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\begin{document}

\title{Magnetic Fabric Signature within a Thrust Imbricate; an analogue
modelling approach}



\author[1]{Thorben Schöfisch}%
\author[1]{Hemin A. Koyi}%
\author[2]{Bjarne Almqvist}%
\affil[1]{Uppsala University}%
\affil[2]{Uppsala Universitet}%


\vspace{-1em}



  
  \date{June 07, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
In this study, we report results from three analogue models with similar
initial setup and different amounts of bulk shortening, to simulate a
development of a pop-up structure in fold-and-thrust belts at different
stages. Samples are taken in different places of the deformed models for
analysis using anisotropy of magnetic susceptibility. Shortening of the
models resulted in the formation of a pop-up structure, which is bounded
by backthrust(s) and complex forekink zone(s). Several forethrusts at
different degrees of maturity developed in front of the pop-up
structure. Three distinct types of magnetic fabric can be identified
throughout the models: (i) a compactional oblate fabric that changes as
function of distance towards a localized deformation zone (e.g., thrust
or kinkzone), (ii) a thrust-induced fabric with magnetic foliation
parallel to the thrust surface, and (iii) a complex forekink zone fabric
with broad girdle distributions of principal axes and magnetic lineation
perpendicular to shortening direction. The latter indicate interplay
between folding and thrusting of the shortened sand layers.
Additionally, a decrease in degree of anisotropy with appearance of a
quantitatively more prolate fabric can be observed towards the thrusts
and kinkzones. Additionally at thrusts, a variation in strain is
reflected by the magnetic fabric and can be inherited in a
thrust-induced fabric. In conclusion, strain is changing as function of
distance towards localized deformation zones with characteristic fabric,
and differences in magnetic fabric are distinct between data away and
within deformation zones as deformation zones mature.%
\end{abstract}%



\sloppy


\textbf{Magnetic Fabric Signature within a Thrust Imbricate; an analogue
modelling approach}

T. Sch\selectlanguage{ngerman}öfisch\textsuperscript{1}, H. Koyi\textsuperscript{1*} , and B.
Almqvist\textsuperscript{1}

\textsuperscript{1}Hans Ramberg Tectonic Laboratory, Department of Earth
Sciences, Uppsala University, Villavägen 16, 752 36 Uppsala, Sweden.

Corresponding author: Thorben Schöfisch (thorben.schofisch@geo.uu.se)

*current address: Department of Earth Sciences, Khalifa University of
Science and Technology, Abu Dhabi, United Arab Emirates

Key Points:

\begin{itemize}
\tightlist
\item
  Anisotropy of magnetic susceptibility as strain indicator within three
  analogue models simulating a development of a pop-up structure
\item
  Characteristic sets of magnetic fabric are developed for each
  structure in the models, which reveal deformation in more detail
\item
  Gradients in changes in magnetic fabric are recognized as function of
  distance towards a thrust or kinkzone
\end{itemize}

Abstract

In this study, we report results from three analogue models with similar
initial setup and different amounts of bulk shortening, to simulate a
development of a pop-up structure in fold-and-thrust belts at different
stages. Samples are taken in different places of the deformed models for
analysis using anisotropy of magnetic susceptibility. Shortening of the
models resulted in the formation of a pop-up structure, which is bounded
by backthrust(s) and complex forekink zone(s). Several forethrusts at
different degrees of maturity developed in front of the pop-up
structure. Three distinct types of magnetic fabric can be identified
throughout the models: (i) a compactional oblate fabric that changes as
function of distance towards a localized deformation zone (e.g., thrust
or kinkzone), (ii) a thrust-induced fabric with magnetic foliation
parallel to the thrust surface, and (iii) a complex forekink zone fabric
with broad girdle distributions of principal axes and magnetic lineation
perpendicular to shortening direction. The latter indicate interplay
between folding and thrusting of the shortened sand layers.
Additionally, a decrease in degree of anisotropy with appearance of a
quantitatively more prolate fabric can be observed towards the thrusts
and kinkzones. Additionally at thrusts, a variation in strain is
reflected by the magnetic fabric and can be inherited in a
thrust-induced fabric. In conclusion, strain is changing as function of
distance towards localized deformation zones with characteristic fabric,
and differences in magnetic fabric are distinct between data away and
within deformation zones as deformation zones mature.

\textbf{Plain Language Summary}

Deformation within fold-and-thrust belts occurs as thrusting
(displacement along weak zones), folding (bending of rock units) and
internal deformation. The internal deformation, like compaction and
grain realignment, is hard to analyze by the naked eye. Fortunately, the
magnetic properties of grains can be measured and provide information of
grain realignment within an imbricate. In this study, we combine
analogue modelling with magnetic analysis to track the internal
deformation of imbricates in detail. We modelled imbricates and analyzed
the magnetic fabric within the models. Our observations show a gradual
change in magnetic fabric within an imbricate towards thrusts and
kinkzones, which bound the imbricate, showing increasing deformation. At
the thrusts, the magnetic fabric aligns parallel to the thrust surface,
whereas in the kinkzone a complex interplay between folding and
thrusting is revealed. Our results can be compared to natural examples,
as observation from models and published natural analogies are
comparable. Our study provides insights into the strain distribution and
gradients within imbricates.

1 Introduction

Three main components take up deformation in fold-and-thrust belts
(FTBs); layer-parallel shortening (LPS), folding and faulting. In FTBs,
most structures like thrusts and folds can be mapped and analyzed with
different techniques by their optical appearance (e.g., Ramsay and
Huber, 1983). However, in the absence of strain markers, penetrative
strain (i.e., layer-parallel shortening), which is not always easy to
quantify in the field, can also be quantified by focusing on an
intrinsic property of the rocks, i.e., their magnetic susceptibility.
The anisotropy of magnetic susceptibility (AMS) has proven to be a
useful tool to study strain in different tectonic regimes and
lithologies (e.g., Graham, 1966; Hrouda, 1982; Averbuch et al., 1992;
Borradaile and Henry, 1997; Bakhtari et al., 1998; Saint-Bezar et
al.,2002; Borradaile and Jackson, 2010; Ferré et al., 2014; Parés,
2015).

