1. INFLUENCE OF FLEXURAL SLIP ON THE FORM
OF FAULT RELATED FOLDS
Austin M. Hodge
Submitted to the faculty of the University Graduate School
in partial fulfillment of the requirements
for the degree
Master of Science
in the Department of Geological Sciences
Indiana University
May 2013

2. ii
Accepted by the Graduate Faculty, Indiana University, in partial
fulfillment of the requirements for the degree of Master of Science.
Kaj M. Johnson, Ph.D.
Bruce J. Douglas, Ph.D.
Gary L. Pavlis, Ph.D

3. iii
Acknowledgements
I would like to thank my committee members, Dr. Kaj Johnson, Dr. Bruce
Douglas, and Dr. Gary Pavlis, for their help, suggestions, and review of my thesis. I
would especially like to thank Dr. Kaj Johnson for all of his hands on help and
support with this study. Without his guidance and knowledge of geologic modeling
this project would not have gone as smoothly.
I extend my thanks to Chevron Energy Company for providing me with a
fellowship my first year at Indiana University. This extra funding allowed me to
focus more time on my classes and research instead of working as a research
assistant or teaching assistant. The extra time proved very valuable in finishing my
research in the two-year span I had allotted.
On a more personal note, I would like to thank everyone I have come into
contact with during my tenure at Indiana University. It has been a wonderful
experience and the friendships and connections I have made I will take with me into
my future career.
And thank you to the state of Indiana for helping me broaden my horizons as
a person. It has been wonderful getting to know the people, culture, and state of
mind of such a unique state. Indiana has brought a lot of happiness into my life, and
also taught me to be somewhat of a decent basketball player (a great stress-
relieving activity from my research). I may not be a born Hoosier, but I will cherish
the Hoosier mindset in my journeys to come.

4. iv
Austin M. Hodge
Influence of Flexural Slip on the Form of Fault-Related Folds
The complex relationship between folding and faulting in global fold-and-
thrust belts has led to the development of a number of models, both two and three
dimensional, aiming to accurately pinpoint the nature of faulting and the origins of
various fold geometries. These fold geometries range from very broad, rounded fold
forms to extremely localized, sharp-hinged, flat-topped folds.
Previous studies have used different modeling styles to characterize the
varying types of fault-related folds. The two main categories of modeling,
kinematic/geometric reconstructions and mechanical models, both have their
respective advantages and disadvantages. Previous work has been focused more
towards kinematic/geometric constructions, with less attention paid to the
mechanical modeling methods that take into account the physical conditions that
form fault-related folds. However, minimal work has explored what effect flexural
layer-parallel slip has on mechanical models of fault-related folds.
For the purposes of this study a code, Boundary Element Analysis of Flexural
Slip (BEAFS), was developed as a way to recreate multiple fold form geometries by
varying a range of physical conditions, thereby helping to shed light on the role of
layer-parallel slip. BEAFS is a code that allows for the deformation of an elastic
layered medium undergoing frictional slip. A dipping fault is embedded within the
medium with a lower detachment and/or an upper detachment. Initial work with
BEAFS has been aimed towards defining the physical conditions responsible for the
formation of end-member typed fold geometries. The physical conditions that can

5. v
be manipulated are the thickness and number of layers, coefficient of friction (range
0-0.8), and initial uniform differential stress (horizontal-vertical) before folding
(range 0-10MPa).
The study has determined that thickly-layered mediums/mediums with
bonded contacts produce rounded, broad fold geometries, regardless of the fault
geometry. With a fault-propagation fold geometry, thin-layered mediums with
freely slipping layers form concentric folds localized above fault tip; in fault-bend
fold geometries kink-banded, flat-crested folds will form. Introducing friction into a
FPF geometry with thin layers will generate kink-banding and the addition of a
farfield stress to most models will enhance development of kink-bands regardless of
fault shape. Continuing work will be focused on using BEAFS to try and recreate
first-order geometries of folds seen in seismic reflection data to better understand
the role of layer-parallel slip.

6. vi
Table of Contents
Page
Acknowledgements……………………………………………………………… iii
Abstract………………………………………………………………………………. iv-v
List of Figures……………………………………………………………………… vii
1. Introduction……………………………………………………………………. 1
1.1 Kinematic models of fault-related folding 2
1.2 Mechanical models of fault-related folding 4
2. Boundary Element Analysis of Flexural Slip (BEAFS)………… 10
3. Influences of Model Parameters on Fold Geometry…………… 13
3.1 Layer Thickness 13
3.2 Contact Strength on Slip Surfaces 15
3.3 Initial Differential Stress 17
3.4 Fault Shape 19
4. Analysis of Natural Folds in Seismic Section…………………….. 21
4.1 Basil Anticline 22
4.2 Rosario Structure 25
4.3 Toldado Anticline 29
5. Conclusions…………………………………………………………………… 33
References………………………………………………………………………… 36
Vita

