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Joints at high angles to normal fault strike: An explanation using 3-D numerical models of fault-perturbed stress fields
Abstract
Structural methods based on homogeneous stress states predict that joints growing in an extending crust form with strike orientations identical to normal faults. However, we document a field example where the strikes of genetically related normal faults and joints are almost mutually perpendicular. Field relationships allowed us to constrain the fracture sequence and tectonic environment for fault and joint growth. We hypothesize that fault slip can perturb the surrounding stress field in a manner that controls the orientations of induced secondary structures. Numerical models were used to examine the stress field around normal faults, taking into consideration the effects of 3-D fault shape, geometrical arrangement of overlapping faults, and a range of stress states. The calculated perturbed stress fields around model normal faults indicate that it is possible for joints to form at high angles to fault strike. Such joint growth may occur at the lateral tips of an isolated fault, but is most likely in a relay zone between overlapping faults. However, the angle between joints and faults is also influenced by the remote stress state, and is particularly sensitive to the ratio of fault-parallel to fault-perpendicular stress. As this ratio increases, joints can propagate away from faults at increasingly higher angles to fault strike. We conclude that the combined remote stress state and perturbed local stress field associated with overlapping fault geometries resulted in joint growth at high angles to normal fault strike at a field location in Arches National Park, Utah.
... As normal fault segments propagate, the stress field adjacent to isolated or interacting faults is perturbed relative to the remote tectonic stress field, resulting in a range of possible fracture orientations and patterns (e.g., Price and Cosgrove, 1990;Rives et al., 1992;Kattenhorn et al., 2000). Based on numerical modeling and field data, Kattenhorn et al. (2000) showed that fractures can grow at high angles to a normal fault plane near the lateral tips of normal faults, and they also demonstrated that a perturbed stress field extends furthest from fault segments proximal the lateral fault tipline and within relay zones between normal fault segments. ...
... As normal fault segments propagate, the stress field adjacent to isolated or interacting faults is perturbed relative to the remote tectonic stress field, resulting in a range of possible fracture orientations and patterns (e.g., Price and Cosgrove, 1990;Rives et al., 1992;Kattenhorn et al., 2000). Based on numerical modeling and field data, Kattenhorn et al. (2000) showed that fractures can grow at high angles to a normal fault plane near the lateral tips of normal faults, and they also demonstrated that a perturbed stress field extends furthest from fault segments proximal the lateral fault tipline and within relay zones between normal fault segments. The location of the VOM outcrop in the footwall of and near the southern tip of the Spencer Bench segment (Fig. 2), likely experienced a perturbed stress field during slip along that fault segment. ...
... Using this model, the Spencer Bench segment adjacent to the study site would have acted as a weak fault section that was a stress barrier between the footwall and hanging wall during fracture initiation and propagation. However, the orientation of joints in the footwall might also be explained by a perturbed stress field adjacent to the tip of the Spencer Bench segment as it propagated to the south (e.g., Kattenhorn et al., 2000;Maniatis and Hampel, 2008) or by stress-field deviation associated with interacting normal fault segments (e.g., Kattenhorn et al., 2000) (Fig. 2). ...
Fractures strongly influence the permeability of geologic formations, and because most fractures in the subsurface are below the resolution of geophysical methods, predicting the spatial evolution of fracture networks is important for groundwater resources, oil and gas production, and geothermal energy. Previous researchers have established that variations in lithologic mechanical properties influence the propagation of joints and fractures in layered rocks under stable stress conditions, but few studies have addressed how instabilities in local stress fields, in conjunction with variations in rock mechanical properties, lead to fracture branching.
We investigate NE-striking fractures in the footwall of the west-dipping Sevier fault in Utah, USA, where canyons expose the sub-horizontal Jurassic Navajo Sandstone. We analyzed field data, petrographic data, and unmanned-aerial-vehicle (UAV) imagery to document the fracture network. We also used structure-from-motion (SfM) software to build a 3D virtual outcrop model, measuring 100 m high and 260 m wide, to aid our analysis of fracture network geometry, intensity, and spacing variations.
Data reveal an up-section increase in fracture intensity and decrease in spacing regularity partly accommodated by upward fracture branching. We suggest that branching was initiated by a combination of changes in mechanical behavior within cross-bed sets and twist hackle propagation associated with mixed mode fracture systems. These tree-like fracture geometries may be associated with high-velocity, earthquake-related fracture propagation events. Fracture branching strongly influences permeability and should be considered by researchers investigating fracture development in subsurface systems.
... L'arrangement spatial de ces familles de fractures forme des réseaux de fractures plus ou moins complexes (e.g. Pollard and Aydin 1988;Rives et al. 1992;Kattenhorn et al. 2000;Peacock et al. 2018;Sanderson and Nixon 2018;Sanderson et al. 2019). Les intersections entre les fractures formées dans le réseau de fractures peuvent être déterminantes pour la compréhension et la chronologie des processus à l'origine de ces fractures. ...
... Ces perturbations sont cohérentes avec la fracturation observée en périphérie et une perturbation de la distribution du déplacement sur les plans de failles (e.g. Aydin and Schultz 1990;King et al. 1994;Willemse et al. 1996;Willemse 1997;Crider and Pollard 1998;Crider 2001;Kattenhorn et al. 2000;Maerten et al. 1999Maerten et al. , 2002Maerten et al. , 2006. Les variations de rejet dans les zones de relais augmentent localement l'intensité des contraintes et favorisent la fragmentation de la zone de relais par des fractures et failles d'orientation variable en fonction du champ de contraintes appliqué et de la friction des failles (Figure 1.23, Crider and Pollard 1998;Kattenhorn et al. 2000;Soliva et al. 2010). ...
... Aydin and Schultz 1990;King et al. 1994;Willemse et al. 1996;Willemse 1997;Crider and Pollard 1998;Crider 2001;Kattenhorn et al. 2000;Maerten et al. 1999Maerten et al. , 2002Maerten et al. , 2006. Les variations de rejet dans les zones de relais augmentent localement l'intensité des contraintes et favorisent la fragmentation de la zone de relais par des fractures et failles d'orientation variable en fonction du champ de contraintes appliqué et de la friction des failles (Figure 1.23, Crider and Pollard 1998;Kattenhorn et al. 2000;Soliva et al. 2010). King et al. (1994), montrent en particulier, par des modèles élastiques, les perturbations du critère de Coulomb lors de ruptures sismiques. ...
L’étude des failles affectant la croûte supérieure suscite un intérêt particulier pour la modélisation de leur impact sur l’écoulement des fluides et le comportement mécanique de la croûte terrestre. Les zones d’endommagements de failles sont d’importantes structures aux multiples implications pour les problématiques de gestions des ressources et de risque/aléa sismiques. Cette thèse a pour objectif de déterminer la distribution de l’endommagement autour des failles, comprendre sa croissance et étudier son impact sur la loi d’échelle Déplacement – Epaisseur d’endommagement (D-T). Pour répondre à cette problématique, deux approches complémentaires sont développées : des études tectoniques d’exemples naturels et des modélisations analogiques de failles normales. Ce manuscrit présente de nouvelles cartographies de l’endommagement, une première loi D-T pour les failles dans des roches carbonatées, ainsi que les premières expériences de modélisation analogique dédiées à l’étude de l’endommagement. Les résultats montrent que la distribution de l’endommagement autour des failles est hétérogène et asymétrique, principalement influencée parles nombreuses interactions de failles lors de leur croissance (segmentation, failles conjuguées). Une loi D-T spécifique à l’endommagement de type wall damage est établie, qui montre une corrélation normale entre D et T pour les failles de rejet inférieur à 100 m et confirme l’existence d’un seuil d’épaisseur d’endommagement au-delà de 100 m de rejet. Pour expliquer cette loi nous proposons un modèle de croissance de zone d’endommagement contrôlée par les processus d’interaction et de coalescence de la segmentation précoce. Les expériences de modélisations analogiques ont permis de décrire deux nouveaux types d’endommagement (graben damage et dip-change link damage), et d’identifier unetransition de mode de déformation, depuis un cisaillement dilatant segmenté vers un cisaillement compactant localisé dans les zones de failles. Elles démontrent également que l’initiation de la segmentation, la sélection de l’activité des segments, leurs interactions et leurs coalescences sont des processus essentiels contrôlant le développement des zones d’endommagement et la loi D-T. Nous proposons que l’épaisseur de l’unité fragile contenant les failles est un paramètre principal du contrôle de l’évolution de la segmentation, de la localisation de la déformation et donc du seuil d’épaisseur d’endommagement observé.
... This fault initiation process, which probably relies more on 3-D stress perturbation around the first initiated faults or pre-existing defect (e.g. Crider and Pollard, 1998;Kattenhorn et al., 2000;Maerten et al., 2002; also see Olson and Pollard, 1991, for a critical analysis of the Coulomb theory for fault initiation), does not discredit the applicability of the Coulomb theory on reactivation of preexisting fault surface and stress magnitude at failure (Reches and Dieterich, 1983). It can, however, justify the need to consider friction as a potential variable in a wider range than provided by common triaxial test data. ...
... Quasi-static fault displacement (net slip) can be computed on fault planes using linear elasticity (see Thomas, 1993;Maerten et al., 2010Maerten et al., , 2014Maerten et al., , 2018; for full explanation), taking into account static friction and cohesion, mechanical interaction due to stress perturbation between faults (e.g. Crider and Pollard, 1998;Kattenhorn et al., 2000;Soliva et al., 2008;Maerten et al., 2014), and using Young's modulus (E) and Poisson's ratio (ν) of 1 GPa and 0.25, respectively. This quasi-static displacement, rather than the coseismic value of displacement which must also be affected by dynamic rupture processes, is considered the fault ability to initiate and accumulate slip along fault. ...
... Although in the range of possible friction, cohesion, and angle of σ 1 with respect to the main fault trend (around 30 • ), the parametric conditions shown in Fig. 5 must be considered nonrealistic since the stress loading is purely uniaxial. The absence of stress perturbation in orientation is due to this uniaxial condition and the absence of fluid pressure in this parametric study (see Kattenhorn et al., 2000, andMaerten et al., 2018). More realistic stress conditions must consider the 3-D tensor and its variation through space and time. ...
By combining a 3-D boundary element model, frictional slip theory, and fast computation method, we propose a new tool to improve fault slip analysis that allows the user to analyze a very large number of scenarios of stress and fault mechanical property variations through space and time. Using both synthetic and real fault system geometries, we analyze a very large number of numerical simulations (125 000) using a fast iterative method to define for the first time macroscopic rupture envelopes for fault systems, referred to as “fault slip envelopes”. Fault slip envelopes are defined using variable friction, cohesion, and stress state, and their shape is directly related to the fault system 3-D geometry and the friction coefficient on fault surfaces. The obtained fault slip envelopes show that very complex fault geometry implies low and isotropic strength of the fault system compared to geometry having limited fault orientations relative to the remote stresses, providing strong strength anisotropy. This technique is applied to the realistic geological conditions of the Olkiluoto high-level nuclear waste repository (Finland). The model results suggest that the Olkiluoto fault system has a better ability to slip under the present-day Andersonian thrust stress regime than for the strike-slip and normal stress regimes expected in the future due to the probable presence of an ice sheet. This new tool allows the user to quantify the anisotropy of strength of 3-D real fault networks as a function of a wide range of possible geological conditions and mechanical properties. This can be useful to define the most conservative fault slip hazard case or to account for potential uncertainties in the input data for slip. This technique therefore applies to earthquake hazard studies, geological storage, geothermal resources along faults, and fault leaks or seals in geological reservoirs.
... Stress perturbations are also significant for evaluating secondary fracturing near faults and its associated permeability, which encompasses joint orientation, secondary faulting, and bed-parallel slip (e.g. Kattenhorn et al., 2000;Maerten et al., 2002;Delogkos et al., 2022). ...
... The stress state in such a block is then dominated by gravity only. One potential example of this is the Arches National Park in Utah, USA, where the joints are almost perpendicular to the normal faults and are constant over several hundred metres (Kattenhorn et al., 2000). Secondary faulting also provides a possible explanation for the complex stress pattern within the Viking Graben (North Sea, Maerten et al., 2002). ...
The impact of faults on the contemporary stress field in the upper crust has been discussed in various studies. Data and models clearly show that there is an effect, but so far, a systematic study quantifying the impact as a function of distance from the fault is lacking. In the absence of data, here we use a series of generic 3-D models to investigate which component of the stress tensor is affected at which distance from the fault. Our study concentrates on the far field, located hundreds of metres from the fault zone. The models assess various techniques to represent faults, different material properties, different boundary conditions, variable orientation, and the fault's size. The study findings indicate that most of the factors tested do not have an influence on either the stress tensor orientation or principal stress magnitudes in the far field beyond 1000 m from the fault. Only in the case of oblique faults with a low static friction coefficient of μ=0.1 can noteworthy stress perturbations be seen up to 2000 m from the fault. However, the changes that we detected are generally small and of the order of lateral stress variability due to rock property variability. Furthermore, only in the first hundreds of metres to the fault are variations large enough to be theoretically detected by borehole-based stress data when considering their inherent uncertainties. This finding agrees with robust stress magnitude measurements and stress orientation data. Thus, in areas where high-quality and high-resolution data show gradual and continuous stress tensor rotations of >20∘ observed over lateral spatial scales of 10 km or more, we infer that these rotations cannot be attributed to faults. We hypothesize that most stress orientation changes attributed to faults may originate from different sources such as density and strength contrasts.
... Our database suggests this is not always the case, however. For example, growth folds are documented on the flanks of Kilauea, Hawaii (Kattenhorn et al., 2000;Parfitt and Peacock, 2001;Peacock and Parfitt, 2002;Holland et al., 2006;Martel and Langley, 2006;Kaven and Martel, 2007;Podolsky and Roberts, 2008), the Modoc Plateau, USA (White and Crider, 2006;Blakeslee and Kattenhorn, 2013;Crider, 2015;Kattenhorn et al., 2016), and the Reykjanes Peninsula, Iceland (Bull et al., 2003;Grant and Kattenhorn, 2004;Bull et al., 2005;Trippanera et al., 2015) suggesting that cover rheology is not the principal control on growth fold occurrence. Cover lithology and rheology may affect the geometry and size of growth folds (Fig. 8D). ...
