Quantifying strain in analogue models simulating fold-and-thrust

belts using magnetic fabric analysis

Thorben Schöfisch

Licentiate thesis to be presented via Zoom https://uu-se.zoom.us/j/62084848216. Meeting-ID: 620 8484 8216. Thursday, 30 September 2021 at 14:00. The examination will be conducted in English.

Abstract Schöfisch, T. 2021: Quantifying strain in analogue models simulating fold-and-thrust belts us-ing magnetic fabric analysis. 42 pp. Uppsala.

Applying the anisotropy of magnetic susceptibility to analogue models provides detailed in-sights into the strain distribution and quantification of deformation within contractional tectonic settings like fold-and-thrust belts (FTBs). Shortening in FTBs is accommodated by layer-par-allel shortening, folding, and thrusting. The models in this research reflect the different defor-mation processes and the resulting magnetic fabric can be attributed to thrusting, folding and layer-parallel shortening. Thrusting develops a magnetic foliation parallel to the thrust surface, whereas folding and penetrative strain develop a magnetic lineation perpendicular to the short-ing direction but parallel to the bedding. These fabric types can be observed in the first model of this study, which simulated a FTB shortened above two adjacent décollements with different frictional properties. The different friction coefficients along the décollements have not only an effect on the geometric and kinematic evolution of a FTB, but also on the strain distribution and magnitude of strain within the belt.

The second series of models performed in this study show the development of a thrust im-bricate and the strain distribution across a single imbricate in more detail. Three models, with similar setup but different magnitudes of bulk shortening, show strain gradients by gradual changes in principal axes orientations and decrease in degree of anisotropy with decreasing distance to thrusts and kinkzones. These models show that at the beginning of shortening, strain is accommodated mainly by penetrative strain. With further shortening, formation of thrusts and kinkzones overprint the magnetic fabric locally and the degree of anisotropy is decreasing within the deformation zones. At thrusts, an overprint of the magnetic fabric prior deformation towards a magnetic foliation parallel to the thrust surfaces can be observed. A rather complex interplay between thrusting and folding can be analysed in the kinkzones.

In general, this thesis outlines the characteristics of magnetic fabric observed in FTBs, relates different types of magnetic fabric to different processes of deformation and provides insights into the strain distribution of FTBs.

Keywords: analogue modelling, AMS, fold-and-thrust belt, strain distribution, décollement, magnetic fabric

Thorben Schöfisch, Department of Earth Sciences, Mineralogy, Petrology and Tectonics, Villavägen 16, Uppsala University, SE-75236 Uppsala, Sweden.

© Thorben Schöfisch 2021

urn:nbn:se:uu:diva- 451977 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-451977)

"Work it harder, make it better

Do it faster, makes us stronger

More than ever, hour after

Hour work is never over.”

Daft Punk (2001)

Harder, Better, Faster, Stronger

List of Papers

This thesis is based on the following papers, which are referred to in the text

by their Roman numerals. Paper I is published in the Journal of Structural

Geology. Paper II is a manuscript, which is submitted to Tectonics.

I Schöfisch, T., Koyi, H., Almqvist, B. (2021) Influence of dé-

collement friction on anisotropy of magnetic susceptibility in a

fold-and-trust belt model. Journal of Structural Geology,

144:104274

II Schöfisch, T., Koyi, H., Almqvist, B. Magnetic fabric signature

within a thrust imbricate; an analogue modelling approach (sub-

mitted to Tectonics)

Reprints were made with permission from the respective publishers.

Personal Contribution

The articles that compose this thesis are the collaborative work of several

authors. The individual contributions to each publication are listed below:

I. The conceptual idea of the model was given by Hemin Koyi.

After two test models, the final model was created by me. Af-

ter model preparation and shortening, AMS sampling and

measurements were executed by me with advice by my super-

visors Hemin Koyi and Bjarne Almqvist. I summarised the

data and interpretations were discussed with both supervisors.

I wrote the initial draft and improved it after substantial advice

of my co-authors.

II. Together with Hemin Koyi, I developed the fundamental idea

of this study. After the first insights and discussions with my

supervisor, I created two additional models. Sampling and

measurements were performed by me. I summarised and in-

terpreted the data with fruitful discussions with Hemin Koyi

and Bjarne Almqvist. The final draft was written by me and

improved after suggestions from my co-authors.

Contents

1. Introduction ............................................................................................... 13

1.1. Motivation ......................................................................................... 13

1.2. Objective ........................................................................................... 14

2. Background ............................................................................................... 15

2.1. Analogue Modelling .......................................................................... 15

2.2. Strain in Fold-and-Thrust Belts ......................................................... 16

2.2.1. Anisotropy of Magnetic Susceptibility ...................................... 18

2.2.2. AMS as strain indicator ............................................................. 19

3. Methodological workflow ......................................................................... 23

3.1. Model setup and preparation ............................................................. 23

3.2. Sampling, measuring the magnetic signal and data evaluation ......... 23

4. Summary of publications .......................................................................... 25

4.1. Paper I Influence of décollement friction on anisotropy of magnetic

susceptibility in a fold-and-thrust belt model ........................................... 25

4.2. Paper II Magnetic fabric signature within a thrust imbricate; an

analogue modelling approach ...................................................................... 28

5. Conclusion ................................................................................................ 30

6. Outlook ..................................................................................................... 31

Summary in Swedish .................................................................................... 33

Acknowledgment .......................................................................................... 35

References ..................................................................................................... 36

Abbreviations and symbols

AMS anisotropy of magnetic susceptibility

FTB fold-and-thrust belt

LPS layer-parallel shortening

Mi magnetization

Hi applied magnetic field intensity

ki magnetic susceptibility

kmax maximum principal axis of susceptibility

kint intermediate principal axis of susceptibility

kmin minimum principal axis of susceptibility

L magnetic lineation

F magnetic foliation

ni natural logarithm of ki

Pj corrected degree of anisotropy

T shape of anisotropy

13

1. Introduction

1.1. Motivation

Following Charles Lyell’s well-known quote “The present is the key to the

past”, understanding the past could in turn provides clues about scenarios of

geologic development in the future. Estimating strain from field observations

is one approach to learn about geological processes. Another approach is to

create models to simulate the development of geological structures and to dis-

cuss potential outcomes based on previous observations and experiences.

Therefore, models help us to understand geological processes, e.g., the devel-

opment of a fold-and-thrust belt (FTB). Shortening in FTBs is accommodated

by thrusting, folding and penetrative strain, such as layer-parallel shortening

(LPS). LPS includes processes like recrystallisation of minerals, volume loss

by porosity reduction (compaction) and grain realignment (e.g., Hossack,

1979; Geiser, 1988; van der Pluijm and Marshack, 2004; Fossen, 2010). How-

ever, LPS is not easy to quantify in the field, especially in the absence of strain

markers. This results in underestimation of strain and deformation. In contrast,

in models, the initial state before deformation is known and deformation pro-

cesses and strain partitioning can be monitored during evolution of the models

(e.g., Hossack, 1979; Mulugeta and Koyi, 1992; Koyi, 1995; Groshong et al.,

2012). Nevertheless, models are simplifications of natural processes and com-

parison between models and natural analogies need to be discussed carefully.

However, with models, we can systematically study factors that influence de-

formation. For example, interpreting grain alignment within rocks at different

locations, by e.g., analysing its magnetic fabric, provides insights in defor-

mation. The magnetic fabric, described by measuring the anisotropy of mag-

netic susceptibility (AMS), has been demonstrated as a useful technique for

studying petrofabrics in Geosciences and especially in structural geology to

identify strain on grain scale (e.g., Graham, 1966; Hrouda, 1982; Borradaile

and Henry, 1997; Parés, 2015). While AMS has mainly been applied at natural

cases, Almqvist and Koyi (2018) introduced AMS in analogue modelling and

illustrated the potential of using AMS in analogue models. Their findings

served as the basis for this thesis: to investigate strain using AMS in models

and comparing the results to natural examples. The method of analysing mag-

netic fabric in analogue models provides a great opportunity to improve the

understanding and breakdown of strain distribution and partitioning in models

and leads to further material of discussion about their natural analogues.

14

1.2. Objective

This thesis summarises the work done in the first part of my PhD-project,

which targets the problem of quantifying penetrative strain within analogue

models and in nature. Following Almqvist and Koyi (2018)’s initial study on

the potential of magnetic fabric analysis in analogue models, further studies

are needed to understand AMS analysis for describing strain in analogue mod-

els. Two such studies were performed and are outlined in this thesis. The first

study (Paper I) investigates the strain distribution within FTBs shortened

above two adjacent décollements with different friction coefficients and, ad-

ditionally, discusses the influence of décollement friction on AMS within

FTBs. The second study (Paper II) illustrates a general strain distribution

within and across thrust imbricates in more detail. In the following, I give a

broad overview of analogue modelling, AMS and its use, the main methodical

workflow, and I end with summarising the current work.