7. vii
List of Figures
Figure Page
1 Experimental folding of photoelastic rubber strips……………….. 2
2 Geometric evolution of a fault-bend fold………………………………. 3
3 Geometric evolution of a fault-propagation fold…………………… 4
4 Diagrammatic illustration of flexural layer-parallel slip………. 6
5 Isolated multilayer folding with BEAFS model…………………….. 8
6 Kink folds in Perdido Fold Belt, Gulf of Mexico…………………….. 9
7 Diagrammatic explanation of BEAFS model…………………………. 11
8 Effects of varying layer thickness………………………………………… 14
9 Effects of varying contact strength between layers……………… 16
10 Development of slip in frictional vs. freeslip model……………… 17
11 Effects of varying initial differential stress……………………………. 18
12 Effects of varying fault shape………………………………………………. 20
13 13.1 Basil Anticline seismic data compared with model……….. 24
13.2 Varying contact strength on best-fit Basil model…………… 25
14 Stratigraphic column of the Maracaibo Basin, VZ…………………. 26
15 15.1 Rosario Structure seismic data compared with model…… 28
15.2 Varying contact strength on best-fit Rosario model………. 29
16 16.1 Toldado Anticline seismic data compared with model……. 32
16.2 Varying contact strength on best-fit Toldado model………. 33

8. 1
1. Introduction
It has been known for decades that the form of folded layers under layer-
parallel shortening is controlled by the nature of contact strength between layers
and the relative stiffness of interbeds. Much insight into folding processes has been
gained from a number of theoretical and experimental studies of multilayer folding.
Classical theoretical analyses of single layer and multilayer folding by Biot (1957,
1964,1965) and Fletcher (1974, 1979) developed the notion of a dominant
wavelength which establishes the wavelength that grows most rapidly during
folding.
Experimental studies of folding of elastic multilayers by, for example,
Cobbold (1971) and Honea and Johnson (1976) demonstrate that fold form is
strongly influenced by contact strength. Figure 1 illustrates two end-member cases
of experimental folding by Honea and Johnson (1976) of photoelastic rubber strips
subjected to layer-parallel shortening where the experimental conditions are
identical except for contact strength. Figure 1a shows rounded, concentric folds
within layers lubricated at contacts with silicone grease (low frictional resistance to
slip). Figure 1 b shows sharp-hinged, localized kink folds in layers with dry contacts
(high frictional resistance to slip). A theory of kink folding and the influence of
contact strength on fold form was developed for elastic layers by Honea and Johnson
(1976) and viscous layers by Pfaff and Johnson (1989). As in the experimental folds,
the primary ingredient in the theoretical analyses for transition from rounded,
concentric folds to sharp-hinged, localized kink folds is nonlinear contact strength
(such as friction or cohesion).

9. 2
Figure1: Experimental folding of photoelastic rubber strips from Honea and
Johnson (1976). Stack of rubber strips subjected to layer-parallel shortening with
vertical confinement. A. Contacts lubricated with silicone grease. B. Dry, frictional
contacts.
Unlike isolated folding of multilayers, the influence of contact strength on multilayer
fault-related folding has not been systematically studied. The purpose of this thesis
is to examine the influence of contact strength on fold form in an elastic multilayer
containing a fault. Model results are compared to real folds imaged in seismic
section . First, we review some of the classic fault-related fold geometries and
kinematic and mechanical analyses.
1.1 Kinematic models of fault-related folds
The complex relationship between faulting and folding has led to the
development of a number of models, both two and three dimensional, aiming to
accurately pinpoint the nature of faulting and the origins of various fold geometries.
Early models of fault-related folding (e.g. Suppe, 1983) were strictly geometric
constructions of uniformly thick strata deforming over a flat-ramp-flat fault

10. 3
orientation, dubbed fault-bend folds (Figure 2). These early geometric models did
not take into account any mechanical parameters of bed deformation and followed a
strict set of geometric rules.
Figure 2: Geometric evolution of a fault-bend fold (Suppe, 1983)
Figure 2 illustrates the kinematic construction of the evolution of a fault-bend fold
by Suppe (1983). The fold is assumed to have a backlimb parallel to the fault ramp, a
flat anticlinal top, and a dipping forelimb. The dip of the forelimb is determined
from the dip of the ramp and an assumption of no change in bed thickness. The flat-
ramp-flat fault geometry is fairly diagnostic of a fault-bend fold, but other fault-
propagation folds have been identified where an upper detachment/flat is non-
existent. Geometric constructions of these folds have been devised by, for example,
Suppe (1985), Suppe and Medwedeff, (1990) and Chester and Chester (1990) (Figure
3). The predominant component of fault-propagation fold geometries is the
presence of an advancing fault-tip that simultaneously transports and propagates
through hanging wall strata. Similar to fault-bend folds, a majority of the research in
fault-propagation fold modeling has been kinematic/geometric in nature.

