
arcs, which simulate natural cases of arcuate fold-and-thrust
belt migrating toward the foreland pushed from behind
by an inner orogenic domain (crystalline internal zones)
in orogenic arc systems associated with back-arc extension
(area increase).
We will focus on several major questions concerning: (a)
how this thin-skinned, arcuate fold-and-thrust belt progressively
acquires its curvature, (b) what factors control its shape
and internal geometry (in particular, the role of strain
partitioning), (c) whether or not deformational structures
passively—or actively—rotate during arc evolution, and (d)
how the geometrical relationships between structures and
displacement vectors evolve with increasing deformation. In our
models, the strain partitioning modes generate highly arcuate
wedges, segmented in blocks that rotated differentially. We will
compare our results with those features observed in the Gibraltar
Arc natural case in terms of deformation sequence, geometry
of the progressive arc external wedge, and timing of vertical-
axis rotations.
THE GIBRALTAR ARC EXTERNAL WEDGE,
A NATURAL CASE OF PROGRESSIVE ARC
FOLD-AND-THRUST BELT
Bearing in mind that our purpose is to model an arcuate
fold-and-thrust belt formed in front of a flexible indenter that
simulates the backstop of a progressive arc, several constraints
extracted from a natural case must be imposed on our laboratory
model setups. We selected the external zones of the Gibraltar
Arc System, the alpine orogenic system formed by the Betic-
Rif mountain chains, which close the western Mediterranean
(Figure 1B). Indeed, its mode of deformation, strain partitioning,
kinematics, timing, and vertical axis-rotations are reasonably
well-known, particularly in its northern branch (see review in
Crespo-Blanc et al., 2016, 2018).
Within this orogenic system, we will zoom on the arcuate fold-
and-thrust belt located in the Western Gibraltar Arc (WGA).
Frontiers in Earth Science | www.frontiersin.org 2March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 1 | (A) Map of the Mediterranean region with a sketch of the structural trend lines of the orogenic arcs. (B) Simplified structural map of the Gibraltar Arc with
structural trend and kinematic vectors (Crespo-Blanc et al., 2016). Representative cross section (cs) of the external wedge (Crespo-Blanc, 2007). (C) Comparison of
the geometry and degree of protrusion of the Carpathian (CarpA), Calabrian (CalA), and Gibraltar (GibA) arcs (reference line: internal–external zone boundary
according to Linzer, 1996; Crespo-Blanc et al., 2016; Gutscher et al., 2017, respectively). (D,E) Simplified tectonic maps of the Calabrian and Carpathian arcs,
respectively, with displacement vectors along thrusts and vertical-axis rotations (see text for references).
Frontiers in Earth Science | www.frontiersin.org 3March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
This arc is defined as the westernmost salient of the Gibraltar
Arc System (west of 4◦30′). Its transition zones to the adjacent
recesses are two strike-slip dominated shear zones (Figure 1B):
the Torcal shear zone in the Betics and the Jebha fault zone in the
Rif (Balanyá et al., 2007, 2012; Barcos et al., 2015).
The key data to constrain our analog model setup are the
following: (1) the chord line length of the WGA measured at
the external–internal zone boundary is around 185 km for an
amplitude of 90 km; accordingly, the WGA degree of protrusion,
that is, the ratio between arc amplitude and chord line (Macedo
and Marshak, 1999) reaches 0.5; (2) the external fold-and-thrust-
belts were pushed from behind by the internal zones, while
the internal–external zone boundary underwent a significant
length increase simultaneous with an area increase of the internal
zones due to back-arc extension (Comas et al., 1999; Balanyá
et al., 2012; Crespo-Blanc et al., 2018); (3) deformation velocities
in the external wedge measured around the arc apex in the
WGA northern branch vary between 0.9 and 1.5 cm/year
(geometry of Luján et al., 2006a combined with timing data
of Crespo-Blanc et al., 2016); (4) the WGA external fold-and-
thrust belt is mainly formed by palaeomargin derived, Mesozoic–
Cenozoic sedimentary covers; (5) in the Betics (WGA northern
branch), 1,300–2,000 m of carbonate sequence overlays 100–
1,000 m of Triassic evaporites (Vera, 2004; Jiménez-Bonilla et al.,
2016), whereas in the Rif (WGA southern branch), a minimum
of 4,000 m of clastic sediments are present (Chalouan et al.,
2008); (6) the structural style of the external wedge in the
northern branch of the Gibraltar Arc corresponds to a fold-and-
thrust belt developed on an evaporitic, viscous substrate (see
representative cross-section in Figure 1B), with pop-up and pop-
down structures separated by large synclines (Crespo-Blanc and
Campos, 2001; Expósito et al., 2012; Crespo-Blanc et al., 2016).
EXPERIMENTAL SETUP
Material Properties
The experiments were performed in the Analog Modeling
Laboratory of the Geodynamics Department-IACT of the
University of Granada-CSIC (Spain). Sand and silicone were
used as analog materials in a natural gravity field to simulate
the brittle, rate-independent behavior of most sedimentary
rocks and the ductile, rate-dependent flow of evaporitic rocks,
respectively (Schellart and Strak, 2016; and references therein).
The quartz sand was dry and rounded, with a grain size
varying between 0.2 and 0.3 mm, a coefficient of internal
friction of 37◦, and a density δbM =1.77 g/cm3(Table 1).
Colored sand provided horizontal passive markers within the
undeformed experimental multilayer. The silicone putty used
in our experiments (transparent Rhodosil Gum FB of Rhone-
Poulenc) is a Newtonian material at experimental strain rates
(10−6s−1), with a density δdM =0.98 g/cm3and a viscosity ηM
=5×104Pa s at room temperature (Table 1;Funiciello et al.,
2003). The initial analog silicone and sand parallelepiped (from
now on, sandpack) was underlain by a Mylar sheet (coefficient
of basal friction 0.43), and its boundaries were confined by sand,
with the exception of the one limited by the indenter.
TABLE 1 | Scaling parameters between natural cases and models.
Parameter Natural
cases (N)
Model (M) Scaling
factor (M/N)
Length (m) 1 ×1035×10−30.5 ×10−5
Density δbrittle
(kg·m−3)
2,400a1,770 0.74
Density
δviscous(kg·m−3)
2,200b980 0.45
Density contrast
δb/δv
1.1 1.8 –
Viscosity η(Pa·s) 1018 to 1021
(5 ×1019)c
5×10410−15
Shortening
velocity in the
arc apex (m·s1)
2.9 ×10−10
to 4.8 ×
10−10
(0.9–1.5
cm/year)d
1.9 and 2.5 ×
10−6
(0.7 and 0.9 cm
h−1)
0.4 ×10−4to
0.86 ×10−4
aBonini (2001).
bWeijermars et al. (1993).
cMukherjee et al. (2010) and Sadeghi et al. (2016), see text.
dCrespo-Blanc (2008), this paper.
Model Setup
The sandbox is schematically illustrated in Figure 2A, and the
terms used in this paper to describe the parts of the experimental
arc are shown in Figure 2B. The innovation of our models comes
from the fact that the curvature of the backstop employed to
deform the sandpack progressively increased. We used a plastic
strip pushed from behind in its apex by a screw attached to
a motor drive. We obliged this strip to go through a 62 cm
wide gate, which represents the chord line of our experimental
arcs. The chord line remained constant, while the amplitude
and perimeter of the arc increased progressively as the limbs
rotated (observe the progressive shape change of the strip in
Figure 2C, from S0 to S3). Consequently, the protrusion degree
of the indenter progressively increased. It must be stressed that
the strip was sufficiently rigid to keep a convex shape and push
the sandpack.
At the beginning of each experiment, the increase of the
protrusion grade took place hand in hand with the decrease
of the backstop curvature ratio (S1 in Figure 2C). When the
apex displacement reached ca. 20 cm, the plastic strip attained its
maximum possible curvature. From that moment, the backstop
moved toward the front similar to a rigid indenter (the protrusion
grade increased, but the curvature ratio at the apex remained
constant). During the whole experiment, the path of selected
points along the indenter displayed a slightly convergent pattern,
particularly in the arc limbs (Figure 2C).
The indenter apex moved at a constant velocity (0.7 or 0.9
cm/h, Table 2). The maximum amplitude reached by the indenter
varies between 20 cm and 40 cm, which corresponds to indenter
degrees of protrusion between 0.32 and 0.65, respectively.
A reference 3 ×3 cm grid was sieved on top of the
sandpack. The progressive deformation was monitored by
time lapse photography of the model surface every 10 min,
and its final geometry was recorded by oblique photographs.
Frontiers in Earth Science | www.frontiersin.org 4March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 2 | (A) Simplified sketch of the experimental apparatus and model setup. (B) Sketch showing the terminology used in the paper. (C) Shape and particle
displacement paths of the deformable indenter for different deformation stages (S1 to S3). (D) Sketch of the measurement of a displacement vector (arrow) between
two successive deformation stages (S1 and S2).
Representative cross sections of the deformed models were
also made. At the end of some of the experiments, the sand
was carefully removed to observe the final 3D geometry of
the silicone.
Scaling
The characteristic values of density (δ), length (l), viscosity
(η), and velocity (v) for both the natural case (subscript N)
and the analog model materials (subscript M), together with
the relative scaling factors of these main physical parameters,
are summarized in Table 1 for natural gravity conditions (gN
=gM=9.81 m/s2). It can be observed that the density
contrast between sedimentary rocks and evaporites in the
natural case is lower than that between sand and silicone
in the models (1.1 vs. 1.8). That means that the buoyancy
of the ductile layer in the model is larger than that in the
natural cases. This limitation is common in sand–silicone analog
experiments, and it has been shown that it does not affect first-
order model results (e.g., Bonini, 2001; Bahroudi and Koyi,
2003; Ferrer et al., 2016; Roma et al., 2018). For the viscous
layer, we used the Hormuz evaporites as reference, with a
viscosity range from 1018 to 1021 Pa s (Mukherjee et al.,
2010; Sadeghi et al., 2016;Table 1). Indeed, the structure of
the Zagros fold-and-thrust belt is similar to that observed
in the external zones of the Gibraltar Arc northern branch
(e.g., Sherkati et al., 2005).