15

2. Background

2.1. Analogue Modelling

Analogue models are simplifications of nature to study mechanical rules and

physical properties that influence geological processes and especially defor-

mation. In a systematic way, deformation through time and space is quantified

and described by monitoring and analysing analogue models. Compared to

numerical models, where physically based mathematical equations predefine

the model, analogue models use physical materials and many different tech-

niques that have been developed over the past century. With recent inventions

in analogue modelling, complex geologic questions can be addressed in even

more detail than they used to be (reviews by e.g., McClay, 1990; Koyi, 1997;

Ranalli, 2001; Schellart, 2002; Graveleau et al., 2012; Schellart and Strak,

2016). These reviews highlight the usage and development of analogue mod-

elling during its 200-year history. The first analogue model was described in

the beginning of the 19th century by Hall (1815), who contracted layers of

cloths explaining the process of folding. Since then, many approaches, setups

and materials were used to understand the development of structures in nature.

The first models used colours or a material contrast as passive markers to

depict the deformation within a model (e.g., review by McClay, 1990). Pas-

sive markers play an important role to illustrate deformational change and es-

timate strain. For example, coloured circles or a grid with squares of the same

material can be imprinted at the surface of the model and, during model short-

ening, surface deformation can be monitored by examining the change in

shape of the passive markers (e.g., Davy and Cobbold, 1988; see review by

Graveleau et al., 2012; see review by Schellart and Strak, 2016). Also, during

model preparation, passive marker layers can be included in the modelling

studies to quantify deformation at deeper parts of the model and for cross-

section balancing (e.g., McClay, 1990; Mulugeta and Koyi,1992; Koyi et al.,

2003). Laser scanning (e.g., Nilforoushan et al., 2008), pixel tracking/PIV

(e.g., Hampel et al., 2004; Adam et al., 2005), and other optical methods, as

summarised in Schellart and Strak (2016), were introduced to analogue mod-

elling for more detailed analysis, quantification, and scaling of the model re-

sults. Cutting sections in models during subsequent stages of deformation pro-

vides further information on internal deformation across the model and dis-

plays the 4D evolution of the model (e.g., Mulugeta and Koyi, 1992). How-

ever, the procedure of evaluating a 4D evolution of models is time consuming

16

and is therefore replaced in some cases by X-ray tomography (Colletta et al.,

1991). In order to quantify strain and trace deformation in models in detail,

high-resolution optical techniques are used (e.g., Adam et al., 2005; Dotare et

al. 2016). Since Almqvist and Koyi (2018) started exploring the potential of

AMS in analogue models recently, strain in models can also be described by

the magnetic fabric in a modelled FTB. In this thesis AMS is used to study

strain within FTBs shortened above two different adjacent décollements (Pa-

per I), and across thrust imbricates in more detail (Paper II).

2.2. Strain in Fold-and-Thrust Belts

Fold-and-Thrust Belts (FTBs) are common around the world and develop

mainly in compressional regimes. They form where layers of the upper crust

of the Earth are shortened under low-grade metamorphic conditions and are

mainly adjacent to a main internal orogen with decreasing deformation inten-

sity towards its foreland (Fig. 1) (van der Pluijm and Marshack, 2004). FTBs

encompass sequences of imbricates with mainly fore- and backthrusts, folded

rocks and pop-up structures (Fig. 1). Shortening in FTBs is accommodated by

penetrative strain, folding and thrusting. To quantify strain in a FTB, cross-

section balancing is performed from field observations and/or geophysical

data (Dahlstrom, 1969). The amount of shortening accommodated by thrust-

ing and folding can be calculated by restoring the constant bed length of de-

formed rock units. However, to account for LPS in nature, strain markers (e.g.,

fossils, reductions spots, pressure solution cleavage, calcite twinning, or peb-

ble rotation) need to be analysed. Here, methods like the Fry method, the cen-

ter-to-center method and others (e.g., van der Pluijm and Marshack, 2004;

Fossen, 2010) are useful tools to provide further information about strain in

rocks. The results from strain marker analyses need to be included in cross-

section balancing to quantify strain partitioning of a FTB (e.g., Hossack, 1979;

Woodward et al., 1986; Koyi et al., 2003; Fossen, 2010; Groshong et al.,

2012). Where strain markers are absent in nature, the initial state before de-

formation cannot be restored completely and thus strain is often underesti-

mated. In contrast, in analogue models, deformation can be monitored from

the initial state to the final stage of deformation. Balancing cross-sections from

analogue models gives a detailed overview of strain accommodation. The

missing distance between the restored bed length by folding and thrusting

compared to the initial bed length of the model provides the amount of LPS

and illustrates the importance of penetrative strain during deformation (Hos-

sack, 1979; Mulugeta and Koyi, 1992; Koyi, 1995; Koyi at al., 2003; Gro-

shong et al., 2012). The distribution of strain can vary vertically and laterally

and changes with time during deformation (Mulugeta and Koyi, 1982; Koyi,

1995; Koyi et al., 2003). These previous modelling studies show, that at the

onset of deformation, most of the bulk shortening is accommodated by

17

compaction and grain reorientation. With further bulk shortening of the model,

folding and thrusting increase in importance until deformation propagates far-

ther into the foreland and a new imbricate is accreted.

In general, cross-section balancing, and analyses of strain markers provide

insights into the strain distribution and development of a FTB. However, the

tools and strain markers described above are limited from their macroscopic

appearance. To provide further insight, especially in describing and quantify-

ing penetrative strain, other methods like thin section analysis or measuring

AMS are decisive.

Figure 1: Schematic overview of a fold-and-thrust belt. Fold-and-thrust belts are form-ing in the foreland adjacent to main orogen an consist of a series of imbricates.

18

2.2.1. Anisotropy of Magnetic Susceptibility

The anisotropy of magnetic susceptibility (AMS) is a useful tool to describe

strain within the field of geosciences (e.g., Graham, 1966; Hrouda, 1982; Bor-

radaile and Henry, 1997; Parés, 2015). AMS is based on measuring the mag-

netic susceptibility of minerals within samples taken from the field or models

and interpreting the orientation of the resulting principal axes of magnetic sus-

ceptibility.

In general, the magnetic susceptibility (k) is the ability of a mineral being

magnetised by an applied magnetic field. However, in the laboratory, we

measure the bulk susceptibility, as samples consists out of many mineral

grains and each grain contributes to the bulk signal. At the end, it is possible

to normalize the bulk susceptibility by volume, mass or treat it as not normal-

ized. Nevertheless, k can be described as a response, i.e., the magnetization

(M), of a mineral to an applied magnetic field intensity (H):

M = kH (1)

The shape of the mineral and its crystallographic order determine the magnetic

response of the mineral within an applied magnetic field. This magnetic re-

sponse can be different in different mineral orientations when the magnetic

field is applied in different directions and therefore the magnetic susceptibility

is referred as anisotropic. Within a three dimensional coordinate system,

where the axes correspond to k1, k2, and k3, the anisotropy of magnetic sus-

ceptibility (k) is described by a second-rank tensor resulting in the following

relations to relate the induced field (Mi) with the applied field (Hi):

M1 = k11H1 + k12H2 + k13H3

M2 = k21H1 + k22H2 + k23H3 (2)

M3 = k31H1 + k32H2 + k33H3

Since the k-matrix is symmetric, only six independent elements need to be

defined (k11, k22, k33, k12=k21, k13=k31, and k23=k32), which derive from six in-

dependent measurements. From the resulting matrix, we can calculate three

eigenvectors, which are also called principal axes of susceptibility, and its ei-

genvalues (Tauxe, 2018). The principal axes correspond to the minimum, in-

termediate and maximum axis of susceptibility and describe an ellipsoid (kmax

≥ kint ≥ kmin). This ellipsoid is consequently a function of the chemical compo-

sition (mineral susceptibility and anisotropy) and structure of the measured

grain (crystallography, shape and size) and therefore depends on its orienta-

tion in the measurement coordinate system (Rochette et al., 1992). Parameters

derived from measurements of the principal axis of susceptibility describe the

magnitude of AMS, the shape of the AMS ellipsoid and the relationship of the

magnitudes of principal axes with each other (see also Jelinek, 1981; Hrouda,

19

1982; Tarling and Hrouda, 1993; Tauxe, 2018). These parameters are useful

to describe the petrofabric and relate changes in magnetic fabric to strain.