11. 4
Figure 3: Geometric evolution of a fault-propagation fold (Suppe and Medwedeff,
1990)
A third, and more recent, category of fault-related folds, the trishear kinematic
model (Erslev, 1991; Cardozo, 2008), has gained a lot of popularity in recent
literature because it produces rounded fold forms and has been used to model
forced-folds and fault-tip folds. This model assumes distributed shear in a
triangular zone ahead of the propagating fault tip.
1.2 Mechanical Models of fault-related folding
A primary reason why geometric/kinematic construction models are so
prevalent in the literature is their ability to help generate complete cross-sections in
situations where subsurface geological information is incomplete or at times non-
existent. The constructions provide rules for constructing fold shapes that are
retro-deformable, that is the fold can be “pulled” backwards to form originally
horizontal strata. Being able to complete a cross-section of a fold using only surface
data can be very useful, however, as mentioned previously, these constructions are
only geometric and do not account for any physical conditions that take place before
and during folding. Therefore, the models provide very little physical insight of the
folding mechanism. However, a second class of fold modeling, numerical

12. 5
mechanical modeling, has concentrated on understanding the physical processes
involved in fault-related folding. A handful of workers (Strayer and Huddleston,
1997; Liu and Dixon, 1995; Greggerickson and Jamison 1995) have created physical
numerical models (variety of finite-element and finite-difference models) of fault-
related folds to better understand the important physical processes involved in
these fold types. The primary disadvantage of mechanical models, however, is that
these models are more complicated to compute and often require setting
parameters that are not known (stress levels, strength, etc.).
Previous research concerning geometric constructions and kinematic
modeling has taken into account strict geometric rules for section balancing and
well-defined rules of flexural layer-parallel slip folding, a type of folding that is
accommodated by frictional slip between layers (Figure 4).

13. 6
Figure 4: Diagrammatic illustration of flexural layer-parallel slip. Folding is accommodated
by slipbetween layers, analogous to the slip between pages as a book is folded. (Connors,
Shaw, Suppe, 2004)
However, minimal work has explored the effect of flexural layer-parallel slip on
mechanical models of fault-bend and fault-propagation folds. Some mechanical
models have dealt with varying the relative stiffness of layers (plastic strength or
viscosity), but have neglected to consider layer-parallel slip.
Along with layer-parallel slip, buckling is yet another important mechanism
of folding that has been largely ignored in mechanical analysis of fault-related folds.
Buckling and layer-parallel slip are both fairly well understood processes and are
known to be intimately related. Buckling of layers tends to occur when strong
contrasts in stiffness are present across layers (interbedded soft and stiff layers)
and/or through layer-parallel slip. Previous work on buckling analysis is quite
mature (e.g. Biot, 1964a and 1964b; Chappel, 1969; Fletcher, 1977; Johnson, 1977;

14. 7
Johnson and Fletcher, 1994) and has mostly focused on understanding the buckling
phenomenon in a layered medium, without the complication of faulting. This work,
supplemented with our own mechanical buckling models, illustrates that layer-
parallel slip has a direct effect on buckling in an isolated fold setting. Figure 5
depicts the results from a numerical physical model called BEAFS and described in a
later section. The stack of layers is subjected to layer-parallel shortening with
vertical confinement. In figure 5a, the layers are allowed to freely slip past each
other without any frictional resistance, forming a broad, rounded, concentric fold
geometry. In figure 5b, friction is introduced between the layers and frictional-layer
parallel slip takes over, resulting in sharp-hinged kink folds. When closely
examining seismic reflection images of various types of fault-related folds around
the world, we notice a similar pattern of certain folds having sharp-hinged, flat-
topped folds (Figure 6), while others have more rounded, broad folding geometries.
This pattern in fault-related folds mirrors the patterns we observe in isolated folds,
implying that layer-parallel slip and buckling play a vital role in the development of
these fold geometries. However, it remains unclear how much the fold form is
related to fault slip, which is the focus of this thesis.

15. 8
Figure5: Multilayer folding with BEAFS. This figure illustrates the influence of contact
strength on fold form (withno fault). The loading conditions are identical in (a) and (b)
consisting of 10^8 Pa confinement and 20 km of shortening over 100 km. However, in (a)
the coefficientof friction is set to zero (freely slipping) whereas in (b) the coefficientof
frictionis 0.6. Freely slipping layers produce concentric folds whereas layers with frictional
contacts produce kink folds.

16. 9
Figure6: Kink folds in Perdido fold belt, Gulf of Mexico. The foldtrain consists of
several sharp-hinged, flat-crested folds, very similarly shaped to the BEAFSmodel
result presented in figure 4b. These folds could have resulted from the influence of
frictionallayer-parallel slip at the contactinterfaces.
We suspect the role of buckle folding and layer-parallel slip should not be
neglected in mechanical models of fault-related folding. We have designed a new
model, combining the manipulation of physical aspects of numerical models with
the flexural layer-parallel slip component of geometric and kinematic
reconstructions, that will allow for the growth of fault-bend or fault-propagation
fold in a medium with elastic layers that slip at the contacts. To aid in assessing the
relevance of the model, the results will be focused towards recreating fault-bend
and fault-propagation folds seen in seismic reflection data obtained from “Seismic
Interpretation of Contractional Fault-Related Folds: An AAPG Seismic Atlas”
(Connors, Shaw, Suppe, 2004). By recreating various types of fold geometries, we
can better understand the role of layer-parallel slip in fault-related folds.