... On the flanks of Kilauea, Hawaii (e.g. Macdonald, 1957;Duffield, 1975;Kattenhorn et al., 2000;Parfitt and Peacock, 2001;Martel and Langley, 2006;Kaven and Martel, 2007;Podolsky and Roberts, 2008;Bubeck et al., 2018) and in the eastern Gulf of Corinth (e.g. Vita-Finzi and King, 1985), fault-propagation folds are currently forming despite very high regional extension rates (Kilauea Volcano -9-12 cm/yr from Owen et al., 1995;Gulf of Corinth -5-15 mm/yr from Bell et al., 2011). ...
Growth folds above the upper tips of normal faults are ubiquitous in extensional settings, especially during the early phases of extension and in salt-rich basins. As slip accumulates on the underlying normal fault, the geometry and size of the fold changes. These changes reflect the dip, throw, displacement and propagation rate of the underlying normal fault, as well as the thickness and rheology of the overlying cover. These changes also have a marked impact on the architecture and distribution of synkinematic sediments, as well as the styles of secondary deformation accommodating strain within the growing fold. Here, we analyse a large dataset of natural, and physically- and numerically-modelled growth folds to: (i) characterise their diagnostic features; (ii) investigate the controls on their geometry, size and differences; and (iii) describe how they grow with increasing extensional strain. We demonstrate that larger fault throws and a thicker and weaker cover are associated with larger growth folds. In contrast, small fault throws as well as thin and strong brittle cover are associated with smaller growth folds. We show that the geometry and size of growth folds vary through time; the width (and thus, the wavelength) of the fold is established relatively early during fold growth, whereas fold amplitude increases gradually with increasing fault throw. Fold width and amplitude become increasingly similar during fold evolution, until the fold is breached by the underlying normal fault. We also derive a number of preliminary empirical relationships between readily observable structural and stratigraphic parameters in our dataset that may help estimate the geometry and size of poorly exposed (i.e. in the field) or imaged (i.e. in the subsurface) growth folds. In addition, we discuss how fault growth models (i.e. constant-length vs. propagating) may impact the three-dimensional evolution of growth folds. Finally, our work shows that growth folds are likely more common than previously thought. For example, although they are well-documented in areas characterised by weak, ductile cover strata and low strain rates, our dataset illustrates that growth folds may also occur in brittle, relatively strong rocks and in regions with high strain rates. However, the underlying controls on fold occurrence remain elusive.
... Other modelling results show that it is possible for the lower part of PFs to appear permeable and critically stressed in the contemporary stress field, while the upper parts are neither permeable nor critically stressed (Wiprut and Zoback, 2000;Zoback, 2007). In the anisotropic stress area (salt tectonic area), stress generated by the overpressured fluid in host rocks leads to the propagation of planar fractures in PF hanging walls; this likely indicates that fluid pressure was not high enough to open the upper fault plane, but only high enough to overcome the minimum horizontal stress plus the fracture strength of the fault blocks (Delaney et al., 1986;Kattenhorn et al., 2000). Therefore, once the gas trapped in the lower part of the footwalls becomes overpressured (Fig. 16a-b), hydraulic fractures propagate from the footwall to pierce the overlying strata and breach the impermeable barrier; as a result, the chimneys were initiated and originated along the lower part of polygonal fault planes. ...
... Anisotropic PFs follow the orientations of salt tectonic structures, indicating that the PFs are heavily influenced by the stress states resulting from salt activities (Carruthers, 2012). The presence of faults can perturb the surrounding stress field and affect the adjacent fracture propagation (Rawnsley et al., 1992;Kattenhorn et al., 2000). Thus, degree of horizontal stress anisotropy and the dominant direction of horizontal intermediate stress play a determinant role in both the formation and geometry of anisotropic PFs and hence the planforms of chimneys. ...
A new type of gas chimney exhibiting an unconventional linear planform is found. These chimneys are termed “Linear Chimneys”, which have been observed in 3-D seismic data offshore of Angola. Linear Chimneys occur parallel to adjacent faults, often within preferentially oriented tier-bound fault networks of diagenetic origin (also known as anisotropic polygonal faults, PFs), in salt-deformational domains. These anisotropic PFs are parallel to salt-tectonic-related structures, indicating their submission to horizontal stress perturbations generated by the latter. Only in areas with these anisotropic PF arrangements do chimneys and their associated gas-related structures, such as methane-derived authigenic carbonates and pockmarks, have linear planforms. In areas with the classic “isotropic” polygonal fault arrangements, the stress state is isotropic, and gas expulsion structures of the same range of sizes exhibit circular geometry. These events indicate that chimney's linear planform is heavily influenced by stress anisotropy around faults. The initiation of polygonal faulting occurred 40 to 80 m below the present day seafloor and predates Linear Chimney formation. The majority of Linear Chimneys nucleated in the lower part of the PF tier below the impermeable portion of fault planes and a regional impermeable barrier within the PF tier. The existence of polygonal fault-bound traps in the lower part of the PF tier is evidenced by PF cells filled with gas. These PF gas traps restricted the leakage points of overpressured gas-charged fluids along the lower portion of PFs, hence controlling the nucleation sites of chimneys. Gas expulsion along the lower portion of PFs preconfigured the spatial organisation of chimneys. Anisotropic stress conditions surrounding tectonic and anisotropic polygonal faults coupled with the impermeability of PFs determined the directions of long-term gas migration and linear geometries of chimneys. Methane-related carbonates that precipitated above Linear Chimneys inherited the same linear planform geometry, and both structures record the timing of gas leakage and palaeo-stress state; thus, they can be used as a tool to reconstruct orientations of stress in sedimentary successions. This study demonstrates that overpressure hydrocarbon migration via hydrofracturing may be energetically more favourable than migration along pre-existing faults.
... As an example, the NNE-SSW to NE-SW (3) and NW-SE (4) mainly appear near the NW-SE Concud Fault or the NE-SW Tortajada Fault. This suggests that they represent local deflections of stress trajectories, as those modelized by e.g., and Katterhorn et al. (2000), and identified by Simón (1989) and Arlegui et al. (2006) in this region. Apart from the older compressional and strike-slip episodes, the Neogene stress field evolution has been therefore characterized from the whole analysis of the distribution of azimuths and R values of extensional stress states affecting the sedimentary sequence (Fig. 6), mesostructural evidence on their relative age (Tables 1 and 2), and the heterogeneous spatial distribution of stress directions attributed to stress deflection (Fig. 4). ...
... First, trajectories of the minimum stress axis (σ 3 ) undergo frequent deflections, veering to become either parallel or perpendicular to NNW-SSE and NNE-SSW major faults, which follow the numerical models of stress deflections (e.g. Katterhorn et al., 2000). A progressive variation of the shape of stress ellipsoids, from near-multidirectional to triaxial tension, frequently accompanies such deflection as approaching active faults (Arlegui et al., 2006). ...
The Teruel Basin is a NNE-SSW trending intracontinental extensional basin located in central-eastern Iberia. It is asymmetrically bounded to the east by a major fault zone, but intrabasinal faults with diverse orientation (NNE-SSW to NE-SW, E-W, or NW-SE) also appear. Offsets of the successive sedimentary units and of two planation surfaces reveal that tectonic activity initiated at the border faults, while intrabasinal ones mainly developed in a later stage. Fractures on a map scale show a prevailing N-S strike in Neogene synrift rocks, while a dense network made of four main fracture sets (NE-SW, E-W to ESE-WNW, N-S and NNW-SSE), likely inherited from Mesozoic rifting stages, is observed in pre-rift units. The results of palaeostress analyses indicate an overall predominance of σ3 directions around E-W, although two stress episodes have been distinguished during the Late Miocene-Pleistocene: (i) triaxial extension with σ3 E-W; (ii) almost ‘radial’ extension (σ1 vertical, σ2 ≈ σ3) with a somehow prevailing σ3 ENE-WSW. A scenario in which the evolving extensional stress field was able to gradually activate major basement structures with different orientation, inherited from previous tectonic events, is proposed as responsible for the evolution and overall pattern of both the eastern active margin and central parts of the central-northern sector of the Teruel Basin.
... Fig. 2 in Hardy, 2013), however, this is not always the case. For example, growth 681 folds are documented in the flanks of Kilauea, Hawaii (Kattenhorn et al., 2000;Parfitt and 682 Peacock, 2001;Peacock and Parfitt, 2002;Holland et al., 2006;Martel and Langley, 2006;683 Kaven and Martel, 2007;Podolsky and Roberts, 2008), the Modoc Plateau, USA (White and 684 Crider, 2006;Blakeslee and Kattenhorn, 2013;Crider, 2015;Kattenhorn et al., 2016), and the 685 Reykjanes Peninsula, Iceland (Bull et al., 2003;Grant and Kattenhorn, 2004;Bull et al., 2005;686 Trippanera et al., 2015) suggesting that cover rheology is not the principal control on growth 687 fold occurrence, although it may affect their geometry and size (Fig. 7D). Although it is possible 688 intra-basaltic heterogeneity e.g. ...
... In the flanks of Kilauea, Hawaii (e.g. Macdonald, 1957;Duffield, 1975;Kattenhorn et al., 2000;708 Parfitt and Peacock, 2001;Martel and Langley, 2006;Podolsky and 709 Roberts, 2008;Bubeck et al., 2018) and in the eastern Gulf of Corinth (e.g. Vita-Finzi and 710 King, 1985), fault-propagation folds are forming at the present-day despite very high regional 711 extension rates (Kilauea Volcano -9 -12 cm/yr from Owen et al., 1995;Gulf of Corinth -5 -712 15 mm/yr from Bell et al., 2011). ...
Growth folds above the upper tips of normal faults are ubiquitous in extensional settings, especially during the early phases of extension and in salt-rich basins. As slip accumulates on the underlying normal fault, the geometry and size of the fold changes. These changes reflect the dip, throw, displacement and propagation rate of the underlying normal fault, as well as the thickness and rheology of the overlying cover. These changes also have a marked impact on the architecture and distribution of synkinematic sediments, as well as the styles of secondary deformation accommodating strain within the growing fold. Here, we analyse a large dataset of natural, and physically- and numerically-modelled growth folds to: (i) characterise their diagnostic features; (ii) investigate the controls on their geometry, size and differences; and (iii) describe how they grow with increasing extensional strain. We demonstrate that larger fault throws and a thicker and weaker cover are associated with larger growth folds. In contrast, small fault throws as well as thin and strong brittle cover are associated with smaller growth folds. We show that the geometry and size of growth folds vary through time; the width (and thus, the wavelength) of the fold is established relatively early during fold growth, whereas fold amplitude increases gradually with increasing fault throw. Fold width and amplitude become increasingly similar during fold evolution, until the fold is breached by the underlying normal fault. We also derive a number of preliminary empirical relationships between readily observable structural and stratigraphic parameters in our dataset that may help estimate the geometry and size of poorly exposed (i.e. in the field) or imaged (i.e. in the subsurface) growth folds. In addition, we discuss how fault growth models (i.e. constant-length vs. propagating) may impact the three-dimensional evolution of growth folds. Finally, our work shows that growth folds are likely more common than previously thought. For example, although they are well-documented in areas characterised by weak, ductile cover strata and low strain rates, our dataset illustrates that growth folds may also occur in brittle, relatively strong rocks and in regions with high strain rates. However, the underlying controls on fold occurrence remain elusive.
... Unbreached RIZs show no apparent structural connection and no drainage connection, while partially breached RIZs may have a breaching fault that partially connects the rift basins, although drainage integration has not occurred yet. RIZs may also show a perturbed local strain field due to the influence of the adjacent, bounding rift faults (Crider and Pollard, 1998;Kattenhorn et al., 2000;Maerten, 2000;Kolawole et al., 2024). The development of these zones may be aided by basement fabrics that strike obliquely relative to the main extension direction (Fossen and Rotevatn, 2016); however, basement fabrics may also influence linkage across these zones (Morley et al., 2004;Heilman et al., 2019;Kolawole et al., 2021a). ...
Many rifts are influenced by pre-existing structures and heterogeneities during their evolution, a process known as structural inheritance. During rift evolution, these heterogeneities may aid rift nucleation, rift growth, and the segmentation of faults; encourage the linkage of various segments; or even inhibit the formation of faults. Understanding how structural inheritance influences early rift evolution could be vital for evaluating seismic risk in tectonically active areas. The Shanxi Rift in the north of China is an active rift system believed to have formed along the trend of the Proterozoic Trans-North China Orogen; however, the influence of these pre-existing structures on the present-day rift architecture is poorly understood. Here, we use tectonic geomorphological techniques, e.g. the hypsometric integral (HI), channel steepness (ksn), and local relief, to study the evolution of the Shanxi Rift and identify areas of higher tectonic activity. We found that the HI was less sensitive to lithology and more valuable in evaluating the tectonic signal and that activity is concentrated in two rift interaction zones (RIZs) formed between the Xinding, Taiyuan, and Linfen basins. We then evaluated the relationship between the active faults and mapped pre-existing structures, finding that many faults formed parallel to inherited structures, while faults in the RIZs often cross-cut these structures. Based on these observations, we propose a new model for the evolution of the Shanxi Rift, where inherited structures play an important role in the initial segmentation of the rift, which, in turn, controls the development of the RIZ structures.
... Within these networks, various interactions can occur as the faults establish both geometric and kinematic relationships with one another (Duffy et al., 2015;Fossen et al., 2005;Frankowicz and McClay, 2010;Nixon et al., 2014). These fault interactions result in areas with localized stress concentrations, which influence the geometry and kinematics of the faults (Bourne and Willemse, 2001;Kattenhorn et al., 2000;Maerten et al., 2002). deformation is challenging due to the complex interplay of fault planes with sub-vertical orientations and non-planar geometries. ...
... This suggests that formerly active faults act as a wider zone of preweakened material, where stresses deflect sequentially rather than with a rapid jump. Similar observations have been made in previous studies of numerical models (Gudmundsson et al., 2010;Kattenhorn et al., 2000). These experiments suggest that earlier fractures lead to subzones (within a broader damage zone), wherein stresses subsequently rotate away from the regional stress field. ...
Continental rifts evolve by linkage and interaction of adjacent individual segments. As rift segments propagate, they can cause notable re-orientation of the local stress field so that stress orientations deviate from the regional trend. In return, this stress re-orientation can feed back on progressive deformation and may ultimately deflect propagating rift segments in an unexpected way. Here, we employ numerical and analog experiments of continental rifting to investigate the interaction between stress re-orientation and segment linkage. Both model types employ crustal-scale two-layer setups wherein pre-existing linear heterogeneities are introduced by mechanical weak seeds. We test various seed configurations to investigate the effect of (i) two competing rift segments that propagate unilaterally, (ii) linkage of two opposingly propagating rift segments, and (iii) the combination of these configurations on stress re-orientation and rift linkage. Both the analog and numerical models show counterintuitive rift deflection of two sub-parallel propagating rift segments competing for linkage with an opposingly propagating segment. The deflection pattern can be explained by means of stress analysis in numerical experiments wherein stress re-orientation occurs locally and propagates across the model domain as rift segments propagate. Major stress re-orientations may occur locally, which means that faults and rift segment trends do not necessarily align perpendicularly to far-field extension directions. Our results show that strain localization and stress re-orientation are closely linked, mutually influence each other, and may be an important factor for rift deflection among competing rift segments as observed in nature.