2.2.2. AMS as strain indicator

Measuring the AMS of a sample taken from the field or model, provides the

bulk orientation of the principal axes of all grains within the sample, whereas

ferromagnetic grains (i.e., mineral with a magnetic remanence) dominate the

AMS signal. For example, quartz (diamagnetic) has a bulk susceptibility of ~-

15 µSI (see data compilation by Hunt et al., 1995), whereas magnetite ranges

values higher than 1 SI (see data compilation by Hunt et al., 1995). Therefore,

the AMS measurement preferentially reflects a preferred alignment of the

more magnetic minerals, such as magnetite, which can be referred as “mag-

netic fabric”. In structural geology, we are interested in the orientations and

alignment of grains because grain analyses provide insight into strain on a

grain scale. The basic ideas of using magnetic fabric in structural geology are

to sample different locations within a tectonic setting and to compare the mag-

netic fabric from each location. Interpretation of these fabric observations can

reveal the deformation process within the sampled region and can help to es-

timate differences in deformation between different regions. Pioneering work

was performed by Ising (1942) and Graham (1954; 1966), who recognized the

magnetic fabric and related it to deformation. During the past four centuries,

several studies were outlined to better understand AMS and its usage in struc-

tural geology (reviews by e.g., Hrouda, 1982; Borradaile, 1988; Borradaile

and Henry, 1997; Borradaile and Jackson, 2010; Parés, 2015). In summary,

the resulting orientation and shape of the AMS ellipsoid provide information

of the alignment and sorting of grains, which can be related to deformation

and especially to LPS. Several studies tried to correlate the change in the fabric

carrying AMS signal with strain (e.g., Owens 1974; Hrouda, 1976, 1978,

1982, 1987; Hrouda and Janák, 1976; Kneen, 1976; Rathore, 1979; Bor-

radaile and Tarling, 1981; Kligfield et al., 1981; Kissel et al., 1986; Borradaile,

1988, 1991; Hirt et al., 1988, 2000, 2004; Averbuch et al., 1992; Borradaile

and Henry, 1997; Mattei et al., 1997; Pueyo-Morer et al., 1997; Sagnotti et al.,

1998; Parés et al., 1999; Parés and van der Pluijm, 2002, 2003; Schwehr and

Tauxe, 2003; Larrasoaña et al., 2004, 2011; Burmeister et al., 2009; Cifelli et

al., 2009; Weil and Yonkee, 2009; Pueyo-Anchuela et al., 2010; Levi and

Weinberger, 2011; Ferré et al., 2014; Levi et al., 2014, 2018; Pocoví Juan et

al., 2014 and references therein; Anastasio et al., 2015; Weinberger et al.,

2017). However, many factors are contributing to the AMS signal (e.g., min-

eral composition, crystallography, recrystallization, deformation, subfabrics)

and many strain increments are accumulated in the finite fabric (e.g., Uyeda

et al., 1963; Borradaile, 1987, 1988; Rochette and Fillion, 1988; Henry 1992;

Borradaile and Dehls, 1993; Borradaile and Henry, 1997; Ferré et al., 2004;

Martín-Hernández and Ferré, 2007; Hirt and Almqvist, 2011; Parés and van

20

der Pluijm. 2014). Therefore, AMS analysis needs to be discussed carefully in

relation with the magnitude of strain (Rochette, 1987; Borradaile, 1991; Aver-

buch et al., 1992; Borradaile and Jackson, 2010). Nevertheless, the composi-

tion of the AMS signal is known in a controlled environment, as in analogue

models. Consequently, magnetic fabric changes in the models provide evi-

dence of strain change, especially, as the models are constraint by grain rear-

rangement and rotation. Grain reorientation is reflected in the change in prin-

cipal axes distribution, shape and degree of anisotropy. These three parame-

ters are significant for our studies and are discussed in the following.

2.2.2.1. Principal axes rotation and fabric

The orientation of the principal axis of susceptibility is often classified using

equal-area lower-hemisphere projections (Fig. 2). The magnetic fabric of un-

deformed rocks is described as an initial or depositional fabric, that is over-

printed by deformation to a tectonic fabric (Fig. 2). Since the models simulate

deformation of sedimentary rocks in a FTB, the description of magnetic fabric

change reflects the magnetic fabric change in sedimentary rocks. The evolu-

tion of magnetic fabric starts with an initial sedimentary fabric. The sedimen-

tary fabric is described by a magnetic foliation (kmax-kint-girdle distribution)

parallel to bedding with kmin clustering with a pole to bedding (Fig. 2a). In

contrast, the tectonic fabric is characterised by a magnetic foliation perpen-

dicular to the shortening direction (Graham, 1966; Averbuch et al., 1992;

Bakhtari et al., 1998; Parés et al., 1999; Parés, 2015) (Fig. 2d). With onset of

deformation and increase in LPS, the principal axes are reorienting, and, as

the axes are distributed in different directions, clusters or girdles, a composite

fabric can be interpreted (Figs. 2b, and 2c). Such composite fabric, that is also

called intermediate fabric, is characterised by a magnetic lineation (kmax clus-

tering) perpendicular to the shortening direction (e.g., Parés et al., 1999; Parés

and van der Pluijm, 2002) (Figs. 2b, and 2c). In many cases of sedimentary

rocks, such magnetic lineation occurs parallel to the intersection lineation of

bedding and cleavage formation (e.g., Parés, 2015) or parallel to fold axis

(e.g., Borradaile and Henry, 1997). Nevertheless, kmin sustains still vertical to

bedding with the creation of magnetic lineation by kmax clustering. But with

further increase in strain, kmin rotates towards the tectonic fabric and creates a

girdle distribution, whose overall pattern can be referred as another type of

intermediate fabric (Fig. 2c; Parés, 2015). Such intermediate fabrics or com-

posite fabrics are common in FTBs and represent a contribution from LPS

(Bakhtari et al., 1998; Parés et al., 1999). Additionally, as indicated by in-

creasing strain, folding, thrusting or cleavage formation influence the orienta-

tion of principal axes as well. For example, with bedding rotation, the mag-

netic foliation can remain parallel to bedding, but has an angle to the initial

fabric (e.g., Averbuch et al., 1992; Saint-Bezar et al., 2002). Also, grains are

realigning into parallelism with cleavage and thrust surfaces (e.g., Kligfield et

al., 1981; Hirt et al., 2004). Note, in cleavage zones and at thrust surfaces,

21

recrystallisation of magnetic contributors is influencing the AMS signal and

careful interpretations of the fabric is needed (Borradaile, 1991; Rochette et

al., 1992; Parés and van der Pluijm, 2002; Borradaile and Jackson, 2010).

However, principal axes reorientation are useful indicators to assess degree of

tectonic deformation (e.g., Graham, 1966; Averbuch et al., 1992; Bakhtari et

al., 1998, Parés, 2015).

Figure 2: Schematic overview of principal axis distribution with increasing strain, that acts in x-direction.

2.2.2.2. Shape and degree of anisotropy

The shape of the AMS ellipsoid can be described by the magnetic lineation

(L) and magnetic foliation (F), analogously to the Flinn-diagram (Hrouda and

Janák, 1976; Kligfield et al., 1977):

𝐿 = 𝑘𝑚𝑎𝑥 𝑘𝑖𝑛𝑡⁄ (3)

𝐹 = 𝑘𝑖𝑛𝑡 𝑘𝑚𝑖𝑛⁄ (4)

F is related to a girdle distribution of kmax and kint, while L relates to the clus-

tering of kmax. In order to integrate all principal axes in the description of the

shape of the ellipsoid, the shape factor T is defined, which ranges from T = +1

for oblate, T = 0 for neutral to T = -1 for prolate ellipsoids and uses the natural

logarithms (ln) of the principal axes: 𝑛𝑚𝑎𝑥 = ln (𝑘𝑚𝑎𝑥), 𝑛𝑖𝑛𝑡 = ln (𝑘𝑖𝑛𝑡),

𝑛𝑚𝑖𝑛 = ln (𝑘𝑚𝑖𝑛), and 𝑛𝑚𝑒𝑎𝑛 = (𝑛𝑚𝑎𝑥 + 𝑛𝑖𝑛𝑡 + 𝑛𝑚𝑖𝑛)/3.

𝑇 = 2 𝑛𝑖𝑛𝑡 − 𝑛𝑚𝑎𝑥 − 𝑛𝑚𝑖𝑛

𝑛𝑚𝑎𝑥 − 𝑛𝑚𝑖𝑛 (5)

22

Similarly, the degree of anisotropy (Pj) can be defined as function of grain

alignment and sorting within a sample, which was mathematically established

by Jelinek (1981) and corrected with integrating the logarithms by Hrouda

(1982).

𝑃𝑗 = 𝑒𝑥𝑝 √{ 2 [(𝑛max − 𝑛𝑚𝑒𝑎𝑛)2 + (𝑛𝑖𝑛𝑡 − 𝑛𝑚𝑒𝑎𝑛)2 + (𝑛𝑚𝑖𝑛 − nmean)2]} (6)

Plotting both parameters (T and Pj) provide a diagram that expresses the de-

gree of anisotropy as a function of ellipsoid shape. This diagram, known in-

formally as the “Jelinek” plot, has been used to describe a strain path of rocks

and sediments, based on the AMS dataset (Jelinek, 1981; Hrouda, 1982; Bor-

radaile, 1988, 1991; Borradaile and Henry, 1997) (Fig. 3). It is suggested that

the oblate sedimentary fabric is decreasing in the degree of anisotropy with

the onset of deformation and moves into the prolate field, representing a par-

tially tectonised fabric (Fig. 3). A further increase in degree of anisotropy and

change into the oblate fabric field, as seen in Fig. 3. However, this fabric type

is not further explored in this thesis, as such change includes often recrystal-

lisation, metamorphism and ductile deformation, which cannot be taken into

account in our models. Some studies try to illustrate differences in the degree

of deformation by plotting the change in inclination of kmax as a function of

shape of anisotropy (T) (Robion et al., 2007) or classifying seismites by plot-

ting L vs T (Levi et al., 2018).