17. 10
2. Boundary Element Analysis of Flexural Slip (BEAFS)
For this work we use a boundary element model to examine folding of
multilayer containing a fault. The boundary element model BEAFS (Boundary
Element Analysis of Flexural Slip) is described in (K. Johnson and W.-J. Huang,
unpublished manuscript).
In layered sedimentary rocks, mechanical interfaces between sedimentary
layers may form because of differences in physical properties at the interfaces such
as grain size and cementation. Soft layers interbedded with stiff layers may localize
shear, allowing the stiff layers to slide past each other. These conditions are
important in folding because the bedding-plane slip can allow the strata to
mechanically buckle with flexural slip. We model these conditions with multiple
elastic layers with frictional contacts (Figure 7). The model consists of a ramp fault
with a lower detachment, an optional upper detachment, and an arbitrary number
of elastic layers. The fault and layers are embedded in an elastic halfspace. For the
fault-propagation case, there is no upper detachment and the fault is loaded at the
right-hand side (Figure 7a) with imposed slip on the detachment. For the fault-
bend-fold geometry, the system is loaded with imposed slip on the upper and lower
detachments. Uniform confinement stresses, σc, are imposed (equal vertical and
horizontal stress) as an approximation to the gravitational load. An additional
arbitrary horizontal far-field stress, σff, may also be imposed (as is the case for this
study). The elastic response is defined by the elastic shear modulus, , and
Poisson’s ratio, . Layer contacts are assigned a coefficient of friction, f. We

18. 11
model initially horizontal layers of finite length embedded in an otherwise
homogeneous elastic half-space. In general, the layers and the fault are assumed to
slip according to a cohesionless Coulomb friction law, | s|≤ σn, where s is
shear stress and σn is normal stress (compression is positive).
Figure 7: Diagrammatic explanation of the BEAFS model.
We follow the displacement discontinuity method of Crouch and Starfield
(1983) and discretize the fault surfaces and layer contacts using the solution for

19. 12
plane-strain edge dislocations in an elastic half-space. We discretize the faults and
layer interfaces into elements with equal length. We specify zero discontinuity in
normal displacement across elements to prevent faces from pulling apart or
overlapping. The evolution of folding is computed by small increments of elastic
deformation. During each increment of deformation, far-field slip on the detachment
is imposed, slip on all interfaces is computed, and new positions of layer interface
and fault elements are computed.
The elastic medium is semi-infinite (i.e., half-space) such that the normal
traction, σn, and shear tractions, σs, are zero at the ground surface. The y-
coordinate of the origin of the coordinate system is fixed at the free surface and the
free surface remains flat (material points that move above the free surface
disappear). The elastic properties of the host medium and the layers are the same. A
semi-infinite dislocation is applied at the depth of the upper and lower detachments
at the edge of the layer interfaces. The imposed semi-infinite dislocation
approximates a uniform displacement of the hanging wall block above the
detachment.

20. 13
3. Influences of Model Parameters on Fold Geometry
The BEAFS model allows for the input and control of a number of physical
parameters, each having variable effects on the resulting fold form. The
manipulation of the model’s physical parameters is crucial in understanding the
effects of flexural layer parallel slip on the formation of fault-related folds. Within
BEAFS, we vary the thickness of layers (related to the number of layers), contact
strength between slip surfaces, initial far-field differential stress, and fault
geometry. In order to understand the influence of each of these parameters on the
resulting fold geometries, each adjustable condition must be isolated from the
others and subsequently examined. To achieve this, a modeled reference fold is
created and only one parameter at a time is changed in a systematic fashion. In the
following subsections, we present results from this systematic examination for both
fault-propagation and fault-bend folds. For our fault-propagation fold analysis, the
reference fault-fold geometry is derived from a 15-layered model with a coefficient
of friction of 0.5, an initial differential stress of 2 MPa, and 7km of shortening. For
our fault-bend fold analysis, the reference figure is a 15-layered model with a
coefficient of friction of 0.5, an initial differential stress of 6 MPa and 3km of
shortening.
3.1 Layer Thickness
Within the initial model interface, both the fault geometry and the number of
layers to be deformed can be selected. Designating a higher number of layers will
create a thinner, more densely layered package, whereas a lower number of layers

21. 14
will cause the layering to be thicker. Figure 8 illustrates folds formed with layer
thicknesses of 1 km (10layers), 0.67 km (15 layers), and 0.33 km (30 layers).
Decreasing the number of layers, thereby thickening them, leads to broad, rounded,
more gentle folds compared to folds in thinner layers. In thinner layers, tight,
sharp-hinged, flat-crested folds tend to form. The width (from upper to lower
hinge) of the forelimb and backlimb of the fold decreases with thinner layers. Also,
the limb dip angle increases with decreased thickness. The reason for the difference
in geometry is that thinner layers (and therefore thinner mechanical stratigraphy)
enhance kink-folding in the forelimb and backlimb of the fold.
Figure 8: Effects of varying the thickness of layers. The middle row represents the reference
models mentioned in the section 3 introduction. Decreasing the number of layers (thicker
layers) yields broad, gentle folds. Increasing the number of layers (thinner layers) yields
tight, sharp-hinged, flat-topped folds.