... Models utilising the orientation and magnitude of strain to calculate stress fields perturbed by large-scale structures have been combined with rock failure criteria (e.g. Figure 3.3) to model natural fracture network characteristics (e.g. Bourne et al., 2000;Bourne and Willemse, 2001;Davatzes et al., 2005;Kattenhorn et al., 2000;Maerten et al., 2006;Maerten et al., 2002). In addition to the enhanced predictability of this approach, elastic dislocations are commonly used to represent stress perturbations in idealised geomechanical models due to their computational simplicity and ability to adequately characterise deformation observed in nature (Maerten et al., 2014). ...
... Zealand (e.g., Rowland & Simmons, 2012). Likewise, other studies have mentioned the importance of secondary structures as fluid flow conduits along active faults (e.g., Martel, 1990;Kattenhorn et al., 2000;Tamagawa & Pollard, 2008). ...
We investigated the relationship between the geothermal activity and fracture networks that control storage and fluid pathways of geothermal systems in the northern part of the Malawi Rifted Zone (MRZ). It is suggested that low to medium temperature geothermal systems in the MRZ are mainly non-magmatic and structurally controlled. However, structural controls and favorable settings of geothermal activity are poorly understood in this region. We used an approach of remote sensing and aeromagnetic data analysis to 1) identify and characterize fracture networks to better understand the structural controls of geothermal activity in the northern part of the rift, 2) quantify and identify permeable areas using topological analysis of fracture intensity and connectivity frequency proxies, 3) understand the role that inherited structures play in the geothermal systems of the northern part of the rift, and 4) build preliminary geothermal conceptual models of selected geothermal systems. Our findings show that fracture networks in the Karonga and Nkhata regions comprise a varying degree of complexity along strike. This structural complexity occurs mainly in favorable structural settings such as 1) two fault segments coalescing to form hard and soft-linked relays, 2) two different oriented fracture segments intersecting each other, and 3) on the tips of major normal faults. The hot springs are located where one or more of these favorable settings occur. The remote sensing analysis shows that Quaternary normal faults are the primary controlling structures of thermal waters at shallow depths in the Karonga (NW-SE to N-S strike) and Nkhata (N-S strike) regions. The aeromagnetic data revealed that permeable NW-striking foliation planes of the Precambrian Mugesse Shear Zone and WNW to ENE-striking foliation planes of the Mwembeshi Shear Zone are important structural controls of geothermal fluids at greater depths in the Karonga and Nkhata region, respectively. The Mwankeja-Mwesia and Chiweta geothermal systems in the Karonga region show favorable structural settings for geothermal fluids related to NNW and NW-striking normal faults segments that coalesce to form hard and soft-linked relay ramps and NW, and NNE -striking faults intersecting each other and NW-striking foliation planes. The Mtondolo geothermal area in the Nkhata region shows that the intersection of N-striking normal faults and ENE-striking foliation planes is the favorable structural setting that controls the emergence of hot springs through the surface. We conclude that high fracture intensity and connectivity are related to the location of the hot springs at the surface and can be used to determine permeable zones and hidden geothermal fluids together with other methodologies. The aeromagnetic data analysis suggested that buried faults and inherited structures (e.g., foliation planes) are controlling the geothermal fluids at depth. Additionally, our aeromagnetic analysis of magnetic basement depth estimation suggests that some of the geothermal reservoirs in the northern part of the MRZ could have an estimated depth of ~500 to ~1000 m.b.g.l. Finally, the low-cost methodology applied in this study can reduce the risk of drilling non-productive wells in the early exploration stages and become an exploration strategy for similar geothermal systems in countries of the Western Branch of the East African Rift System.
... The use of linear elasticity for modelling deformation and fractures is supported by numerous research studies over the past halfcentury. These studies have used linear elasticity to effectively explain observed geological structures such as fractures (Kattenhorn et al. 2000;Bourne & Willemse, 2001), veins (Soliva et al. 2010), dykes (Odé, 1957;Muller & Pollard, 1977;Baer & Reches, 1991), fault slip (Maerten, 2000), faultrelated deformation and even salt-related deformation (Luo et al. 2012). We therefore believe that such mechanical elastic behaviour is appropriate as a first approximation for modelling dyke propagation from magma chambers or stocks. ...
In volcano-tectonic regions, dyke propagation from shallow magmatic chambers is often controlled by the interaction of the local and regional stress fields. The variations of the stress fields result from a combination of factors including the regional tectonic stress, the geometry of pressurized magma chambers, the layering and the pre-existing discontinuities (e.g. fractures). In this contribution, we describe and apply a new multiparametric inversion technique based on geomechanics that can invert for both the far field stress attributes and the internal pressure of magma chambers or stocks, constrained by observed dyke or eruptive fissure orientations. This technique is based on the superposition principle and uses linear elastic models that can be solved using many types of numerical methods. For practical reasons, we chose a 3D boundary element method (BEM) for a heterogeneous elastic half-space, where magma chambers are modelled as pressurized cavities. To verify this approach, the BEM solution has been validated against the known 3D analytical solution of a pressurized cylindrical cavity. Then the effectiveness of this technique and its practical use is demonstrated through application to natural examples of dyke network development around two different volcanic systems, the Spanish Peaks (USA) and the Galapagos Islands (Ecuador). Results demonstrate that regional stress characteristics as well as the internal pressure of magma chambers can be estimated from observed radial and circumferential dyke patterns and some knowledge of magma chamber geometry.
... The reorientation of the main fault plane at this location may be characteristic of a tip-damage zone in which the deformation would be associated with an increase in stress, with a local reorientation of the stress field [Cowie and Scholtz, 1992, Peacock et al., 2017, Kattenhorn et al., 2000, Nixon et al., 2020]. ...
Increasing displacement along an isolated fault is generally associated with fault propagation within the host rock. This propagation is controlled by several factors, including host-rock lithology, tectonic context and the presence of preexisting structures. Consequently, fault propagation is rarely linear and continuous, instead often alternating between periods of propagation and arrest, or propagation locking. We present structural data collected in a field at the terminal tip of the Argence Fault, one of the regional normal faults in the northern part of the Aquitaine Basin. At the outcrop, the fault cuts a heterogeneously layered sequence of limestones, marls and clays. We observed a well-exposed tip of this fault, and analyzed the deformation patterns. This analysis provided insights into the processes involved in the formation of fault zones, the fault damage zone in particular, and the effects of contrasting mechanical properties on modes of fault growth.
... Although at far distance from our study area and not clearly kinematically consistent, such process involving mantle flux perturbations may have implied stress changes at far distances in the Pyrenean lithosphere. Another potential source of stress perturbation could be the mechanical interaction and linkage (e.g., Crider & Pollard, 1998;Kattenhorn et al., 2000) between the Cevennes and the Catalan lithospheric normal faults, through a very large-scale relay zone located in the Eastern Pyrenees. Such large-scale mechanical interaction could have favored stress changes and strain distribution along multiple faults in this eastern part of the Pyrenees. ...
The timing of transition between the contractional and extensional regimes along the Pyrenean range remains debated. Compared to its central and western parts, the eastern part of the chain was significantly affected by extensional tectonics mostly related to the opening of the Gulf of Lion. The Têt normal fault is the best example of this tectonic activity, with topographic reliefs above 2,000 m in its footwall. In this study, we synthetized previous thermochronological data and performed new (U‐Th)/He and fission track dating in the Eastern Pyrenean massifs. Output apparent exhumation rate and thermal modeling in the hanging wall of the Têt fault highlight a rapid exhumation (0.48 km/Ma) and cooling (∼30°C/Ma) phase between 38 and 35 Ma, followed by slower exhumation/cooling afterward. In the footwall, cooling subsequently propagated westward along the fault during Priabonian (35–32 Ma), upper Oligocene and lower Miocene (26–19 Ma), and Serravallian‐Tortonian times (12–9 Ma). These data and modeling outcomes suggest that the exhumation of the Têt fault hanging wall related to southward thrusting ended at 35 Ma, and was followed by different extensional stages, with a propagation of the deformation toward the West during the upper Miocene. We propose that the onset of extension in the Eastern Pyrenees occurred during the late Priabonian period, contemporaneously with the large‐scale rifting episode recorded in Western Europe. After this event, the Têt fault activity and the westward propagation of the deformation appear mainly controlled by the opening of the Gulf of Lion.
... Activity of the Dombjerg and Thomsen Land faults in the post-rift stage has not been reported. However, the presence of the transfer zone should still cause local stress perturbations and may therefore influence deformation in response to any regional tectonic activity (e.g., Kattenhorn et al., 2000). Nevertheless, as the vein density increases towards the Dombjerg Fault , activity of the fault also in the post-rift stage does seem plausible, albeit this cannot be independently confirmed by our data. ...
Faults commonly form loci for high fluid flux in sedimentary basins, where fluids, rocks and deformation processes frequently interact. Here, we elucidate the interaction of fluid flow, diagenesis and deformation near basin-bounding faults in sedimentary basins through a study in the vicinity (0–3.5 km) of the Dombjerg Fault in the NE Greenland rift system. Due to fault-controlled fluid circulation, fault-proximal syn-rift clastics underwent pervasive calcite cementation, whereas uncemented clastics at some distance from the fault remained highly porous and friable. Correspondingly, two distinct deformation regimes developed to accommodate continued deformation: discrete brittle fractures formed in calcite cemented rocks, whereas cataclastic deformation bands formed in uncemented deposits.
We show that low-permeable deformation bands forming in highly porous rocks were associated with localized host rock alteration, and chemical reduction of porosity along bands. In rocks with cementation-induced low porosity, brittle fractures created new pathways for fluids, but were subsequently filled with calcite. Occasionally, veins comprise multiple generations of microcrystalline calcite, likely precipitated from rapidly super-saturated fluids injected into the fractures. This suggests cemented deposits sealed uncemented compartments, where fluid overpressure developed. We conclude that compartmentalized flow regimes may form in fault-bounded basins, which has wide implications for assessments of potential carbon storage, hydrocarbon, groundwater, and geothermal sites.
... Furthermore, the radial extensive tectonic regime inferred from the reactivated faults indicates that the lower stress axis (σ3) may have suffered deflections, becoming parallel or perpendicular to the reactivated plane, which agrees with numerical stress field models (e.g., Simon et al., 1988;Kattenhorn et al., 2000). The deflection of the lower stress axis (σ3) due to reactivated structures was also observed in recent earthquakes in NE Brazil, where shear zones were reactivated as normal faults in a strike-slip regime (Ferreira et al., 2008). ...
Margens Continentais Passivas Elevadas (MCPEs) são caracterizadas por apresentarem extensas elevações topográficas, como serras escarpadas, localizadas na transição entre platôs interiores elevados e planícies costeiras estreitas. Entretanto, a localização da escarpa, bem como sua morfologia, pode variar consideravelmente e, em alguns casos, ao longo de uma mesma MCPE. Esta situação é observada na margem Sudeste do Brasil, onde a porção sul exibe as escarpas íngremes das serras do Mar e da Mantiqueira, marcando divisores de drenagem regionais próximos a costa, e a região norte, caracterizada pela ausência do escarpamento proeminente, com divisores regionais posicionados a mais de 100 km no interior continental. Em particular, na região norte da Serra da Mantiqueira, a intepretação de eventos neotectônicos a partir do estudo de sedimentos neogênicos restritos à margem costeira contrasta com a quiescência tectônica pós-miocênica indicada por idades de denudação e soerguimento em porções no interior continental. Neste estudo, exploramos os padrões de topografia e estruturas tectônicas para investigar a evolução geológica pós-rifte e a influência das estruturas rúpteis na evolução topográfica na terminação norte da Serra da Mantiqueira. Para tanto, realizamos análises geomórficas quantitativas para a extração de métricas da topografia, um extensivo levantamento de campo para levantamento de estruturas geológicas rúpteis e análises mineralógicas de materiais de preenchimento em estruturas rúpteis. Os resultados indicam um grande número de estruturas rúpteis orientadas a NE-SW e NW-SE formadas pela concentração de tensões locais desenvolvidas nas descontinuidades do embasamento pré-cambriano. Falhas rúpteis, cujas estrias são marcadas nos materiais de preenchimento, originaram-se após a precipitação mineral (no caso dos óxidos de manganês) ou durante (no caso da illita), com idade máxima de deformação no Mioceno. Três eventos tectônicos pós-rifte foram determinados: uma transcorrência sinistral E-W e uma distensão WNW-ESE, ambos atuantes entre o Mioceno e o Plioceno; e um evento distensivo NE-SW a NNE-SSW, posicionado no Pleistoceno. Os padrões de topografia, de drenagem e a deformação rúptil indicam a presença de uma knickzona de direção NE-SW ancorada em limites estruturais reativados, associada a um rejuvenescimento topográfico mais recente do que a época Mioceno. Contudo, a morfologia da paisagem em grande escala e, em particular, a origem dos divisores de drenagem regionais deve ser anterior à deformação rúptil e ao rejuvenescimento pós-miocênico, implicando que elementos topográficos mais antigos e mais recentes coexistem na paisagem. A terminação norte da Serra da Mantiqueira, uma MCPE não caracterizada por uma escarpa proeminente, sofreu rejuvenescimento topográfico e deformação rúptil relativamente recentes, e estes processos não estão necessariamente ligados à formação ou persistência de uma "Grande Escarpa".
... The basement shear zones' geometry influences reactivated fault planes as observed in the moment tensor triangle plots, suggesting local stress variation. Furthermore, the radial extensive tectonic regime inferred from the reactivated faults indicates that the lower stress axis (σ3) may have suffered deflections, becoming parallel or perpendicular to the reactivated plane, which agrees with numerical stress field models (e.g., Simon et al., 1988;Kattenhorn et al., 2000). The deflection of the lower stress axis (σ3) due to reactivated structures was also observed in recent earthquakes in NE Brazil, where shear zones were reactivated as normal faults in a strikeslip regime (e.g., Ferreira et al., 2008). ...