Frontiers in Earth Science | www.frontiersin.org 5March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
TABLE 2 | Model settings.
Experiment
type
Material (rheology) Layer thickness Size of the initial parallelepiped Total
displacement of
the apex
Protrusion
degree of the
indenter
Screw velocity
(cm/h)
1 Sand 1.5 cm (3,000 m) 66 cm ×51 cm (132 km ×102 km) 26.7 cm (54 km) 0.43 10.4 cm/h
2 Sand (brittle)
Silicone (viscous)
1.5 cm (3,000 m)
0.5 cm (1,000 m)
66 cm ×51 cm (132 km ×102 km) 20.0 cm (40 km) 0.32 0.7 cm/h
3 Sand (brittle)
Silicone (viscous)
1.5 cm (3,000 m)
1.0 cm (2,000 m)
66 cm ×51 cm (132 km ×102 km) 21.7 cm (44 km) 0.35 0.9 cm/h
4 Sand (brittle)
Silicone (viscous)
1.5 cm (3,000 m)
0.5 cm (1,000 m)
100 cm ×65 cm (200 km ×130 km) 39–40 cm
(78–80 km)
0.63–0.65 0.9 cm/h
Numbers within brackets: sizes corresponding to natural cases. Width of the gate (arc chord line) through which the plastic stripe went: 62 cm (124 km) for all models.
We set a length ratio (lM/lN) of 0.5 ×10−5(1 cm in the
experiments represents 2,000 m in nature), and with the values
of Table 2, we estimated the shortening velocity of the models
according to Weijermars and Schmeling (1986):
νN−ηM
ηNδN
δM
gN
gM
l2
N
l2
MνM
The variability of the different parameters, in particular the
viscosity range of the natural case, introduces a significant
uncertainty in the calculation of the shortening velocity of the
models, which varies from 0.6 ×10−6to 1.7 ×10−3m s−1,
that is, 0.2 to 612 cm h−1. However, as we had to ensure that the
silicone employed in our analog models behaves as a Newtonian
material, we restricted the shortening velocity to 0.7–0.9 cm h−1
(Luján et al., 2006b; Borderie et al., 2018). With these values of
shortening velocity, we calculated the strain rate of our analog
models as ε=vM/w, where w is the width of the deformable
zone measured in the apex parallel to the shortening direction
(between 51 and 65 cm). The calculated strain rates vary between
3.7 ×10−6s−1and 4.9 ×10−6s−1. Moreover, these velocities
of 0.7–0.9 cm h−1in the models correspond to viscosities in the
natural ductile layers of around 5 ×1019 Pa s (viscosity value
inside the brackets in Table 1).
Tested Parameters: Size and Thicknesses
We tested the influence of the rheological stratification by varying
the thickness of the ductile layer at the bottom of the undeformed
analog pack. After a first round of experiments, we also increased
the size of the models with the double purpose of reducing
the border effects observed in the first experiments as well as
reaching a higher bulk shortening in front of the indenter hinge
zone. Accordingly, we made four types of models (Table 2): (1) a
66 cm ×51 cm initial analog pack built only with a brittle layer
composed of sand (1.5 cm thick); (2 and 3) a 66 cm ×51 cm
initial analog pack floored by a ductile layer of silicone, 0.5 cm
and 1 cm thick, respectively, overlain by a 1.5 cm thick sand layer;
and (4) a 100 cm ×65 cm initial analog pack floored by a 0.5 cm
thick silicone layer overlain by a 1.5 cm thick sand layer. The
dimensions to which these values correspond in a natural case
using a scale factor of 0.5 ×10−5figure into brackets in Table 2.
For all experiments, we used the same gate of 62 cm (chord line,
equivalent to 124 km in a natural case).
Measurement of Displacement Vectors
For all models, displacement vectors along selected thrusts have
been depicted for successive deformation stages. They are drawn
by joining reference points of the selected thrust hanging wall
in successive deformation stages. For example, the displacement
vector along the thrust sketched in Figure 2D corresponds to
the mean direction and total displacement of the hanging-wall
movement from S1stage to S2stage, using a reference point as
near as possible to the thrust. Consequently, the vectors on any
selected structure at a determined Sxstage represent the mean
direction and total displacement of the hanging-wall movement
from that stage and the previous one, that is, from Sx−1to Sx
stage. The corresponding arrows have been drawn with their
origin on the selected thrust, or eventually on the normal fault.
ANALOG MODELING OF PROGRESSIVE
ARCS: RESULTS
Small Sandpack Composed Only by Sand:
Model 1
When a backstop simulating a progressive arc is indented in a
sandpack composed only by sand, a typical piggyback, foreland-
verging thrust system is formed (Figure 3A). These thrusts are
rooted at the bottom of the sandpack and are associated with
accommodation folds. In the line drawing of the final stage of the
experiment, the relative chronology of the structures is shown by
numbering (Figure 3A). Additionally, the complete deformation
sequence can be observed in Supplementary Video 1.
The trend-line pattern displays an arcuate geometry, which
mimics as a whole the indenter shape, although with a slightly
higher degree of protrusion. This is due to the effect of two
conjugate strike-slip faults that extrude a salient at the hinge zone
of the arcuate wedge, defined by the most external thrust (thrust
9, Figure 3A).
The first thrusts formed subparallel to the backstop
boundary (see Supplementary Video 1). Then, the length
of the most external arcuate thrust increased together with
the width of the area affected by shortening. Nevertheless,
when the indenter amplitude reached ∼10 cm, the width
Frontiers in Earth Science | www.frontiersin.org 6March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 3 | Line drawings of experiments with an initial sandpack: (A) Model 1: final stage. The numbering indicates the chronology of the structures. (B) Model 1:
progressive displacement of the frontal thrust (dashed line) for various positions of the indenter (numbers: apex movement) and displacement vectors along this thrust
(arrows). (C,D) idem (B,C), respectively, from a model of Crespo-Blanc and González-Sánchez (2005) with a rigid indenter.
of the deformed wedge in front of the indenter hinge zone
remained relatively constant until the end of the experiment (see
Supplementary Video 1).
At the beginning of the experiment, displacement vectors
were at 90◦to the strike of the new, most external thrust
(arrows in Figure 3B), but as shortening proceeded, this angle
diminished from the arcuate wedge hinge toward both limbs,
from 90◦to ∼65◦, respectively. Accordingly, at the first stage
of the experiment, the displacement vectors directions defined
a range of around 60◦along the arcuate wedge frontal thrust,
whereas this range decreased to only 10◦at the end. The
outward radial transport produced an arc-parallel lengthening
of the grid markers, which was accommodated in the sandpack
by arrays of millimetric-spaced normal faults. Because of
their very small spacing (see photograph of Figure 4A), these
normal faults have been grouped in Figure 3A into single
fault trace.
During the whole experiment, as the indenter curvature
increases, the lateral parts of the wedge and the previously formed
thrusts rotated around vertical axes. At the end of the experiment,
grid markers depict 20–25◦clockwise and counterclockwise
rotations, left and right of the arc apex, respectively (Figure 3A).
Frontiers in Earth Science | www.frontiersin.org 7March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 4 | Photographs of various models. (A) Model 1: millimetrical-spaced normal faults (situated to the right of Fault 7 in Figure 3A). (B) Model 2: Conjugated
strike-slip faults system and small normal faults (situated to the right of Fault 11 in Figure 5B). (C) Cross section in the arc apex zone of Model 3 (location on
Figure 5F).
In Figures 3C,D, for comparison purposes (see discussion),
we present the results of the analog experiment of Crespo-
Blanc and González-Sánchez (2005), which used the same
Model 1 rheology (1.5 cm thick sand layer) and an elliptical,
rigid backstop. The curvature ratio of that backstop is similar
to the minimum reached in our experiments. In the model
of Crespo-Blanc and González-Sánchez (2005), displacement
vectors along the frontal thrusts are slightly divergent (10◦range)
and their directions relatively constant during deformation
(Figure 3D).
Small Sandpack With Silicone Substratum:
Models 2 and 3
Using a constant, 1.5cm thick upper sand layer, two different
experiments were carried out with 0.5 and 1 cm thick lower
silicone layers, respectively. The size of the initial sand–silicone
pack was 66 ×51 cm (Table 2). The deformation sequence
is illustrated by line drawings that compare three different
deformational stages with similar indenter amplitude for both
models (Figure 5, see also Supplementary Videos 2,3). In both
experiments, the deformation was accommodated by thrusts,
backthrusts, and strike-slip faults, all of them rooted within
the silicone, as well as thrust-related folds and normal faults.
Regardless of their initial kinematics, the regime of some of these
faults changed along the experiments. Although the distribution
of these structures is different in both types of experiment,
the final result was a non-cylindrical, segmented, arcuate fold-
and-thrust belt in which apparently undeformed blocks, shown
by undistorted grid, rotated differentially. Moreover, buoyant
silicone locally reached the model surface.
Model 2 (Silicone Thickness: 0.5 cm)
The relative chronology of the structures involved in the
deformed wedge is shown by numbering in Figures 5A–C (see
also Supplementary Video 2). Shortening was accommodated by
a few forethrusts that initiated with a wide spacing and one
small subordinate backthrust (number 8). Due to the difference
in displacement between thrust sheets, four transfer faults
appeared at early stages (faults 4–7 of Figure 5A). They acted
as dextral or sinistral faults, in accordance with their position
with respect to the arc limbs. The transfer faults facilitated the
formation of three blocks (ca. 20 cm wide) that rotated while
deformation proceeded. The central block A underwent little
vertical axis rotation, whereas blocks B and C significantly rotated
counterclockwise and clockwise, respectively. These vertical-axis
block rotations were accompanied by arc-parallel lengthening
of the wedge front. Such lengthening was accommodated
by small normal faults that developed in the hinge zone,
subperpendicular to the structural trend of the arcuate wedge.