22. 15
3.2 Contact Strength on Slip Surfaces
Within the model we vary the contact strength of layer slip surfaces by
varying the coefficient of sliding friction. The model result shown in Figure 9 was
designed to understand the effects of contact strength on fold form. There we
compare end member contact strengths with one end consisting of freely slipping
layers and the other layers bonded together. The reference figure represents
frictional slip between the layers (coefficient of friction = 0.5). It is already well
understood that within isolated folds, friction between layers leads to sharp-hinged,
kink-like folds and a lack of friction leads to concentric, rounded folds (e.g., Figure
5). Figure 9 shows that the same characteristics are observable in the fault-
propagation folds. Folds in layers with frictional contacts are formed with localized
kink folding in the limbs, whereas the folds in frictionless (freeslip) layers are
rounded. The round, localized, relatively high amplitude fold above the tip of the
propagating fault in frictionless layers is not observed in the ramp fold with an
upper detachment. The fault-bend fold in frictionless layers shows localized kinks
at the upper and lower bends in the fault. The difference between these two folds is
that the upper termination of the fault in the fault-propagation fold promotes
buckling of the layers. In Figure 9 we also illustrate the effects of having layers
bonded together, essentially behaving as one large mass moving over a fault.

23. 16
Figure 9: Effects of varying contact strength (layer friction). The middle row represents the
reference models mentioned in the section 3 introduction. Frictional contacts lead to tight,
sharp-hinged, flat-topped folds (middle row). Bonded, non-slipping contacts lead to
asymmetric, broad folds (top row). Free-slipping, frictionless contacts lead to more
rounded, concentric folds (bottom row). Note: the fault-propagation free-slip figure is taken
at 5km shortening due to numerical constraints during the model run.
Both in isolated and fault-related folds, having frictional contacts helps localize the
slip into kink bands, leading to the typical kink-band, flat-crested, sharp-hinged
geometry. If the layers were to freely slip past one another without friction we
would observe more rounded, concentric folds. In figure 10, we provide a
sequential step-by-step evolution of the layer slip in a fault-propagation fold. The
model for this figure was produced using the reference model for fault-propagation
folds mentioned previously in the introduction to section 3.

24. 17
Figure 10: Step-by-step evolution of a fault-propagation fold at 2, 5, and 7km and the
development of slipin frictional (left) vs. freely-slipping (right) contacts. Color bar scale
represents kilometers of slip. Positive values represent top to the left shear and negative
values represent top to the right shear. Left: Slip is localized on the limbs and begin to form
kink-bands. Right: Slip is distributed across the fold, leading to more concentric, round folds.
Figure 10 emphasizes the localization of slip in kink bands on the forelimbs of the
fault-propagation fold in the case of frictional contacts (left-hand side). Slip between
layers occurs throughout the fold in frictionless layers (right-hand side).
3.3 Initial Differential Stress
Both in nature and in the BEAFS model, a pre-existing far-field stress (σff)
needs to exist in order for folding to initiate and continue. Furthermore, a vertical
confining pressure (σcc) must also be present. The difference between these two
variable stresses is called the differential stress (σDiff=σff-σc), a parameter that can be
manipulated in BEAFS. For the purposes of this study, the confining pressure was

25. 18
not altered as we only concentrated on varying the horizontal far-field loading.
Increasing or decreasing the amount of horizontal loading would in turn lead to a
higher or lower differential stress respectively. Figure 11 illustrates the results
from varying the initial differential stresses. Overall, higher values of differential
stress lead to tight, sharp-hinged, flat-crested folds with higher amplitudes whereas
lower values of initial differential stress generally reduces the amplitude of the fold.
Furthermore, lower values of initial differential stress only affected the fault-bend
fold geometries. A “Suppe-like” fault-bend fold geometry only tends to form under
higher amounts of differential stress.
Figure 11: Effects of varying initial differential stress. Vertical confining pressure remains
at a default 2MPa. Higher initial differential stress leads to more well-developed, higher
amplitude folds with sharp-hinged, flat-topped geometries. Lower initial differential stress
leads to lower amplitude folds (observed only in fault-bend fold models). Higher values of
initial stress are needed to create the traditional “Suppe-like” fault-bend fold geometry.

26. 19
3.4 Fault Shape
Through experimentation with the BEAFS model, we discovered that the
shape of the fault embedded in the layered medium had an important role in
governing the shape of the resultant fold. Curved, broad faults with gentle
transitions to the lower detachment yield very asymmetrical folds. The backlimbs
in these folds are very gentle and broad with shallow dips, but the forelimbs tend to
form very tight kink bands with steep dips above the fault tip (Figure 12). Straight
faults, with sharp transitions into the lower detachment tend to form asymmetrical
folds as well, but with an opposite sense of asymmetry (Figure 12). These folds
have two kink bands instead of the singular kink band seen in the curved fault
shape. One kink band forms over the fault tip, similar to the curved fault, but the
second forms over the sharp transition between the lower detachment and the
ramp. Similar experimentation of fault shape with fault-bend folds did not provide
any insight.

27. 20
Figure 12: Effects of varying fault shape. Both folds are from a model run with 15 layers,
frictional contacts, 2 MPa initial differential stress, and 7km of shortening. Top: Having a
curved, gentle sloping fault leads to asymmetry. The forelimb dips are much steeper than
the backlimb dips. The forelimb kink band forms over the fault tip. Bottom: Having a
straight fault with a sharper transition to the lower detachment leads to asymmetry as well.
The backlimb kinks propagate over the transition from the lower detachment to the ramp
and the forelimb kinks propagate over the fault tip.

