Stuart Hardy

Numerical modeling of trishear fault propagation folding

In contrast to kink band migration modeling methods, trishear numerical models produce fault propagation folds with smooth profiles and rounded hinges. Modeled fold hinges tighten and converge downward, within a triangular zone of distributed deformation which is focused on the fault tip. Such features have been reported from field studies and are also seen in analogue models of compressional deformation. However, apart from its initial application to Laramide folds, little quantitative work has been undertaken on trishear fault propagation folding in other settings. In addition, no study has been undertaken into the growth strata which might be associated with such structures. This paper uses an equivalent velocity description of the geometric model of trishear, together with models of erosion and sedimentation, to investigate trishear fault propagation folding of both pregrowth and growth strata. The trishear model is generalized to include a variety of fault propagation to slip ratios and fault propagation from a flat decollement. The models show continuous rotation of the forelimb with the characteristic development of cumulative wedges within growth strata. When total slip on a structure is high, the model predicts overturned pregrowth and growth strata. During the initial stages of deformation, beds in the forelimb thicken but later thin when they become steep or overturned. The effect of variations in fault propagation to slip ratios on two-dimensional finite strain in the models is assessed by the use of initially circular strain markers. High fault propagation to slip (p/s) ratios lead to narrow zones of high finite strain, while lower p/s ratios lead to more ductile deformation and broader zones of high strain. In all cases, hanging wall anticlines and footwall synclines originate as early ductile folds which are later cut by the propagating fault. Modeled structures are compared with natural examples.

Progressive evolution of a fault-related fold pair from growth strata geometries, Sant Llorenç de Morunys, SE Pyrenees

New structural-stratigraphical mapping constrains the three-dimensional kinematics and mechanisms of Eocene-Oligocene growth folding at Sant Llorenc de Morunys (NE Ebro basin, Spain). A 1 km wide sub-vertical panel of syntectonic alluvial gravels passes southwards via a highly asymmetrical growth fold-pair to shallowlydipping strata. The axial surface of the anticline comprises either continuous or en echelon segments while that of the syncline is concave and usually continuous. While converging upwards, the axial surfaces do not define growth triangles. Principal and subsidiary growth unconformities and thickness changes occur across both axial surfaces and the common limb. Dips within the common limb decrease up-stratigraphy and up-dip. Mesostructures indicate that internal deformation was ongoing during folding at all stratigraphical levels, and concentration of cleavage in the syncline indicates that this hinge was essentially fixed. Sequential restoration of three profiles shows that folds amplified principally by limb rotation but incorporated minor passive hinge migration. Particle movement vectors, generated by section restoration, are arcuate about a hinterland pinpoint. A new trishear model of fault propagation folding involving non-rigid limb rotation reproduces the rounded hinge forms, thickening geometries and limb dip variations observed. Simple kink band migration models (fixed axis and constant thickness theories) do not replicate these features.

Kinematic modelling of extensional fault-propagation folding

Abstract Many studies have shown that in extensional basins discrete faulting at depth is commonly linked to more distributed deformation, in particular folding, at higher levels. Such extensional fault-propagation folds are particularly common where there is a distinct mechanical contrast between faulted basement and sedimentary cover. Outcrop and analogue modelling studies indicate that such folds form as upward widening zones of distributed deformation (monoclines) above discrete faults at depth. With increasing displacement (strain) the folds are cut by faults as they propagate upwards into the cover. To date, however, there has been little investigation into the kinematics of linked basement faulting and extensional fault-propagation folding. Here we present a two-dimensional kinematic model of linked basement faulting and fault-propagation folding which is based upon trishear. The model allows investigation of the influence of shear zone geometry and the rate of fault propagation upon the style of folds and the strains associated with them. The evolution of linked basement faulting and folding predicted by the model is compared in detail to that observed in an analogue model. The kinematic model reproduces well many of the features seen both in the analogue model and reported from outcrop and seismic studies.

Discrete element modelling of contractional fault-propagation folding above rigid basement fault blocks