Figure 3: Idealised strain path of rock samples shown in a “Jelinek” plot, from an initial sedimentary fabric (a) via an intermediate fabric (b) to a fully tectonised fabric (c) (after Borradaile and Henry, 1997).

23

3. Methodological workflow

The models of both studies have certain parameters and a general workflow

in common, which are described in the next sections.

3.1. Model setup and preparation

Loose quartz sand (0.124-0.356 mm) was mixed with same-sized, subangular

magnetite grains (<0.1 volume%). Note, that the fraction of magnetite is one-

tenth smaller than used in Almqvist and Koyi (2018). This still gives sufficient

signal, even though the size of our samples had a volume of 2.2 cm³, which is

smaller than regular sized cubes used in palaeomagnetism (~8 cm3)., The

smaller cubes have the advantage of targeting smaller structures in the models

in detail. The granular, dry mixture of sand and magnetite has a cohesion of µ

= 0.49.

Starting from the backstop, the mixture was scraped layer by layer, sepa-

rated by thin coloured layers of sand. The thin coloured layers were sieved

and used as marker layers to trace deformation in deeper parts of the models.

On top of the undeformed models, grids of circles were sieved using coloured

sand to monitor surface deformation. Additionally, coloured reference points

were placed between some circles at the surface for referencing the models

and pictures, which were taken during model shortening. Finally, a backstop

shortened the models by moving forward and pushing the models from one

side (Fig. 4). After a pre-defined increment of model shortening, photos were

taken for surface observations.

3.2. Sampling, measuring the magnetic signal and data

evaluation

After shortening the models, the sand was carefully wetted. The wet sand has

a cohesion that enables sectioning by cutting pieces out of the model without

collapsing. Different sections were taken with regular spacing across the mod-

els by cutting from the backstop (model north) to the model south, i.e., per-

pendicular to the shortening direction. Each section was photographed, and

samples were taken by pushing the cubic containers carefully into the model

24

before the next section was cut. This sampling strategy enables to sample the

surface as well as deeper parts of the models. Cross-section balancing was

performed on referenced images, which allows a comparison between strain

estimation derived from the deformed passive markers (i.e., coloured sand)

with analyses of the magnetic fabric.

Measurements of the AMS were performed with a MFK1-FA Kappabridge

(Agico Inc.) using an AC field strength of 200 A/m with a frequency of 976

HZ. With the instrument related software Anisoft, the measurement results are

illustrated in different diagrams, tables and by equal-area lower hemisphere

projections, where the orientations of the principal axes are plotted and means

as well as confidence ellipses were calculated (Jelinek, 1978). Additionally,

Excel, ArcGiS, Matlab, ImageJ, Move and Leapfrog were used to interpret and

depict the results in this thesis.

Figure 4: Initial model setup with an initial model length (l) and an initial model height (h). Laser scans and pictures are taken during model shortening. The backstop is grad-ually moving into the model, creating the deformed sand wedge.

25

4. Summary of publications

Paper I utilises AMS analysis on a model to explore the importance of dé-

collement friction on penetrative strain in a FTB. Paper II focusses on the

strain distribution across a thrust imbricate. The main outcomes from these

papers are summarised in this chapter.

4.1. Paper I Influence of décollement friction on anisotropy of magnetic susceptibility in

a fold-and-thrust belt model

Basal friction has an important influence in the structural geometry and kine-

matics within a FTB shortened above different décollements. The influence of

décollement friction is reflected in the magnetic fabric in our models and nat-

ural examples of similar settings, like the Zagros FTB (Bakhtari et al., 1998;

Aubourg et al., 2010), the Potwar Region in Pakistan (Robion et al., 2007) or

in the Spanish Pyrenees (Robion et al., 2007; Muñoz et al., 2013).

In this paper, we present the results of a model shortened above two adja-

cent décollements with different friction in order to analyse the influence of

the décollement friction on the penetrative fabric, detected through the mag-

netic fabric. The model shows that deformation varies above each décollement

(Fig. 5). The initial model fabric, which is influenced by the scraping during

model preparation, has a magnetic lineation (kmax alignment) which is parallel

to the shortening direction with a vertical kmin cluster (Fig. 5f and h). Even

after shortening of the models, this initial fabric is detected in the undeformed

foreland. Above the high-friction décollement, a stack of imbricates is pro-

duced, which creates a magnetic fabric that is related to the observed closely

spaced thrusts. The thrust-affected fabric has a magnetic foliation (kmax-kint-

girdle distribution) parallel to the thrust surfaces (Fig. 5a). In comparison,

above low-friction décollement, the deformation front propagates farther into

the foreland and consists of a sequence of boxfolds. The magnetic fabric ob-

served in the hinterland above the low-friction décollement has both a thrust-

induced component (Fig. 5c), which also reflects the vergence of the thrust, as

well as a penetrative-strain induced component (Fig. 5d). The latter compo-

nent is expressed by the magnetic lineation being perpendicular to the short-

ening direction and a kmin cluster vertical (pole) to bedding. The change in

26

magnetic fabric from the foreland to the hinterland above the low-friction dé-

collement occurs gradually, defined by a transition zone. The magnetic fabric

in this transition zone is characterised as a penetrative-strain induced fabric

(Fig. 5e). However, above the high-friction décollement the magnetic fabric

change from the foreland towards the hinterland is sharp and fabrics are dis-

tinct from each other (compare Figs. 5a and 5h). As the deformation front

propagated differently above the two décollements, a deflection zone with

strike slip-faults is formed to compensate the boundary of the adjacent dé-

collements. In the deflection zone, a magnetic fabric is observed that repre-

sents the change between the fabric produced by the thrust imbricates in the

hinterland of the high-friction décollement and the boxfolds from the hinter-

land of the low-friction décollement (Fig. 5b). Approaching the deflection

zone, the magnetic lineation is rotated towards parallelism with the arcuate

forethrusts in the model. Additionally, strike-slip faults formed in the interior

of the deflections zone. At the strike slip-faults, kmax rotated into parallelism

with the strike-slip fault surfaces, whereas kmin rotated away from its vertical

orientation towards subhorizontal inclination, perpendicular to the thrust sur-

face (Fig. 5g). Above each décollement, characteristic magnetic fabrics de-

velop, which can be compared to natural examples of FTBs shortened above

different frictional décollements. For example, the Zagros mountains are de-

formed mainly above a low frictional salt décollement that produced, similar

to our model, mainly intermediate magnetic fabric with magnetic lineation

perpendicular to shortening direction and parallel to fold axis and thrusts

(Bakhtari et al., 1998; Aubourg et al., 2010). Similar orientation of magnetic

fabric is observed in the Potwar Region, where the development of a low-

friction décollement is interpreted by Robion et al. (2007). Above high-fric-

tion décollements, a higher quantity of intermediate and tectonic fabric can be

characterised, compared to areas that were deformed above low-friction dé-

collement (Robion et al., 2007), which coincides with our observations in the

model.

In conclusion, this paper highlights the importance of décollement friction

on the evolution of a FTB and its associated magnetic fabric. It furthermore

provides insights in strain distribution and magnitude in FTBs shortened

above different frictional décollements.

27

Figure 5: Overview of AMS fabric in model shortened above two adjacent different frictional décollements with a high-friction (blue colour on model surface) and low-friction (green colour on model surface). Zones can be separates by structural differ-ences and show characteristic magnetic fabric in a) thrust-affected fabric in the hin-terland above the high-friction décollement, b) mixed fabric in the hinterland above the transition between décollements, c) thrust-affected fabric and d) penetrative-strain affected fabric above low-friction décollement, e) penetrative-strain affected fabric in transition between fore- and hinterland and g) fabric in deflection zone. f) and h) show data from the undeformed foreland and represent the initial model fabric. Each fabric in presented in equal-area projections with confidence ellipses and their mean (filled white symbols).

28

4.2. Paper II Magnetic fabric signature within a thrust imbricate;

an analogue modelling approach

This study investigates the strain distribution and development within and at

different parts of a thrust imbricate. Three models with a comparable setup

were shortened by different amounts (Model A: 16%, Model B: 24.5% and

Model C: 34%). In Model A, a pop-up structure was developed, bounded by

a backthrust and a forekink zone. In Model B (Fig. 6) and Model C, which

experienced higher bulk shortening, further backthrusts and forekink zones

developed, bounding the main pop-up structure. Additional forethrusts were

created in front of the pop-up structure in all three models. AMS samples were

taken at different parts of the models for analysis of the magnetic fabric. Gen-

erally, all three models developed similar magnetic fabric. In areas away from

thrusts and kink zones, a penetrative-strain induced fabric is observed that is

generally oblate (Figs. 6e, and 6f). Towards the thrusts and kinkzones, the

magnetic fabric is changing gradually. The gradual change in magnetic fabric

is seen by changes in the inclination of principal axes, a decrease in degree of

anisotropy, and by the development of prolate fabric (Fig. 6f). At the thrusts,

a tectonic fabric with magnetic foliation (kmax-kint girdle distribution) parallel

to thrust surface is detected (Figs. 6a, and 6c). Furthermore, the degree of an-

isotropy at a thrust is lower compared to the magnetic fabric away from a

thrust or a kinkzone (Fig. 6f). An additional decrease in degree of anisotropy

can be observed downwards along all thrusts. The magnetic fabric of all

thrusts from the three models are similar, even though the thrusts differ in

amount of displacement and inclination. This decrease in degree of anisotropy

with depth at thrusts is interpreted to arise from the original magnetic fabric

prior to thrusting, as strain is generally distributed heterogeneously in a model