28. 21
4. Analysis of Natural Folds in Seismic Section
Having a fundamental understanding of the variable physical parameters
within BEAFS and their affects on fold geometries allows us to take a step further
and begin investigating the physical conditions responsible for generating natural,
real-world folds. Folds in nature take on a wide range of different shapes and
arrangements, so the BEAFS model must be robust enough to recreate an
assortment of different fold geometries. The dataset we used to gather these
various fold geometries was an AAPG compilation (atlas) of fault-related folds from
around the world, imaged with seismic seismic reflection surveys with
interpretations included by the authors (Shaw, Connors, Suppe, 2005). The goals of
this study are aimed towards capturing the essence of folds in seismic section, not
necessarily recreating them in an exact, quantitative fashion. We use the BEAFS
model to produce a general, qualitative shape that is similar to the fold, capturing
the folding style and key characteristics (e.g., asymmetrical vs. symmetrical, high
amplitude vs. low amplitude, broad vs. localized). The three primary reasons for
resorting to a qualitative analysis are: 1. Limitations of the BEAFS model, 2. Lack of
depth conversion on seismic lines : Most of the seismic lines in the AAPG Seismic Atlas
(Shaw, Connors, Suppe, 2005) are not depth converted and therefore cannot be
assumed to display the true fold and fault geometry -- time/depth conversion of
seismic lines commonly skews the vertical placement of reflection horizons and may
not reflect the true fold geometry, and 3. Steep dips on forelimbs are not well imaged
in the available seismic section: A common problem in seismic sections is the lack of
imaging capability on steep horizons without the aid of proper processing. Little to

29. 22
no resolution exists for these steep horizons, so true dips on the steep limbs of folds
cannot be accurately interpreted. Below we provide our “best-fit” models for three
different types of fold geometries:
1. Sharp-hinged, flat-topped, asymmetrical fault-propagation fold (Basil Anticline),
2. Rounded, broad, asymmetrical fault-propagation fold (Rosario Structure)
3. Sharp-hinged, flat-topped, symmetrical fault-bend fold (Toldado Anticline).
4.1 Basil Anticline
The Basil Anticline example is a Pliocene-aged fault-propagation fold within
the Apennines folds and thrust belt, in the Northern Adriatic Sea off the eastern
coast of Italy. The stratigraphy of the Pliocene foreland deposits in the northern
Adriatic are characterized as turbidite sequences which are famously thinly
interbedded sequences (Ghielmi et al., 2013). The structure verges to the Northeast
with a gently dipping backlimb and a much steeper forelimb that is poorly imaged in
the seismic section (Figure 13.1). The fault ceased propagation and deformation
terminated before any breakthrough into overlying units could occur, leaving the
forelimb mostly intact. In a qualitative sense, the fold is very angular and flat-
topped, with kink bands developed on either side of the fold crest.
The first order fold geometry characteristics of the fold in seismic are similar
to those of a thinner layered model with frictional slip contacts and a higher initial
differential stress (See figures from section 3). However, the crucial geometric
feature that defines the Basil Anticline is the presence of a very steep forelimb
versus a much broader backlimb. This type of asymmetry is observed when we

30. 23
introduce a curved fault geometry into BEAFS (see Figure 12), and should therefore
be applied to the starting model of the Basil Anticline as well. The presence of a
curved fault geometry allows the forelimb kink band to develop earlier in the fold
generation than the backlimb kink band, producing much steeper angles of dip in
the forelimb. In Figure 13.1, we present our “best-fit” solution for matching the
overall fold geometry characteristics of the Basil Anticline seismic section. The
physical conditions required to create the fold are: layer thickness of 0.4 km (25
layers), frictional contacts (μ=0.5), 6 MPa initial differential stress, and 7km of
shortening. Figure 13.2 displays the best-fit model for the Basil Anticline alongside a
frictionless model and a bonded model. When comparing the three models, it is
apparent that frictional layer slip must be present to generate the flat-topped, kink-
band fold geometry.

31. 24
Figure 13.1: Seismic reflection data of the Basil Anticline with interpretations from authors
(Shaw, Connors, Suppe 2005) compared with “best-fit” solution from the BEAFS model.
“Best-fit” solution is compared to folded strata beneath Pliocene and Pleistocene growth
wedges. Scales for X and Y axes are in kilometers. “Best-fit” solution captures the
asymmetry of the Basil Anticline with a very steep forelimb and broad backlimb. Both the
seismic data and modeled solution are fairly sharp-hinged and flat-topped.

32. 25
Figure 13.2: Bottom: “Best-fit” solution for the Basil Anticline. Scales for X and Y axes are in
kilometers. Physical conditions needed are listed above the model result. The key features
of the fold to note are the steep forelimb and very broad backlimb and a flat-topped fold
crest. Top left: “Best-fit” model run with layers bonded together. No slipbetween layers
yields little folding and heavy asymmetry. Top right: “Best-fit” model run with frictionless
contacts. Slip is distributed across the fold, generating a rounded, concentric fold. Note-all
above models are the mirror image of figure 13.1
4.2 Rosario Structure
The Rosario Structure is a broad, asymmetrical fault-related fold located
within the Maracaibo Basin, Venezuela roughly 70 kilometers west of Lake
Maracaibo. The anticline is documented as forming during the Andean Orogeny of
middle Miocene time (Roure et al, 1997). A roughly 3,000m thick lithostratigraphic
package is entrained in the fold. The subsurface stratigraphy and structure of the
Maracaibo Basin is for the most part well recorded due to the occurrence of large
amounts of oil and gas reserves in the basin. The oldest formation involved in the
folding of the Rosario structure is the Cretaceous Rio Negro, followed by the Cogollo