Strike-slip faults developed oblique to the wedge trend (faults
10 and 11 of Figures 5B,4B). They acted as conjugate faults to
the early transfer faults and show a slight normal component
of displacement that also contributed to this lengthening. These
structures produced small recesses of the wedge front, in the
sense of Macedo and Marshak (1999).
As deformation proceeded, a new foreland-verging thrust split
block C into two (C1 and C2) and new arc-perpendicular normal
faults and strike-slip faults oblique to the wedge trend developed
(Figures 5B,C). The rotation of blocks was accommodated not
only by these faults but also by the different horizontal heave
along the most frontal thrusts. At the final stage, block B rotated
22◦counterclockwise and block C1 rotated 26◦clockwise (C2 is
Frontiers in Earth Science | www.frontiersin.org 8March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 5 | (A–C) Line drawings of different stages of Model 2 (silicone layer of 0.5 cm). (D–F) Line drawings of different stages of Model 3 (silicone layer of 1 cm). The
numbering indicates the relative chronology of the structures. The apex displacement is indicated for each stage. Arrows: displacement vectors along some thrusts
[drawn between stages (B,C,E,F)]. The length of the arrows represents the magnitude of the displacement with the same scale of the line drawings. Cs, cross section
of Figure 4C.
considered to be influenced by the model border and probably
did not rotate freely), whereas the central block A did not rotate
significantly (Figure 5C). Thrust displacement vectors between
stages B and C were divergent, and their trend varied around 70◦
(see arrows on Figure 5C).
Model 3 (Silicone Thickness: 1.0 cm)
The relative chronology of the structures is illustrated by the
line drawings in Figures 5D–F and Supplementary Video 3.
Apart from several similarities with Model 2, the presence
of a thicker layer of silicone under the sand layer induced
some differences with Model 2: (a) backthrusts occurred more
frequently and, together with forethrusts, defined pop-up and
pop-down structures (see backthrusts 5, 9, 10, and 14 of
Figures 5D–F); (b) two conjugated strike-slip faults formed
in the external part of the arcuate deformed wedge (strike-
slip faults 2 and 8), and they subsequently evolved into
thrusts with a lateral slip component; (c) the size of the
Frontiers in Earth Science | www.frontiersin.org 9March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 6 | Line drawings of Model 4-1 at different stages (S1–S4). The numbering indicates the relative chronology of the structures. The apex displacement is
indicated for each stage. A–E: localization of cross sections of Figure 9.
individual blocks was smaller, and the amount of vertical-
axis rotations increased from the arcuate wedge hinge toward
the limbs (blocks B1 and B2 rotated counterclockwise, 33◦
and 42◦, respectively; blocks C1 and C2 clockwise, 34◦and
35◦, respectively; block A did not rotate; Figure 5F); (d)
buoyant silicone walls and canopies were more widespread
than in Model 2; and (e) deformation reached the frontal
boundary of the initial sand–silicone pack, and the localization
of thrust 13 and associated backthrust 15 are considered as
border effect.
The total displacement of the wedge front, excluding the
faults related to border effect, was similar in both experiments,
but Model 3 generated a narrower thrust wedge than Model 2.
Shortening in the hinge zone of the arcuate wedge was reached
through a rather complex geometry in which two retrovergent
folds developed in the footwall of thrust 1 of Figure 5D (see cross
section in Figure 4C).
Finally, displacement vectors related to thrusts between stages
E and F were divergent and showed a strike range around 60◦,
similar to those in Model 2.
Large Sandpack With Silicone Substratum:
Models 4
In order to reduce the border effects observed in Models
2 and 3, and to reach a higher degree of protrusion, the
initial sand–silicone pack was enlarged up to 100 cm ×65 cm
(Table 2). The silicone and sand thicknesses were 0.5 cm and
1.5 cm, respectively. In order to check their reproducibility, two
experiments were performed with the same initial setting. The
final stage of both experiments, with an indenter degree of
protrusion of 0.6 and ∼40 cm of shortening in front of the arc
apex, was similar in terms of type and evolution of the structures.
Frontiers in Earth Science | www.frontiersin.org 10 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 7 | Line drawings Model 4-2 at different stages (S1–S4). The numbering indicates the relative chronology of the structures. The apex displacement is
indicated for each stage.
In both cases, the result was a segmented, highly arcuate fold-
and-thrust belt, although the distribution of thrusts, backthrusts,
strike-slip, and normal faults was slightly different. This is likely
due to the unavoidable heterogeneities in the preparation of
such large analog models, such as small variation of sand or
silicone thicknesses or different packing of the sand grains when
the sand layers are made even. We will describe the results
pointing out the key aspects of the structures developed in
each model. Line drawings of S1 to S4 deformational stages for
both experiments are illustrated in Figures 6 (Model 4-1) and 7
(Model 4-2), in which the chronology of structures is indicated by
numbering. To facilitate comparison between models, the apex
displacement in S2 corresponds to that of the final deformation
stage of Models 2 and 3 (∼20 cm). The deformation sequence
in Models 4-1 and 4-2 can also be seen in the corresponding
Supplementary Videos 4,5, respectively.
Photographs of these models are shown in Figure 8 (final stage
together with some details of the structures). At the end of the
experiment, systematic cross sections were made in Model 4-1.
Sand in Model 4-2 was carefully removed to observe the viscous
substratum 3D geometry.
Deformation Sequence
At the onset of deformation in both experiments (S1 stage),
the radial outward shortening in the sand–silicone pack was
accommodated by both forelandward and backward thrusts
(thrusts 1, 5, and 6 in Figure 6; thrusts 4 and 8 in Figure 7). In
both models, a thrust mimics the frontal boundary of the pack
and is considered as a border effect (thrust 3).
As deformation proceeded, these thrusts were linked by
transfer zones with a main component of thrusting (e.g., fault
4 in Figure 6) or strike-slip (fault 6 in Figure 7). At this stage,
one or two strike-slip faults appeared, connecting the central part
of the fold-and-thrust belt to the frontal boundary of the sand–
silicone pack (dextral fault 8 in Figure 6 and sinistral faults 5 and
11 in Figure 7).
As shortening increased (S2 stage, with a backstop apex
displacement of ca. 21 cm), the deformation front propagated
toward the foreland with the nucleation of curved thrusts
and backthrusts (faults 11 and 13 in Figure 6; faults 12 and
15 in Figure 7), generating pop-up and pop-down structures.
Meanwhile, ongoing thrusting and tilting of the previous
structures thickened the wedge. Differential displacements of
Frontiers in Earth Science | www.frontiersin.org 11 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 8 | Photographs of Models 4. (A) Oblique photograph of Model 4-2 at its final stage. (B) Millimetrical-spaced normal faults (localized on A). (C) Transpressive
bands at the arc limb (localized on A). (D) Silicone topography of Model 4-2 once the sand is removed at the final stage. (E) Zenithal view of Model 4-1 at the
completion of the experiment. (F) Millimetrical-spaced normal faults (localized on E). (G) Conjugate strike-slip fault systems (localized on E). (H) Silicone outcropping
on the model surface (localized on E).
the thrusts led to the lengthening of the transfer zones
and the vertical-axis rotations of the earlier structures. For
example, between stages S1 and S2, faults 5 (Figure 6) and
4 (Figure 7) rotated 5◦, clockwise and counterclockwise at
the left and right arc limbs, respectively. The kinematics of
some faults changed with further deformation, as in the case
of fault 5, which evolved from a pure strike-slip fault to a
transpressive zone where restraining bends formed (Figure 7).
Along-strike lengthening of the arcuate fold-and-thrust belt
resulted in arc-parallel extension, mainly accommodated by
milli- to centimetric spaced normal faults, mostly oriented
subperpendicular to the indenter boundary. These defined
conjugated systems form graben structures (Figures 6,7,
8B,F). Conjugate strike-slip faults also contributed to arc-
lengthening (e.g., fault 24 in Figure 6 and fault 6 in Figures 7,
8A,E,G). At this stage, different types of structures delineated
discrete blocks that subsequently underwent clockwise or
counterclockwise vertical-axis rotations, depending on their
location relative to the left or right flank of the arcuate
backstop, respectively.
Between stages S2 and S4, shortening was mostly
accommodated either by the previously formed thrusts or
by the development of new arcuate thrusts, subparallel to the
curved indenter boundary (e.g., faults 28 and 30–33 in Figure 6).
At the same time, rotation of early structures proceeded,
sometimes associated with variations in their kinematics (e.g.,
thrusts evolving to transpressive bands; faults 25 and 26 of
Figure 7, photographed in Figure 8C). Buoyant silicone pierced
the sand layer, preferentially along graben structures (Figures 6,
7,8A,E,H).
Relay zones between thrust traces correspond to either relay
deformation zones where grid markers were rotated ca. 5◦(e.g.,
between 28 and 33 in Figure 6) or strike-slip faults that acted
as transfer faults (e.g., fault 26 in Figure 7). Thrusts also formed
along the lateral boundary of the confining sand (border effect).
Final Architecture of the Deformed Wedge
The arcuate fold-and-thrust belts generated in Models 4-1 and
4-2 have complex geometries. They show salients and recesses
and are sharply segmented along-strike (stage S4 of Figures 6,
Frontiers in Earth Science | www.frontiersin.org 12 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 9 | Series of cross sections (A–E) of Model 4-1 (location on Figure 6).
7,8A,E). The deformed wedge is formed by blocks bounded by
different types of structures. These blocks underwent clockwise
or counterclockwise vertical-axis rotations coherent with their
position with respect to the symmetry axis of the indenter. At
the completion of the experiments, the grid marker rotations
diminished progressively from ca. 60–70◦in front of the limbs
of the indenter down to 0◦in front of its apex.
Arc-parallel lengthening was achieved by conjugate strike-
slip and normal faults. Both types of faults played a crucial
role on the along-strike segmentation of the fold-and-thrust
belt (Figures 6–8). The normal faults did not produce any
observable deformation in the silicone layer (Figure 8D) and are
consequently detached at the top of the silicone layer or within
the sand layer.