A sharp escarpment lying close to the coast or more in the continental interior defines the morphology of Elevated Passive Continental Margins (EPCMs). Most studies on the dynamics and evolution of EPCMs, including numerical modeling exercises, concentrate on the geometry and evolution of escarpments located at or near a continental drainage divide. However, topographic relief varies considerably along the length of an EPCM, as one can observe in southeastern Brazil and southeastern Australia, and in some cases, the steep, wall-like escarpment may not be present. Here we investigate the post-rift geomorphic evolution in an EPCM lacking a sharp escarpment (southeastern Brazil), focusing on exploring topographic rejuvenation and links with potential controls such as the arrangement of pre-existing structures and lithological variability. We present topographic data showing a regional zone of high channel steepness and local relief extending continuously through the middle part of all seaward-dipping catchments. In this regional “belt” of high topography lies many knickpoints, and all rivers crossing it are marked by non-linear shapes in elevation-χ space. The structural data show a large number of NE-SW and NW-SE oriented brittle structures with slickensides recorded on filling materials following the orientation of pre-existing basement structures, suggesting a multiphase brittle deformation with at least two main paleostress tectonic regimes between the Miocene and Pleistocene. Our results indicate post-Miocene topographic rejuvenation and brittle deformation, probably driven by the accumulation of far-field stresses in pre-existing weakness zones. Nevertheless, the origin of the regional drainage divide and adjacent areas, located considerably upstream of the regional knickzone, must predate the topographic resurgence we infer, implying that older and more recent topographic elements coexist in the landscape. Our study demonstrates that post-rift topographic rejuvenation (and brittle deformation) in an EPCM is not necessarily linked to the formation or persistence of a “Great Escarpment”.
... Sample area 2784 is farthest from the lineament and has the lowest fracture density (3.73). Contrary to what was expected if the study area is associated with a damage zone, there is no maximum direction parallel to the lineament (N45E), although it is possible for joints to form at high angles to the strike of a fault (Kattenhorn et al., 2000). Fracture density in basalts varies depending on the internal lava flow structure. ...
The variation in the structural characteristics (cooling joints and tectonic fractures) of basaltic flows implies potential variability in the intensity of erosion by plucking. The erosive behavior of the rivers that sculpt these areas depends on their interaction with the diverse fracture systems. In view of this, we analyzed the effect of fracture variability in basalts on erosion in a bedrock river reach located in the Continental Volcanic Province of the Paraná Basin, southern Brazil. The 120-m-long reach is influenced somewhat by a possible fault that crosses it near one end. The fracture density and fracture direction were evaluated through field photogrammetry in seven sample areas distributed along the reach. The fracture direction and main erosion axes were also surveyed by remote piloted aircraft (RPA) aerial imaging. Tectonic fractures were identified in the field; they do not always appear in the survey of the sample areas but are evident in the RPA survey. The main erosion axes coincide with the principal fracture directions (tectonic fractures), which are disposed obliquely to the channel flow direction, making an average angle of 50°. The more abundant and multidirectional cooling joints act to control the plucking process and not to determine the erosion direction. The fracture density decreases with increasing distance from the fault crossing zone (from 9.62 to 3.73 m/m²), although the lower value is influenced by the presence of an amygdaloidal basalt zone. The higher fracture density favors more intense plucking.
... Sample area 2784 is farthest from the lineament and has the lowest fracture density (3.73). Contrary to what was expected if the study area is associated with a damage zone, there is no maximum direction parallel to the lineament (N45E), although it is possible for joints to form at high angles to the strike of a fault (Kattenhorn et al., 2000). Fracture density in basalts varies depending on the internal lava flow structure. ...
The variation in the structural characteristics (cooling joints and tectonic fractures) of basaltic flows implies potential variability in the intensity of erosion by plucking. The erosive behavior of the rivers that sculpt these areas depends on their interaction with the diverse fracture systems. In view of this, we analyzed the effect of fracture variability (tipology, density and direction) in basalts on erosion in a bedrock river reach located in the Continental Volcanic Province of the Paraná Basin, southern Brazil. The fracture density and fracture direction were evaluated through field photogrammetry in seven sample areas distributed along a reach of 120 m. The fracture direction and main erosion axes were also surveyed by remote piloted aircraft (RPA) aerial imaging. The main erosion axes coincide with the principal fracture directions (tectonic fractures), which are disposed obliquely to the channel flow direction, making an average angle of 50°. The small, more abundant, and multidirectional cooling joints control the plucking process, but do not determine the erosion direction. The fracture density systematically decreases upstream from 9.62 to 3.73 m/m², probably related to distance from a structural lineament which river crosses downstream. The higher fracture density favors more intense plucking due to decrease in the size of the rock blocks. The lower fracture density limits the plucking and favors the macroabrasion, mainly if associated with vesicular-amygdaloidal basalt.
... Both opening mode I and shear mode II and III fractures in normal and thrust fault system generally strike parallel to the main or secondary faults (e.g., Savage and Brodsky (2011) and Mayolle et al. (2019)). However, some of the mode I fractures can be observed normal to fault strike in the specific conditions where the horizontal maximum stress is very close to the horizontal minimum stress (Kattenhorn et al., 2000). For strike-slip faulting, both opening mode and shear mode fracture orientation can be different than the main fault strike (e.g., Riedle structures in the in-plane dimension, Fossen (2016)) and stress perturbations can occur quite far from the main strike-slip fault (e.g., King et al. (1994) and Chéry et al. (2001)). ...
Studying hydrothermal systems in basement environments requires knowledge of fault and fracture network distributions. This study addresses this through multi-scale structural analysis of the Têt fault and its surrounding fracture systems (Eastern Pyrénées) using remote sensing and field data. This study aims to achieve this through: 1) precisely mapping and describing the brittle fault network, 2) analysing the distribution of lineaments and outcrop-scale fractures related to these faults, 3) making comparisons to fault-kinematic evidence combined in a new regional review, 4) examining the relations between fractures features and lithology, 5) applying statistical analysis to highlight relations between different scales of deformation. The complex fault network is inherited from consecutive tectonic stages (Hercynian, Pyrenean compression, Neogene extension) and has been reactivated since the middle-Miocene. NE–SW secondary faults are abundant at the regional scale, even away from the Têt fault. Major NW–SE faults are constituted by 10s-m wide brittle core zones, and NW–SE secondary faults are concentrated around the Têt fault, attesting that they had formed at shallow crust levels after the Oligo-Miocene extension. N–S fractures, formed during Pyrenean compression, are part of the background fracturing and are scattered throughout the study area. Intersections of fault and fracture networks provide efficient permeable pathways for meteoric and hydrothermal fluids. Finally, a dislocation model reveals a lithological control on fracture apertures in crystalline rocks, which appears more preserved at depth than in metasediments. All of these elements are integrated in a global model of the hydrothermal system establishment in accordance with the faulting sequence, with the damage distribution and with the lithology. This distributed fault system could represent the surface expression of the crustal thinning revealed by recent geophysical data. The realized identification of the lithological and structural characteristics of the surrounding mountains, allowing hydrothermal circulation to establish itself, provides a better understanding of the orogenic-belt related hydrothermal systems necessary to the geothermal exploration.
... B. J. Andrews et al.: Growth of faults and fracture networks at Spireslack SCM Pre-existing weaknesses (e.g., joints and faults) also play an important role in the nucleation, orientation, and length of later faults (Crider and Peacock, 2004;Peacock, 2001;Walsh et al., 2002). The mechanical response of a pre-existing joint to faulting will depend on its orientation relative to far field stress , the ratio of principal stresses (Lunn et al., 2008;Healy et al., 2006;Moir, 2010;Chang and Haimson, 2000;Haimson and Chang, 2000), and local variations in the stress field due to the interaction of joints in the preexisting network (Crider and Peacock, 2004;Kattenhorn et al., 2000;Moir et al., 2010;Peacock, 2001). Where joints or cleats are orientated perpendicular to the growth direction of faults, they can act as a strength contrast and restrict fault growth (Wilkins and Gross, 2002). ...
Fault architecture and fracture network evolution (and resulting bulk hydraulic properties) are highly dependent on the mechanical properties of the rocks at the time the structures developed. This paper investigates the role of mechanical layering and pre-existing structures on the evolution of strike–slip faults and fracture networks. Detailed mapping of exceptionally well exposed fluvial–deltaic lithologies at Spireslack Surface Coal Mine, Scotland, reveals two phases of faulting with an initial sinistral and later dextral sense of shear with ongoing pre-faulting, syn-faulting, and post-faulting joint sets. We find fault zone internal structure depends on whether the fault is self-juxtaposing or cuts multiple lithologies, the presence of shale layers that promote bed-rotation and fault-core lens formation, and the orientation of joints and coal cleats at the time of faulting. During ongoing deformation, cementation of fractures is concentrated where the fracture network is most connected. This leads to the counter-intuitive result that the highest-fracture-density part of the network often has the lowest open fracture connectivity. To evaluate the final bulk hydraulic properties of a deformed rock mass, it is crucial to appreciate the relative timing of deformation events, concurrent or subsequent cementation, and the interlinked effects on overall network connectivity.
... -45 - Willemse et al. 1996). π π α υ α π α α α απ α α π α α (Segall and Pollard 1983, Dawers and Anders 1995, Crider and Polard 1998, Kattenhorn et al. 2000, Maerten et al. 2002. υ υ α απ α π υ α α α α υ υ (Trudgill andCartwright 1994, Dawers andAnders 1995). ...
... The formation of wing cracks is an interesting phenomenon that has been found in a wide range of earth and planetary science phenomena. For example, secondary cracks have been observed on opposite ends of a fault, as a result of the faulting process [81][82][83][84][85][86], associated with splitting, exfoliation, and rock burst [12], and have also been observed at the tip of strike-slip faults in the ice shell of Europa, Jupiter's moon [87]. While these initial static measurements allowed interesting observations, they did not allow to capture the evolution of dynamic ruptures. ...
The last few decades have seen great achievements in dynamic fracture mechanics. Yet, it was not possible to experimentally quantify the full-field behavior of dynamic fractures, until very recently. Here, we review our recent work on the full-field quantification of the temporal evolution of dynamic shear ruptures. Our newly developed approach based on digital image correlation combined with ultrahigh-speed photography has revolutionized the capabilities of measuring highly transient phenomena and enabled addressing key questions of rupture dynamics. Recent milestones include the visualization of the complete displacement, particle velocity, strain, stress and strain rate fields near growing ruptures, capturing the evolution of dynamic friction during individual rupture growth, and the detailed study of rupture speed limits. For example, dynamic friction has been the biggest unknown controlling how frictional ruptures develop but it has been impossible, until now, to measure dynamic friction during spontaneous rupture propagation and to understand its dependence on other quantities. Our recent measurements allow, by simultaneously tracking tractions and sliding speeds on the rupturing interface, to disentangle its complex dependence on the slip, slip velocity, and on their history. In another application, we have uncovered new phenomena that could not be detected with previous methods, such as the formation of pressure shock fronts associated with “supersonic” propagation of shear ruptures in viscoelastic materials where the wave speeds are shown to depend strongly on the strain rate.
... Fig. 3) to model natural fracture network characteristics (e.g. Bourne et al., 2000;Bourne and Willemse, 2001;Davatzes et al., 2005;Kattenhorn et al., 2000;Maerten et al., 2006;Maerten et al., 2002). In addition to the enhanced predictability of this approach, elastic dislocations are commonly used to represent stress perturbations in idealised geomechanical models due to their computational simplicity and ability to adequately characterise deformation observed in nature (Maerten et al., 2014). ...
Effective storage and containment of injected fluids, over a range of spatial and temporal scales, is reliant upon the sealing capacity of the lithologies overlying geological stores. Low-permeability mudrocks are considered effective candidates to restrict the migration of injected fluids from the host formation, owing to their low matrix permeabilities (< 10−19 m2). Fluid-conductive fault and fracture systems can threaten seal integrity by creating high permeability pathways (> 10−19 m2), potentially compromising subsurface storage operations. To safeguard and expedite the initialisation of storage projects on an impactful scale, rigorous comprehension of the intrinsic flow properties of fractures in mudrocks is key. The distribution of fractures within fracture networks, and the degree to which these configurations promote interconnectivity, is a primary factor influencing fluid transport. At the individual fracture scale, a fractures ability to transmit fluid is a function of the aperture distribution, which is itself governed by a series of hierarchical controls operating across various scales. Accurate understanding, characterisation and quantification of the physical transport mechanisms and fluid flow dynamics prevalent in rock fractures is frustrated by the existence of heterogeneous aperture distribution, caused by fracture surface roughness. Further hindrances to understanding the fundamental transport properties of fractures stem from our limited knowledge of the breadth and complexity of hydromechanical responses that emerge from the coupling of pore pressure, effective stress and multiphase flow. In this review paper, we have collated and analysed the large body of experimental and theoretical literature pertaining to single- and two-phase fluid transport, and the geomechanical properties of single fractures and fracture networks in relation to fluid conductivity. We focus upon naturally occurring fractures in mudrocks and the current understanding of the physical and transport properties which impact the risks to secure containment in geological reservoirs.
... However, relay-damage zones involve the interacting stress fields of two fault tips, which inhibits tip propagation and increases displacement gradients as well as causes local rotations in the stress field between the two faults (c.f. Willemse et al., 1996;Crider and Pollard, 1998;Gupta and Scholz, 2000;Kattenhorn et al., 2000). Thus, the resultant damage zones will exhibit greater fracture intensities and varied fracture orientations in comparison to isolated fault tip-damage zones (e.g. ...
Using outcrop-based examples, we investigate the topological and graph characteristics of various fault damage zones in carbonate rocks on Malta. The damage zone fracture networks are analysed as a series of nodes (isolated I-nodes; connected Y/X-nodes) and branches (II-, IC-, CC-branches), which may link to form connected components and fracture-bounded regions. We compare the metrics of the different nodes, branches, regions and components that make-up each damage zone fracture network, calculating parameters that assess their connectivity. Results identify distinct topological signatures and graph metrics for different tip-, relay- and splay-damage zones, providing a new classification that describes and quantifies their arrangement and connectivity. Placing the studied damage zones in a fault evolutionary model highlights topological pathways whereby tip-damage zones, dominated by I-nodes and II-branches, give way to relay-damage zones, dominated by Y-nodes and CC-branches. During this process, tree-like components link to form larger interconnected components with many regions. This systematically changes the graph metrics of the network increasing the number of branches and regions relative to nodes and components. The topological pathways and graph metrics provide important insights into how damages zones might develop as faults propagate, interact and link and could have implications when assessing their importance for fluid-flow.