33. 26
Group, La Luna Formation, Colon Shale, and into younger Paleocene to Miocene
sediments (Figure 14). Qualitatively, the fold geometry is weakly asymmetric with a
slightly steeper forelimb versus backlimb (Figure 15.1). Truncation occurs only in
the deeper regions of the fold within the Cretaceous Rio Negro and La Luna
formations.
Figure 14: Generalized stratigraphic section of the Maracaibo Basin (Shaw, Connors, Suppe
2005). Units included in deformation of the Rosario Structure are the Rio Negro, Cogollo
Group, La Luna, Colon Shale, and more recent Cenozoic Deposits.
The fold is fairly rounded with no kink-band development whatsoever, a
geometry that is more akin to folds formed in thickly layered media as seen in

34. 27
Figure 8. The similarity to our thick-layered model helps us infer that the carbonate
packages of the Rio Negro Fm., Cogolla Group, and La Luna Fm. that are involved in
the deformation are potentially more thickly layered sediments with stiff-layer
mechanical stratigraphy, reinforcing the occurrence of a rounded fold form in the
seismic section. The asymmetry can be modeled by inputting a curved fault, leading
to a much broader backlimb versus forelimb. The AAPG Seismic Atlas (Shaw,
Connors, Suppe, 2005) interprets the structure as a fault-bend fold having both an
upper and lower detachment, however we were unable to use BEAFS to model the
fold form with a fault-bend fold geometry. Instead, we have successfully modeled
the structure as a fault-propagation fold, lacking an upper detachment. A potential
explanation for this discrepancy could be that the Rosario Structure has very
recently developed a breakthrough upper detachment. A majority of the
deformation could have taken place as fault-propagation fold, like the model
predicts, with an upper detachment forming at a later stage. In Figure 15.1, we
present our “best-fit” solution for matching the overall fold geometry characteristics
of the Rosario Structure seismic section. The physical conditions required to create
the fold are: layer thickness of 1.11km (9 layers), frictional contact (with coefficients
of friction of 0.5), 2 MPa initial differential stress, and 11 km of shortening. Figure
15.2 illustrates the “best-fit” model for the Rosario Structure alongside a frictionless
model and a bonded model.

35. 28
Figure 15.1: Seismic reflection data of the Rosario Structure with interpretations from
authors (Shaw, Connors, Suppe 2005) compared with “best-fit” solution from the BEAFS
model. Scales for X and Y axes are in kilometers. “Best-fit” solution captures the asymmetry
of the fold with a steeper forelimb versus a broader backlimb. The rounded character of the
Rosario Structure is also represented in the best-fit solution, produced by using a more
thickly layered package.

36. 29
Figure 15.2: Bottom: “Best-fit” solution for the Rosario Structure. Scales for X and Y axes are
in kilometers. Physical conditions needed are listed above the model result. The key
features of the fold to note are the steep forelimb and very broad backlimb and a with a
more rounded fold crest lacking kink bands. Top left: “Best-fit” model run with layers
bonded together. No slip between layers yields a less developed fold with asymmetry. Top
right: “Best-fit” model run with frictionless contacts. Slip is distributed across the fold,
creating a “pop-up” like structure. The amplitude of the frictionless fold is much higher than
the best-fit solution.
4.3 Toldado Anticline
The Toldado Anticline, deriving its name from its location in the Toldado
Oilfield in the Upper Magdalena basin, Tolima, Colombia, is a subsurface, sharply
hinged fault-bend fold superimposed on the larger and farther-reaching Avechucos
Syncline. The Toldado Anticline is part of the NNE trending Ortega fold and thrust
belt, involving the deformation of late Cretaceous to Oligocene aged lithologic units,
predominantly interbedded sandstones and shales of marine shelf, shoreface, and
coastal plain origin. The authors of the AAPG Seismic Atlas (Shaw, Connors, Suppe
2005) provide two separate kinematic interpretations of the fold and fault geometry
of the anticline. For the purposes of our modeling we decided the best course of

37. 30
action would be to model the second, and according to the authors, more plausible
interpretation, found in Figure 16.1. This interpretation has the geometry of a
traditional “flat-ramp-flat” fault-bend fold, reminiscent of the Suppe, (1983) models
of fault-bend folds. The slope of the fault ramp is relatively low-angle and the
geometry of the fold is fairly symmetrical, displaying sharp-hinged kink bands both
in the forelimb and back-limb and a very flat, moderate amplitude fold crest, a shape
very similar to Figures 5 and 6 of an isolated, frictionally slipping fold. Interestingly,
the entire fold, including the fault, is tilted with respect to the backlimb. The fold
could have either been rotated or developed on an inclined section. While modeling
this fold we did not include this rotating of the fold and fault, but instead modeled
the geometry as if the upper and lower detachments were at their original
horizontal positions prior to tilting, using the fault takeoff angle from the lower
detachment as reference. In order to capture the essence of the Toldado Anticline,
the BEAFS model needed to model the sharp-hinged kink-banded limbs, the flat-fold
crest, and the symmetrical nature. Looking back at Figure 8 from section 3, sharp-
hinges and flat fold crests tend to form with more thinly layered packages, but must
also have frictionally slipping contacts (Figure 9). When compared to the
interbedded sand and shale nature of the Toldado Anticline, a thinner layer package
would make sense for this model. However, to further develop and exaggerate the
kink bands on the limbs, as displayed by the fold in the seismic reflection, higher
amounts of initial differential stress need to be present in the model (Figure 11).
The combination of these physical parameters helped us to accurately model the
essence of the Toldado anticline, creating our best-fit model in Figure 16.1. The