A series of cross sections from Model 4-1 are illustrated
in Figure 9. The deformed wedge is characterized by
foreland and hinterland-verging thrusts and folds (ca.
7 cm-spaced) rooted within the silicone layer, which
generate pop-up and pop-down structures. The shortening
is maximum in the central part of the model, where a
backthrust overlies not only the pop-down structure itself
but also the following pop-up structure (rear part of cross
section D).
Displacement Vectors Along Selected Structures
Displacement vectors associated with the main structures
at different stages of Models 4-1 and 4-2 are shown in
Figures 10A,B, respectively. Throughout the experiments,
the displacement vectors display a radial pattern swinging
roughly 90◦across the indenter symmetry axis (Figures 10A,B).
It should be noted that some displacement vectors changed
direction with increasing deformation, but they did
not vary as much as the strike of their corresponding
thrusts (irrespective of their vergence). Moreover, as
deformation proceeded, most of structures rotated, but
the direction of their associated displacement vectors
Frontiers in Earth Science | www.frontiersin.org 13 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 10 | Displacement vectors associated with the main structures at the different stages of Models 4-1 (A) and 4-2 (B). The length of the arrows represents the
magnitude of the displacement with the same scale of the line drawings. Black arrows: movement on thrust. Gray arrows: movement on normal fault. Other symbols:
Idem Figures 6,7.
Frontiers in Earth Science | www.frontiersin.org 14 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 11 | (A) Sketch of the paleomagnetical orocline test applied to our models. (B1, B2) Oroclinal test for Model 1 at early and final stages. (C) Oroclinal test for
Model 4-1 at final stage. (D1, D2) Oroclinal test for Model 4-2 at early and final stage. (E,F) Oroclinal test for models of sand and silicone–sand of Crespo-Blanc and
González-Sánchez (2005), respectively.
Frontiers in Earth Science | www.frontiersin.org 15 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
FIGURE 12 | Line drawings of analog models of arcuate fold-and-thrust belts previously published compared with our results. (A–F) Sand models.
(G–M) Silicone–sand models. References on the figure.
did not. Therefore, the relative orientation between
structures and displacement vectors changed over time.
Available displacement vectors along the normal faults that
contributed to arc lengthening were subparallel to the strike of
the indenter.
Orocline Test
The orocline test assesses to what extent vertical-axis rotations
have played a role in the acquisition of an orogen’s curvature.
It is graphically represented by the deflection of a primary,
predeformational linear marker D, from a reference direction
Frontiers in Earth Science | www.frontiersin.org 16 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
Dr, plotted against the deviation between the strike of regional
structures S, and a reference strike Sr (Schwartz and Van der
Voo, 1983; Weil and Sussman, 2004). Such D-Dr vs. S-Sr plots
are represented in Figure 11.
In natural cases, declination of paleomagnetical poles are
used as the primary marker to quantify vertical-axis rigid body
rotations, but others can be used, such as joints or paleocurrent
directions (Weil et al., 2012). Such test can be applied to
the analog models presented in this paper by using the grid
markers as a proxy for paleomagnetical directions (see Costa and
Speranza, 2003).
For the structures, the thrust traces drawn in the final stage
of the experiments were divided into 3 cm-long segments and
their mean orientation was measured. For both parameters, the
E-W direction was used as the reference orientation, that is, the
strike of the indenter in its undeformed stage. Thus, each point
of the plots in Figure 11 represents the angle between the strike
of the selected structure and the E-W direction (S-Sr) vs. the
angle between the initial E-W lines of the grid marker closest to
that structure and the E-W direction (D-Dr angle). If structures
formed obliquely with respect to the E-W reference direction, but
the grid did not rotate, oroclinal test will yield slopes around 0
(Figure 11A), corresponding to ideal primary arcs. By contrast, if
both structures and grid markers rotated equally, slopes around
1 will be obtained, corresponding to ideal oroclinal arc. Slopes
between 0 and 1 have been associated with progressive arcs (Weil
et al., 2012).
This test has been applied to the final stages of sand model
(Model 1) and large, sand–silicone models (Model 4-1 and Model
4-2), in order to test the influence of the presence of viscous
substratum on the formation mechanism of the curved fold-
and-thrust belts generated in our experiments (Figures 11B1,
C,D1). The test was also applied at intermediate stages of Model
1 and Model 4-2 (Figures 11B2,D2). Moreover, for comparison
purposes (see discussion), similar plots were made for two analog
models of Crespo-Blanc and González-Sánchez (2005), with an
elliptical, rigid backstop. One of them consisted of a sandpack
(see Figure 3D), and the second one included a 0.5 cm silicone
layer overlain by a 1.0 cm sand layer (see their Figure 4). These
plots are presented in Figures 11E,F, respectively.
The slopes of the regression line yielded by the orocline tests
for the final stages of our models vary between 0.5 and 0.6
(Figures 11 B1,C,D1). In Model 1 and Model 4-2, the slope
is significantly smaller at intermediate stages (0.3 and 0.4,
respectively; Figures 11B2,D2). In all cases, the linear regression
is well-determined (R2higher than 0.8). It is worth to note
that in the two experiments with a rigid elliptical indenter, the
oroclinal test yields much lower slope values (between 0.2 and
0.3; Figures 11E,F).
DISCUSSION
Kinematics and Deformation Sequence of
Analog Models
As described above, the progressive deformation caused by
a backstop with increasing degree of protrusion and whose
curvature ratio diminished with time indenting in a sand–
silicone parallelepiped led to the formation of highly segmented
arcuate fold-and-thrust belts. In both types of progressive
arc models (with and without a viscous substratum), arc-
perpendicular shortening was accommodated by radial outward
thrusting, while arc-parallel lengthening was achieved by means
of conjugated strike-slip fault systems and normal faults.
Nevertheless, this strain partitioning mode varies significantly
depending on the rheology of the initial analog pack. In the
case of an initial sandpack, the geometry of the resulting
arcuate thrust wedge is relatively simple (Figure 3). This sharply
contrasts with the complex geometry of non-cylindrical thrusts
and independent blocks rotating differentially that developed
over a viscous substratum (Figures 5–7). In the next paragraphs,
we will compare our results with other experiments that
modeled arcuate fold-and-thrust belts with sand and silicone as
analog materials.
Initial Sandpack
In our sandpack model (Model 1), the shortening mode is
similar to the classical modeling of thrust wedges that developed
in front of a straight, rigid indenter (Liu et al., 1992). It is
achieved by foreland-verging thrusts rooted at the bottom of a
sandpack in a piggyback sequence. In map view, the structural
trend line of the final stage of Model 1 displays an arcuate
geometry that mimics as a whole the indenter shape (Figure 3A).
Moreover, a few structures accommodated arc lengthening. The
displacement vectors along the frontal thrust structures are
moderately divergent (Figure 3B).
Arcuate fold-and-thrust belts developed from sandpacks in
front of rigid vertical indenters of different shapes and/or with
a wide range of motion paths have been previously modeled.
The final stages of selected ones are compiled in Figures 12A–F
(this work; Marshak, 1988; Calassou et al., 1993; Zweigel, 1998;
Lickorish et al., 2002; Crespo-Blanc and González-Sánchez,
2005, respectively).
As in Model 1, rigid indenters simulating a primary arc
with a step or with an angular or curved shape create curved
thrust wedges with structural trend mimicking the indenter shape
(Figures 12B–E). Nevertheless, such models differ from our
Model 1 in the following characteristics: (a) the deformation took
place only in front of the indenter (note that to generate folds
and thrusts beyond the leading edge of the indenter, a curved
displacement of the rigid indenter is necessary; Figure 12E);
(b) the lateral boundaries of the deformed wedge are occupied
by slumped areas, such that no thrusts form beyond these
boundaries; (c) the overall transport direction of the thrusts
is broadly parallel to the translation path of the indenter; (d)
no significant arc-parallel lengthening occurred, and (e) the
thrusts formed at early stages underwent only small vertical-axis
rotations, if any.
Initial Sand–Silicone Pack
In our sand–silicone models, the propagation sequence of thrusts
and backthrusts is characteristic of fold-and-thrust wedges
developed over a viscous substratum, as modeled by other
Frontiers in Earth Science | www.frontiersin.org 17 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
authors (e.g., Letouzey et al., 1995; Cotton and Koyi, 2000;
Bahroudi and Koyi, 2003; Luján et al., 2003).
In the map view of our experiments, the deformed wedge
acquired its arcuate geometry from the early stages of the
experiments. The progressive indenter protrusion led to the
formation of independent blocks, bounded by normal and/or
strike-slip faults, which rotate differentially. These highly non-
cylindrical structures together with the vertical-axis rotations
are the identifying characteristics of the resulting fold-and-
thrust belts (Figure 12G). This is favored by the localization of
transpressive and transtensive zones. When compared with the
final stages of selected sand–silicone models with rigid indenters,
this is a striking difference. In the experiments of Lickorish et al.
(2002),Bahroudi and Koyi (2003),Costa and Speranza (2003),
Luján et al. (2003), and Crespo-Blanc and González-Sánchez
(2005) (Figures 12H–M; respectively), the main factor that
controls the curvature of the fold-and–thrust belts, regardless of
the rigid indenter shape, is the geometry of the silicone layer in
the initial analog pack. Moreover, rigid indenters with straight
motion paths generate arcuate fold-and-thrust belts only in front
of the indenter, whereas the lateral deformation zone around the
indenter is very narrow (Figures 12J–M), as in models formed
only by sand. Moreover, in these models with rigid indenter, the
vertical-axis rotations are limited to a dozen degrees, if any (as in
the model of Figures 12J,M).
In our sand–silicone models, we showed that the pattern of
the displacement vectors on particular structures that contribute
to the strain partitioning was rather complex both in space and
time (Figures 5C,F,10A,B). During the deformation sequence,
the transport directions of thrusts and backthrusts were broadly
radial, which contrasts with sand models (Figure 3). Moreover,
several early formed structures progressively rotated, in such a
way that the angle between the displacement vector and the strike
of a particular rotating structure changed with time.