(Mulugeta and Koyi, 1992; Koyi 1995) and LPS is increases with depth (Koyi

et al., 2003). Kinkzones in the three models, which developed different geom-

etries and kinematics, display different magnetic fabric (Fig. 6b). Generally,

the magnetic fabrics of the kinkzones reflect the different contribution in strain

by LPS, folding and thrusting. Here, a magnetic lineation (kmax clustering) rep-

resents an intersection lineation from folds and forethrusts. In general, scatter-

ing of the principal axes orientation of the kinkzone fabric indicates the struc-

tural complexity of the kinkzones. However, in the kinkzone of Model A, a

thrust-induced fabric can be interpreted by kmax being distributed parallel to

the forethrust surfaces. This thrust-induced fabric in kinkzone of Model A in-

dicates that thrusting dominates deformation in steep kinkzones. In contrast,

shallower inclined kinkzones reflect higher strain, accommodated by folding,

as the kinkzone in Model B developed a broad cluster of kmin axes that are

distributed parallel to the poles of the folds within the kinkzone. Most of mag-

netic fabric change is created during thrusting and kinkzone development. The

29

results of this modelling study are comparable to natural examples like in the

French Alps (Kligfield et al., 1981), Corbières in the Pyrenees (Averbuch et

al. 1992), Central Appalachian FTB (Hirt et al., 2004), in the Barbados Ac-

cretionary Prism (Housen et al., 1996) and the Hikurangi Subduction Margin

in New Zealand (Greve et al., 2020). These natural examples, similar to our

model results, show an increase in strain revealed by changes in magnetic fab-

ric towards the main deformation zones with most fabric change at the thrusts.

In conclusion, magnetic fabric reflects changes in strain and distribution

within a thrust imbricate and provides insights into deformation kinematics at

thrusts and kinkzones.

Figure 6: Overview of magnetic fabric developed in the models, using Model B as representative model. The orientations of the principal axes from samples taken at a) backthrust, b) forekink zone, c) and d) forethrusts, and e) for samples taken away from thrusts and kinkzone are plotted on equal-area projections. f) shows the distribution of the degree of anisotropy (Pj) against the shape of anisotropy (T) as function of distance to the thrusts or kinkzone (color code).

30

5. Conclusion

This thesis demonstrates the use of AMS in analogue modelling and provides

insights into the strain distribution in FTBs simulated by sandbox modelling.

Furthermore, it underlines the importance of décollement friction on the mag-

netic fabric in FTBs above different frictional décollements (Paper I) and re-

veals gradients and kinematics in the strain distribution as a function of dis-

tance to localised deformation zones (a thrust or kinkzone), (Paper II).

With the onset of shortening, the model compacts and creates a penetrative-

induced magnetic fabric. With further shortening, thrusts and kinkzones are

forming that overprint the penetrative-induced magnetic fabric locally to-

wards a magnetic fabric characteristic by thrusts (magnetic foliation parallel

to thrust surface) or kinkzones (intersection lineation between thrusts and

folds). Towards the thrusts and kinkzones, the magnetic fabric is modified

with the development of deformation zones like thrusts and kinkzones and

develops gradients in the change of magnetic fabric. The gradients in magnetic

fabric indicate changes in strain, which are influenced by the maturity of the

deformation zone (Paper II). The distribution of strain and geometry of

thrusts and kinkzones within a FTB are influenced by the friction of the dé-

collement. Consequently, the appearance of different types of magnetic fabric,

associated to certain structures, is reflecting the different development of

FTBs above different frictional décollements. Generally, strain is increasing

from the foreland to the hinterland in FTB, but gradients in strain change along

profile are determined by the friction of the décollement below (Paper I).

In conclusion, this thesis provides insights into the strain distribution and

development of FTBs in sandbox models using AMS. The strain distribution

revealed by magnetic fabric is dependent on the formation of deformation

zones and distance towards such deformation zones. Different accommoda-

tion of model shortening is reflected by different types of magnetic fabric

characteristic for LPS, folding and thrusting.

31

6. Outlook

Further models are planned in the second part of the PhD-project aiming to

improve the method of strain quantification with AMS in analogue models

using different materials, as well as different techniques for model preparation

(sieving vs scraping) on the magnetic fabric change due to deformation. A

benchmark study from 15 different analogue laboratories has shown, that even

following the same strict modelling protocol for preparing the same model and

using similar material, the deformed models developed a variation of geome-

tries of thrust wedges (Schreurs et al., 2016). It is concluded by the authors,

that the human influence plays an important role during modelling. Even small

changes in the model setup have a significant impact on the mechanical prop-

erties of the material and therefore, on the deformation within the model

(Schreurs et al., 2016). To increase the understanding of the influence of

model preparation during modelling, I performed test models (comparable

workflow as the models performed in this thesis) comparing sieving and

scraping as two model preparation techniques, which are common techniques

in the analogue modelling world (e.g., review by Graveleau et al., 2012). Pre-

liminary AMS results from the test models indicate variances in magnetic fab-

ric for similar structures. Results from such study can have influence on the

interpretation of depositional effects on AMS data in nature (e.g., compare to

Rees 1965, 1966). However, further test will be performed for further insights.

Additionally, different carriers of a magnetic signal, i.e., different minerals,

create different AMS signals in deformed rocks and therefore, interpretation

and comparison of magnetic fabric created by different minerals need to be

done carefully (e.g., Borradaile and Jackson, 2010 and references therein).

Mixing sand with different minerals, e.g., like biotite or haematite, and per-

forming simple compressional sandbox models with these different mixtures,

will provide interesting insights in the correlation of strain with AMS.

To complement the modelling studies, model results will be compared to

the magnetic fabric distribution of a stack of imbricates in the Spanish Pyre-

nees, where samples are collected for later analysis. The Aragüés thrust sys-

tem in the south-central Spanish Pyrenees is a stack of thrust imbricates and a

great example to study tectonic deformation of thrust systems in the field

(Teixell and Koyi, 2003). We collected several samples from different parts

of the limbs and the crestal area from the fault-related folds across different

lithological units from the Aragüés thrust system during a field campaign in

32

spring 2019. The purpose of this AMS study of a well-studied tectonic area is

to investigate and quantify strain in such tectonic settings with AMS in more

detail.

33

Summary in Swedish

Denna avhandling belyser användningen av magnetisk anisotropi inom ana-

log modellering och ger en inblick i hur en berkskedja deformas genom si-

mulering med hjälp av sandlådemodellering. Uppsatsen understryker vikten

av basal friktion på i utevecklingen av en berkskedja (Artikel 1), och visar

gradienter och kinematik i deformation som en funktion av avståndet till en

överskjutning eller en veckningszon (Artikel 2).

Artikel 2 beskriver deformationen och den magnetiska anisotropin för en

sandlådemodell med överskjutningszoner med olika basalfriktion . I det initi-

ala stadiet av modelleringen kompakteras sand, vilket skapar en penetrativt

deformerad struktur som är karaktäriserad av en magnetisk lineation (kmax

kluster) som ligger vinkelrät mot riktningen av model komprimering, samti-

digt som den magnetiska foliationen (kmax-kint ) till mestadels förblir horison-

tell. Med kompaktion sker vecking och överskjutning. Veckning roterar den

magnetiska foliationen, vilken förblir parallell till lagerföljden. Överskjutning

ändrar istället den magnetiska anisotropin lokalt, d , där den magnetiska foli-

ationen är parallell till överskjutningsytan. Överskjutningens vergens reflek-

teras av den magnetiska foliationens riktning. Veckningszoner producerar i

vissa fall en komplex magnetisk anisotropi som reflekterar samverkan mellan

veckning och överskjutning. Däremot kan magnetiska anisotropin vid över-

skjutningar eller veckningszoner ärva den magnetiska susceptibiliteten som

fanns före den slutliga deformationen. De magnetiska egenskaperna ändras

gradvis mot överskjutningar och veckningszoner, vilket påvisar en ökad de-

formation mot dessa strukturer. Detta visar sig av förändringar i variationen

av den magnetiska huvudaxelns riktning, samt en minskande grad av ani-

sotropi.

På en större skala så kan resultaten från artikel 1 representera deformation

genom ett berkskedja fastställd av den basala friktionsytan. Deformationsfron-

ten sprids längre in i modellen ovanför lågfriktionsyta, jämfört med den ovan-

för en högfriktionsyta. Förändringen i deformation ovanför en låg-friktionsyta

sker gradvis, medan övergången i deformation ovanför en hög-friktionsyta är

skarp. Friktionsytan påverkar följaktligen gradienten i den magnetiska anis-

otropin observerad i den modellerade berkskedjan. Generellt sätt kan resulta-

ten från den här uppsatsen jämföras med verkliga exempel, då kompaktion i

modellen inträffar på ytor med olika friktion eller till exempel som visar ut-

vecklingen av olika strukturer i ett berkskedja. Sammanfattningsvis ger den

34

här avhandlingen en inblick i deformationen och utvecklingen av en

berkskedja i sandlådemodeller med hjälp av magnetisk anisotropi.