Many studies have shown that discrete (blind) faults at depth are commonly linked to more distributed deformation, in particular folding, at higher levels. One category of fault-related folds, forced folds, is common where there is a distinct mechanical contrast between faulted basement and sedimentary cover. Outcrop, numerical and analogue modelling studies indicate that such folds form as upward widening zones of distributed deformation (monoclines) above discrete faults at depth. With increasing displacement the folds are often cut by faults as they propagate upwards into the cover. While the trishear kinematic model of fault-propagation folding appears to approximately represent the geometric development of such structures, comparatively little is known of the mechanical controls on their development. Here we present a 2D discrete element model of sedimentary cover deformation above a contractional fault in rigid basement. The elements consist of a series of soft spheres that obey Newtons equations of motion and initially interact with elastic forces under the influence of gravity. Particles are bonded until the separation between them exceeds a defined breaking strain at which time the bond breaks, simulated by the transition from repulsive–attractive forces to solely repulsive forces. The model is used to investigate the influence of basement fault dip and sedimentary cover strength on the geometry of the folds developed and the rate of fault propagation. In all cases an upward widening monocline occurs above the basement fault. We find that shallow basement fault dips produce homogenous thickening of the monocline limb while steeper dips produce contemporaneous thinning and thickening within the monocline. Thinning and thickening within the monocline are accommodated by a combination of small-scale faulting and folding. With decreasing cover strength, the zone of deformation becomes wider, localization does not occur on a single fault and fold geometries resemble trishear fold profiles with low propagation to slip ratios (p/s∼1). In contrast, a stronger cover produces a narrower zone of deformation, localization on a single fault and more rapid fault propagation (similar to trishear fold profiles where p/s∼2–3). The fault propagates into the cover at approximately the same angle as the basement fault. The model reproduces well many of the features observed in analogue modelling and reported from outcrop and seismic studies.

Architecture and depositional sequences of Tertiary fault-block carbonate platforms ; an analysis from outcrop (Miocene, Gulf of Suez) and computer modelling

Abstract This study combines outcrop with seismic data, and tectonostratigraphic modelling to characterise the stratigraphy of Tertiary fault-block carbonate platforms. Seismic sections from the Middle East and Southeast Asia indicate that carbonate platforms commonly develop on fault-blocks in the late syn-rift to post-rift stage of basin evolution, they are characterised by retrogradational or drowning morphologies with deep water clastics/evaporites sealing the platforms. A new tectono-stratigraphic modelling program simulates the development of carbonate platforms on domino-style fault blocks and predicts a distinctive tectonic control on the evolving syn-rift stratigraphy. Detailed field work from a three-dimensionally exposed Miocene syn-rift platform from the Gulf of Suez (Gebel Abu Shaar, Egypt) shows the existence of unconformity-bound depositional sequences which are predicted by the program and are interpreted to have formed in response to fault-block rotation. The sequences are characterised by synchronous hangingwall subsidence and footwall uplift and erosion. The seismic images, the modelling and the outcrop study provide different levels of information on fault-block platforms and their characteristic stratigraphy. The scale of the modelling is of particular value as it provides a link between the seismic-scale imaging and outcrop data.

The velocity description of deformation. paper 2: sediment geometries associated with fault-bend and fault-propagation folds

Abstract A general tectono-sedimentary forward modelling equation is used to derive two-dimensional numerical models of sediment geometries associated with developing fault-bend and fault-propagation folds. These styles of folding are described in terms of velocity models of deformation and are linked with syn-tectonic erosion, transport and sedimentation. The resultant two-dimensional numerical models simulate pre-growth and growth strata in both submarine and subaerial settings. The geometries and relationships produced by the models are broadly similar to those seen in natural examples. However, complex stratal geometries may be generated which are significantly different to those produced by previous models. Growth strata associated with fault-bend and fault-propagation folds are also compared and the distinguishing features of each mode of folding discussed. The forward models presented in this paper have predictive capabilities in terms of possible sediment geometries associated with fault-bend and fault-propagation folds and also in terms of the amount of deformation or erosion that a part of a structure may have undergone.

Structural evolution of calderas: Insights from two-dimensional discrete element simulations

The manner in which calderas develop is a key question in volcanology and has important implications for associated volcanogenic risk and geothermal and ore exploitation. To better understand the structural evolution of calderas, I use a discrete element model of a frictional cover undergoing piston-like subsidence at its base, simulating magma chamber deflation and cover collapse. These novel simulations capture not only the initiation of cal deras but also much of the complexity of faulting during their later development. In all models, both normal and reverse faults accommodate deeper subsidence at higher structural levels. Curved, outward-dipping reverse faults are consistently the first structures to develop; subsequent caldera growth is mainly the result of movement on vertical or steeply inward-dipping normal faults. This may be followed by a later phase of lateral collapse on shallower normal faults. The roof aspect ratio ( R = cover thickness/piston width) is seen to be an important factor: calderas with low aspect ratios ( R ≤ 1) exhibit a coherent central subsiding block, while those with higher aspect ratios have a complexly faulted internal structure.