... Swanson, 1989Swanson, , 2005. Cementation of wide, deeply penetrating, sub-vertical, fault-perpendicular cross-fractures like those described at fault step-overs by Kattenhorn et al. (2000) and asymptotic, curving-upward, dilatant pinnate fractures bound by subparallel slip surface described in other fault systems by Bruhn et al. (1994) and Micklethwaite (2009) help to isolate and encapsulated lozenges of variably weakened footwall material ( Fig. 12a and b). Cementation of or around fault asperities may have contributed to instability of the principal slip surface (Fig. 12c). ...
Abstarct
Faults vary in structural style, from simple planes to complex systems composed of fault cores and damage zones. Increased fault complexity results from the interaction of mechanical and chemical processes, including fracture growth, shear, and linkage, and mineral dissolution and precipitation. Although water-rock interaction is traditionally associated with fault rock weakening and shear localization, we investigate processes of fault core widening by water-rock interactions that resulted in quartz precipitation. We combine field and petrographic observations with prior mechanical characterization to assess the impact of alteration and cementation on fault architecture at the Dixie Comstock epithermal gold deposit, Nevada, USA. Mineralized portions of the fault contain strong, thick, silicified fault cores and wide, weak damage zones, with evidence for widening of the core through entrainment of damage zone material and repeated cycles of embrittlement, dilation, and cementation. We present a model of fault zone evolution in which the hydrothermal regimes favoring either alteration-weakening or precipitation-strengthening result in distinct fault zone architecture and mechanical and flow properties of fault systems. Alteration-weakening favors localization of the fault into thinner, clay-rich, low permeability fault cores. Precipitation-strengthening promotes thick, strong, and low permeability fault cores, with mineralization-embrittlement enhancing transient permeability following coseismic failure.
... Some areas with local stress concentration and perturbation are produced by the fault interaction, which affects the geometry and kinematics of faults (e.g., Kattenhorn et al., 2000;Bourne and Willemse, 2001;Maerten et al., 2002;Rashidi et al., 2017Rashidi et al., , 2018. These stress concentrations can form the secondary structures in damage zones, where they typically have different orientations in comparison to the surrounding areas (e.g., Kim et al., 2004;Fossen et al., 2005;Bastesen and Rotevatn, 2012;Choi et al., 2016). ...
We used satellite images, earthquake catalogues and field observations to study several active fault systems and their interactions in Sabzevaran Area in SE Iran. The focus of this study is to verify the link between the active faults, their kinematics and seismic activity. Field observations and geomorphological analysis highlight the interaction of the active faults. Moreover, most of the tectonic activity is observed in the area, related to the Chahmazrae-North Faryab shear zone. Most of the earthquakes in this shear zone are reverse and occur in the deeper crust while aftershocks dominantly occur in the shallower crust. The Main Zagros Reverse Fault (MZRF) is the source of reverse events and the Chahmazrae- North Faryab shear zone is source of left- lateral, oblique reverse faulting events, and strike- slip events. These types of the earthquakes in the study area confirm the idea of tectonic proximity of the root faults and shear zone. In the interaction area, minor fractures begin to develop and are progressively linked to the main faults. In the en échelon arrangement of the faults, the minor faults have grown and linked the en échelon segments of the faults. It seems that the earthquake ruptures can spontaneously propagate across both extensional and compressional fault steps. This propagation occurs along strike- slip faults such as Sabzevaran fault and its branches.
... One suggestion for the subtle angle of joints relative to the faults is that joints could develop in response to perturbed local stresses within the overlap zone of faults. In fact, the movement of the faults in the overlap zones results in the perturbation of local stress fields and gives rise to the development of various joints at higher angle to the strike of normal faults (Kattenhorn et al., 2000). ...
... One suggestion for the subtle angle of joints relative to the faults is that joints could develop in response to perturbed local stresses within the overlap zone of faults. In fact, the movement of the faults in the overlap zones results in the perturbation of local stress fields and gives rise to the development of various joints at higher angle to the strike of normal faults (Kattenhorn et al., 2000). ...
... The strike of the fault strands fluctuates between NE-SW and E-W (Fig. 11). This trend variation could be caused by faults with a minor left-lateral component and by the interaction with NNW-striking faults, which perturbs the local stress field (e.g., Kattenhorn et al., 2000;Mennella et al., 2000). Based on these strike fluctuations, the Tarímbaro graben can be divided into three graben segments (Fig. 11). ...
Twelve monogenetic volcanoes formed during the last 7 Ma within the Tarímbaro graben, northwest of the city of Morelia, in the central-eastern part of the Michoacán-Guanajuato volcanic field (México). These include four scoria cones (Pelón, Tetillas, Jamanal, and Parastaco), four lava domes (La Cruz, Divisadero, Estadio, and Tetillas), two small shield volcanoes (Quinceo and Tetillas) and two lava flows (Cuto and Cerritos). Based on a detailed geological map and stratigraphy aided by new 40Ar/39Ar and 14C radiometric dates, and whole-rock chemical analyses, we established the eruptive chronology of these monogenetic volcanoes. These volcanoes were built upon four early Miocene successions of regional volcanism named Cuitzeo lavas (18.7 Ma), Cuitzeo ignimbrite (17.4 Ma), Atécuaro ignimbrite (16.8 Ma), and Punhuato lavas (16.3 Ma). Late Miocene to Pliocene activity consisted of the La Cruz, Divisadero, and Estadio domes and the Cuto lava flow (6.7–3.1 Ma). Pleistocene activity included the Cuitzeo fallout pyroclastic sequence (1.48 Ma), the Quinceo small shield volcano (1.36 Ma), the Pelón scoria cone (0.84 Ma), the Tetillas small shield volcano, two lava domes and a scoria cone (0.56–0.34 Ma), the Jamanal and Parastaco scoria cones and the Cerritos lava flow (0.11 Ma). Magma volumes from these volcanoes vary from <0.1 to 4 km3. We ascribe their variety of magma volumes, morphology, volcanic styles, and spatio-temporal distribution to tectonic changes and evolution of the ENE Tarímbaro graben, whose faults belong to the Tarímbaro-Álvaro Obregón fault segment in the central part of the Morelia-Acambay Fault System. Quinceo (2 km3) and Tetillas (4 km3) small shield volcanoes are by far the most voluminous centers dominating the landscape of the city of Morelia. All rock samples have compositions varying from 49.3 to 61.6 wt % in silica with medium-K contents (0.43–1.83 wt %).
... The formation of wing cracks is an interesting phenomenon that has been found in a wide range of earth and planetary science phenomena. For example, secondary cracks have been observed on opposite ends of a fault, as a result of the faulting process [81][82][83][84][85][86], associated with splitting, exfoliation, and rock burst [12], and have also been observed at the tip of strike-slip faults in the ice shell of Europa, Jupiter's moon [87]. While these initial static measurements allowed interesting observations, they did not allow to capture the evolution of dynamic ruptures. ...
The last few decades have seen great achievements in dynamic fracture mechanics. Yet, it was not possible to experimentally quantify the full-field behavior of dynamic fractures, until very recently. Here, we review our recent work on the full-field quantification of the temporal evolution of dynamic shear ruptures. Our newly developed approach based on digital image correlation combined with ultrahigh-speed photography has revolutionized the capabilities of measuring highly transient phenomena and enabled addressing key questions of rupture dynamics. Recent milestones include the visualization of the complete displacement, particle velocity, strain, stress and strain rate fields near growing ruptures, capturing the evolution of dynamic friction during individual rupture growth, and the detailed study of rupture speed limits. For example, dynamic friction has been the biggest unknown controlling how frictional ruptures develop but it has been impossible, until now, to measure dynamic friction during spontaneous rupture propagation and to understand its dependence on other quantities. Our recent measurements allow, by simultaneously tracking tractions and sliding speeds on the rupturing interface, to disentangle its complex dependence on the slip, slip velocity, and on their history. In another application, we have uncovered new phenomena that could not be detected with previous methods, such as the formation of pressure shock fronts associated with "supersonic" propagation of shear ruptures in viscoelastic materials where the wave speeds are shown to depend strongly on the strain rate.
... 3d and 5a; Morley and Wonganan (2000); Mansfield and Cartwright (2001) spatial stress heterogeneity should also be taken into account. Numerical models (e.g., Sim� on et al., 1988;Kattenhorn et al., 2000) show that, where previous oblique faults do exist, trajectories of the minimum stress axis (σ 3 ) undergo sharp deflection, veering to become either parallel to the fault (close to the tips) or perpendicular to it (close to the centre). Swapping of σ 2 and σ 3 axes is also a common phenomenon, which result in e.g. ...
A new type of fault relay zone in extensional contexts, dominated by distributed along-strike or longitudinal fractures, is defined. It contrasts with the classical models reported in the literature, in which transverse connecting faults controlled by the own relay kinematics prevail. The new model is based on structural features of the Teruel graben system, as well as on analogue modelling. Relay zones between the NW-SE to NNW-SSE striking faults that delimit the eastern boundary of the Jiloca Graben (Calamocha, Sierra Palomera and Concud
faults), together with the Teruel Fault, have been studied. All of these relay faults show recent (Neogene-Quaternary) ruptures at different scales, mostly parallel to the macrostructural trend and to the maximum horizontal stress (SHmax) trajectories (i.e., orthogonal to the ENE-WSW regional extension direction that characterises
the nearly biaxial or radial stress regime active during Upper Pliocene-Quaternary times). Transverse ruptures are almost absent, with the exception of the northern relay zone (Calamocha-Sierra Palomera), where an incipient NE-SW striking connecting fault does exist. Analogue models have been run under a biaxial extension regime similar to the regional one. They allowed analysing the main factors controlling fracture propagation, depending on the ratio of extension velocities and the orientation of the master faults relative to extension directions. Laboratory fracture patterns, as in the natural studied examples, are mostly controlled by the inherited anisotropies and, in a greater extent, by the imposed extension trajectories, which results in a clear prevalence of longitudinal fractures. Such external controls, usually disregarded in numerical and analogue modelling, tend to induce fault coalescence through along-strike (parallel or at very-low-angle) propagation resulting in a final braided fault pattern.
... This second extensional episode matches with the oblique extension during the Paleocene-Eocene during the Scottish Highlands uplift as suggested by Roberts et al. (1990). The orientation of the dilatant structures from N140°to N190°could mark a gradual east-west reorientation of this latter extensional episode or potential stress perturbation because of fault interactions (e.g., Kattenhorn et al., 2000). Both the close orientation and the formation time of dilation bands and joints suggest a genetic similarity of these structures. ...
... Pollard and Segall, 1987;Petit and Mattauer, 1995;Homberg et al., 1997), in overstep areas (e.g. Kattenhorn et al., 2000;Agosta et al., 2009), in bends along the fault trace (e.g. Maerten et al., 2002), and within relay zones (e.g. ...
Rugged peaks, large intermontane basins and frequent seismicity all characterize the active extensional tectonic setting of the southern Apennines. The Matese ridge typifies the active tectonic setting of the southern Apennines with steep carbonate mountain fronts and large depositional centres. Moderate to high magnitude earthquakes have affected the northern, western and eastern sectors of the Matese ridge in historical times. However, the seismogenic potential of the extensional fault system bounding the southern Matese mountain front has not been fully assessed to date. To unravel the active tectonic setting of the southern Matese mountain front, we have carried out a comprehensive geomorphological and tectonic-geomorphology investigation of the mountain front and its piedmont and have constrained results through chronological (i.e., tephrostratigraphical and 40Ar/39Ar) and structural data.
Our study highlights that in the last ~600 ka, activity along E-Wtrending normal faults has identified a locus of higher slip rate tectonic activity in the central part of the analysed mountain front. These active E-W-striking normal faults are inherited, reactivated structures, which have interacted with newly formed NW-SE-striking normal faults during NE-SWextension active on the regional scale, causing fault bending and local extension to be oriented N-S. Consequently, lower slip rates have been recorded along the NW-SE-striking normal faults at the north-western and south-eastern tips of the southern Matese
front. The long-term displacement rate of the fault system at the boundary of the central part of the southern Matese front is consistent with mean values of displacement of faults that, in the southern Apennines, show evidence of activity during the late Quaternary. Despite strong historical seismicity clustering primarily around the study area, our data highlight that it cannot be ruled out that moderate to high magnitude seismicity could affect the southern Matese mountain front.
Our case study represents an example of the possible modes of formation and evolution of mountain front-basin systems in extensional setting, and shows how the combination of different data sets allows unravelling the interaction between tectonic, erosional and sedimentary processes, which lead to landscape evolution of active mountain belts.
... Such structural setting is consistent with the recent, Pliocene-Quaternary stress regime at the eastern Iberian Chain: biaxial or 'multidirectional' extension (σ 1 vertical, σ 2 ≈ σ 3 ) (Simón 1989;Arlegui et al. 2005). According to the notion of strain/stress partitioning (Simón et al. 2008), biaxial extensional deformation could be accommodated by slip on faults of diverse orientations, through a non-linear sequence of rupture episodes linked to systematic, not chaotic stress changes (stress deviation, stress switching; Simón et al. 1988;Caputo 1995Caputo , 2005Kattenhorn et al. 2000;Bai et al. 2002). Since each slip event can be considered as geologically 'instantaneous', paleoseismology provides a useful tool for analysing incremental deformation within a narrow time window. ...
The E–W trending, nearly pure extensional Valdecebro fault zone is a transverse structure at the central sector of the N–S Teruel graben. It was activated by the Late Ruscinian (Early Pliocene, ca. 3.7 Ma), giving rise to structural rearrangement of the graben margin. Until the Late Pleistocene, it has accommodated a net slip ca. 205 m, with slip rate of 0.055 mm/a. Paleoseismicity has been analysed in a 29-m-long, 5-m-deep trench excavated through a fault branch that offsets a Pleistocene pediment surface. The paleoseismic succession includes a minimum of 6–7 events occurred since ca. 142 ka BP, although a model with 12 events could be more realistic. The following paleoseismic parameters have been inferred, assuming a minimum of 6 and a maximum of 12 events: average coseismic slip = 58–117 cm; recurrence period = 8.4–28.4 ka; potential moment magnitude Mw = 5.8–5.9. The recorded displacement since ca. 142 ka BP totalizes 7.0 m, with slip rate of 0.05–0.07 mm/a. Slip on the transverse Valdecebro fault zone has critically contributed to bulk deformation under a prevailing ‘multidirectional’ extensional regime. Drainage patterns have been rearranged, recurrently switching between westward and southward directions as a consequence of diverse slip episodes at the Valdecebro fault zone (E–W) and the neighbouring La Hita (N–S) and Concud (NW–SE) faults. The ultimate westward drainage of the Valdecebro depression incised and dismantled a southward-sloping Pleistocene pediment sourced at the Valdecebro mountain front, representing a capture by the Alfambra river occurred between 124 and 22 ka BP.