Quantifying penetrative strain in fold-thrust belts is not always
possible due to lack of strain markers and outcrops and difficulty of
accessing deeper levels. However, in analogue models, where initial and
subsequent deformation stages are well documented and different parts
are accessible, strain partitioning in model FTBs and accretionary
wedges can be quantified, which assists in interpreting field
observations and the development of FTBs (e.g., Davis et al., 1983;
Dahlen et al., 1984; Mulugeta, 1988; Mulugeta and Koyi, 1992; Liu et
al., 1992; Koyi, 1995; Gutscher et al., 1996; Storti et al., 2000; Koyi
et al., 2003; Sans et al., 2003; Adam et al., 2005; Graveleau et al.,
2012; Dotare et al., 2016). It has been reported that in most of the
model studies simulating FTBs, the granular material (simulating
sedimentary rocks) is compacted, and the deformation front propagates
from the backstop towards the foreland of the model. Shear bands precede
thrust initiation (Dotare et al., 2016) and with further shortening
thrusts act as ramps (e.g., Suppe, 1983) where strain is refracted into
the hangingwall (Maillot and Leroy, 2003; Maillot and Koyi, 2006; Koyi
and Maillot, 2007). Imbricates between the thrusts deform internally
(Koyi, 1995) and overall strain varies both with time and depth
(Mulugeta and Koyi, 1992; Koyi et al., 2003). To monitor and quantify
penetrative deformation in analogue models, passive markers printed on
the surface of the models are monitored by photogrammetry or laser
scanning (reviews by Koyi, 1997; Graveleau et al., 2012; Schellart and
Strak, 2016). LPS in models is estimated by cross-section balancing and
area calculation (e.g., Koyi et al., 2003; Groshong, 2019), analysis of
surface deformed strain markers and volumetric strain (Nilforoushan et
al., 2008). Recently, AMS has also been introduced in analogue modelling
to quantify strain in models simulating FTBs (Almqvist and Koyi, 2018).
In FTBs, the evolution of the magnetic fabric depends on the amount of
shortening and location within a FTB. With increasing strain, a primary
fabric, i.e., sedimentary fabric, will be overprinted to a completely
reoriented tectonic fabric. A mixture of magnetic fabric patterns
between primary and tectonic fabric indicates an intermediate fabric,
that results from a moderate tectonic overprint of the sedimentary
fabric. Intermediate and tectonic magnetic fabric are typical in FTBs
and paths in strain change described by tectonic overprint derive from
field observations (e.g., Graham, 1966; Borradaile and Tarling, 1981;
Kligfield et al., 1981; Averbuch et al., 1992; Bakhtari et al., 1998;
Parés et al., 1999; Hirt et al., 2004). A similar magnetic fabric
evolution with increasing strain, as seen from field data, is observed
in analogue models (Almqvist and Koyi, 2018), with the possibility to
differentiate between fabric influenced by thrusting and by grain
reorientation due to compaction (Schöfisch et al., 2021).

As a continuation of such modelling studies, in this study, we use the
results of a series of shortened sandbox models simulating the evolution
of a pop-up structure at different amount of bulk shortening, to
investigate the evolution of the magnetic fabric, mainly within an
imbricate and at the developed structures. Specifically, the aim of this
study is to describe the strain distribution within a pop-up structure
and compare the magnetic fabric that develops at different stages of
finite strain across the imbricate.

2 Methods

\textbf{2.1 Model setup and sampling}

Three models (A, B, and C) with a similar setup are shortened to
different extent in order to analyze the magnetic fabric along thrust
faults at different stages that are associated with a development of a
pop-up structure (Table 1). To initiate a pop-up structure bounded by
active back- and forethrusts, an artificial wedge is sieved and built on
top of the model next to the backstop in models A and C. In Model B, a
basal plate is attached to the backstop, as a velocity discontinuity, to
transmit shortening away from the backstop and initiate a boxfold in the
middle of the model away from the backstop. To increase sampling
capacity and target individual parts of the boxfold, the models were
thick (8 cm) and had an initial dimension of 71x30 cm (Fig. 1). Loose
sand was mixed with magnetite grains (\textless{}0.1vol\%) of the same
grain size (0.124-0.356 mm) to enhance magnetic susceptibility. This
mixed composition (cohesion \selectlanguage{greek}μ \selectlanguage{english}= 0.49) was used to construct layers that
were scraped to an individual thickness of one centimeter each. Between
each 1 cm-thick layer, a thin marker horizon is sieved using different
colored sand. To monitor surface deformation, a colored grid of circles
is imprinted on the model surface by sieving. After shortening, the
models are carefully wetted, and vertical sections are taken parallel to
the shortening direction (Table 1). Each section is photographed, and
oriented cubic samples (volume 2.2 cm\selectlanguage{ngerman}³) are taken across the sections in
specific parts of the structure (forethrust, backthrust, forekink zone,
crestal areas, undeformed part in the foreland, etc.) for AMS analyses.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1:} Sketch of model setups. A pre-existing wedge was
placed next to the backstop on top of the surface of models A and C. In
Model B, a metal plate that moved with the backstop was used as velocity
discontinuity.

\textbf{Table 1:} Overview of setup of the three models. The three
models share the same thickness and lateral dimensions but vary in the
amount of bulk shortening and sampling.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
& bulk shortening & setup variation & sections/samples\tabularnewline
\midrule
\endhead
Model A & 12 cm = 16\% & artificial wedge on top of model next to
backstop; 7x12 cm, slope: 30\selectlanguage{ngerman}° & 8 / 289\tabularnewline
Model B & 17.5 cm = 24.5\% & velocity discontinuity by underlying moving
metal plate; length: 20 cm & 7 / 320\tabularnewline
Model C & 24 cm = 34\% & artificial wedge on top of model next to
backstop; 4x8 cm; slope: 26\selectlanguage{ngerman}° & 5 / 170\tabularnewline
\bottomrule
\end{longtable}