Even with a viscous substrate, it is not possible to generate
a highly segmented arcuate wedge with a rigid indenter that
moves with a straight motion path: a backstop with a variable
protrusion grade and curvature ratio is needed. As such, strongly
divergent displacement vectors in an arcuate fold-and-thrust
wedge represent a solid argument for a progressive arc mode
of formation.
Finally, it must be stressed that in our models, the buoyancy
of the ductile layer is higher than in the natural cases (Table 1),
which should have some influence on the experiment dynamics.
Nevertheless, this behavior is assumed in most of the analog
modeling set for the simulation of deformation in upper crustal
levels (see models of Ferrer et al., 2016; Li and Mitra, 2017;
Borderie et al., 2018; Roma et al., 2018 who used the same analog
materials as in this paper). Moreover, at the beginning of our
experiments, the lateral flow of the silicone was limited, as it was
confined by sand. When deformation proceeds, silicone can flow
toward zones of low-gravity potential and diapirs can eventually
pierce the experiment surface.
Orocline Test Applied to the Analog Models
Concerning the orocline test applied to our models, the test
values fall into the field of the progressive arcs, with slopes
between 0.3 and 0.6 (Figure 11). This was expected, as our
experimental setting included a deformable indenter to model
progressive arcs. Nevertheless, it is remarkable that the test
values increased as the experiments proceeded, approaching to
orocline values (slope =1). Indeed, they varied from 0.3–0.4
to 0.5–0.6, with both types of substratum (sand and silicone).
This is a surprising tendency, as during the late stage of the
experiments, the backstop acted close to a rigid indenter (fixed
apex shape and minor limbs rotation), more similar to a primary
arc. Accordingly, a decrease of the test slopes should be expected.
The increasing “oroclinal component” is also observed when
this test is applied to previous experiments with a rigid indenter
and a sand–silicone pack (Crespo-Blanc and González-Sánchez,
2005). In this case, the obtained values are lower (0.2–0.3) than
those calculated for our experiments, but not equal to zero,
which would represent an ideal primary arc. Consequently, our
results suggest that the absolute values obtained from the orocline
test alone may not be sufficient to distinguish between the
formation modes of orogenic arcs if they are not compared to
other kinematic information. In this sense, the analysis of the
operating strain partitioning modes, and more specifically the
amount and localization of arc-parallel stretching, seems to be a
more useful and efficient approach (Hindle and Burkhard, 1999;
Balanyá et al., 2007).
Comparison Between our Analog Models
of Progressive Arcs, the Gibraltar Arc, and
Other Natural Cases
Our experiments with a silicone layer systematically led to the
formation of arcuate fold-and-thrust belts, which exhibit the
following strain partitioning mode: (a) in cross section, the
structural style is characterized by bivergent thrusts with pop-
up and pop-down structures; (b) in map view, shortening in
the external wedge was accommodated by thrusts with a pattern
that broadly mimics the indenter curvature; (c) the displacement
vectors along the thrusts define a fan, subperpendicular to the
structural trend-line pattern at the hinge zone and oblique at
the limbs; (d) normal and conjugate strike-slip faults, which
accommodated arc-parallel stretching, contributed to the along-
strike segmentation of the deformed wedge in blocks; (e) these
blocks underwent clockwise and counterclockwise vertical-axis
rotations of up to 65◦, coherently with their position in the arc;
and (f) major strike-slip dominated fault zones developed at the
lateral parts of the arc.
The aforementioned strain partitioning mode of our models,
both in cross section and map view, is very similar to that
observed in the external zones of the Western Gibraltar Arc
(Balanyá et al., 2007), which imposed our laboratory model
setups in terms of rheology, convergence velocity around the
progressive arc apex, arc chord line, and amplitude (degree
of protrusion). In Table 3, we compare the main geological
features of the Western Gibraltar Arc external fold-and-thrust
belt of the northern branch with the main characteristics
of our analog models, regarding transport direction, types
and localization of structures, trend-line pattern, vertical-axis
rotations, and size of the rotated blocks. We also include
Frontiers in Earth Science | www.frontiersin.org 18 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
TABLE 3 | Structural characteristics of the external wedge of the Gibraltar Arc system compared with those of our analog models.
Natural case
(Gibraltar Arc
fold-and-thrust belt)a
Rigid elliptical
indenter (sand)b
Model 1 (sand)cModels 2 and 3 (silicone
and sand, small)c
Models 4 (silicone and
sand, large)c
Backstop
protrusion grade
∼0.5 <0.5 0.43 0.32–0.35 0.63–0.65
Thrust transport
directions
Very highly divergent
(direction variation up
to 140◦)
Slightly divergent
(direction variation
of 25◦)
Moderately divergent
(direction variation of 65◦)
Moderately divergent
(direction variation of 65◦)
Very highly divergent
(direction variation up to
130◦)
Structures in the
apex zones
Fold-and-thrust belt.
Normal and strike-slip
fault systems
Fold-and-thrust
belt
Fold-and-thrust belt Fold-and-thrust belt. Normal
and strike-slip fault systems
Fold-and-thrust belt. Normal
and strike-slip fault systems
Structures in the
lateral zones
Fold-and-thrust belt.
Transpressive or
transtensional bands
oblique to the main
trend
No fold-and-thrust
belt. Strike-slip
bands parallel to
the backstop
movement
No fold-and-thrust belt.
Strike-slip bands parallel to
the backstop movement
Fold-and-thrust belt.
Strike-slip faults oblique to
the main trend
Fold-and-thrust belt.
Transpressive or
transtensional bands oblique
to the main trend
Structures
accommodating
arc-parallel
lengthening
Normal and strike-slip
fault systems
Not observed Normal and strike-slip fault
systems
Normal and strike-slip fault
systems
Normal and strike-slip fault
systems
Arc-parallel
lengthening
localization
Apex and laterals – Laterals Mostly laterals Apex and laterals
Structural trend-line
pattern
Discontinuous Continuous Continuous (frontal part) Discontinuous Discontinuous
Maximum rotation
of passive lines
Around 50◦
(paleomagnetic vectors
from 9 Ma onwards)
<10◦Around 25◦Around 25–40◦Around 70◦
Size of rotated
blocks
More than 100 km long No block
individualization
No block individualization Individualization of 3–5
blocks
Individualization of 5–8
blocks
aGeological data from Balanyá et al. (2007),Jiménez-Bonilla et al. (2015, 2016), and Crespo-Blanc et al. (2016).
bCrespo-Blanc and González-Sánchez (2005, first stage of Figure 3C op.cit).
cThis paper.
results from the model with a rigid indenter (Figure 3D)
of Crespo-Blanc and González-Sánchez (2005). It must be
stressed that we zoom on the northern branch of the Gibraltar
Arc external wedge as its structural evolution is much better
known than the southern one, and it is underlaid by a
viscous substrate.
Models 4-1 and 4-2 are those that best fit with the strain
partitioning mode observed in the natural case (Table 3). In
both the models and the natural case study: (1) the transport
direction of thrusts swings significantly (up to 90◦in the model
and 130◦in the natural case study, compare Figures 1B,10);
(2) arc-parallel stretching is accommodated by arc-perpendicular
normal faults (e.g., the intermontane Ronda basin faults in
Figure 1B;Jiménez-Bonilla et al., 2015) and conjugate strike-slip
fault systems that localize cuspate recesses in map view (e.g.,
compare the Gaucín fault shown in Figure 1B with Figures 6,
7;Balanyá et al., 2007; Jiménez-Bonilla et al., 2015, 2016, 2017);
(3) transpressive and transtensive bands developed oblique to
the main trend at the lateral zones of the arcs, and likely
contributed to their protrusion increase (compare the Torcal
Shear Zone or Jebha fault in Figure 1B with Figures 6,7,
8C,G; see also Barcos et al., 2015; Crespo-Blanc et al., 2018);
and (4) independent blocks rotated significantly clockwise or
counterclockwise related to their position at the right or left arc
limbs, respectively.
The horizontal dimensions of independent blocks were 20-
30 cm in the models, which, applying the scaling factor of 0.5
×10–5 (Table 1), corresponds to 40–60 km in nature. This
represents a block size about a half of the arc chord length, which
is broadly the same magnitude of the four blocks described by
Crespo-Blanc et al. (2016) in the Gibraltar Arc System, which
are 100–200 km long (measured along-strike, that is 0.5–1 time
the arc chord length). In the natural case, these blocks rotated
in the same sense as our experiments during the last 9 Ma, and
the maximum amount of rotation of passive lines observed in the
Gibraltar Arc System (53◦in the western Betics block) is similar
to the maximum rotations observed in models with a silicone
layer (Models 2–4). For all these reasons, the development of an
arcuate fold-and-thrust belt such as the Gibraltar Arc external
wedge is likely similar to the models of progressive arc described
in this paper.
Other natural examples of Mediterranean progressive arcs
could have formed in a comparable way in terms of kinematics
and strain partitioning as the Calabrian or the Carpathian
Arcs (Figure 1A). As the Gibraltar Arc, these arcs formed in
convergent systems in which outward radial thrusting is coupled
Frontiers in Earth Science | www.frontiersin.org 19 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
with severe back-arc extension. A significant increase in the
area and perimeter of their internal zones took place while
these latter pushed from behind and intruded progressively
the external fold-and-thrust belts (Horvath and Berkhemer,
1982). Both arcs also show similar chord line lengths measured
at the external–internal zone boundary (ca. 185–290 km) and
degree of protrusion (0.4–0.5) with respect to the Gibraltar Arc
(Figure 1C).