35

Acknowledgment

First of all, I would like to thank my supervisors, who applied for funding for

this PhD-project. I am very happy, that I got the chance to follow my partner

Paula to Sweden and that we can both experience a new chapter of life. How-

ever, this chapter is very challenging, and we both have our good and bad

moments in conducting research. I am very grateful, that we can support each

other during the PhD-time, the pandemic and, recently, that Paula tries to give

me silent moments, when she takes care about our beloved daughter Ronja.

Many thanks to Hemin, who introduced me to the field of analogue modelling

and who is very patient with the progress of his PhD-student. I enjoyed the

moments of discussion and learning from his lectures. Additionally, I thank

Bjarne for introducing me into the world of AMS and explaining me, how to

measure all my samples. Furthermore, I have to admit, that I challenge Hemin

and Bjarne with my manuscripts and my confusing thoughts. Therefore, I am

very grateful for the comments, which they provide to sort out my ideas.

An additional gratitude is given to Stefan. Unfortunately, we did not have the

chance to work together more intense, but I am looking forward to the future,

where we can continue our discussion and to progress our ideas. Many thanks

as well to Tobias Schmiedel and further colleagues in MPT and Geophysics.

Thanks for your help, interesting seminars, field trips and corridor discussions.

Here, I also want to thank the other PhD- and MSc-students for great Fika

breaks and further social events. Especially, many thanks to Susanna Åberg

for helping me with the Swedish translation of the summary. I am also very

lucky to get the support from the Geologiska Sektionen and the Otterborg

Scholarship. Additionally, I would like to thank Fatima, who is great help in

sorting out administrative problems during the PhD as well as the Hans Ram-

berg Tectonic Laboratory and Uppsala University for supporting my PhD. Fi-

nally, I want to thank the editors and reviewers of my publications and my

opponent, Ram Weinberger, of the licentiate seminar. Thanks for your time!

Thank you very much! Together, we can solve the puzzle!

36

References

Adam, J., Urai, J. L., Wieneke, B., Oncken, O., Pfeiffer, K., Kukowski, N., et al. (2005). Shear localisation and strain distribution during tectonic faulting - New insights from granular-flow experiments and high-resolution optical image correlation techniques. Journal of Structural Geology, 27(2), 283–301. https://doi.org/10.1016/j.jsg.2004.08.008

Almqvist, B. S. G., & Koyi, H. (2018). Bulk strain in orogenic wedges based on insights from magnetic fabrics in sandbox models. Geology, 46(6), 483–486. https://doi.org/10.1130/G39998.1

Anastasio, D., Pares, J. M., Kodama, K. P., Troy, J., & Pueyo, E. L. (2015). Anisotropy of Magnetic Susceptibility ( AMS ) records synsedimentary deformation kinematics at Pico del Aguila anticline , Pyrenees , Spain Anisotropy of magnetic susceptibility ( AMS ) records synsedimentary deformation kinematics at Pico del Aguila anti, (January 2016). https://doi.org/10.1144/SP425.8

Aubourg, C., Smith, B., Eshraghi, A., Lacombe, O., Authemayou, C., Amrouch, K., et al. (2010). New magnetic fabric data and their comparison with palaeostress markers in the western Fars Arc (Zagros, Iran): Tectonic implications. Geological Society Special Publication, 330(June 2010), 97–120. https://doi.org/10.1144/SP330.6

Averbuch, O., Frizon de Lamotte, D., & Kissel, C. (1992). Magnetic fabric as a structural indicator of the deformation path within a fold-thrust structure: a test case from the Corbières (NE Pyrenees, France). Journal of Structural Geology, 14(4), 461–474. https://doi.org/10.1016/0191-8141(92)90106-7

Bakhtari, H. R. ., Frizon de Lamotte, D. ., Aubourg, C. ., & Hassanzadeh, J. . (1998). Magnetic fabrics of Tertiary sandstones from the Arc of Fars (Eastern Zagros, Iran). Tectonophysics, 284, 299–316. https://doi.org/PIIS0040-1951(97)00179-0

Borradaile, G. (1987). Anisotropy of magnetic susceptibility: rock composition versus strain. Tectonophysics, 138(2–4), 327–329. https://doi.org/10.1016/0040-1951(87)90051-5

Borradaile, G.J., & Henry, B. (1997). Tectonic applications of magnetic susceptibility and its anisotropy. Earth-Science Reviews, 42(1–2), 49–93. https://doi.org/10.1016/S0012-8252(96)00044-X

Borradaile, Graham J. (1991). Correlation of strain with anisotropy of magnetic susceptibility (AMS). Pure and Applied Geophysics, 135(1), 15–29. https://doi.org/https://doi.org/10.1007/BF00877006

Borradaile, Graham J., & Jackson, M. (2010). Structural geology, petrofabrics and magnetic fabrics (AMS, AARM, AIRM). Journal of Structural Geology, 32(10), 1519–1551. https://doi.org/10.1016/J.JSG.2009.09.006

Borradaile, Graham J., & Tarling, D. H. (1981). The influence of deformation mechanisms on magnetic fabrics in weakly deformed rocks. Tectonophysics, 77(1–2), 151–168. https://doi.org/10.1016/0040-1951(81)90165-7

37

Borradaile, Graham J, & Dehls, J. F. (1993). Regional kinematics inferred from magnetic subfabrics in Archean rocks of Northern Ontario, Canada. Journal of Structural Geology, 15(7), 887–894. https://doi.org/10.1016/0191-8141(93)90182-A

Borradaile, Graham John. (1988). Magnetic susceptibility, petrofabrics and strain. Tectonophysics, 156(1–2), 1–20. https://doi.org/10.1016/0040-1951(88)90279-X

Burmeister, K. C., Harrison, M. J., Marshak, S., Ferré, E. C., Bannister, R. A., & Kodama, K. P. (2009). Comparison of Fry strain ellipse and AMS ellipsoid trends to tectonic fabric trends in very low-strain sandstone of the Appalachian fold-thrust belt. Journal of Structural Geology, 31(9), 1028–1038. https://doi.org/10.1016/j.jsg.2009.03.010

Cifelli, F., Mattei, M., Chadima, M., Lenser, S., & Hirt, A. M. (2009). The magnetic fabric in “undeformed clays”: AMS and neutron texture analyses from the Rif Chain (Morocco). Tectonophysics, 466(1–2), 79–88. https://doi.org/10.1016/j.tecto.2008.08.008

Colletta, B., Letouzey, J., Pinedo, R., Ballard, J. F., & Bale, P. (1991). Computerized X-ray tomography analysis of sandbox models: examples of thin-skinned thrust systems. Geology, 19(11), 1063–1067. https://doi.org/10.1130/0091-7613(1991)019<1063:CXRTAO>2.3.CO;2

Dahlstrom, C. D. A. (1969). Balanced cross sections. Canadian Journal of Earth Sciences, 6(4), 743–757. https://doi.org/10.1139/e69-069

Davy, P., & Cobbold, P. R. (1988). Indentation tectonics in nature and experiment. 1. Experiments scaled for gravity. Bull. Geol. Inst. Univ. Uppsala, NS, 14(May 2014), 129–141.

Dotare, T., Yamada, Y., Adam, J., Hori, T., & Sakaguchi, H. (2016). Initiation of a thrust fault revealed by analog experiments. Tectonophysics, 684, 148–156. https://doi.org/10.1016/j.tecto.2015.12.023

Ferré, E. C., Martín-Hernández, F., Teyssier, C., & Jackson, M. (2004). Paramagnetic and ferromagnetic anisotropy of magnetic susceptibility in migmatites: Measurements in high and low fields and kinematic implications. Geophysical Journal International, 157(3), 1119–1129. https://doi.org/10.1111/j.1365-246X.2004.02294.x

Ferré, E. C., Gébelin, A., Till, J. L., Sassier, C., & Burmeister, K. C. (2014). Deformation and magnetic fabrics in ductile shear zones: A review. Tectonophysics, 629(C), 179–188. https://doi.org/10.1016/j.tecto.2014.04.008

Fossen, H. (2010). Structural Geology. Cambrige University Press (Vol. 84). Retrieved from http://ir.obihiro.ac.jp/dspace/handle/10322/3933

Geiser, P. A. (1988). The role of kinematics in the construction and analysis of geological cross sections in deformed terranes (pp. 47–76). https://doi.org/10.1130/SPE222-p47

Graham, J. W. (1954). Magnetic susceptibility anisotropy, an unexploited petrofabric element. Geol. Soc. Am. Bull. 65, 1257–1258.