\textbf{2.2 AMS measurements and fabric evolution}

AMS measurements were performed with a MFK1-FA Kappabridge (Agico Inc.)
using an AC field strength of 200 A/m and a frequency of 976 Hz. From
each measurement, the bulk orientation of the principal axes of
susceptibility (k\textsubscript{max} [?] k\textsubscript{int} [?]
k\textsubscript{min}) of magnetite grains within one sample is
calculated and plotted on a lower-hemisphere equal-area projection with
the backstop defining the North. Note that the matrix sand, consisting
mainly of weakly diamagnetic quartz, is considered to have a negligible
contribution to the AMS compared to the magnetite. Furthermore, the
principal axes define an ellipsoid, which can be described by the shape
of anisotropy (\(T\ =\ [2n_{\text{int}}\ n_{\max}\ \ n_{\min}]/[n_{\max}\ \ n_{\min}]\)) and degree of anisotropy
(\(Pj\ =\ exp\{2(n_{\max}\ n_{\text{mean}})+(n_{\text{int}}\ \ n_{\text{mean}})+(n_{\min}\ \ n_{\text{mean}})]\}\)) with \(n_{\max}=ln(k_{\max})\),\(n_{\text{int}}=ln(k_{\text{int}})\),
\(n_{\min}=ln(k_{\min})\), and \(n_{\text{mean}}=(n_{\max}+n_{\text{int}}+n_{\min})/3\)(Jelinek, 1981; Hrouda, 1982).
The shape of anisotropy (\emph{T} ) ranges from \emph{T} = -1 for
prolate, \emph{T} = 0 for neutral to \emph{T} = +1 for oblate
ellipsoids. The degree of anisotropy describes a ratio between the
principal axes, hence a change in the alignment of the magnetic grains
(magnetite in this model) within a sample will result in a different
degree of anisotropy (Hrouda, 1982), e.g., high values indicate a
preferred orientation. Analyzing the magnetic fabric throughout the
model enables a description of strain changes due to principal axes
rotation and it is used to describe a strain path from an oblate
depositional fabric towards an intermediate and tectonic fabric with
lower \emph{Pj} and occurrence of more prolate susceptibility ellipsoids
(e.g., Kligfield et al.,1981; Rochette et al., 1992; Borradaile and
Henry, 1997; Bakhtari et al., 1998). Note that since we neither model
ductile deformation, grain fracturing nor recrystallisation, which
influence the bulk orientation of the magnetic fabric in cleavages zones
(Borradaile and Tarling, 1981; Hirt et al., 2004; Ferr\selectlanguage{ngerman}é et al., 2014),
the magnetic fabric development is limited to rigid body rotation of
grains in our models. However, a reworking of the magnetic fabric due to
rigid body rotation caused by an increase in LPS, folding and thrusting
are often interpreted for FTBs (e.g., Averbuch et al., 1992; Borradaile
and Henry, 1997; Bakhtari et al., 1998; Saint-Bezar et al., 2002;
Burmeister et al., 2009) and are observed in analogue models (Almqvist
and Koyi, 2018; Schöfisch et al., 2021).

3 Results

\textbf{3.1 Model kinematics and evolution}

The three models (Models A, B and C) are shortened to different amounts
(12 cm, 17.5 cm, and 24 cm, respectively) (Table 1), but share a
relatively similar evolution and comparable development of structures.
The main structure that developed during the shortening of the models is
a pop-up structure with a well-defined backthrust and a broad forekink
zone (Figs. 2a, b, and c). In addition to the pop-up structure, the
models developed other structures in their foreland. For example, in
front of the pop-up structure in Model A (16\% bulk shortening), two new
forekinks were initiated as indicated by bending of the surface markers
and slight increase in topography (dashed lines in Fig. 2b). These
forekinks represent an early stage of forethrust creation. In Model B
(24.5\% bulk shortening), an additional forethrust (FT1) developed
simultaneously with the splay of the backthrust (BT) of the major pop-up
structure. Farther into the foreland of Model B, a second forethrust
(FT2) formed, represented by a mm-scale fore-kink (Fig. 2b). However,
compared to models A and B, Model C (34\% bulk shortening) developed a
more complex set of structures (Fig. 2c). In this model, a ``lower''
backthrust (BT1) formed simultaneously with the ``upper'' forekink zone
(FKZ1). At a later stage, an ``upper'' gently-dipping backthrust (BT2)
formed and uplifted FKZ1. Simultaneously with initiation of BT2, a
``lower'' forekink zone formed (FKZ2). With further shortening, a second
pop-up structure formed in the foreland. This additional foreland-pop-up
consists of a narrower forekink zone (FKZ3) and a foreland-backthrust
(BT3). This BT3 offsets the upper layers of the FKZ2, which in turn is
offset by a forethrust (FT) that initiated during further shortening
(after 21 cm of shortening, representing 90\% of final bulk shortening
of Model C). This FT, located beneath FKZ2, splayed and is related to
the deformation of the main pop-up structure, where a new backthrust is
about to form above BT2 as counterpart (Fig. 2c, dashed red line in
Model C above BT 2) (Fig. 2c). Overall, the three models show a similar
evolution of a pop-up structure at different stages of shortening (Figs.
2a, b, and c). Faults and kinks in each model steepen with depth and
displacement along all faults decreases with depth (Figs. 2d, e, and f).

\textbf{3.2 Cross-section balancing}

During shortening of the models, strain is partitioned between the three
deformation components: layer-parallel shortening (LPS), folding, and
thrusting. The amount of deformation taken up by thrusting and folding
is proportional to the percentage of bulk shortening. However, most of
the strain in all models is accommodated by LPS, i.e., penetrative
strain (Figs. 2d, e, and f). Even though LPS increases with bulk
shortening, its contribution to the overall strain decreases relative to
that of folding and thrusting with progressive bulk shortening. In
general, the amount of LPS and folding are changing with depth in all
models, whereas thrusting decreases (Figs. 2d, e, and f). Additionally,
the distribution of strain and its trend with depth is different in
Model B compared to models A and C (Figs. 2d, e, and f). In Model B, LPS
decreases from the surface to layer 4 and then increases again towards
the deeper layers (Fig. 2e), whereas the opposite is the case for
folding. Thrusting in Model B mainly decreases with depth as seen in
models A and C (Figs. 2d, e, and f).

\textbf{3.3 Magnetic fabric}

In the three models, 779 samples were taken and analyzed for AMS
signature (Table 1). We separated the datasets from the models by their
location relative to the main structures (thrusts and forekink zone) and
describe the characteristic magnetic fabric in detail in the following
sections. The distance of a sample to a thrust or a kinkzone is measured
by using the center of the sample. Consequently, we assume that samples,
whose centers are lying in a range of 0.8 cm (length from center to
corner of the cubic samples) to a thrust or kinkzone, are carrying a
signal that is attributed to thrust or kinkzone and are summarized
within the datasets showing magnetic fabrics of such a structure. The
complete dataset is provided in the data repository (Schöfisch, 2021)
and an overview of AMS distribution across the pop-up structures are
presented as supplementary material (S1-S8).