Onshore, the limbs of the emerged Calabrian arc are
composed by the fold-and-thrust belts of the Sicilian
Maghrebides to the southwest and of the Southern Apennines
to the northeast, related to the African and Adriatic continental
margins, respectively. Offshore, in the outer part of the apex zone
of the arc, a submerged accretionary prism developed (Polonia
et al., 2011). Cifelli et al. (2008, 2016) show that blocks ca. 200 km
long rotated clockwise and counterclockwise in the NE and
SW arc limbs, respectively. In the Southern Apennines, these
vertical-axis rotations measured from middle-upper Miocene
can reach 100◦(Patacca et al., 1990; Scheepers and Langereis,
1994; Maffione et al., 2013), having rotated up to 56◦in the last
9 Ma, a similar rotation as the Models 2–4 (Cifelli et al., 2008,
2016;Figure 1D). Moreover, these rotations are accompanied
by normal faulting, associated with arc-parallel stretching and
responsible for the development of several intermontane basins
(Aucelli et al., 2014), which is also observable in Models 2–4.
Nevertheless, it must be stressed that the rheological profile
of the Sicilian-Maghrebides and the Southern Apennines fold-
and-thrust belt of the Calabrian Arc differ from the Gibraltar
Arc. Indeed, neither the fold-and-thrust belt of the Sicilian
Maghrebides nor that of the Southern Apennines detached
over evaporites.
In the same way, in the Carpathian Arc external wedge, the
strike of the folds and thrusts associated with arc-perpendicular
shortening varies ∼125◦, from NW-SE in the northeastern part
of the arc to E-W in the southern one (Linzer, 1996;Figure 1E).
The transport directions along the thrusts fan around the arc
ca. 90◦, that is, a significantly smaller angle than their strike
variation. This differs from the models with silicone layer, but
is similar to the first stages of the sand models (Figure 3C). As
a matter of fact, the basal layer in the external Carpathian Arc
is not composed of evaporites, as reported in the Gibraltar Arc
northern branch, but of lutites, weaker than other sedimentary
rocks although still with a brittle behavior. Major strike-slip shear
zones develop at low angles to the structural trend in the lateral
parts of the Carpathian arc: sinistral wrench faults in the northern
branch (Linzer, 1996) and a large-scale dextral transpressive zone
to the south in which displacement is partitioned into thrust
shear, pure shear distributed deformation, and dextral wrench
shear (Ratschbacher et al., 1993). Finally, Cretaceous to lower
Miocene paleomagnetical declinations reveal severe differential
rotations (more than 90◦) fanning outwards around the entire
Carpathian arc. Zooming in the eastern Carpathian salient, these
rotations are predominantly of dextral sense and reach 60◦,
although they were accomplished during various events from the
very beginning of the arching (Linzer, 1996). In Figure 1E, only
the last vertical axis rotational event has been indicated.
CONCLUSIONS
1. The analog experiments presented here model the progressive
deformation of analog packs in front of an indenter that
moved toward the foreland with an increasing degree of
protrusion and whose curvature ratio diminished with time,
that is, a progressive arc. The experiments led to the formation
of arcuate fold-and-thrust belts in which strain was partitioned
between: (a) arc-perpendicular shortening accommodated
by thrusts with slightly divergent (sand) or approximately
radial outward transport direction (sand–silicone), and (b)
arc-parallel stretching accommodated by both normal and
conjugate strike-slip faults, which would lead, in natural
progressive arcs, to the development of intermontane basins.
Such strain partitioning occurred from the very beginning of
the experiments.
2. In the experiments with a silicone lower layer, normal
and strike-slip faults, developed mainly in the lateral parts
of the arcs, contributed to the along-strike fold-and-thrust
belt segmentation in blocks, resulting in a highly non-
cylindrical arcuate wedge. These blocks suffered clockwise and
counterclockwise rotation (up to 65◦) in the right and left
flanks of the progressive arc, respectively (referenced to the
direction of apex movement). The kinematics of the structures
that separate blocks were complex and varied with time.
By contrast, models that employed only sand generated an
arcuate piggyback forethrust sequence, which was extended
along strike by somewhat evenly distributed normal faults.
3. In fold-and-thrust wedges over a frictional decollement
(sandpack), the tectonic transport associated with thrusting
shows a slightly divergent pattern and is relatively constant
during progressive deformation. By contrast, in the sand–
silicone experiments, the displacement vectors along
particular thrusts display a radial pattern swinging ∼90◦
from one part to the other of the indenter symmetry axis. As
deformation proceeded, most structures rotated clockwise
or counterclockwise and the angle between their strikes and
their displacement vectors changed with time. Hence, the
tectonic regime of some faults significantly changed during
the experiments.
4. Orocline tests applied to our models yielded values that
are consistent with those of progressive arcs. As the degree
of protrusion of the indenter increases, the test values
approached orocline values, even though primary arc values
would have been expected.
5. The strain partitioning mode in our progressive arc models
is similar to that observed in the external zones of
the northern branch of the Gibraltar Arc System in
terms of degree of protrusion, transport directions, types
and localization of the structures, trend-line pattern and
vertical-axis rotations. Other two natural cases of the
Mediterranean arcs that developed during a thin-skinned
regime are similar to our analog models. Although the
natural case studies are more complex due to intrinsic
heterogeneities (e.g., variations of the rheology of the
decollement level, variations in the ratio of competent/weak
Frontiers in Earth Science | www.frontiersin.org 20 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
rock thickness, a.s.o.), analog modeling of progressive arcs
with a deformable backstop in map view can be used to
shed light on the type and kinematics of the structures
that develop during progressive development of arcuate
fold-and-thrust belts.
DATA AVAILABILITY STATEMENT
All datasets generated for this study are included in the
article/Supplementary Material.
AUTHOR CONTRIBUTIONS
AJ-B and AC-B realized the experiments. JB, IE, and MD-A
help to conceived the experiments. All of us participated to the
manuscript redaction.
FUNDING
This study was supported by projects RNM-0451, EST1/00231,
CGL2017-89051-P, PGC2018-100914-B-I00, and UPO 1259543.
SUPPLEMENTARY MATERIAL
The Supplementary Material for this article can be found
online at: https://www.frontiersin.org/articles/10.3389/feart.
2020.00072/full#supplementary-material
Supplementary Video 1 | Small sandpack composed only by sand (Model 1).
Supplementary Video 2 | Small sandpack with silicone substratum (Model 2).
Supplementary Video 3 | Small sandpack with silicone substratum (Model 3).
Supplementary Video 4 | Large sandpack with silicone substratum (Model 4-1).
Supplementary Video 5 | Large sandpack with silicone substratum (Model 4-2).
REFERENCES
Aucelli, P., D’Argenio, B., Della Seta, M., Giano, S. I., and Schiattarella, M.
(2014). Foreword: intermontane basins: quaternary morphoevolution
of Central-Southern Italy. Red. Fis. Acc. Lincei 25, 107–110.
doi: 10.1007/s12210-014-0356-3
Bahroudi, A., and Koyi, H. A. (2003). Effect of spatial distribution of Hormuz salt
on deformation style in the Zagros fold and thrust belt: an analogue modelling
approach. J. Geol. Soc. Lond. 160, 719–733. doi: 10.1144/0016-764902-135
Balanyá, J. C., Crespo-Blanc, A., Díaz Azpiroz, M., Expósito, I., and Luján,
M. (2007). Structural trend line pattern and strain partitioning around the
Gibraltar Arc accretionary wedge: insights as to the mode of orogenic arc
building. Tectonics 26:TC2005. doi: 10.1029/2005TC001932
Balanyá, J. C., Crespo-Blanc, A., Díaz-Azpiroz, M., Expósito, I., Torcal, F., Pérez-
Peña, V., et al. (2012). Arc-parallel vs back-arc extension in the Western
Gibraltar arc: is the Gibraltar forearc still active? Geol. Acta 10, 249–263.
doi: 10.1344/105.000001771
Barcos, L., Balanyá, J. C., Díaz-Azpiroz, M., Expósito, I., and Jiménez-Bonilla,
A. (2015). Kinematics of the Torcal Shear Zone: transpressional tectonics in
a salient-recess transition at the northern Gibraltar Arc. Tectonophysics 663,
62–77. doi: 10.1016/j.tecto.2015.05.002
Bonini, M. (2001). Passive roof thrusting and forelandward fold propagation in
scaled brittle-ductile physical models of thrust wedges. J. Geophys. Res. 106,
2291–2311. doi: 10.1029/2000JB900310
Borderie, S., Graveleau, F., Witt, C., and Vendeville, B. (2018). Impact of an
interbedded viscous décollement on the structural and kinematic coupling in
fold-and-thrust belts: insights from analogue modelling. Tectonophysics 722,
118–137. doi: 10.1016/j.tecto.2017.10.019
Calassou, S., Larroque, C., and Malavieille, J. (1993). Transfer zones of deformation
in thrust wedges: an experimental study. Tectonophysics 221, 325–344.
doi: 10.1016/0040-1951(93)90165-G
Chalouan, A., Michard, A., El Kadiri, K., Negro, F., Frizon de Lamotte, D.,
Soto, J. I., et al. (2008). “The Rif belt,” in Continental Evolution: The Geology
of Morocco.Lecture Notes in Earth Sciences, eds A. Michard, O. Saddiqi,
A. Chalouan, and D. Frizon de Lamotte (Berlin: Springer-Verlag), 116.
doi: 10.1007/978-3-540-77076-3_5
Cifelli, F., Caricchi, C., and Mattei, M. (2016). “Formation of arc-shaped orogenic
belts in the Western and Central Mediterranean: a palaeomagnetic review,” in
Palaeomagnetism in Fold and Thrust Belts: New, eds E. L. Pueyo, F. Cifelli,
A. J. Sussman, and B. Oliva-Urcia (London: Special Publications; Geological
Society), 425. doi: 10.1144/SP425.12
Cifelli, F., Mattei, M., and Porreca, M. (2008). New paleomagnetic data from
Oligocene-upper Miocene sediments in the Rif chain (northern Morocco):
insights on the Neogene tectonic evolution of the Gibraltar arc. J. Geophys. Res.
