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Evolution of dilatant fracture networks in normal
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faults – evidence from 4D model experiments
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Marc Holland1*, Heijn van Gent1, Loïc Bazalgette2, Najwa Yassir2 , Eilard H. Hoogerduijn
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Strating3, Janos L. Urai1
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Structural Geology Tectonics Geomechanics, www.ged.rwth-aachen.de,
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RWTH Aachen University, Lochnerstrasse 4-20, D-52066 Aachen,
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Germany
Shell International Exploration and Production B.V., Kesslerpark 1, 2288
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GS Rijswijk ZH, The Netherlands
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Street, Houston, TX 77002, United States of America
Shell Exploration & Production Company, Two Shell Plaza, 777 Walker
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Dilatant segments of normal fault zones are widely recognized as major
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pathways of fluid flow in the upper crust, but the structure of these fracture
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networks in 3D, their connectivity and their temporal evolution is poorly known.
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Here we show, using a series of CT scans of a scaled physical model, how the
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dilatant fracture network evolves in a normal fault zone, as a complex self-
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organizing system with self-similar geometry. Dilatant jogs initiated along the
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evolving fault plane coalesce into a fractal percolating volume (Fd=1.91). The
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fracture volume increases non-linearly with progressive displacement as the
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velocity of the fault blocks diverges from the master fault orientation and the
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normal stress on the fault decreases correspondingly. This process continues
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until the system triggers the formation of antithetic faults, with a corresponding
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decrease in the rate of fracture porosity creation. We infer that the processes
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and geometries in our model are robust and relevant to a wide range of normal
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fault zones in nature.
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Corresponding author. E-mail address: [email protected] (M. Holland).
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Fault zones occur at a wide range of length scales; they are first order mechanical
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discontinuities in the Earth’s crust and form major barriers or conduits for fluid flow.
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In those parts of the upper crust where the compressive strength of rocks is much
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higher than the mean effective stress, deformation in releasing sections of normal
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faults is massively dilatant and generates open fractures. These can be pathways
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controlling the fluid flow. Examples are found in basalts, crystalline rocks, cemented
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carbonates and cemented mudrocks in the deeper parts of sedimentary basins where
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diagenetic processes have led to a strong increase of compressive strength1-6.
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Dilatant fractures can also be formed deeper in the crust where total stresses are
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much larger but fluid pressures are close to lithostatic. Here, fault-valve processes
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and invasion percolation2, 7-9 become important. Networks of open fractures in the
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Crust are difficult to access or image in 3D, so that their connectivity and temporal
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evolution is not fully understood10, 11.
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Here we focus on the evolution of physical models scaled to represent rocks in which
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open fractures can form in normal fault zones. We ask the question if, and how the
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dilatant segments commonly observed in normal fault zones connect in 3D during
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progressive deformation, and what the geometry of such fracture networks can be.
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Figure 1 (Experiment series, visualization of the void volume)
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The physical model consists of a 15 cm thick package of fine grained cohesive
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powder1, 12 (CaSO4 • ½ H2O) with a depth dependent tensile strength and cohesion12.
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The powder’s tensile strength and cohesion are high in comparison with the mean
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stress in the model1, 12-14. The model is deformed above a rigid basement containing a
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60° dipping normal fault (basement fault). At successive deformation stages the
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radiological density was imaged using a computer tomograph for the acquisition of a
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4D dataset.
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Processing included cropping and the application of a threshold filter to isolate the
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void voxels. Clusters of less than four interconnected voxels were excluded from the
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analysis. Assuming interconnectivity of the voxels for face-to-face and edge-to-edge
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bridging, we visualized and analyzed the progressive development of fault-related
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tensile fractures and dilatant segments which form the interconnected voids in the
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deforming model. Based on the spatial resolution of the scanner (0.5 mm) and the
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radiological contrast of the materials, void apertures down to 130 μm (±30 μm) are
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resolved. Data is shown of the lower 80% of the experiment, (subset ‘b’, Figure 2,
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inset), whereas a smaller subset ‘a’ is examined for statistical analysis (Figure 2,
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inset). Avoiding edge effects, analysis of subset ‘a’ involved tracking the number of
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interconnected voids and their mean volume over time (Figure 2)
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Figure 2 (Development of void sizes and numbers, Inset with setup)
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At the onset of deformation, incipient strain occurs above the basement fault in
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shear and at the surface with mode I fractures propagating downward. This is
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followed by propagation of the master fault to the surface, and later by the initiation
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of an antithetic fault (Figure 1). In profile, all these faults are associated with
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numerous dilatant jogs. Processes modifying the dilatant volume are gravity-driven
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movement of fragments and reworking of asperities.