3.3.1 M\emph{agnetic fabric away from thrust and kinkzone}

An oblate shape of anisotropy, where kmin axes are clustered vertically
relative to bedding, is observed in all models in areas away from a
thrust or kinkzone, i.e., the footwall of the backthrusts next to the
backstop, the interlimb zone between the main backthrust and main
forekink zone, and the areas between the ``minor foreland'' thrusts in
front of the main forekink zones (Fig. 3). Both kmax and kint define a
horizontal to subhorizontal magnetic foliation around the primitive
circle parallel to the sand layers in these areas, where kmax is
generally aligned along the model north (towards backstop)-south axis,
and kint clusters mainly in the east and\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2:} Three models A,B,C are shortened to different amount
of bulk shortening (16\%, 24.5\%, 34\%). They show the evolution of a
pop-up structure. a,b,c) show representative cross-sections for each
model. d,e,f) show the restoration of cross-sections, which provide a
partitioning of strain. Additionally, the heave at major structures is
plotted for each layer counting from the top.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3:} a) plots of the inclination of the principal axes
(kmax [?] kint [?] kmin) as a function of distance to a thrust or kinkzone.
b) equal-area projection showing distribution of principal axis for
samples with a distance \textgreater{} 0.8 cm to a thrust or kinkzone
with backstop to the North. c) illustrates the distribution of degree
and shape of anisotropy using the Jelinek-plot. Circles coincide with
samples taken away from a thrust of kinkzone, whereas crosses represent
data from thrust and kinkzone.

west direction (Fig. 3b). The degree of anisotropy in these areas lies
in the interval between 1.1 [?] Pj [?] 1.6 (Fig. 3c).

All three models show a general trend in principal axes rotation as a
function of distance to a thrust or kinkzone (Fig. 3a). The closer the
sample is to such a structure, the larger is the variety of inclinations
of the principal axes, e.g., kmax and kint axes rotate from mainly
horizontal inclinations to broad range of inclinations (Fig. 3a). The
opposite is observed for the inclination of kmin axes. The degree of
anisotropy (\emph{Pj} ) generally decreases towards a thrust or kinkzone
(Fig. 3c). Furthermore, the shape of anisotropy is oblate for most of
the samples away from a thrust or kinkzone, whereas in the vicinity of a
such structure both prolate and oblate shapes are observed (Fig. 3c).

3.3.2 \emph{Magnetic fabric at thrust surfaces}

An evolution of magnetic fabric for thrusts can be recognized in the
models. The thrusts from the models show different amounts of
displacement and therefore the observed magnetic fabric at each thrust
can be related to the different degree of thrust maturity (Figs. 2, and
4). The kinks in front of the pop-up structure in Model A are described
as an early stage of thrust development and samples from the kinks show
vertical k\textsubscript{min} axis distribution with horizontal
k\textsubscript{max} and k\textsubscript{int} axes. The principal axes
orientation of the kinks is similar to the principal axes orientation
observed in samples away from the thrusts or kinkzones (Fig. 4a).
Nevertheless, samples from the kinks show a lower degree of anisotropy
(\emph{Pj} ) with some tendency towards a prolate fabric, which is
different compared to samples away from thrusts and kinkzones (Figs. 3c,
5a, and 5d). The principal axes for samples from the forethrust (FT2) in
the foreland of Model B are less clustered, as observed for the kinks in
Model A (Fig. 4a). Additionally, at FT2, k\textsubscript{max} and
k\textsubscript{int} create a magnetic foliation that is subhorizontal
(dipping 10-20\selectlanguage{ngerman}°) and are therefore not as horizontal as observed for
samples away from the thrusts, but also not parallel to the thrust
surface. k\textsubscript{min} axes clusters tightly around the mean,
with a steep inclination (\textasciitilde{}80°) that verges slightly to
the south-west (Fig. 4a). The degree of anisotropy for samples taken at
FT2 is generally lower than for data collected at the kinks in the
foreland of Model A. However, the peaks of the distribution of the
degree of anisotropy for data from FT2 and the kinks in Model A are
similar (Fig. 5d). The forethrust (FT) of Model C as well as the splayed
forethrust (FT1) of Model B developed a magnetic foliation that
converges into the orientation of the thrusts (Fig. 4a). For both
forethrusts, most of the principal axes developed a subhorizontal
magnetic foliation (i.e., girdle distribution of k\textsubscript{max}
and k\textsubscript{int}) that tends into parallelism with the
forethrusts and k\textsubscript{min} axes started to rotate from
vertical towards gentler inclinations in the south (Fig. 4a).
Additionally, the degree of anisotropy at both forethrusts (FT and FT1)
is comparable and is lower than observed for the kinks in Model A and
FT2 in Model B (Fig. 5).

Along the backthrusts of all three models, k\textsubscript{max} and
k\textsubscript{int} develop a magnetic foliation parallel to the thrust
surfaces with k\textsubscript{min} clustering at the pole (Fig. 4b).
However, some principal axes deviate from this general alignment and
clustering, which can be attributed to the local structural complexity
and splaying of the backthrusts. Along the backthrust of Model B, a
clustering of k\textsubscript{max} indicate a clustering of magnetic
lineation (k\textsubscript{max}) parallel to the north-south shortening
direction (Fig. 4b). In all thrusts (fore- and backthrusts) of the three
models, a decrease in the degree of anisotropy can be observed downwards
along the thrust surfaces, i.e., \emph{Pj} decreases with depth for each
thrust (Fig. 4d). Despite that the thrusts show different amount of
displacement (Fig. 2), degree of anisotropy is still comparable between
all thrusts (1.1 \selectlanguage{english}[?] \emph{Pj} \selectlanguage{english}[?] 1.4), except for the kinks (early-stage
thrusts) in the foreland of Model A, which have slightly higher degree
of anisotropy (1.15 \selectlanguage{english}[?] \emph{Pj} \selectlanguage{english}[?] 1.5) (Fig. 5). At depth, where thrusts
are intersecting, slightly higher degree of anisotropy are observed. For
example, at 8 -- 13 cm depth interval of the backthrust in Model C, the
forekink zones are intersecting with the backthrust and a slightly
higher degree of anisotropy is calculated (Fig. 5). The shape of
anisotropy at the thrusts is classified as a mix between prolate and
oblate shapes (Fig. 3c). Nevertheless, the oblate shapes dominate at the
thrusts (Fig. 3c).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4:} Equal-area projections showing principal axes of
magnetic susceptibility with their means and 95 \% confidence ellipses
of the means (ellipses with same color as principal axes) from a) the
forethrusts, b) backthrusts, and from c) the forekink zones from the
three models A, B, and C with backstop to the North. The numbers in the
brackets are the ranges in displacement along each thrust.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5:} Distribution of degree of anisotropy (Pj) with depth
for a) Model A, b) Model B, and c) Model C. The density of distribution
probabilities, calculated with a Kernel distribution function, of the
degree of anisotropy for each structure from the models are given in d)
for forethrusts and foreland kinks, e) backthrusts, and f) forekink
zones. The position of the peak values (maxima) of each curve in d,e,
and f are plotted with short vertical lines in the same color along the
x-axis.