38. 31
physical conditions required to create the fold are: layer thickness of 0.3km (23
layers), frictional contacts (with coefficients of friction of 0.5), 8 MPa initial
differential stress, and 4 km of shortening. Figure 16.2 illustrates the comparison
between the “best fit” model and models of frictionless and bonded contact
strengths with all other physical conditions remaining the same.

39. 32
Figure 16.1: Seismic reflection data of the Toldado Anticline with interpretations from
authors (Shaw, Connors, Suppe 2005) compared with “best-fit” solution from the BEAFS
model. Scales for X axes are in meters and scale for Y axes are in kilometers. Best-fit
solution captures the symmetrical nature of the Toldado Anticline along with the well-
developed, sharp-hinged kink bands on the forelimb and backlimb. A slight footwall syncline
appears to be developed in the seismic section, which we have modeled as well. The seismic
reflection data shows a rotation of the fold toward the backlimb, which we do not model. We
have modeled the fold as if the upper and lower detachment were horizontal, prior to the
tilting of the fold.

40. 33
Figure 16.2: Bottom: “Best-fit” solution for the Toldado Anticline. Scales for X and Y axes are
in kilometers. Physical conditions needed are listed above the model result. The key
features of the fold to note are the symmetrical nature, flat, moderate amplitude fold crest,
and well-developed kink bands in the forelimb and backlimb. Top left: “Best-fit” model run
with layers bonded together. No slipbetween layers results in a very rounded, asymmetric
fold with low amplitude. Top right: “Best-fit” model run with frictionless contacts. Slip is
distributed equally across the layers, creating a sinusoidal fold train.
5. Conclusions
Through our mechanical modeling of both very general fold geometries to
various examples of natural fault-related folds from around the world, we have been
able to better grasp the role of flexural layer-parallel slip in these types of folds. By
creating a general reference fold geometry for both fault-bend and fault-propagation
folds and systematically manipulating one physical parameter at a time, we have a
deeper understanding of the relationship and interconnection between the various
physical conditions that create fold geometries.

41. 34
We have determined that thickly-layered mediums and mediums with
bonded contacts always lead to rounded, broad fold geometries, regardless of the
fault geometry. In most cases, we learned that fault geometry plays a vital role in
the shaping the resulting fold, however the previously mentioned thick-layered
mediums and bonded contacts were an exception. With a fault-propagation
geometry, freely-slipping, thin-layered mediums lead to highly rounded, localized
concentric-like fold forms above the tip of the fault. In contrast, with a fault-bend
fold geometry, freely-slipping, thin-layered mediums lead to kink-like forelimbs and
backlimbs with flat fold crests. When frictional contacts are introduced into a thinly
layered medium with a fault-propagation geometry the resultant fold form would
display kink-like forelimb and backlimb with a flat-fold crest. In most cases, the
addition of an initial farfield differential stress enhances the formation of kink folds
with sharp hinges, regardless of the fault geometry.
With these general results regarding the relationship between varying
physical parameters in the BEAFS model, we were able to analyze the physical
conditions and fault geometry in real-world folds. Using the model, we were able to
reproduce the first-order geometric characteristics of three different fault-related
folds imaged in seismic section: 1. Basil Anticline, Northern Adriatic Sea, 2. Rosario
Structure, Maracaibo Basin, Venezuela, and 3. Toldado Anticline, Magdalena Basin,
Colombia. Reproduction of the Basil Anticline and Toldado Anticline required thinly
layered mediums in the model and frictional contacts in order to generate the sharp
hinges that are observed in both folds. The stratigraphy for both localities
comprises of thin mechanic layering which is consistent with the thinly-layered

42. 35
medium we used to recreate the fold and helps support our results from the BEAFS
model. In contrast, the Rosario Structure required very thick layers to recreate the
broad, rounded fold observed in seismic section. The units involved in the
deformation of the Rosario are massively bedded, thick carbonate sequences
leading to thick, stiff mechanical layering, consistent with the BEAFS model, further
supporting our results. In conclusion, it seems very apparent that the role of
flexural layer parallel slip is crucial in the formation of not only isolated folds, but in
fault-related folds as well.

43. 36
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45. Vita
NAME: Austin M. Hodge
DATE OF BIRTH: May 3, 1989
PLACE OF BIRTH: Warner Robins, Georgia
EDUCATION: B.S., 2011, Clemson University, Clemson, South Carolina
M.S., 2013, Indiana University, Bloomington, Indiana