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Figure 3 (The 1st. percolating fault)
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Vertical connectivity along the master fault (in subset ‘a’, Figure 1) increases with
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fault displacement. The first continuous open fracture system at the scale of the
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model forms between 5 mm and 7 mm offset (Figure 1, Figure 3). The increasing
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structural complexity of the fault network is in good agreement with the evolution of
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the dilatant fracture volume. The total fracture volume increases progressively with
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offset, but the distribution of fractures is much more complex. Initially, the number
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of fractures increases strongly. Fracture coalescence and the onset of percolation
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leads to a drop in the number of individual fractures (Figure 2, throw=5-7 mm,
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arrow). The initiation of the antithetic fault is linked to the formation of additional
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fractures, however without an increase in mean fracture volume (Figure 2, throw>7
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mm). The percolating volume has a horizontal opening up to 6 voxels (3 mm, Figure
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3). 3D box- counting on the isolated percolating volume yields a power-law
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relationship (Fd=1.91), suggesting fractal characteristics of the volume (Figure 3).
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Although dilatant jogs in profiles of fault zones can be relatively simple, this
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experiment suggests that the 3D network along a fault plane has a complex self-
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similar geometry.
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The geometry of the complete dilatant fracture volume in subset ‘a’ of our model
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shows a gradual evolution (Figure 4). For box sizes larger than 30 voxels (edge
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length 15 mm) boundary effects (dimensions of the experiment) generates similar
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slopes, whereas the smaller box sizes produce linear curve segments implying fractal
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characteristics. Extrapolation of the linear trend suggests self-similarity below the
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resolution of the scanner. Throughout the experiment the fractal dimension changes,
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shown as a gradual increase in slope during the ten deformation stages when the
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system evolves from a segmented line (D<1), over a planar structure (D≈2) towards a
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fragmented volume (2<D<3).
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From approximately 7 mm offset on, the curves become sub-parallel. These late
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stages still show an ongoing increase in fracture volume but no further changes in
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the fractal dimension.
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Figure 4 (Fractal development of the experiment series)
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The evolution of the dilatant fracture network in our experiment is controlled by the
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evolution of the stress field and the spatial variation of material properties. In this
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displacement-controlled model the global stress field is heterogeneous15 and the
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patterns of localization are not compatible with the simple kinematics of the
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basement fault, so that complex patterns of deformation evolve over time. In
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addition, in this non-stratified material the roughness of the fractures is influenced
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by material heterogeneity, creating irregular fracture surfaces, which can enhance
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the initiation of dilatant jogs.
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Earlier studies using PIV (particle image velocimetry)12, 16 have shown that with
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progressive displacement of the master fault the mismatch in dip angles of the
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developing master fault plane and the 60˚ basement fault (Figure 5a) leads to
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divergence across the master fault. We infer that this helps the dilatant sections to
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grow and coalesce, in addition to the divergence caused by the dilatancy angle17. This
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is interpreted to cause a decrease of the normal stress on the master fault (Figure
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5b) and with an increase of shear stress in the hanging wall block, until the
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formation of an antithetic fault reverses these conditions and adopts the system
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temporarily to the kinematic framework (Figure 5c).
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Figure 5 (Sketch of the mechanical framework)
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The formation of antithetic faults is a commonly observed feature in extensional
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tectonic systems. Although the width of our deformation zones is not scaled
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correctly, normal fault systems in nature are inferred to show similar cycles of
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normal stress on the master fault plane, along with the formation of antithetic faults.