3.3.3 \emph{Magnetic fabric in forekink zone}

The magnetic fabric within the relatively broad forekink zones can be
summarized by principal axes spreading along north-south and east-west
oriented great circle girdles (Fig. 4c). The forekink zone in Model A
developed a scattered broad
k\textsubscript{max}-k\textsubscript{int}girdle (i.e., magnetic
foliation) dipping to the north with a subhorizontal mean of
k\textsubscript{max} towards east and a mean of k\textsubscript{int}
that is dipping \textasciitilde{}35\selectlanguage{ngerman}° to the north. In contrast,
k\textsubscript{min} scatters as a broad north-south girdle with
inclinations that vary from vertical to horizontal. Nevertheless, the
mean of k\textsubscript{min} is directed towards the south with an
inclination of 52°, although with a very large mean confidence ellipse
(Fig. 4c). By comparison, in the forekink zone of Model B,
k\textsubscript{min} developed a broad north-south girdle distribution
as well, but with a narrower confidence ellipse and a mean clustering of
k\textsubscript{min} that is almost vertical (Fig. 4c). Furthermore, in
the forekink zone of Model B, k\textsubscript{max} is mainly clustering
along an east and west axis, defining a magnetic lineation perpendicular
to the shortening direction. The k\textsubscript{int} axes of the
forekink zone in Model B rotated into the north-south girdle
distribution of k\textsubscript{min} with a horizontal
k\textsubscript{int} mean axis aligned north-south. The two forekink
zones in Model C developed a general principal axes distribution that
can be compared to the magnetic fabric in the forekink zone of Model A
(Fig. 4c). In the two forekink zones of Model C, k\textsubscript{max}and
k\textsubscript{int} define a magnetic foliation trending perpendicular
to the shortening direction with different inclinations but mainly with
a vertical k\textsubscript{int} mean and a suhorizontal east-west
k\textsubscript{max} mean. The k\textsubscript{min} axes cluster
subhorizontally in the two forekink zones of Model C with a north-south
direction with a mean k\textsubscript{min} plunging subhorizontally
towards the south in the lower hemisphere projection (Fig. 4c). Notably,
the minor forekink zone in the foreland of Model C (FKZ3) developed a
similar AMS pattern as seen in the major forekink zones in this model
(i.e., FKZ1 and 2). Overall, the shape anisotropy observed in forekink
zones from all the three models are heterogeneous and range from oblate
to prolate. The degree of anisotropy is comparable between the forekink
zones of all three models and range from 1.05 \selectlanguage{english}[?]\emph{Pj} \selectlanguage{english}[?] 1.35, which
are the lowest ranges observed in this study (Fig. 5f). However, the
peak of the distribution of the degree of anisotropy of the kinkzone in
Model B is higher than the peaks for the forekink zones of Model A and
Model C. (Fig. 5f).

4 Discussion

\textbf{4.1 Strain distribution across the models}

Of the three components of shortening (LPS, folding, and thrusting), LPS
is dominant at the early stage of model deformation, leading to
compaction of the shortened layers until folds and thrusts accommodate
the shortening resulting in formation of an imbricate (Mulugeta and
Koyi, 1992, Koyi, 1995, Koyi et al., 2003). This is also illustrated by
our models, where the amount of LPS increases with bulk shortening but
with a gradual decrease in strain accommodation giving way to an
increase in faulting and folding as the imbricate is uplifted along the
backthrust(s). Displacement of layers by faulting and folding are
visible components of deformation during model shortening and localizes
at certain zones within the models. Nevertheless, LPS, which is
accommodated by grain rotation and repacking (Fig. 2), is not easy to
identify by naked eye. Processes like compaction, grain rearrangement
and grain reorientation contribute to the overall LPS and are
consequences of stress propagation through the model (Koyi et al.,
2003). However, since AMS monitors grain orientation and alignment, it
can be used to indirectly deduce the degree of compaction and hence
penetrative strain distribution. Reworking of the magnetic fabric due to
an increase in LPS, folding and thrusting is typical for FTBs (e.g.,
Averbuch et al., 1992; Borradaile and Henry, 1997; Bakhtari et al.,
1998; Saint-Bezar et al., 2002; Burmeister et al., 2009) and is a
process that is observed in the three models presented in this study.
All three models are shortened to different amount of bulk shortening,
but express similar distribution of principal axes of magnetic
susceptibility, degree of anisotropy (\emph{Pj} ) and shape of
anisotropy (\emph{T} ). In general, there is a distinct difference
between a magnetic fabric that developed away from a thrust or kinkzone
to that within a thrust or kinkzone (Figs. 3 and 4). Consequently, the
AMS data show (i) a change in the magnetic fabric as a function of
distance to a thrust or kinkzone (Figs. 3a and 3c), and (ii) clear
tectonic overprinting of a pre-existing magnetic fabric at faults and
kinkzones.

4.1.1 \emph{Compaction and folding in areas away from thrust and
kinkzone}

Areas away from thrusts and kinkzones show a magnetic fabric that can be
classified as a mixture between the initial fabric and tectonic fabric,
where the tectonic fabric is represented by mainly LPS. The initial
fabric is determined by model preparation as scraping produced an
alignment of a magnetic lineation parallel to the shortening direction
with k\textsubscript{min} vertical to bedding (Almqvist and Koyi, 2018;
Schofisch et al., 2021). This initial fabric is preserved in some
places, regardless of distance to a thrust or kinkzone (Fig. 3b).
However, a variation in principal axes distribution is illustrated by
the distribution of k\textsubscript{max} and k\textsubscript{int} axes
around the primitive circle with horizontal to subhorizontal
(\textasciitilde{}10-20deg dipping) inclinations (Fig. 3b). The change in
magnetic fabric in the areas away from thrusts and kinkzones can be
attributed to mainly penetrative strain, i.e., LPS (Fig. 2a). This
agrees with observations of the penetrative-strain induced fabric from
other modelling studies (Almqvist and Koyi, 2018; Schofisch et al.
(2021) and natural examples (Kissel et al., 1986; Lee et al., 1990;
Averbuch et al., 1992; Bakhtari et al., 1998; Pares and van der Plujim,
2002; Sans et al., 2003) where k\textsubscript{max} is aligned
perpendicular to the shortening direction and
k\textsubscript{min}remained vertical (pole to bedding). However, also
gentle folding can be interpreted in the areas away from thrusts and
kinkzones as bedding changes slightly along profile (Fig. 2). Folding is
responsible for the change in inclination of the magnetic foliation, as
k\textsubscript{max}and k\textsubscript{int} remain parallel to bedding,
which has been reported by Averbuch et al. (1992) and Saint-Bezar et al.
(2002). Consequently, the grain reorientation in areas away from thrusts
and kinkzones, as described by the magnetic fabric, is characterized by
tectonic compaction and folding. However, folding, i.e., bedding
rotation in the areas away from thrusts and kinkzones, is very gentle
and responsible for only few degrees, up to maximum 10deg, of inclination
change of magnetic foliation.