Graham, J. W. (1966). Significance of Magnetic Anisotropy in Appalachian Sedimentary Rocks. In The Earth Beneath the Continents: A Volume of Geophysical Studies in Honor of Merle A. Tuve. (1966), Geophys. Monogr. Ser., vol. 10, edited by J. S. Steinhart and T. J. Smith, pp. 627-648, AGU, Washington, D. C. (pp. 627–648). https://doi.org/10.1029/GM010p0627

Graveleau, F., Malavieille, J., & Dominguez, S. (2012). Experimental modelling of orogenic wedges: A review. Tectonophysics, 538–540, 1–66. https://doi.org/10.1016/j.tecto.2012.01.027

38

Greve, A., Kars, M., Zerbst, L., Stipp, M., & Hashimoto, Y. (2020). Strain partitioning across a subduction thrust fault near the deformation front of the Hikurangi subduction margin, New Zealand: A magnetic fabric study on IODP Expedition 375 Site U1518. Earth and Planetary Science Letters, 542, 116322. https://doi.org/10.1016/j.epsl.2020.116322

Groshong, R. H., Withjack, M. O., Schlische, R. W., & Hidayah, T. N. (2012). Bed length does not remain constant during deformation: Recognition and why it matters. Journal of Structural Geology, 41, 86–97. https://doi.org/10.1016/j.jsg.2012.02.009

Hall, J. (1815). II. On the Vertical Position and Convolutions of certain Strata, and their relation with Granite. Transactions of the Royal Society of Edinburgh, 7(1). https://doi.org/10.1017/S0080456800019268

Hampel, A., Adam, J., & Kukowski, N. (2004). Response of the tectonically erosive south Peruvian forearc to subduction of the Nazca Ridge: Analysis of three-dimensional analogue experiments. Tectonics, 23(5). https://doi.org/10.1029/2003TC001585

Henry, B. (1992). Modelling the relationship between magnetic fabric and strain in polymineralic rocks. Physics of the Earth and Planetary Interiors, 70(3–4), 214–218. https://doi.org/10.1016/0031-9201(92)90185-X

Hirt, A. M., Lowrie, W., Clendenen, W. S., & Kligfield, R. (1988). The correlation of magnetic anisotropy with strain in the Chelmsford Formation of the Sudbury Basin, Ontario. Tectonophysics, 145(3–4), 177–189. https://doi.org/10.1016/0040-1951(88)90194-1

Hirt, A. M., Julivert, M., & Soldevila, J. (2000). Magnetic fabric and deformation in the Navia-Alto Sil slate belt, northwestern Spain. Tectonophysics, 320(1), 1–16. https://doi.org/10.1016/S0040-1951(00)00047-0

Hirt, A. M., Lowrie, W., Lüneburg, C., Lebit, H., & Engelder, T. (2004). Magnetic and mineral fabric development in the ordovician Martinsburg Formation in the Central Appalachian Fold and Thrust Belt, Pennsylvania. Geological Society Special Publication, 238(1995), 109–126. https://doi.org/10.1144/GSL.SP.2004.238.01.09

Hirt, Ann M., & Almqvist, B. S. G. (2011). Unraveling magnetic fabrics. International Journal of Earth Sciences, 101(3), 613–624. https://doi.org/10.1007/s00531-011-0664-0

Hossack, J. R. (1979). The use of balanced cross-sections in the calculation of orogenic contraction; a review. Journal of the Geological Society, 136(6), 705–711. https://doi.org/10.1144/gsjgs.136.6.0705

Housen, B. A., Tobin, H. J., Labaume, P., Leitch, E. C., Maltman, A. J., Shipley, T., et al. (1996). Strain decoupling across the decollement of the Barbados accretionary prism. Geology, 24(2), 127–130. https://doi.org/10.1130/0091-7613(1996)024<0127:SDATDO>2.3.CO;2

Hrouda, F. (1978). The magnetic fabric in some folds. Physics of the Earth and Planetary Interiors, 17(2), 89–97. https://doi.org/10.1016/0031-9201(78)90050-X

Hrouda, F. Š. (1987). Mathematical model relationship between the paramagnetic anisotropy and strain in slates. Tectonophysics, 142(2–4), 323–327. https://doi.org/10.1016/0040-1951(87)90131-4

Hrouda, František. (1976). A model for the orientation process of ferromagnetic minerals in slates. Earth and Planetary Science Letters, 33(1), 107–110. https://doi.org/10.1016/0012-821X(76)90162-X

Hrouda, František. (1982). Magnetic anisotropy of rocks and its application in geology and geophysics. Geophysical Surveys, 5(1), 37–82. https://doi.org/10.1007/BF01450244

39

Hrouda, František, & Janák, F. (1976). The changes in shape of the magnetic susceptibility ellipsoid during progressive metamorphism and deformation. Tectonophysics, 34(1–2), 135–148. https://doi.org/10.1016/0040-1951(76)90181-5

Hunt, C. P., Moskowitz, B. M., & Banerjee, S. K. (1995). Magnetic Properties of Rocks and Minerals. In In Rock Physics & Phase Relations, T.J. Ahrens (Ed.) (pp. 189–204). https://doi.org/10.1029/RF003p0189

Ising, G. (1942). On the magnetic properties of varved clay. Ark. Mat. Astron. Fys. 29a, 1–37.

Jelinek, V. (1981). Characterization of the magnetic fabric of rocks. Tectonophysics, 79(3–4), T63–T67. https://doi.org/10.1016/0040-1951(81)90110-4

Jelínek, V. (1978). Statistical processing of anisotropy of magnetic susceptibility measured on groups of specimens. Studia Geophysica et Geodaetica, 22(1), 50–62. https://doi.org/10.1007/BF01613632

Kissel, C., Barrier, E., Laj, C., & Lee, T. ‐Q. (1986). Magnetic fabric in “undeformed” marine clays from compressional zones. Tectonics, 5(5), 769–781. https://doi.org/10.1029/TC005i005p00769

Kligfield, R., Lowrie, W., & Dalziel, I. W. D. (1977). Magnetic susceptibility anisotropy as a strain indicator in the sudbury basin, Ontario. Tectonophysics, 40(3–4), 287–308. https://doi.org/10.1016/0040-1951(77)90070-1

Kligfield, R., Owens, W. H., & Lowrie, W. (1981). Magnetic susceptibility anisotropy, strain, and progressive deformation in Permian sediments from the Maritime Alps (France). Earth and Planetary Science Letters, 55(1), 181–189. https://doi.org/10.1016/0012-821X(81)90097-2

Kneen, S. J. (1976). The relationship between the magnetic and strain fabrics of some haematite-bearing Welsh slates. Earth and Planetary Science Letters, 31(3), 413–416. https://doi.org/10.1016/0012-821X(76)90123-0

Koyi, H. (1997). Analogue modelling: From a qualitative to a quantitative technique - A historical outline. Journal of Petroleum Geology, 20(2), 223–238. https://doi.org/10.1111/j.1747-5457.1997.tb00774.x

Koyi, H. A., Sans, M., Teixell, A., Cotton, J., & Zeyen, H. (2003). The Significance of Penetrative Strain in the Restoration of Shortened Layers Insights from Sand Models and the Spanish Pyrenees. AAPG Memoir, 1–16.

Koyi, Hemin. (1995). Mode of internal deformation in sand wedges. Journal of Structural Geology, 17(2), 293–300. https://doi.org/10.1016/0191-8141(94)00050-A

Larrasoaña, J. C., Pueyo, E. L., & Parés, J. M. (2004). An integrated AMS, structural, palaeo- and rock-magnetic study of Eocene marine marls from the Jaca-Pamplona basin (Pyrenees, N Spain); new insights into the timing of magnetic fabric acquisition in weakly deformed mudrocks. Geological Society Special Publication, 238(Sintubin 1994), 127–143. https://doi.org/10.1144/GSL.SP.2004.238.01.10

Larrasoaña, J. C., Gómez-Paccard, M., Giralt, S., & Roberts, A. P. (2011). Rapid locking of tectonic magnetic fabrics in weakly deformed mudrocks. Tectonophysics, 507(1–4), 16–25. https://doi.org/10.1016/j.tecto.2011.05.003

Levi, T., Weinberger, R., & Marco, S. (2014). Magnetic fabrics induced by dynamic faulting reveal damage zone sizes in soft rocks, Dead Sea basin. Geophysical Journal International, 199(2), 1214–1229. https://doi.org/10.1093/gji/ggu300

Levi, T., Weinberger, R., Alsop, G. I., & Marco, S. (2018). Characterizing seismites with anisotropy of magnetic susceptibility. Geology, 46(9), 827–830. https://doi.org/10.1130/G45120.1

Levi, Tsafrir, & Weinberger, R. (2011). Magnetic fabrics of diamagnetic rocks and the strain field associated with the Dead Sea Fault, northern Israel. Journal of Structural Geology, 33(4), 566–578. https://doi.org/10.1016/j.jsg.2011.02.001

40

Martín-Hernández, F., & Ferré, E. C. (2007). Separation of paramagnetic and ferrimagnetic anisotropies: A review. Journal of Geophysical Research: Solid Earth, 112(3). https://doi.org/10.1029/2006JB004340

Mattei, M., Sagnotti, L., Faccena, C., & Funiciello, R. (1997). Magnetic fabric of weakly deformed clay-rich sediments in the extensional tectonics ~ N. Tectonophysics, 271, 107–122.