... See text for full discussion. Note also the releasing stepover to the north, between the Tormeno and Melegnon faults ROTEVATN AND PEACOCK EAGE | 1271 1998; Kattenhorn, Aydin, & Pollard, 2000). This is the reason why relay zones are often described as areas of enhanced structural "complexity". ...
Reverse reactivation of normal faults, also termed ‘inversion’, has been extensively studied, whereas little is known about the strike-slip reactivation of normal faults. At the same time, recognizing strike-slip reactivation of normal faults in sedimentary basins is critical, as it may alter and impact basin physiography, accommodation and sediment supply and dispersal. Motivated by this, we present a study of a reactivated normal fault zone in the Liassic limestones and shales of Somerset, UK, to elucidate the effects of strike-slip reactivation of normal faults, and the inherent deformation of relay zones that separate the original normal fault segments. The fault zone, initially extensional, exhibits a series of relay zones between right-stepping segments, with the steps between the segments having subsequently become contractional due to sinistral strike-slip movement. The relay zones have therefore been steepened and are cut by a series of connecting faults with reverse and strike-slip components. The studied fault zone, and comparison with larger-scale natural examples, lead us to conclude that the relays-turned-contractional-steps are associated with (i) complex fault and fracture networks that accommodate shortening, (ii) anomalously high numbers of fractures and faults, (iii) layer parallel slip and (iv) folding and uplift. Comparison with published statistics from global relay zones shows that whereas the reactivated relay zones feature aspect ratios similar to those of unreactivated relay zones, bed dips within reactivated relay zones are significantly steeper than unreactivated relay zones. Given the potential of reactivated relay zones to form areas of local uplift, they may affect basin structure and may also form potential traps for hydrocarbon or other fluids. The elevated faulting and fracturing, on the other hand, means reactivated relays are also likely loci for enhanced up-fault flow.
... The development of faults perturbs the surrounding stress field that can affect fracture formation within their influence zone (e.g. Hafner, 1951;Lajtai, 1969;Couples, 1977;Segall and Pollard, 1980;Pollard and Segall, 1987;Rawnsley et al., 1992, Fig. 9; Reches and Lockner, 1994;Cooke, 1997;Homberg et al., 1997;Martel and Boger, 1998;Kattenhorn et al., 2000;Bourne and Willemse, 2001;Maerten et al., 2002;Bellahsen et al 2006;Savage et al, 2010). ...
Major normal fault systems are composed of segments that link as displacement accumulates, with linkage zone characteristics that reveal fault zone evolution. The steeply west-dipping Sevier fault zone in southwestern Utah, displays a complex fault network that developed between two long (>10 km), en echelon segments near the town of Orderville. Geologic map data and cross-sections of the transfer zone between the Mt. Carmel segment in the south and the Spencer Bench segment in the north reveal more than ten normal faults and four relay ramps displaying a range of geometries, including two relay ramps that display ramp-parallel folds. We suggest that transfer zone deformation was initially dominated by faults subparallel to the primary segments with later cross-faults that hard-linked these faults across most of the transfer zone. When the transfer zone was a soft-linked system, a displacement deficit likely existed relative to fault segments to the north and south. This early fault configuration would have reduced the efficiency of slip propagation associated with major earthquakes (>M7.0). In contrast, the present-day transfer zone, with a complex but hard-linked fault network, shows displacements that transition smoothly from the higher displacement (~800 m) southern segment to the lower displacement (~400 m) northern segment. That transition, combined with extensional strain within the zone, suggests that the Orderville fault network would be unlikely to impede propagation associated with future major earthquakes. The kinematic model of fault evolution presented here has implications for those investigating geothermal energy potential, groundwater flow, natural gas and oil reservoirs, mineral deposit formation, or seismic hazards.
The concept of superposed fracture networks consisting of different generations, and often types, of fractures that have developed sequentially is discussed. Superposed networks can consist of different types of extension or shear fractures, and each fracture may abut, cross or follow (reactivate) earlier fractures. An example of a superposed fracture network in Liassic limestones in Somerset, UK, is presented, which comprises two sets of veins and a later joint network. The veins develop as damage zones around faults, with veins of the later set crossing or trailing along the earlier set. The later joints either cross-cut the earlier veins or reactivate them, the latter being common for the thicker (more than about 5 mm) veins. The veins and joint networks have markedly different geometries and topologies. The veins are spatially clustered and are typically dominated by I-nodes, while the joints are more evenly distributed and tend to be dominated by Y-nodes. The combined network of veins and joints at Lilstock is dominated by X-nodes because so many joints cross-cut the earlier veins. Understanding the development of superposed fracture networks leads to better understanding of the kinematic, mechanical, tectonic and fluid flow history of rocks.
One of the numerical methods in the mechanics of continuous environments is the boundary element method. In this method, the governing differential equations will be converted to integral equations and applied to the problem
boundary. Then the boundary is divided into boundary parts and numerical integration is performed on the boundary elements, from the solution of which a single solution of the problem can be obtained. In the boundary element
method, the partial differential equations defined within a space are converted to integral equations at the boundaries of that space, which reduces one dimension of the problem. For example, an elastodynamic problem defined in a
two-dimensional space is replaced by an integral equation problem defined at its boundaries that has one dimension.
If the problem defined in a three-dimensional space is replaced by a two-dimensional integral equation problem.
Finally, the integral equations will be solved numerically by dividing the boundaries into a network of finite element discrete elements. The boundary element method can be easily applied to borders with complex geometry. Boundary
element method or boundary integral equation (BIEM) is one of the numerical modeling methods that have many applications in numerical simulation of fault dynamics. Its results provide a broad view of the physics of earthquake
rupture. To solve two-dimensional problems, the numerical technique of the boundary element method has been widely used. The boundary element method has been used to model the behavior of faults of overlapping centers,
the growth of junction assemblies, veins and seismic analysis of topographic features. One form of BEM is based on separation, which is called the displacement discontinuity method. The theory of detachments in elastic materials
has been widely used for more than half a century to evaluate the displacement, stress and strain fields around faults.
By integrating Green's functions, the displacement field around the discontinuity surface can be calculated. These displacement fields are the Navier equations that are the governing equations of linear elastic theory. Strain
components are obtained from the spatial derivatives of the displacement components, and the stress components can be calculated using Hooke's law for homogeneous and homogeneous elastic materials. Therefore, the
mathematical tool of detachment theory is able to calculate the displacement, stress and strain fields around faults in
half-elastic space, but it is less accurate compared to geophysical data. In this paper, numerical modeling of faults
using the boundary element method has been reviewed, and studies conducted in the field of numerical modeling of
faults using the boundary element method have been reviewed. Finally, the results show that the boundary element
method is suitable for problems with complex boundaries such as fault geometry and problems with infinite
boundaries. It is also possible to predict slip on the fault and surface deformation using numerical modeling using
the boundary element method. The results of numerical modeling of the fault using the boundary element method
and comparing these results with the observed values show that the boundary element method is a suitable method
for predicting issues such as slip distribution on the fault, surface displacement and slope instability. Also, the
boundary element method is a suitable method for predicting the location of smaller and secondary faults. Therefore,
it can be said that the boundary element method is a powerful tool for numerical modeling of earthquake or fault
rupture dynamics. In the articles studied in this study, the slip distribution at the fault surface has been determined
using the inversion of surface displacements resulting from the main earthquake. If aftershocks also cause surface
displacements, then as a suggestion for future research, the inversion of surface displacements caused by aftershocks
can also be used to determine the secondary slips created on the fault surface.
Research into the geological processes operating on Mars relies on interpretation of images and other data returned by unmanned orbiters, probes and landers. Such interpretations are based on our knowledge of processes occurring on Earth Terrestrial analog studies therefore play an important role in understanding the geological features observed on Mars. This 2007 book presents direct comparisons between locales on Earth and Mars, and contains contributions from leading planetary geologists to demonstrate the parallels and differences between these two neighboring planets. Mars is characterized by a wide range of geological phenomena that also occur on Earth, including tectonic, volcanic, impact cratering, eolian, fluvial, glacial and possibly lacustrine and marine processes. The book provides terrestrial analogs for data sets from Mars Global Surveyor, Mars Odyssey, Mars Exploration Rovers and Mars Express, and will therefore be a key reference for students and researchers of planetary science.
Understanding the factors controlling fracture frequency distribution can greatly improve the assessment of fluid circulation in fault damage zones, with evident implications for fault mechanics, hydrogeology and hydrocarbon exploration. This is particularly important for relay zones that are usually characterized by strong damage and structural complexity. We investigated the fracture frequency within an outcrop adjacent to the front fault segment of a relay ramp, hosted within peritidal carbonates that forms part of the Tre Monti fault (Central Italy). We analysed the distribution of fracture frequency in the outcrop through (1) scanlines measured in the field, (2) oriented rock samples, and (3) scan-areas performed on a virtual outcrop model. Fracture frequency increases with distance from the front segment of the relay ramp. Moreover, supratidal and intertidal carbonate facies exhibit higher fracture frequency than subtidal limestones. This trend of increased fracture frequency has two main explanations. (1) The number of subsidiary faults and their associated damage zones increases moving away from the front segment. (2) the supratidal and intertidal carbonate facies content increases toward the centre of the relay ramp. Our results indicate that the fracture frequency pattern is very complex in relay ramps hosted in shallow-water limestones and that its prediction necessitates a good control on structures and sedimentary facies distribution.
Minor fault geometry and kinematics within relay ramps is strongly related to the stress field perturbations that can be produced when two major fault segments overlap and interact. Here we integrate classical fieldwork and interpretation of a virtual outcrop to investigate the geometry and kinematics of subsidiary faults within a relay ramp along the Tre Monti normal fault in the Central Apennines. Although the Tre Monti fault strikes parallel to the regional extension (NE-SW) it shows predominant dip-slip kinematics, suggesting a NW-SE oriented extension acting at sub-regional scale (1–10 km). Conversely, the slickenlines collected on the front segment of the relay ramp highlight right-lateral kinematics. The subsidiary faults in the relay ramp show a complex geometry (variable attitudes) and slickenlines describe multiple kinematics (left-lateral, dip-slip, right-lateral), independently of their orientation. Our fault slip analysis indicates that a local stress field retrieved from the kinematic inversion of the slickenlines collected on the front segment, and likely promoted by the interaction between the overlapping fault segments that bound the relay zone, can explain most of the geometry and kinematics of the subsidiary faults. Further complexity is added by the temporal interaction with both the regional and sub-regional stress fields.
Cambridge Core - Structural Geology, Tectonics and Geodynamics - Geologic Fracture Mechanics - by Richard A. Schultz
Widespread NW‐SE‐trending faults and Cenozoic basins in the coastal area of Fujian Province demonstrate unique tectonic deformations from the influence of the modern arc‐trench system on the adjacent continent. Field‐based structural analyses in the Zhangzhou region identify two‐stage deformation in the Cenozoic. The early stage was dominated by normal faulting and mafic intrusions. The structural configuration was differentiated as a graben in the estuary area and linear ridges in the western mountains, representing outer arc extension caused by orthogonal flexure of the coast. Late‐stage deformation turned early‐stage normal faults into sinistral strike‐slip faults and induced a transtensional setting that greatly facilitated the evolution of the basin, as well as a small rotation of the segmented structures. The tectonic dynamics are attributed to far‐field effects of the west Pacific subduction zones. Additionally, a strike‐slip fault‐controlled scissor‐like structure is proposed to demonstrate the mechanism of the redefined, fan‐shaped basin. This article is protected by copyright. All rights reserved.
The Moab Fault is a 28 mi (45 km) long, salt-related, normal fault of about 3,100 ft (950 m) maximum surface throw. The fault cuts a Pennsylvanian to Cretaceous sedimentary sequence, and extends northwest wards from the Moab-Spanish Valley salt anticline along the southwestern flank of a salt withdrawal syncline. The surface trace comprises a simple southern segment joined at branch-points to a series of fault splays in the north. Maximum surface throw occurs in the south where the fault is associated with both a footwall high and a hangingwall anticline. The fault trace is bordered by a damage zone, which includes a swarm of minor structures, that is most extensively developed within regions of structural complexity, for example around branch-points, fault bends, overlap zones and fault-related folds. The fault was active from the Triassic until at least the mid-Cretaceous. Distinctive types of veining, calcite cementation and iron oxide reduction are best developed adjacent to the fault, especially in Jurassic Navajo and Entrada sandstones. Calcite, ankerite, barite, and pyrite cemented veins are restricted to the immediate proximity of the fault except within regions of structural complexity. Concre-tionary calcite cements are extensively developed within regions of structural complexity where they extend for tens of metres away from the fault. Reduction of iron oxides in red bed sandstones is more widely distributed than cementation and veining. Within regions of structural complexity adjacent to the fault the Navajo and Entrada sandstone sequences are entirely reduced, whilst reduction fronts extend up to 3 mi (5 km) away from the fault in the most permeable horizons. Field observations indicate that the cementation and iron oxide reduction are broadly synchronous with the latest stages of fault movement.
The Moab Fault is a 28 mi (45 km) long, salt-related, normal fault of about 3,100 ft (950 m) maximum surface throw. The fault cuts a Pennsylvanian to Cretaceous sedimentary sequence, and extends northwest wards from the Moab-Spanish Valley salt anticline along the southwestern flank of a salt withdrawal syncline. The surface trace comprises a simple southern segment joined at branch-points to a series of fault splays in the north. Maximum surface throw occurs in the south where the fault is associated with both a footwall high and a hangingwall anticline. The fault trace is bordered by a damage zone, which includes a swarm of minor structures, that is most extensively developed within regions of structural complexity, for example around branch-points, fault bends, overlap zones and fault-related folds. The fault was active from the Triassic until at least the mid-Cretaceous. Distinctive types of veining, calcite cementation and iron oxide reduction are best developed adjacent to the fault, especially in Jurassic Navajo and Entrada sandstones. Calcite, ankerite, barite, and pyrite cemented veins are restricted to the immediate proximity of the fault except within regions of structural complexity. Concre-tionary calcite cements are extensively developed within regions of structural complexity where they extend for tens of metres away from the fault. Reduction of iron oxides in red bed sandstones is more widely distributed than cementation and veining. Within regions of structural complexity adjacent to the fault the Navajo and Entrada sandstone sequences are entirely reduced, whilst reduction fronts extend up to 3 mi (5 km) away from the fault in the most permeable horizons. Field observations indicate that the cementation and iron oxide reduction are broadly synchronous with the latest stages of fault movement.