Despite the variation in orientation of the principal axis, the degree
of anisotropy for samples away from thrust and kinkzone illustrate a
broad range of values (1.1 \selectlanguage{english}[?] \emph{Pj} \selectlanguage{english}[?] 1.6). In the vicinity of a
thrust or kinkzone prolate shape of anisotropy is recognizable, even
though the overall fabric is oblate (Fig. 3c). This heterogeneous
distribution in orientations of principal axes, degree of anisotropy and
shape of ellipsoids (Fig. 3) describe a varying strain in the areas away
from thrusts and kinkzones. This is known from observing deformation
within an imbricate before fault initiation with optical methods (Adam
et al., 2005; Dotare et al., 2016). Adam et al. (2005) described the
strain distribution within an imbricate as ``diffuse shear strain'',
whereas Dotare et al. (2016) recognized this ``diffuse strain'' as an
accumulation of several short-lived weak shear bands during compaction
of an imbricate. Our model results reveal a further detailed insight
into the strain distribution in imbricates, especially, as the AMS data
from the models show gradients in change of the magnetic fabric towards
a thrust and a kinkzone.

4.1.2 S\emph{train gradient towards thrusts and kinkzones}

Even though the principal axis distribution, degree of anisotropy and
shape of anisotropy are scattered and described as a kind of ``diffuse
strain'' in areas away from thrusts and kinkzones, a gradient in these
magnetic fabric parameters can be described as a function of the
distance to a thrust or kinkzone. With decreasing distance to a thrust
or kinkzone, the variation of principal axis inclination increases, and
a higher variation of principal axes orientations can be found closer to
the thrust or kinkzone (Fig. 3a). Furthermore, a trend of decreasing
degree of anisotropy is observed towards a thrust or kinkzone and the
presence of prolate fabric increases in areas closer to a fault (Fig.
3c). Similar observations in changes of the magnetic fabric towards a
thrust are identified from, for example, the French Alps (Kligfield et
al., 1981), Corbieres in the Pyrenees (Averbuch et al. 1992), Central
Appalachian FTB (Hirt et al., 2004), Gavarnie thrust in the Pyrenees
(Marcen et al., 2018), the Barbados Accretionary Prism (Housen et al.,
1996), and the Hikurangi Subduction Margin in New Zealand (Greve et al.,
2020). Note that the first four studies above show an effect of magnetic
mineral reprecipitation, and the latter two studies show an additional
effect of fluids on the magnetic fabric. However, observations are
similar to what our models show, and there is a compatible decreasing
trend in the degree of anisotropy and alignment of magnetic grains
towards the faults. Irrespective of the influence of fluids and mineral
recrystallisation, our models suggest that brittle deformation plays a
major role in reorientation of grains, and changes in magnetic fabric
due to tectonic compaction and folding are important mechanisms towards
a thrust.

Bulk shortening and hence the amount of deformation in a model, are
reflected in the trends and gradients of the magnetic fabric change
towards a thrust or kinkzone. With larger bulk shortening, more faults
and kinkzones formed in the models, and displacement increased along the
structures bounding the main boxfold, i.e., backthrusts and forekink
zones. It appears, that with increasing shortening within a model,
changes in magnetic fabric between a thrust-induced fabric and magnetic
fabric away from thrusts and kinkzones are more distinct. The increase
in variety of inclination of the principal axes with decreasing distance
to a thrust or kinkzone occurs over smaller distances (Fig. 3a). For
example, the largest amount of strain is accommodated in Model C (Fig.
2f), and the change in principal axes inclination as a function of
distance to thrust and kinkzone is observed for a smaller distance in
this model compared to models A and B, where the gradient is steeper,
more linear and is observed over a longer distance (Fig. 3a). Also, the
degree of anisotropy shows less scattering and a clearer decrease in
Model C (Fig. 3c), which is not a consequence of the differing number of
samples between the models (Table 1). Consequently, the transition of a
magnetic fabric away from a thrust or kinkzone towards a magnetic fabric
at a thrust or kinkzone is defined by the amount of bulk shortening,
which is also reflected in the amount of displacement along a thrust.

Furthermore, most studies interpret an increase in strain, especially
LPS, from the foreland to the hinterland in FTBs over a larger regional
scale. However, such increase in strain as a function of distance to the
hinterland is not linear and it has been observed that accumulation of
strain is rather expressed by localized minor faults and deformation
zones that accretion towards the hinterland (e.g., Groshong et. al.
1984, Averbuch et al., 1992; Dittmar et al., 1994). However, our models
show that strain is also changing and increasing within imbricates,
towards its boundaries on a local scale. Consequently, AMS provides
useful insights into the strain distribution of an imbricate and
therefore the model results encourage studying strain distribution of
natural analogues within FTBs at local scales.

4.1.3 \emph{Tectonic overprinting by thrusting}

The magnetic fabric observed at a thrust is distinct from the other sets
of magnetic fabric observed in the other areas of the models. Moreover,
greatest change in magnetic fabric from the initial fabric is observed
at a thrust, especially where the displacements by thrusts are large.
Thrusts from all three models, i.e., backthrusts and forethrusts,
created a similar fabric pattern that reflects the geometry of the
thrusts, as the magnetic foliation
(k\textsubscript{max}-k\textsubscript{int} girdle) is scattered,
generally along a great circle parallel to the thrust plane, instead of
being parallel to the bedding (Figs. 4a and b). Consequently, thrusting
has a significant impact on the development of the magnetic fabric and
such fabric can be described as ``thrust-induced fabric'' (Schofisch et
al. 2021). Samples from a thrust show a higher variation in the shape of
anisotropy with both oblate and prolate shape anisotropy. Compared to
LPS-produced fabric in areas away from the thrust, more prolate shapes
can be observed with a general lower degree of anisotropy in thrusts
(Fig. 3c). The change from oblate to a more prolate fabric with a lower
degree in anisotropy is consistently observed in the vicinity of a
thrusts in the models and is common in nature as deformation increases
and localizes towards a structure (Kligfield et al., 1981; Hirt et al.,
2004). In general, changes in magnetic fabric, with magnetic foliation
parallel to thrust surface and low degrees of anisotropy, are in
agreement with experiments (Borradaile and Alford, 1988; Borradaile and
Puumala,1989; Housen et al., 1993; Schofisch et al., 2021), numerical
models (Housen et al., 1993), and field observations (e.g., Averbuch, et
al. 1992; Housen et al., 1996; Pares and van der Pluijm, 2002; 2004;
Hirt et al., 2004; Marcen et al., 2018; Greve et al., 2020).