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With differences in growth rates and cycle length, complex patterns of rupture and
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slip can form even without the effects of high fluid pressures2, 7, 8, 18..
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In previous 2D studies we have shown that using simple scaling arguments, the
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structures in these experiments compare well with natural prototypes observable in
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basalts and carbonates. They are robust, with similar fracture geometries for a range
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of parameters. In this study, we have shown how the 3D dilatant fracture volume
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evolves over time, with the formation of fractal fracture networks.
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Keeping in mind the granular nature of our material, the thickness of the
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deformation zone and total fracture volume do not scale with the scaling ratio of the
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model. However, based on the well known self-similar geometry of natural fracture
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surfaces over many orders of magnitude19, we propose that the geometries of
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dilatant sections found in our experiments are similar to the corresponding
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geometries in normal faults in nature, as observed in outcrops and wells and
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suggested by patterns of seismicity
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In nature, additional processes are important such as the transport of sediments
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carried by meteoric fluid flow (limited to shallow depth domains), chemical processes
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of dissolution and cementation and changes in fracture geometry across layering.
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Therefore the dilatant fracture network will show additional complexity depending
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on these factors
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Although formed without invasion, fluid flow in such systems could lower the fault
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strength and trigger further slip2, 3, 7, 8.
. Flow of fluid in such a network will be complex7, 8, 20, 22.
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Acknowledgements:
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We would like to thank Shell SIEP Rijswijk (Axel Makurat, Fons Marcelis) and the staff
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of RWTH University Hospital, Aachen for providing access to the computer
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tomograph and support during the project. This manuscript greatly benefited from
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discussions with Stephen Miller (University Bonn). This work is part of a Shell-
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sponsored research project in collaboration with the RWTH Aachen University and
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was largely carried out at Shell SIEP Rijswijk.
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Figure Captions
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Figure 1 – Visualization of the experiment showing the development of the fracture
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network in nine successive deformation stages. The topmost 3 cm as well as the
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outermost parts are cropped producing volumes of 522×512×302 voxels. The upper
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pictures show grayscale images of the outer surface of volume from the computer
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tomograph, the lower pictures display the isolated void volume. Note the
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propagation of irregular void volumes until after 7 mm offset vertical connectivity is
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reached (Extent of subset ‘b’ shown in Figure 2; Bright interlayers in the CT volumes
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are thin passive marker layers of high density barite powder; See text for details).
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Figure 2 – Statistical analysis of the void characteristics throughout the ten
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deformation stages obtained on subset ‘a’. The number of interconnected void
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clusters increases until 5 mm offset and drops as these coalesce at 7 mm offset,
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forming the first percolating feature. Inset shows the location of ‘b’ subset used for
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visualization and the ‘a’ subset used for statistical analyses excluding the outer
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margins.
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Figure 3 – After 7 mm offset a first feature is detected that spans subvolume ‘a’
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vertically. Projected on a vertical plane, the horizontal opening of this percolating
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volume is up to 6 pxl (color bar with horizontal opening [pxl] applicable to the
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projection only). 3D box-counting on this fracture only shows a power-law pattern
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with a fractal dimension of approximately Fd=1.91 (S is box length in pixel, N(S)
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number of returned boxes with void volume).
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Figure 4 – 3D box-counting on the open-mode volumes of subset ‘a’ show curves
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with linear segments. For smaller box sizes the system changes from a line pattern
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(1 mm offset), over a planar (3-5 mm offset), to a segmented volume pattern (10-25
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mm). Although the last four to five stages show an increase in the detected volume,
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the sub-parallel distributions indicate no significant changes in the geometrical
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pattern (S is box length in pixel, N(S) number of returned boxes with void volume).
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Figure 5 – Kinematic scenario showing the evolution of the normal fault system: (A)
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The formation of early deformation features are oriented non-optimal to the
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kinematic conditions (white stippled line). (B) A curved master fault plane develops
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showing a divergence to the basement fault, which lowers the normal stress on the
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fault plane. (C) Due to an increase of shear strength in the hanging wall block, the
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system adapts by forming an antithetic fault, which temporarily readjusts the system
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with localized decrease or increase of the void volume along the master fault plane.
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