B: Solid Earth 113:B02104. doi: 10.1029/2007JB005271
Comas, M. C., Platt, J. P., Soto, J. I., and Watts, A. B. (1999). “The origin
and tectonic history of the Alborán basin: insights from Leg 161 results,”
in Proceeding of the Ocean Drilling Program, Scientific Results,Vol. 161,
eds R. Zahn, M. C. Comas, and A. Klaus (College Station, TX), 555–579.
doi: 10.2973/odp.proc.sr.161.262.1999
Corrado, S., Di Bucci, D., Naso, G., and Faccenna, C. (1998). Influence of
palaeogeography on thrust system geometries: an analogue modelling approach
for the Abruzzi-Molise (Italy) case history. Tectonophysics 296, 437–453.
doi: 10.1016/S0040-1951(98)00147-4
Costa, E., and Speranza, F. (2003). Paleomagnetic analysis of curved
thrust belts reproduced by physical models. J. Geodyn. 36, 633–654.
doi: 10.1016/j.jog.2003.08.003
Cotton, J., and Koyi, H. (2000). Modeling of thrust front above
ductile and frictional detachments: application to structures in
the Salt Range and Potwar Plateau, Pakistan. Geol. Soc. Am. Bull.
112–113, 351–363. doi: 10.1130/0016-7606(2000)112<351:MOTFAD>
2.0.CO;2
Crespo-Blanc, A. (2007). Superposed folding and oblique structures in the
paleomargin–derived units of the Central Betics (SW Spain). J. Geol. Soc. Lond.
164, 621–636. doi: 10.1144/0016-76492006-084
Crespo-Blanc, A. (2008). Recess drawn by the internal zone outer boundary
and oblique structures in the paleomargin-derived units (Subbetic domain,
central Betics): an analogue modelling approach. J. Struct. Geol. 30, 65–80.
doi: 10.1016/j.jsg.2007.09.009
Crespo-Blanc, A., Balanyá, J. C., Expósito, I., Luján, M., and Suades, E. (2012).
Crescent-like large scale structures in the external zones of the western
Gibraltar arc (Betic–Rif orogenic wedge). J. Geol. Soc. Lond. 169, 667–679.
doi: 10.1144/jgs2011-115
Crespo-Blanc, A., and Campos, J. (2001). Structure and kinematics of the
South Iberian paleomargin and its relationship with the flysch trough units:
extensional tectonics within the Gibraltar Arc fold-and-thrust belt (western
Betics). J. Struct. Geol. 23, 1615–1630. doi: 10.1016/S0191-8141(01)00012-8
Crespo-Blanc, A., Comas, M., and Balanyá, J. C. (2016). Clues for a
Tortonian reconstruction of the Gibraltar Arc: structural pattern,
deformation diachronism and block rotations. Tectonophysics 683, 308–324.
doi: 10.1016/j.tecto.2016.05.045
Crespo-Blanc, A., and González-Sánchez, A. (2005). Influence of indenter
geometry on arcuate fold-and-thrust wedge: preliminary results of analogue
modeling. Geogaceta 37, 11–14.
Crespo-Blanc, A., Jiménez-Bonilla, A., Balanyá, J. C., Expósito, I., and
Díaz-Azpiroz, M. (2018). Models going through analogue experiments: the
Frontiers in Earth Science | www.frontiersin.org 21 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
Gibraltar Arc System revisited in the light of the External Zones structural
evolution. Revista de la Sociedad Geológica de España 31, 23–51.
Dominguez, S., Malavieille, J., and Lallemand, S. E. (2000). Deformation of
accretionary wedge in response to seamount subduction: insight from sandbox
experiments. Tectonics 19, 182–196. doi: 10.1029/1999TC900055
Duarte, J. C., Rosas, F. M., Terrinha, P., Gutscher, M. A., Malavieille, J., Silva, S.,
et al. (2011). Thrust–wrench interference tectonics in the Gulf of Cadiz (Africa–
Iberia plate boundary in the North-East Atlantic): insights from analogue
models. Marine Geol. 289, 135–149. doi: 10.1016/j.margeo.2011.09.014
Eldredge, S., Bachtadse, V., and van der Voo, R. (1985). Paleomagnetism
and the orocline hypothesis. Tectonophysics 119, 153–179.
doi: 10.1016/0040-1951(85)90037-X
Expósito, I., Balanyá, J. C., Crespo-Blanc, A., Díaz-Azpiroz, M., and Luján, M.
(2012). Overthrust shear folding and contrasting deformation styles in a
multiple decollement setting, Gibraltar Arc external wedge. Tectonophysics
576–577, 86–98. doi: 10.1016/j.tecto.2012.04.018
Ferrer, O., McKaly, K., and Sellier, N. C. (2016). “Influence of fault geometries and
mechanical anisotropies on the growth and inversion of hanging-wall synclinal
basins: insights from sandbox models and natural examples,” in The Geometry
and Growth of Normal Faults, eds C. Childs, R. E. Holdsworth, C. A.-L. Jackson,
T. Manzocchi, J. J. Walsh, and G. Yielding (London: Special Publications;
Geological Society) 439. doi: 10.1144/SP439.8
Funiciello, F., Faccenna, C., Giardini, D., and Regenauer-Lieb, K. (2003). Dynamics
of retreating slabs: 2. Insights from three-dimensional laboratory experiments.
J. Geophys. Res. 108, 1–16. doi: 10.1029/2001JB000896
Gutscher, M.-A., Kopp, H., Krastel, S., Bohrmann, G., Garlan, T., Zaragosi,
S., et al. (2017). Active tectonics of the Calabrian subduction revealed by
new multi-beam bathymetric data and high-resolution seismic profiles in
the Ionian Sea (Central Mediterranean). Earth Planet. Sci. Lett. 461, 61–72.
doi: 10.1016/j.epsl.2016.12.020
Hindle, D., and Burkhard,. M. (1999). Strain, displace¬ment and rotation
associated with the formation of curvature in fold belts: the example of the Jura
Arc. J. Struct. Geol. 21, 1089–1101. doi: 10.1016/S0191-8141(99)00021-8
Horvath, F., and Berkhemer, H. (1982). “Mediterranean backarc basins,” in Alpine
Mediterranean Geodynamics, eds H. Berkhemer and M. Hsü (Washington, DC:
American Geophysics Union), 141–173. doi: 10.1029/GD007p0141
Jiménez-Bonilla, A., Expósito, I., Balanyá, J. C., and Díaz-Azpiroz, M. (2017).
Strain partitioning and relief segmentation in arcuate fold-and-thrust belts:
a case study from the western Betics. J. Iberian Geol. 43, 497–518.
doi: 10.1007/s41513-017-0028-0
Jiménez-Bonilla, A., Expósito, I., Balanyá, J. C., Díaz-Azpiroz, M., and
Barcos, L. (2015). The role of strain partitioning on intermontane basin
inception and isolation, External Western Gibraltar Arc. J. Geodyn. 92, 1–17.
doi: 10.1016/j.jog.2015.09.001
Jiménez-Bonilla, A., Torvela, T., Balanyá, J. C., Expósito, I., and Díaz-
Azpiroz, M. (2016). Changes in dip and frictional properties of the basal
detachment controlling orogenic wedge propagation and frontal collapse: the
external central betics case. Tectonics 35, 3028–3049. doi: 10.1002/2016TC0
04196
Johnston, S. T., Weil, A. B., and Gutiérrez-Alonso, G. (2013). Oroclines: thick and
thin. Geol. Soc. Am. Bull. 125, 643–663. doi: 10.1130/B30765.1
Letouzey, J., Colletta, B., Vially, R., and Chermette, J. C. (1995). “Evolution of
salt related structures in compressional setting,” in Salt Tectonics: A Global
Perspective, eds M. P. A. Jackson, D. G. Roberts, and S. Snelson (Tulsa: AAPG
Mem), 65, 41–60. doi: 10.1306/M65604C3
Li, J., and Mitra, S. (2017). Geometry and evolution of fold-thrust structures at
the boundaries between frictional and ductile detachments. Mar. Pet. Geol. 85,
16–34. doi: 10.1016/j.marpetgeo.2017.04.011
Lickorish, W. H., Ford, M., Bürgisser, J., and Cobbold, P. (2002). Arcuate thrust
systems produced by sand-box modelling: a comparison to the external arc of
the Western Alps. Geol. Soc. Am. Bull. 114, 1089–1107.
Linzer, H. G. (1996). Kinematics of Retreating Subduction along the
Carpathian Arc, Romania. Geology 24, 167–170. doi: 10.1130/0091-
7613(1996)024<0167:KORSAT>2.3.CO;2
Liu, H., McClay, K. R., and Powell, D. (1992). “Physical models of thrust
wedges,” in Thrust Tectonics, ed K. R. McClay (London, UK; New
York, NY; Tokyo; Melbourne, VIC; Madras: Chapman and Hall), 71–81.
doi: 10.1007/978-94-011-3066-0_6
Lu, C. Y., and Malavieille, J. (1994). Oblique convergence, indentation and
rotation tectonics in the Taiwan Mountain Belt: insights from experimental
modelling. Earth Planet. Sci. Lett. 121, 477–494. doi: 10.1016/0012-821X(94)
90085-X
Luján, M., Crespo-Blanc, A., and Balanyá, J. C. (2006a). The Flysch Trough thrust
imbricate (Betic Cordillera): a key element of the Gibraltar Arc orogenic wedge.
Tectonics 25, 1–17. doi: 10.1029/2005TC001910
Luján, M., Storti, F., Balanyá, J. C., Crespo-Blanc, A., and Rossetti, F.
(2003). Role of décollement material with different rheological properties
in the structure of the Aljibe thrust imbricate (Flysch Trough, Gibraltar
Arc): an analogue modelling approach. J. Struct. Geol. 25, 867–881.
doi: 10.1016/S0191-8141(02)00087-1
Luján, M., Storti, F., Rossetti, F., and Crespo-Blanc, A. (2006b). Extrusion vs.
accretion at the frictional-viscous décollement transition in experimental
thrust wedges: the role of convergence velocity. Terra Nova 18, 241–247.
doi: 10.1111/j.1365-3121.2006.00685.x
Macedo, J., and Marshak, S. (1999). Controls on the geometry of
fold-thrust belt salients. Geol. Soc. Am. Bull. 111, 1808–1822.
doi: 10.1130/0016-7606(1999)111<1808:COTGOF>2.3.CO;2
Maffione, M., Speranza, F., Cascella, A., Longhitano, S. G., and Chiarella, D. (2013).