High fault-tip stress concentrations are associated with coseismic slip on blind thrust faults and suggest that these structures should readily propagate to the Earth's surface. Seismic profiles of blind-thrust-related earthquakes reveal diffuse zones of aftershocks surrounding the fault tip which are attributed to inelastic deformation, such as flexural-slip or extensional fracturing. The complex interaction between blind thrust faults and secondary structures may control the evolution of blind thrust systems. The influence of bedding-plane slip on fault propagation is simulated with numerical models using the boundary element method. We use two parameters to estimate the tendency for thrust fault propagation, (1) the mode II stress intensity factor and (2) the maximum Coulomb stress near the fault tip. Calculations from both analyses suggest that shallow thrust faults may exhibit an increased tendency to propagate as a result of interaction with the Earth's surface and slip along bedding planes above the fault tip and a decreased tendency to propagate due to slip along bedding planes at or below the fault tip. Our results demonstrate that the magnitude and style of inelastic deformation in active fault systems control fault propagation.
The deformation associated with several small, brittle faults was investigated on both microscopic and macroscopic scales. While the dominant macroscopic structures are solution cleavage planes and secondary shear fractures, the dominant microscopic deformation structures are healed tensile microfractures. The fault-related microfractures display densities and orientations distinct from the background microfracture population. These densities and orientations are consistent with formation within the altered stress fields of propagating shear fracture tips. This microfracture population is used to define the fault process zone associated with growth of the macroscopic fault plane. Process zone microfractures show logarithmic density increases with proximity to the fault, a constant maximum density that is independent of fault length, and orientations which can be used to infer the direction of propagation of the fault plane. The width of the process zone scales linearly with fault length with a proportionality constant of the order of 10-2.
Fault displacements measured in coal mines and from seismic data are used to develop a model describing the near-field displacements associated with an ideal, single normal fault. Displacement on a fault surface ranges from a maximum at the center of the fault to zero at the edge or tip-line. The tip-line is elliptical, with the shorter axis of the ellipse parallel to the displacement direction. Contours of equal displacement form concentric ellipses centered on the point of maximum displacement. Displacement gradients vary with fault size and with mechanical properties of host rock; fault radius to maximum displacement ratios range from 5 to 500. Plotting of displacement contour diagrams and knowledge of displacement gradients are useful in interpreting seismic reflection data, both for quality control of interpretations and for quantitative extrapolation of limited data. Displacements associated with fault decrease systematically with increasing distance along the normal to the fault surface; this decrease is seen as reverse drag in both hanging wall and footwall. Hanging-wall rollover and tilting of the reflectors cannot be used to distinguish listric from planar normal faults; even where fault-block rotation can be demonstrated, neither listric fault geometry nor a flat detachment surface is geometrically necessary. Because faulting is accommodated by ductile deformation, rigid fault-bounded blocks cannot exist except in some special circumstances related to a free surface. The displacements within the rock volume affected by a single fault are not simply related to regional extension. Apparent horizontal extension by faulting varies from one layer to another, and a significant proportion of the extension in a basin may be due to ductile deformation. 13 figures.
We present a new method to estimate stable seismic source parameters, such as energy, moment, and Orowan stress drop, using regional coda envelopes from as few as one broadband station. We use the method to compute path- and site-corrected seismic moment-rate spectra for 117 recent western United States earthquakes. Empirical Green's function corrections were applied to our surface- and body-wave coda envelope measurements to generate S-wave source spectra. These source spectra provide stable, single-station estimates of radiated seismic energy ES and seismic moment MO that for common events are in excellent agreement with network-averaged estimates obtained using local and regional data. Teleseismic moment estimates are compatible with our regional results, but teleseismic energy estimates appear to be nearly an order of magnitude low. We estimated the seismic moment of events ranging between MW 2.2 and 7.3, and energy estimates for which we had measured at least 70% of the total energy, generally events above MW 3.3. We use these estimates to examine the behavior of derived parameters such as the Orowan stress drop (Deltasigma=2muES/MO). While the earthquakes we studied have a small range in Orowan stress drop, generally between 0.1 and 20 MPa, they show a strong tendency for Orowan stress drop to increase with moment, approximately as M0.25O. We believe this is a source effect and is not due to inadequate bandwidth or attenuation correction, and note that this trend appears to continue for microearthquakes as described in a recent deep borehole study in southern California. Many of the large high stress drop earthquakes show complexity in their moment-rate spectra near the corner frequency and cannot be fit by a simple omega-square model. Instead, above the first corner frequency, the spectral decay ranges between f-1.0 and f-1.5. This leads to larger estimates of radiated energy than predicted with a simple omega-square model and has implications for seismic hazard estimation. Coda envelopes have three main advantages over direct arrivals for estimating seismic moment and energy: (1) Coda amplitudes vary little with geology and source-radiation anisotropy and allow accurate single-station applications; (2) path-corrected coda amplitude measurements can be applied to very large regions, allowing a comparison of source parameters throughout the western United States using a common methodology and stations; (3) because long-period coda can last for hours for large local and regional events, it allows the analysis of seismograms with clipped early arrivals.
A radial system comprising more than 200 basaltic and trachytic dikes and two minor systems of parallel dikes intruded the Ramon area, southern Israel, during the Early Cretaceous. Field relations between dikes and fractures in the radial system indicate that the dikes intruded self-generated fractures, and thus indicate the directions of the tectonic stresses. Other field observations indicate that the dikes propagated in subhorizontal directions up to distances of 15 km from their source. Our analysis of the emplacement mechanics of these dikes shows that the horizontal propagation is best explained by the density differences between the intruding magma and the host rocks. The measured mean density for basement rocks at depths greater than 2.4 km is 2.55+/-0.07 g/cm3, and it is 2.36+/-0.21 g/cm3 for the sedimentary cover above. For the magma to be propagating horizontally at its neutral buoyancy level requires a mean magma density of about 2.5 g/cm3. The large distance of horizontal propagation requires a low viscous pressure drop, below 0.1 MPa/km within the dike, and an overpressure of about 1 MPa in the magma chamber. We computed stress trajectories using a two-dimensional elastic model for a pressurized hole in a regional stress field and compared to it to the Ramon radial system. The model reveals that the dikes originated at a central intrusion of about 3 km diameter and intruded under a predominantly radial state of stress with negligible regional stress field. This period of weak tectonic stresses and intensive magmatism falls between the early Mesozoic extensional regime and the late Mesozoic-Cenozoic compressional regime in Israel. The calculated center of the radial system is offset from a large magnetic anomaly south of the Ramon area, suggesting a 3 km right-lateral displacement along the Ramon fault after the intrusion of the radial system.
Numerous published analyses of the nontectonic state of stress are based on Hooke's law and the boundary condition of zero horizonal deformation. This approach has been used to determine the gravitational stress state as well as the effects of processes such as erosion and temperature changes on the state of listhospheric stress. The major disadvantage of these analyses involves the assumption of lateral constraint which seems unrealistic in view of the observational fact that the crust can deform horizontally in response to applied loads. If the same problems are addressed by assuming that the remote stress state is constant, instead of the condition of zero horizontal deformation, then the resulting stress states are entirely different and in good accord with observations. In the absence of applied tectonic forces only likely gravitational stress states are those for which all three principal stresses are nearly equal. To the contrary, the gravitational stress states developed on the basis of the lateral constraint assumption can be ruled out. The processes of erosion and sedimentation have slight tendencies to increase and decrease, respectively, the state of deviatoric stress. In particular, for initial stress states in the range of slightly extensional to compressional, erosion has the effect of enhancing the ratio of average horizontal to vertical stress, which may explain, at least in part, the common observation of high near-surface horizontal stresses. Temperature changes have only minor effects on the stress state, as averaged over the thickness of the lithosphere.
We derive in algebraic form the displacement and stress fields produced by a triangular element of constant slip by superposing the solution of Comninou and Dundurs (1975) for an angular dislocation in an elastic half-space. As an example, triangular elements are used to determine the distribution of slip on a planar surface caused by a prescribed stress drop. The results using uniform slip elements are compared with those from the more elaborate procedure of Wu et al. (1991) that takes proper account of stress singularity at the edge of the slipping zone. The comparison indicates that, for a prescribed uniform stress drop, the uniform slip model slightly overestimates the free surface displacements. -from Authors
Simple strike-slip fault zones mark the third stage of faulting in granitic plutons in the Mount Abbot quadrangle of the Sierra Nevada of California. It is suggested that as some faults linked to form longer structures, a "shear stress shadow' was cast over adjacent smaller faults, causing slip on them essentially to cease. In this manner, displacement progressively became localized on the longer faults and fault zones. If the regional shear strain rate remained constant during this process, then the shear strain rate across the still active faults must have increased. This may have caused cataclastic textures to develop in the boundary faults. -Authors
Opening-mode splay fractures have been observed within clusters near fault tips. The spatial distribution of splay fractures along faults influences fluid flow and lends insight into the mechanical processes of faulting. Slip gradients along faults produce stress concentrations which promote the development of opening-mode splay fractures along faults. Since the slip distribution depends on the distribution of frictional strength along faults, spatial variations in the frictional properties may influence fracture localization. Variations in friction coefficient along faults can reduce the stress singularities at fault tips and promote the development of multiple fractures inwards from the fault tips. The conditions that promote splay crack localization are examined using analytical and numerical fault models. Single splay fractures develop at locations of abrupt friction coefficient change and/or at fault tips when the frictign coefficient near the tips is less than a critical value. Fault models with linearly increasing friction coefficient toward the fault tip promote the development of multiple splay fractures within broad zones near the tip.
The 3-D geometries of normal faults defining the Wytch Farm oilfield, southern England, have been interpreted from a high quality 3-D seismic reflection survey. In the deepest portions of the survey (~1600m depth), where faults were active the longest, the faults are laterally continuous. Higher in the section, younger faults form isolated segments. The deeper faults may thus have formed through the linkage of initially isolated segments. This hypothesis is supported by multiple maxima in the fault surface slip distributions, indicating individual segment nucleation locations. Multiple slip maxima are restricted to specific stratigraphic depths, predominantly in sandstone or limestone, indicating significant lithologic control on fault nucleation. As a result, laterally-segmented fault systems dominated, forming composite fault surfaces as the segments linked together along their lateral edges. Subtle indicators in the seismic data allow the determination and corroboration of such linkages.
Fault interactions play a major role in the definition of tipline shapes. Steep tiplines occur where the through-going fault of a conjugate pair scissors from one fault to the other, or where mechanical interaction arrests the growth of laterally overlapping faults. Horizontal upper and lower tiplines developed as a result of interaction between vertically stepping faults, with vertical offsets occurring across thick shale horizons. Shaley lithologies exert a major control on fault growth, often impeding vertical linkage. Consequently, predominantly lateral propagation and segment linkage produced very long, rectangular faults. Fault seal continuity may thus be expected to extend a great distance along strike, while being more discontinuous down the fault dip as a result of vertical steps. For earthquake-producing normal faults, such a geometry introduces vertical barriers to rupture propagation and may contribute to why aftershock distributions tend to spread out further laterally than vertically.
Viewed from directly above, the spatial arrangement of faults in the fault system defines a systematic quilt-like patchwork geometry in 3-D space, with each fault filling a hole in the patchwork. This pattern of faulting is consistent irrespective of fault dip direction, and implies that the 3-D extent of propagation of each fault is greatly controlled by the geometries and arrangement of other faults in the patchwork. Each individual fault formed through the linkage of numerous smaller segments, thus defining a secondary patchwork system for each composite fault surface. Fault evolution is thus governed by a hierarchical system of segmentation that develops composite faults through segment linkage and controls the relative arrangements of composite faults in 3-D space. These insights into 3-D fault geometry may be useful for the development of fault evolution models and for understanding earthquake rupture propagation, mechanical interaction between faults, leakage points in hydrocarbon reservoirs, and complex slip distributions.
We consider and discuss the presence of discontinuities in the crust as a major source of stress perturbations. Based on 2-D distinct-element modelling, we reconstruct the local stress field around a vertical discontinuity in various geological contexts. The resulting stress distribution reveals that major directional stress changes occur near the tips of the discontinuity so that stress deviations can reach values as large as 50 °. We establish simple relationships controlling stress changes around a pre-existing fault zone as a function of (1) the remote differential stress magnitude, (σ1 − σ3), (2) the friction coefficient on the discontinuity, and (3) the strike of the discontinuity relative to the far-field stress.As a geological example, we present the Morez Fault Zone in the internal Jura. Paleostress reconstruction in forty-two sites indicates that the trends of the Mio-Pliocene compression are N110 ° on average near the fault, whereas they are N130 ° in the surrounding areas. A comparison between the results of the tectonic study and those of theoretical modelling suggests that the 20 ° counterclockwise deviation is directly related to the reactivation of this large weak zone. We thus evaluate the role of mechanical decoupling along pre-existing zones of weakness, especially with consideration to the accommodation of the Alpine deformation in the Jura belt.
In order to eliminate the need for complex geometric definitions when
working with three dimensional engineering problems, boundary element
methods are presented which are applicable to a number of different
common three dimensional engineering problems. Some of the general
advantages of boundary element methods over domain methods in computer
analysis and design are described, including simpler data preparation;
greater accuracy in solving infinite or semi-infinite problems; more
accurate results for stress and flux variables; and internal results for
only the points where they are needed. Some representative applications
of boundary element methods are: for thermo-elastic analysis; cathodic
protection solutions; ideal elastoplasicity problems; tunnelling
problems; time dependent heart transfer analysis; membrane vibrations;
and free vibrations of a shear wall.
Fault zone permeability in outcrop is quantified by detailed geologic mapping and by measurements using a minipermeameter. Deformation bands, zones of deformation bands, and slip planes are structural elements associated with successive stages in the evolution of a fault zone in porous sandstones. Deformation bands have a porosity about one order of magnitude less than the surrounding host rock and, on average, a permeability three orders of magnitude less than the surrounding host rock. The intensity of cataclasis and the clay content control the amount of permeability reduction as measured perpendicular to a band. The wall rock in proximity to slip planes can have permeabilities more than seven orders of magnitude less than the pristine sandstone. Capillary pressure within deformation bands is estimated to be 10-100 times larger than that in the surrounding host rock. Thus, deformation bands and slip planes can substantially modify fluid flow properties of a reservoir and have potential sealing capabilities with respect to a nonwetting phase, as evident in outcrop exposure. 55 refs., 21 figs.