McClay, K. R. (1990). Extensional fault systems in sedimentary basins: a review of analogue model studies. Marine and Petroleum Geology, 7(3), 206–233. https://doi.org/10.1016/0264-8172(90)90001-W

Mulugeta, G., & Koyi, H. (1992). Episodic accretion and strain partitioning in a model sand wedge. Tectonophysics, 202, 319–333. https://doi.org/10.1016/0040-1951(92)90117-O

Muñoz, J. A., Beamud, E., Fernández, O., Arbués, P., Dinarès-Turell, J., & Poblet, J. (2013). The Ainsa Fold and thrust oblique zone of the central Pyrenees: Kinematics of a curved contractional system from paleomagnetic and structural data. Tectonics, 32(5), 1142–1175. https://doi.org/10.1002/tect.20070

Nilforoushan, F., Koyi, H. A., Swantesson, J. O. H., & Talbot, C. J. (2008). Effect of basal friction on surface and volumetric strain in models of convergent settings measured by laser scanner. Journal of Structural Geology, 30(3), 366–379. https://doi.org/10.1016/J.JSG.2007.09.013

Owens, W. H. (1974). Mathematical model studies on factors affecting the magnetic anisotropy of deformed rocks. Tectonophysics, 24(1–2), 115–131. https://doi.org/10.1016/0040-1951(74)90133-4

Parés, J. M. (2015). Sixty years of anisotropy of magnetic susceptibility in deformed sedimentary rocks. Frontiers in Earth Science, 3, 4. https://doi.org/10.3389/feart.2015.00004

Parés, J. M., & van der Pluijm, B. A. (2003). Magnetic fabrics and strain in pencil structures of the Knobs Formation, Valley and Ridge Province, US Appalachians. Journal of Structural Geology, 25(9), 1349–1358. https://doi.org/10.1016/S0191-8141(02)00197-9

Parés, J. M., & van der Pluijm, B. A. (2014). Low-temperature AMS and the quantification of subfabrics in deformed rocks. Tectonophysics, 629(C), 55–62. https://doi.org/10.1016/j.tecto.2014.03.005

Parés, J. M., & Van Der Pluijm, B. A. (2002). Evaluating magnetic lineations (AMS) in deformed rocks. Tectonophysics, 350(4), 283–298. https://doi.org/10.1016/S0040-1951(02)00119-1

Parés, J. M., Van der Pluijm, B. A., & Dinarès-Turell, J. (1999). Evolution of magnetic fabrics during incipient deformation of mudrocks (Pyrenees, northern Spain). Tectonophysics, 307(1–2), 1–14. https://doi.org/10.1016/S0040-1951(99)00115-8

Pluijm, vand der B. A., & Marshack, S. (2004). Earth structure. An introduction to structural geology and tectonics. Nature. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/21455154

Pocoví Juan, A., Pueyo Anchuela, Pueyo, E. L., Casas-Sainz, A. M., Román Berdiel, M. T., Gil Imaz, A., et al. (2014). Magnetic fabrics in the Western Central-Pyrenees: An overview. Tectonophysics, 629(1), 303–318. https://doi.org/10.1016/j.tecto.2014.03.027

Pueyo-Morer, E. L. ., Millán-Garrido, H. ., Pocoví-Juan, A. ., & Parés, J. M. . (1997). Determination of the Folding Mechanism by AMS Data. Study of the Relation Between Shortening and Magnetic Anisotropy in the Pico del Aguila Anticline (Southern Pyrenees). Phys. Chem. Earth, 22(1), 195–201. https://doi.org/S0079-1946(97)00 102-X

41

Pueyo Anchuela, Ó., Pocoví Juan, A., & Gil Imaz, A. (2010). Tectonic imprint in magnetic fabrics in foreland basins: A case study from the Ebro Basin, N Spain. Tectonophysics, 492(1–4), 150–163. https://doi.org/10.1016/j.tecto.2010.06.016

Ranalli, G. (2001). Experimental tectonics: From Sir James Hall to the present. Journal of Geodynamics, 32(1–2), 65–76. https://doi.org/10.1016/S0264-3707(01)00023-0

Rathore, J. S. (1979). Magnetic susceptibility anisotropy in the Cambrian slate belt of North Wales and correlation with strain. Tectonophysics, 53(1–2), 83–97. https://doi.org/10.1016/0040-1951(79)90355-X

Rees, A. I. (1965). The use of anisotropy of magnetic susceptibility in the estimation of sedimentary fabric. Sedimentology, 4(4). https://doi.org/10.1111/j.1365-3091.1965.tb01550.x

Rees, Anthony I. (1966). The Effect of Depositional Slopes on the Anisotropy of Magnetic Susceptibility of Laboratory Deposited Sands. The Journal of Geology, 74(6), 856–867. https://doi.org/10.1086/627216

Robion, P., Grelaud, S., & Frizon de Lamotte, D. (2007). Pre-folding magnetic fabrics in fold-and-thrust belts: Why the apparent internal deformation of the sedimentary rocks from the Minervois basin (NE - Pyrenees, France) is so high compared to the Potwar basin (SW - Himalaya, Pakistan)? Sedimentary Geology, 196(1–4), 181–200. https://doi.org/10.1016/j.sedgeo.2006.08.007

Rochette, P., & Fillion, G. (1988). Identification of multicomponent anisotropies in rocks using various field and temperature values in a cryogenic magnetometer. Physics of the Earth and Planetary Interiors, 51(4), 379–386. https://doi.org/10.1016/0031-9201(88)90079-9

Rochette, P., Jackson, M., & Aubourg, C. (1992). Rock Magnetism and the Interpretation of AMS, (92), 209–226.

Rochette, Pierre. (1987). Magnetic susceptibility of the rock matrix related to magnetic fabric studies. Journal of Structural Geology, 9(8), 1015–1020. https://doi.org/10.1016/0191-8141(87)90009-5

Sagnotti, L., Speranza, F., Winkler, A., Mattei, M., & Funiciello, R. (1998). Magnetic fabric of clay sediments from the external northern Apennines (Italy). Physics of the Earth and Planetary Interiors, 105(1–2), 73–93. https://doi.org/10.1016/S0031-9201(97)00071-X

Saint-Bezar, B., Hebert, R. L., Aubourg, C., Robion, P., Swennen, R., & Frizon De Lamotte, D. (2002). Magnetic fabric and petrographic investigation of hematite-bearing sandstones within ramp-related folds: Examples from the South Atlas Front (Morocco). Journal of Structural Geology, 24(9), 1507–1520. https://doi.org/10.1016/S0191-8141(01)00140-7

Schellart, W. P. (2002). Analogue modelling of large-scale tectonic processes: An introduction. Journal of the Virtual Explorer, 7, 1–6. https://doi.org/10.3809/jvirtex.2002.00045

Schellart, Wouter P., & Strak, V. (2016). A review of analogue modelling of geodynamic processes: Approaches, scaling, materials and quantification, with an application to subduction experiments. Journal of Geodynamics, 100, 7–32. https://doi.org/10.1016/j.jog.2016.03.009

Schreurs, G., Buiter, S. J. H., Boutelier, J., Burberry, C., Callot, J. P., Cavozzi, C., et al. (2016). Benchmarking analogue models of brittle thrust wedges. Journal of Structural Geology, 92, 116–139. https://doi.org/10.1016/j.jsg.2016.03.005

Schwehr, K., & Tauxe, L. (2003). Characterization of soft-sediment deformation: Detection of cryptoslumps using magnetic methods. Geology, 31(3), 203–206. https://doi.org/10.1130/0091-7613(2003)031<0203:COSSDD>2.0.CO;2

42

Tarling, D. H., and Hrouda, F. (1993). The Magnetic Anisotropy of Rocks. London: Chapman and Hall.

Tauxe, L., Banerjee, S. K., Butler, R. F., & van der Voo, R. (2018). Essentials of Paleomagnetism: Fifth Web Edition (5th ed.). Retrieved from https://earthref.org/MagIC/books/Tauxe/Essentials/#x1-80001.5

Teixell, A., & Koyi, H. A. (2003). Experimental and field study of the effects of lithological contrasts on thrust-related deformation. Tectonics, 22(5). https://doi.org/10.1029/2002TC001407

Uyeda, S., Fuller, M. D., Belshé, J. C., & Girdler, R. W. (1963). Anisotropy of magnetic susceptibility of rocks and minerals. Journal of Geophysical Research, 68(1), 279–291. https://doi.org/10.1029/jz068i001p00279

Weil, A. B., & Yonkee, A. (2009). Anisotropy of magnetic susceptibility in weakly deformed red beds from the Wyoming salient, Sevier thrust belt: Relations to layer-parallel shortening and orogenic curvature. Lithosphere, 1(4), 235–256. https://doi.org/10.1130/L42.1

Weinberger, R., Levi, T., Alsop, G. I., & Marco, S. (2017). Kinematics of Mass Transport Deposits revealed by magnetic fabrics. Geophysical Research Letters, 44(15), 7743–7749. https://doi.org/10.1002/2017GL074471

Woodward, N. B., Gray, D. R., & Spears, D. B. (1986). Including strain data in balanced cross-sections. Journal of Structural Geology, 8(3–4), 313–324. https://doi.org/10.1016/0191-8141(86)90052-0