AMS analysis show that prominent changes in the degree of anisotropy and
alignment of principal axes can be observed at the onset of thrusting
(Figs. 4 and 5). The kinks at the front of the main boxfold in Model A
and the forethrust in Model B with a minor offset show a mixture between
the magnetic fabric observed farther away from the thrust and at more
mature thrusts, with larger displacement like the backthrusts (Figs. 3
and 4). Compaction precedes thrusting (e.g., Adam et al., 2005; Dotare
et al., 2016) and further kinking takes place before the sand layers are
offset by thrusting. Therefore, thrusting will overprint a LPS-affected
fabric, that has also a signature of folding. The kinks in Model A and
the forethrust in Model B illustrate a transition from a ``compactional
fabric'' to a ``thrust-induced fabric'', which occurs with kink
initiation and minimal layer offset in our models. This means that
compaction, kinking and folding are the main components responsible for
principal axes reorientation prior to thrusting.

With larger displacement along a thrust, a ``thrust-induced fabric''
shows a general alignment of magnetic foliation with the thrust surface.
This thrust-induced fabric is seen in the well-developed fore- and
backthrusts of all three models (Figs. 3a and b). Especially at the
backthrusts, overprinting of a compacted and folded magnetic fabric is
more efficient, as deformation within the zone of thrust initiation
created alignment of principal axes with the thrust surface (Fig. 3b).
Nevertheless, variations in principal axis orientation can occur due to
structural complexity, for example, where a fore- and backthrust are
intersecting (Model C), or where a splay developed (Model B). Note that
an increase of degree of anisotropy at lower levels in the models is
related to the intersection of other thrusts (Fig. 5). For example, the
backthrust of Model C is intersecting with the forekink zones at depth
in the model and an influence on the magnetic fabric is expected in this
area (Fig. 6).

As strain, especially LPS, is heterogenous throughout a model (Mulugeta
and Koyi, 1992; Koyi, 1995), notably with depth (Koyi et al., 2003), the
variation in strain will also be reflected in the magnetic fabric prior
to thrusting and can be inherited in further overprinting (e.g., Pares
and von der Pluijm, 2002; Ferre et al., 2014; Marcen et al., 2018). The
models reported here also show a change in strain with depth (Figs. 2d,
e, and f), especially by decreasing displacement along the thrusts (Fig.
2). The changes in displacement and strain accommodation with depth in
the models can explain a general decreasing trend in the degree of
anisotropy downwards the thrusts (Fig. 5). Relatively higher values in
degree of anisotropy reveal a preferred alignment of the magnetic grains
within the samples, whereas lower degrees show less preferred alignment
of grains (e.g., Borradaile and Jackson, 2010; Pares, 2015). This means
that thrusting was less efficient in realigning the grains at depth, and
an AMS signal prior to thrusting is inherited in the final modelled
magnetic fabric. A similar observation is made at the Gavarnie thrust in
the Pyrenees (Marcen et al., 2018), where an intersection lineation
prior the Alpine deformation is inherited during reactivation of the
thrust and a low degree of anisotropy is observed at the reworked
Variscan fabric.

Additionally, the trend of decreasing degree of anisotropy with depth
along a thrust seems to be independent of the amount of displacement at
a thrust, as the same trend can be interpreted at each thrust from the
three models, whereas each thrust differs in amount of displacement. The
changes in AMS signal at a thrust needs to be discussed considering
relative changes in deformation along an individual thrust instead of
comparing absolute numbers of displacement for each thrust. Larger
displacement, which is observed in upper segments of the thrusts,
produce higher degree of anisotropy and therefore grains are more
aligned compared to deeper segments of the thrusts, where lower
displacements and lower degree of anisotropy are observed. However,
comparing data between different segments of different thrusts, but with
similar amount displacement, is deceiving, because different segments of
thrusts and, in general, thrusts from different models have different
deformation histories in general.

The trend of decreasing degree of anisotropy with depth at a thrust is
less obvious for thrusts in Model B and C compared to thrusts in Model A
(Figs. 5a, b, and c). This further emphasizes that strong changes in
magnetic fabric are observed at the beginning of thrust initiation, as
the thrusts in Model A are less mature compared to the thrusts from the
other models. With increasing deformation and further displacement at a
thrust, differences in magnetic fabric (e.g., inclination of principal
axes or degree of anisotropy) between upper and lower parts of a thrust
will decrease. Our models are limited to grain reorientation only and
therefore, alignment of principal axes of susceptibility parallel to a
thrust will reach a certain degree of anisotropy. However, AMS data from
the modelled thrusts reveal ``heterogeneous strain'' along thrusts and
shear zones, which are typical observations in nature (e.g., Ferre et
al., 2014). Consequently, this highlights the importance of brittle
reorientation of grains during thrust development.

4.1.4 \emph{The internal deformation of kinkzones}

The initial model setup and the amount of bulk shortening are reflected
in the evolution of the model and, especially, in the creation of the
forekink zones. The geometric variation in width and extent of the
forekink zones from the different models, are also expressed in the
magnetic fabric for each forekink zone. The forekink zones consist of
rotated bedding parallel to the backthrust and many forethrusts with
small displacement (Fig. 2). The small displacement (millimeters) within
the kinkzone is significant enough to rotate grains, which results in a
broad spread of the principal axes of susceptibility (Fig. 4c). Overall,
the magnetic fabric in the forekink zones can be described by an
interplay among LPS, thrusting, and folding, while folding includes
bedding rotation parallel to the backthrust on a larger scale and
internal kinking due to forethrust creation on a smaller scale. The
different mechanisms of deformation contributed differently in each
kinkzone and can be revealed by the magnetic fabric. The kinkzone fabric
from all three models, especially the means of the principal axes of
susceptibility and their confidence ellipses, are comparable and
summarized by a mean of k\textsubscript{max} oriented to the East-West
and by means of k\textsubscript{min} and k\textsubscript{int} within a
broad north-south girdle (Fig. 4c). The k\textsubscript{max} clustering
defines a magnetic lineation normal to the shortening direction and
parallel to the fold axis of the minor kinks and bedding-thrust
intersection within all models. However, the principal axes are rather
scattered, which is also reflected by the appearance of low degree of
anisotropy, which is even lower than observed at thrusts or in areas
away from thrust and kinkzone (Fig. 5). Low degree of anisotropy derives
from the intersection of folding and thrusting, without a dominance of
either of these deformation processes. This agrees with natural
examples, where S-C-structures are producing a low degree of anisotropy
(Ferre et al., 2014; Marcen et al., 2018). However, the composite
magnetic fabric needs to be analyzed carefully, because summarizing
different grain orientations in a bulk susceptibility makes AMS to
strain correlation more difficult (Housen et al., 1993; Ferre et al.,
2014). In contrast, at the intersection between backthrust and forekink
zone, e.g., in Model C, the intersection is well defined and produces a
relatively higher degree of anisotropy compared to the interplay of
thrusting and folding in the kinkzones itself.