A 125◦post-early Serravallian counterclockwise rotation of the Gorgoglione
Formation (Southern Apennines, Italy): new constraints for the formation of
the Calabrian Arc. Tectonophysics 590, 24–37. doi: 10.1016/j.tecto.2013.01.005
Marques, F. O., and Cobbold, P. R. (2002). Topography as a major factor in
the development of arcuate thrust belts: insights from sandbox experiments.
Tectonophysics 348, 247–268. doi: 10.1016/S0040-1951(02)00077-X
Marshak, S. (1988). Kinematics of orocline and arc formation in thin-skinned
orogens. Tectonics 7, 73–86. doi: 10.1029/TC007i001p00073
Marshak, S. (2004). “Salients, recesses, arcs, oroclines, and syntaxes; a review of
ideas concerning the formation of map-view curves in fold-thrust belts,” in
Thrust Tectonics and Hydrocarbon Systems, ed K. R. McClay (AAPG Memoir)
82, 131–156.
Marshak, S., and Wilkerson, M. S. (1992). Effect of overburden thickness
on thrust belt geometry and development. Tectonics 11, 560–566.
doi: 10.1029/92TC00175
Marshak, S., Wilkerson, M. S., and Hsui, A. T. (1992). “Generation of curved
fold–thrust belts: insight from simple physical and analytical models,” in
Thrust Tectonics, ed K. R. McClay (London: Chapman and Hall), 83–92.
doi: 10.1007/978-94-011-3066-0_7
Mitra, G. (1997). “Evolution of salients in a fold-and-thrust belt: the effects of
sedimentary basin geometry, strain distribution and critical taper,” in Evolution
of Geological Structures in Micro- to Macroscales. ed S. Sengupta (London:
Chapman & Hall), 59–90. doi: 10.1007/978-94-011-5870-1_5
Mukherjee, S., Talbot, C. J., and Koyi, H. (2010). Viscosity estimates of salt in the
Hormuz and Namakdan salt diapirs, Persian Gulf. Geol. Mag. 147, 297–507.
doi: 10.1017/S001675680999077X
Musgrave, R. J. (2015). Oroclines in Tasmanides. J. Struct. Geol. 80, 72–98.
doi: 10.1016/j.jsg.2015.08.010
Patacca, E., Sartori, R., and, Scandone, P. (1990). Tyrrhenian Basin and appeninic
Arcs: kinematic relations since late tortonian times. Mem. Soc. Geol. Ital.
45, 425–451.
Polonia, A., Torelli, L., Mussoni, P., Gasperini, L., Artoni, A., and Klaeschen, D.
(2011). The Calabrian Arc subduction complex in the Ionian Sea: regional
architecture, active deformation, and seismic hazard. Tectonics 30:5018.
doi: 10.1029/2010TC002821
Ratschbacher, L., Frisch, W., and Linzer, H. G. (1993). The Pieniny
Klippen Belt in the Western Carpathians of northeastern Slovakia,
structural evidence for transpression. Tectonophysics 226, 471–483.
doi: 10.1016/0040-1951(93)90133-5
Rauch, M. (2013). The oligocene–miocene tectonic evolution of the northern
outer carpathian fold-and-thrust belt: insights from compression-and-
rotation analogue modelling experiments. Geol. Mag. 150, 1062–1084.
doi: 10.1017/S0016756813000320
Reiter, K., Kukowski, N., and Ratschbacher, L. (2011). The interaction of two
indenters in analogue experiments and implications for curved fold-and-thrust
belts. Earth Planet. Sci. Lett. 302, 132–146. doi: 10.1016/j.epsl.2010.12.002
Roma, M., Ferrer, O., Roca, E., Pla, O., Escosa, O., and Butillé, M. (2018).
Formation and inversion of salt detached ramp-syncline basins. Results
Frontiers in Earth Science | www.frontiersin.org 22 March 2020 | Volume 8 | Article 72

Jiménez-Bonilla et al. Analog Models of Progressive Arcs
from analog modeling and application to the Columbrets Basin (Western
Mediterranean). Tectonophysics 745, 214–228. doi: 10.1016/j.tecto.2018.08.012
Sadeghi, S., Storti, F., Yassaghi, A., Nestola, Y., and Cavozzi, C. (2016).
Experimental deformation partitioning in obliquely converging orogens with
lateral variations of basal décollement rheology: Inferences for NW Zagros,
Iran. Tectonophysics 693, 223–238. doi: 10.1016/j.tecto.2016.05.014
Scheepers, P. J. J., and Langereis, C. G. (1994). Magnetic fabric of the Pleistocene
clays from the Tyrrhenian arc: a magnetic lineation induced in the final
stage of the middle Pleistocene compressive event. Tectonics 13, 1190–1200.
doi: 10.1029/94TC00221
Schellart, W., and Strak, V. (2016). A review of analogue modelling of
geodynamic processes: approaches, scaling, materials and quantification,
with an application to subduction experiments. J. Geodyn. 100, 7–32.
doi: 10.1016/j.jog.2016.03.009
Schreurs, G., Haenni, R., and Vock, P. (2001). Four-dimensional analysis of analog
models; experiments on transfer zones in fold and thrust belts. Mem. Geol. Soc.
Am. 193, 179–190. doi: 10.1130/0-8137-1193-2.179
Schwartz, S. Y., and Van der Voo, R. (1983). Palaeomagnetic evaluation of the
orocline hypothesis in the central and southern Appalachians. Geophys. Res.
Lett. 10, 505–508. doi: 10.1029/GL010i007p00505
Sherkati, S., Molinaro, M., Frizon de Lamotte, D., and Letouzey, J. (2005).
Detachment folding in the Central and Eastern Zagros fold-belt (Iran): salt
mobility, multiple detachments and late basement control. J. Struct. Geol. 27,
1680–1696. doi: 10.1016/j.jsg.2005.05.010
Soto, R., Casas, A. M., Storti, F., and Faccenna, C. (2002). Role of lateral
thickness variations on the development of oblique structures at the Western
end of the South Pyrenean Central Unit. Tectonophysics 350, 215–235.
doi: 10.1016/S0040-1951(02)00116-6
Storti, F., Soto Marín, R., Rossetti, F., and Casas Sainz, A. M. (2007). Evolution
of experimental thrust wedges accreted from along-strike tapered, silicone-
floored multilayers. J. Geol. Soc. 164, 73–85. doi: 10.1144/0016-764920
05-186
Ter Borgh, M. M., Oldenhuis, R., Biermann, C., Smit, J. H. W., and Sokoutis, D.
(2011). The effects of basement ramps on deformation of the Prebetics (Spain):
a combined field and analogue modelling study. Tectonophysics 502, 62–74.
doi: 10.1016/j.tecto.2010.04.013
Vera, J. A. (Eds.) (2004). Geología de España. Madrid: Sociedad Geológica de
España; Instituto Geológico y Minero de España.
Weijermars, R., Jackson, M. P. A., and Vendeville, B. (1993). Rheological
and tectonic modeling of salt provinces. Tectonophysics 217, 143–174.
doi: 10.1016/0040-1951(93)90208-2
Weijermars, R., and Schmeling, H. (1986). Scaling of Newtonian and non-
Newtonian fluid dynamics without inertia for quantitative modelling of rock
flow due to gravity (including the concept of rheological similarity). Phys. Earth
Planet. In. 43, 316–330. doi: 10.1016/0031-9201(86)90021-X
Weil, A., Gutiérrez-Alonso, G., Johnston, S. T., and Pastor-Galán, D. (2012).
Kinematic constraints on buckling a lithospheric-scale orocline along the
northern margin of Gondwana: a geologic synthesis: Tectonophysics 582, 25–49.
doi: 10.1016/j.tecto.2012.10.006
Weil, A. B., and Sussman, A. J. (2004). Classifying curved orogens based on timing
relationships between structural development and vertical-axis rotations. Geol.
Soc. Am. 383, 1–15. doi: 10.1130/0-8137-2383-3(2004)383[1:CCOBOT]2.0.
CO;2
Weil, A. B., Yonkee, A., and Sussman, A. (2010). Reconstructing the
kinematic evolution of curved mountain belts: internal strain patterns in the
Wyoming Salient, Sevier thrust belt, U.S.A. Geol. Soc. Am. Bull. 122, 3–23.
doi: 10.1130/B26483.1
Wu, J., McClay, K., and Frankowicz, E. (2015). Niger Delta gravity-driven
deformation above the relict Chain and Charcot oceanic fracture zones, Gulf
of Guinea: insights from analogue models. Mar. Petrol. Geol. 65, 43–62.
doi: 10.1016/j.marpetgeo.2015.03.008
Zweigel, P. (1998). Arcuate accretionary wedge formation at convex plate margin
corners: results of sandbox analogue experiments. J. Struct. Geol. 20, 1597–1609.
doi: 10.1016/S0191-8141(98)00052-2
Conflict of Interest: The authors declare that the research was conducted in the
absence of any commercial or financial relationships that could be construed as a
potential conflict of interest.
Copyright © 2020 Jiménez-Bonilla, Crespo-Blanc, Balanyá, Expósito and Díaz-
Azpiroz. This is an open-access article distributed under the terms of the Creative
Commons Attribution License (CC BY). The use, distribution or reproduction in
other forums is permitted, provided the original author(s) and the copyright owner(s)
are credited and that the original publication in this journal is cited, in accordance
with accepted academic practice. No use, distribution or reproduction is permitted
which does not comply with these terms.
Frontiers in Earth Science | www.frontiersin.org 23 March 2020 | Volume 8 | Article 72