We present a methodology to describe fault geometry at different scales and to characterize the distribution of these scales on the flanks of a salt intrusion in the Colorado Plateau (Arches National Park, United States). This methodology is based on the recognition of the physical processes of faulting and on the quantitative characterization of the structural and petrophysical properties of faults in porous sandstones. The methods used include a variety of mapping techniques (photography, aerial photography, string mapping, theodolite surveys, etc.), as well as techniques for determining fluid flow properties. The resulting study is a prototype for understanding seismic and subseismic scales of heterogeneity related to faulting and fracturing in subsurface reservoirs. Slip planes, which are not interconnected, may have poor geometric sealing characteristics. In the hanging wall of a major normal fault, the quantitative spatial distribution of the faults can be correlated with bending of the strata, probably associated with the salt intrusion. The number of deformation bands, the most ubiquitous element, is proportional to the amount of slip on a single major fault. Deformation bands also have a very high density (>100 mâ»Â¹) in stepovers between slip planes. In these areas we find the largest anomalies in permeability. In zones of high strata curvature, the average orders of magnitude with respect to the host rock; if complex fault zones are present, the average permeability can drop more than four orders of magnitude in the direction normal to the faults. Finally, by using outcrop and laboratory data that describe the effect of distinctive structural units on fluid flow, we quantify the three-dimensional distribution of permeability in a reservoir analog at any scale, and we show that such permeability distribution could be implemented in a geology-based reservoir simulator.
Fracture mechanics theory and field observations together indicate that the shear stress on many faults is non-uniform when they slip. If the shear stress were uniform, then: (a) a physically implausible singular stress concentration theoretically would develop at a fault end; and (b) a single curved ‘tail fracture’ should open up at the end of every fault trace, intersecting the fault at approximately 70 °. Tail fractures along many small faults instead range in number, commonly form behind fault trace ends, have nearly straight traces and intersect a fault at angles less than 50 °. A ‘cohesive zone’, in which the shear stress is elevated near the fault end, can eliminate the stress singularity and can account for the observed orientation, shape, and distribution of tail fractures. Cohesive zones also should cause a fault to bend. If the cohesive zone shear stress were uniform, then the distance from the fault end to the bend gives the cohesive zone length. The nearly straight traces of the tail fractures and the small bends observed near some fault ends implies that the faults slipped with low stress drops, less than 10% of the ambient fault-parallel shear stress.
Detailed studies of stress-induced wellbore breakouts in wells drilled through active faults reveal stress field discontinuities that are apparently associated with recent fault movements. These discontinuities are expressed as localized rotations in wellbore breakout orientation in the vicinity of the fault penetrated by the borehole. This phenomenon is observed in a variety of tectonic environments and rocks types. Utilizing cases where relatively complete knowledge of the horizontal principal stresses is available from in situ measurements, we use three-dimensional dislocation modeling to demonstrate that these discontinuities can be explained as the superposition of a reference stress state and a perturbation caused by movement on preexisting faults. Case studies from normal, strike-slip and reverse faulting stress state indicate that nearly complete stress drop is required to match the observed breakout orientation anomalies. Hydraulic fracturing data independently confirm the occurrence of near-complete stress drop on some faults penetrated by drilling. Modeling of the observed interactions between breakouts and fractures can also be used to obtained information about the magnitude of in situ stress.
Sedimentary rocks intruded by Tertiary mafic dikes on the Colorado Plateau typically display systematic dike-parallel joints. These closely spaced joints occur only near dikes, their spacing commonly increasing with distance from the dike contacts. Igneous breccias along some of these joints indicate that the joints are not younger than the dikes and, therefore, did not form during cooling. Field relations are best explained if the joints form in host rocks beyond the dike tip, becoming juxtaposed against the dike with continued propagation: an interpretation supported by previously reported descriptions of ground surface cracks formed near eruptive fissures and of microcracks formed near the tips of larger extension cracks during laboratory experiments. Tensile stress generated by magmatic pressure is sufficient to fracture host rocks beyond dike tips. The tensile maxima are located on either side of the dike plane, beyond the tip. The stresses increase in magnitude closer to the tip, thus explaining the greater abundance of joints near the dike plane. Noting that dikes may parallel regional joint sets, we contrast (1) emplacement along older joints oriented arbitrarily with respect to the principal stress directions acting at the time of intrusion and (2) emplacement along self-generated fractures propagated in a plane perpendicular to the least compressive stress direction. Magma can invade along older joints if magmatic pressure exceeds the horizontal stress acting across the joint plane. This situation is most common if the horizontal principal stress difference is small compared to the magmatic driving pressure or if joints are nearly perpendicular to the direction of least compressive regional stress. Magma must advance by filling self-generated fractures if older, suitably oriented, joints are absent.
The Sleipner Vest field, located in blocks 15/6 and 15/9 on the Norwegian Continental Shelf, contains hydrocarbons (mainly gas condensates) within the marginal marine units of the Middle Jurassic Hugin Formation. The field is segmented into fault-bounded compartments, which exhibit differences in gas-water contacts of between 10 and 100m. Microstructural analysis of core samples has identified three principal fault types; cataclasites, developed from clean sandstones, framework phyllosilicate fault rocks created from impure sandstones and clay smears developed from phyllosilicate-rich units. The distribution of these has been linked to the phyllosilicate content of the undeformed Hugin reservoir at the time of deformation. Petrophysical property analysis has been used to quantify the representative permeabilities and threshold capillary pressures of the fault rocks and their undeformed equivalents. Juxtaposition/seal diagrams and detailed fault plane maps were also constructed and provide a basis for mapping sand-sand juxtapositions and the distributions of the different fault rock types with assigned permeabilities and capillary threshold pressures. The results provide an explanation of the mapped variations in gas-water contacts. An important correlation exists between the type of fault rock predicted to dominate the fault plane near the hydrocarbon-water interface and the difference in hydrocarbon depths across the faults. Compartments separated by faults with windows of juxtaposed clean sandstone cataclasites have small hydrocarbon-water level differences (7–11 m), suggesting that the low capillary threshold pressure (more permeable) cataclastic fault rocks control communication. Compartments separated by faults predicted to have extensive phyllosilicate-rich fault rocks (developed from impure sandstones and clay rich units) with high capillary threshold pressures correlate to larger hydrocarbon-water differences (>39 m), reflecting the reduced communication.
Fieldwork within a series of mesoscale grabens in southeast Utah has revealed a particularly well-exposed system of interlinked extensional faults. A series of down-faulted grabens consist of two or more overlapping elements, which are composed of fault segments. These segments may be hard-linked (fault surfaces are joint) or soft-linked (fault surfaces are isolated, but linked by ductile strain of the rock volume between them) in map view. Relay structures are defined as zones connecting the footwalls and hanging walls of overlapping fault segments representing soft linkage of fault segments. In the Canyonlands grabens, the transfer of displacement between soft-linked fault segments is characterized by well-defined, dipping relay ramps commonly rotated and extended to accommodate the ductile strain between the overlapping fault segments. -from Authors
Simple strike-slip fault zones mark the third stage of faulting in granitic plutons in the Mount Abbot quadrangle of the Sierra Nevada of California. Deformation began with the opening of nearly vertical subparallel joints. These joints were filled mostly with epidote and chlorite, are up to a few tens of meters long, and typically are less than 1 cm wide. Next, some of these joints slipped left-laterally and became small faults. Small faults accommodated up to ∼2 m of displacement and are characterized by mylonitic fabrics and ductilely deformed quartz. Oblique fractures commonly developed near the ends of small faults and in many cases linked faults end-to-end. Simple fault zones developed as abundant oblique fractures linked small faults side-to-side. These fractures opened and were filled with chlorite, epidote, and quartz. Such fractures are scarce outside the two faults that mark the boundaries of a zone. Simple fault zones typically are 0.5-3 m wide, hundreds of meters long, and laterally displace dikes up to ∼10 m. Displacement is concentrated along the boundary faults, which are characterized by cataclastic textures and brittlely deformed quartz. The fault zones consist of noncoplanar segments a few tens of meters long that join at steps or bends. The segmentation reflects the initial joint pattern and indicates that fault zones grew in length as noncoplanar faults linked end-to-end. Away from bends, the most prominent internal fractures have straight traces and strike 20°-60° counterclockwise from the boundaries, whereas near bends they have gentle S-shaped traces and are nearly perpendicular to the boundaries.
We suggest that as some faults linked to form longer structures, a "shear stress shadow" was cast over adjacent smaller faults, causing slip on them essentially to cease. In this manner, displacement progressively became localized on the longer faults and fault zones. If the regional shear strain rate remained constant during this process, then the shear strain rate across the still active faults must have increased. This may have caused cataclastic textures to develop in the boundary faults.
The origin of en echelon second order shear fractures and tension gashes associated with first order, or primary, faults is examined analytically and experimentally. It is postulated that en echelon second order structures form under the influence of a stress mechanism similar to the one occurring in the direct shear test. The direct shear or modified direct shear state of stress could develop at certain points along a forming primary fault as a result of a local reduction in the normal stress acting on planes perpendicular to the displacement direction. It is argued that in most en echelon arrays the orientation of the individual fractures reflects the existence of a local state of stress, and cannot directly be correlated with the regional (primary) stress field. The zone in which they occur, however, may represent planes of high effective shear stress within the regional framework. The direct shear model (full relief of transverse normal stress) offers a stress mechanism which can explain the origin of not only en echelon tension gashes but also second order faults. For a given set of strength parameters, the type of en echelon fractures that will develop depends on the normal stress acting in the primary fault plane. In general, tension fractures form at low normal stress, shear fractures at intermediate values of normal stress, and at high normal stress a crush or shear zone is produced. If the state of stress is one of modified direct shear (only partial relief of transverse normal stress), the development of second order faults is favored.
Mixed mode I+III loading of a fracture front results in out-of-plane propagation into echelon stepping fractures. Because a planar fracture geometry is the exception rather than the rule, and because the introduction of even a minor component of mode II or III loading is known to promote out-of-plane propagation, an understanding of mixed mode fracture growth is imperative to analyze fracture behavior. We have loaded cracks in mixed mode I+III within polymethyl methacrylate (PMMA or Plexiglas) rectangular blocks resembling conceptual fracture mechanics models of mixed mode loading and have analyzed the resulting geometries. The observed angle of twist of echelon fractures from the parent crack plane increases with the ratio KIII/KI and falls below theoretical predictions. Fracture propagation paths depend not only on the load ratio applied but also on sample geometry, loading configuration, and interaction among growing fractures. Sample geometry and loading configuration are approximately accounted for using analytical determinations of the stress intensity factors. We propose that interaction among growing fractures may contribute to the discrepancy between theoretically predicted twist angles and those observed in these and other mixed mode I+III experiments. Analysis of these experimental results has motivated the design of a new sample and loading configuration to test the propagation paths of uniformly loaded mixed mode I+III fractures.
We present a model for the nucleation and growth of faults in intact
brittle rocks. The model is based on recent experiments that utilize
acoustic emission events to monitor faulting processes in Westerly
granite. In these experiments a fault initiated at one site without
significant preceding damage. The fault propagated in its own plane with
a leading zone of intense microcracking. We propose here that faults in
granites nucleate and propagate by the interaction of tensile
microcracks in the following style. During early loading, tensile
microcracking occurs randomly, with no significant crack interaction and
with no relation to the location or inclination of the future fault. As
the load reaches the ultimate strength, nucleation initiates when a few
tensile microcracks interact and enhance the dilation of one another.
They create a process zone that is a region with closely spaced
microcracks. In highly loaded rock, the stress field associated with
microcrack dilation forces crack interaction to spread in an unstable
manner and recursive geometry. Thus the process zone propagates unstably
into the intact rock. As the process zone lengthens, its central part
yields by shear and a fault nucleus forms. The fault nucleus grows in
the wake of the propagating process zone. The stress fields associated
with shear along the fault further enhance the microcrack dilation in
the process zone. The analysis shows that faults should propagate in
their own plane, making an angle of 20 deg-30 deg with the maximum
compression axis. This model provides a physical basis for 'internal
friction', the empirical parameter of the Coulomb criterion.
On the basis of the analysis of the stability of an interacting system of straight edge cracks it is shown that when the fracture strength of the ice is taken to be nonzero, there exists a minimum spacing for water-free crevasses (about 6-8 m). This spacing is, in general, much larger than the minimum crack spacing (about 1/3 m) needed in order to be able to attain the critical value of the stress intensity factor; and therefore, in general, the minimum spacing of the water-free crevasses is dictated by the stability consideration, rather than by the consideration of the stresses alone. In terms of dimensionless parameters a master chart is developed which separates stable and unstable states. It is shown that the minimum spacing decreases with decreasing fracture strength of the ice, and when the fracture strength of the ice is taken to be zero, the spacing can be very small. At this limit the penetration depth is approximately given by the value found by Nye, which is then independent of the corresponding spacing.
Many fault arrays consist of echelon segments. Field data on ancient and active faults indicate that such segmented geometries have a pronounced effect on the distribution of fault slip. Outcrop measurements of slip on arrays of fault segments show that: (i) the point of maximum fault slip generally is not located at the centre of a fault segment; (ii) displacement gradients steepen towards the adjacent fault for underlapping faults; and (iii) displacement gradients become more gentle near the tips of overlapping faults.Numerical analyses suggest that mechanical interaction between neighbouring faults may cause such asymmetrical slip distributions. This interaction occurs through local perturbation of the stress field, and does not require the faults to be connected. For normal faults, the degree of fault interaction, and hence the degree of asymmetry in the slip distribution, increases with increasing fault height and fault overlap and with decreasing fault spacing. The slip magnitude along a discontinuous fault array can be nearly equal to that of a single larger continuous fault provided the segments overlap with small spacing.Fault interaction increases the ratio between fault slip and fault length, especially for closely spaced, overlapping faults. Slip-to-length ratios also depend on the three-dimensional fault shape. For normal faults, the slip-to-length ratio increases with increasing fault height. The effects of fault interaction and three-dimensional fault shape together can lead to more than one order of magnitude variation in slip-to-length ratio for the simple case of a single slip event in a homogeneous isotropic rock. One should expect greater variation for the more complex conditions found in nature. Two-dimensional fault scaling models can not represent this behaviour.