As bedding within the forekink zone is generally parallel to the
backthrust, the magnetic fabric depicts this bedding rotation. Several
previous studies have shown that the magnetic foliation remains parallel
to the bedding during folding (Averbuch et al., 1992; Bakhtari et al.,
1998; Saint-Bezar et al., 2002). However, the models presented in this
study show that several minor forethrusts are developed within a
forekink zone. Consequently, the fabric in these forekink zones is not
only the product of bedding rotation, but the effect of thrusting needs
to be considered too. In a steep forekink zone inclination, which cause
larger throw, thrusting within the kinkzone will have a greater impact
on AMS signature, as seen in Model A by the development of broad gridle
of k\textsubscript{max} and k\textsubscript{int} subparallel to the
fault surface (Figs. 2 and 4c). An even clearer magnetic foliation and
clustering of k\textsubscript{min} (seen by narrower confidence ellipses
compared to forekink zone in Model A) is observed in the forekink zones
of Model C (Fig. 4c). However, in the kinkzones of Model C, the magnetic
foliation does not align with the forethrust and is rather parallel to
the intersection lineation of bedding and forethrusts of the forekink
zone. Nevertheless, k\textsubscript{min} distribution of the kinkzones
in Model A and C are clustering to the pole of the forethrusts within
the kinkzones. AMS data from the forekink zone in Model B create
compatible narrow confidence ellipses as the forekink zones in Model C,
but here the position of k\textsubscript{min} and
k\textsubscript{int}are swapped (Fig. 4c). Obvious step-like kinks
developed in the forekink zone in Model B (Fig. 2b), which are less
visible in the other models. Consequently, additional internal folding
needs to be discussed for the forekink zone of Model B, which explains,
that k\textsubscript{min} is rather distributed in a girdle as poles to
the internal folds instead of clustering perpendicular to the thrust
surface. However, k\textsubscript{max} lineation is still parallel to
the intersection of the forethrusts and bedding in the forekink zone of
Model B, as observed in all forekink zones of all models. Generally, the
magnetic fabric highlights the influence of different deformation
processes within a kinkzone and reveals strain in more detail.

The observation that the ``kinkzone fabric'' in the models is a
consequence of an interplay between folding and faulting is similar to
the observation of Greve et al. (2020). In Greve et al. (2020), the zone
right above the major fault zone, called the `mid hangingwall' in their
study, is pervaded by thrusts and has steep bedding. The analyzed AMS
fabric from this zone is very similar to the ``kinkzone fabric'' in our
models, where k\textsubscript{max} clusters perpendicular and a
k\textsubscript{int}-k\textsubscript{min} girdle is defined parallel to
the shortening direction. Another comparison can be done with
observations from the shear zone at the Gavarnie thrust in the Pyrenees
(Marcen et al., 2018). S-C-structures create a composite magnetic fabric
producing magnetic lineation parallel to the intersection of S- and
C-planes. Similar magnetic lineation is produced in our case by the
intersection of folding and thrusting. In general, it is known from
natural examples, that the intersection of bedding and cleavage in a
deformed rock creates a magnetic lineation parallel to it (e.g.,
Borradaile and Tarling, 1981; Kligfield et al., 1981; Pares and van der
Pluijm, 2002; Hirt et al., 2004). However, competing fabric within in
one AMS sample lead to a composite fabric, that may not reflect the
strain within the deformation zone (Housen, 1993; Ferre et al., 2014).
Nevertheless, AMS data from the modelled kinkzones can be associated to
different accommodation of deformation within the kink zone as described
above. Consequently, AMS reveals different contributions to strain
within the kinkzone and vice versa, different deformation processes
within a kinkzone lead to complex sets of heterogenous kinkzone fabric.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Figure 6:} Schematic sketch of grain alignment in the models.

5 Conclusions

Measurements of the magnetic fabric in three different shortened
analogue models describe strain distribution across a thrust imbricate,
i.e., pop-up structure with associated thrusts and kinkzones. The AMS
data reflect a strain gradient from (i) an initial to compactional
magnetic fabric towards a (ii) thrust-induced fabric or (iii) composite
fabric within forekink zones (Fig. 6). Generally, the geometry of a
thrust determines the alignment of the magnetic fabric shown by
clustering and girdle distribution of the principal axes. In contrast,
folded layers displaced by minor thrusts display a more complicated AMS
pattern within the kinkzones. However, fabric analysis in the kinkzones
indicates the importance of strain accommodation of different
deformation mechanism like thrusting or folding. In addition, at
thrusts, AMS signatures from deformation prior thrusting can be
inherited in the finite magnetic fabric, which explains a varying strain
distribution and interpretation along thrusts in general. Overall, this
AMS study outlines strain distribution and magnitude within different
parts of an imbricate in more detail. Strain is changing as function of
distance towards localized deformation zones (e.g., thrusts and
kinkzones) and with larger bulk shortening, the change in strain between
areas away and within deformation zones is more distinct.

\textbf{Acknowledgement} This study is supported by a research grant
from the Swedish Research Council to HK and BA (VR 2017-04519). The
authors acknowledge LKAB Minerals Lule\selectlanguage{ngerman}å (Sweden) for providing the
magnetite for modelling. We thank the editor for editorial handling, and
anonymous reviewers for constructive comments. There are no conflicts of
interest.

\textbf{Data Availability Statement}AMS data from the three models of
this study will be available at doi:10.17632/zs7n4t57k4.1, an
open-source online data repository hosted at Mendeley Data (Schöfisch,
2021). Additionally, uncommented plots illustrating magnetic fabric
distribution in the models can be found in the supporting information
(Figures S1-S8).

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