Three-Dimensional Numerical Modeling of Deltaic Depositional Sequences 2: Influence of Local Controls

ABSTRACT We investigate the influence of three local controls (sediment supply, subsidence, and physiography) on delta development and sequence variability, using the three-dimensional numerical model of deltaic deposition presented in a companion paper (Ritchie et al. 2004). Independently varying a single local control within geologically constrained limits produces marked differences in three-dimensional morphology, cross-sectional stratal geometry, and delta evolution during a cycle of sea-level change. Sediment supply strongly influences not only the timing of transgressive and maximum flooding surface development during sea-level rise, and hence the diachroneity of lowstand, transgressive, and highstand systems tracts, but also the timing of onset of fluvial incision and the characteristics of incised valleys and forced regressive wedges. Low sediment supply leads to early drowning of forced regressive and lowstand prograding wedges, high-magnitude transgressions, and the late development of maximum flooding surfaces. During relative sea-level fall, low sediment supply results in early initiation of fluvial incision and development of few, but major incised valleys that route sediment to elongate forced regressive lobes at their mouths. In contrast, high sediment supply leads to early onset of normal regression and late transgression during relative sea-level rise, and numerous, poorly developed incised channels and a broad, laterally continuous forced regressive apron during relative sea-level fall. On basin margins with a shelf-slope morphology, base-of-slope deepwater deposits may occur at times of sea-level highstand due to sediment bypass across the slope. During relative sea-level fall fluvial incision is enhanced by the relatively steep gradient of the slope, leading to the early onset of incision and rapid headward propagation. As a result, major, deep incised valleys develop that capture sediment and feed it directly to thick shelf-edge forced regressive and lowstand prograding wedges. The greater water depth ahead of the shelf edge and the steep slope gradients result in limited forced and normal regression compared to a ramp setting. In contrast to other controls, tectonic subsidence (or uplift) leads to modification of accommodation, so that relative sea-level change may vary significantly along a basin margin. In high-subsidence settings, relative sea level may continue to rise even at times of high rates of background sea-level fall. In such settings, deltas lack incised valleys, forced regressive delta lobes, and prominent sequence boundaries. Furthermore, normal regression and even transgression in high-subsidence locations can be contemporaneous with forced regression and incised-valley development in adjacent lower-subsidence locations. The results of this sensitivity analysis suggest that systems tracts and their bounding surfaces are likely diachronous along many basin margins and may locally be absent. More than one control can produce a similar stratigraphic response, making interpretation of controlling processes from the stratigraphic product equivocal. The models provide a framework for understanding the stratigraphy of natural basin fills, but further research on the interplay between the controls is required in order to understand the climatic, tectonic, and sea-level signals concealed in the stratigraphic record.

Three-Dimensional Numerical Modeling of Deltaic Depositional Sequences 1: Influence of the Rate and Magnitude of Sea-Level Change

ABSTRACT A three-dimensional numerical model of deltaic deposition is used to investigate the influence of sea-level changes on delta development and sequence variability. Results illustrate the three-dimensional morphology of key stratal surfaces and architecture of stratal units (systems tracts) and highlight the importance of the rate and magnitude of sea-level change in controlling the evolution of deltaic depositional sequences. High rates of sea-level fall lead to the development of a limited number of major incised channels that focus sediment supply to a few elongate, finger-like forced regressive lobes separated by large areas of nondeposition. In contrast, low rates of sea-level fall cause only minor channel incision, which occurs late during sea-level fall. As a result, sediment is supplied more uniformly to the delta front, leading to an attached, laterally continuous forced regressive apron. During lowstand and subsequent sea-level rise, the delta morphology and internal geometry are strongly controlled by the rate of rise. High rates lead to: i) poorly developed lowstand wedges that are drowned early, ii) high-magnitude transgressions, and iii) the late development of maximum flooding surfaces. The stratigraphy developed during sea-level rise is also strongly influenced by the incised-valley system created during the preceding sea-level fall. If deep, major valleys developed that captured most of the sediment supply, the resultant stratigraphy has well developed lowstand wedges that are flooded relatively late during sea-level rise. Even within a single delta, systems tracts and key stratal surfaces show three-dimensional variability and two-dimensional sections often lack significant elements of the stratigraphy. As a result, analysis of two-dimensional sections can often lead to miscorrelation and erroneous interpretations of the controlling processes.

Effects of variations in fault slip rate on sequence stratigraphy in fan deltas: Insights from numerical modeling

Results from a newly developed numerical model incorporating tectonic subsidence, eustasy, and sedimentation are presented for rift-basin settings. In particular, we simulate contemporaneous fan-delta deposition, subsidence, and eustatic sea-level variations to investigate the three-dimensional nature of depositional sequences in the hanging wall of a normal fault. A random-walk algorithm is used for sediment delivery from source to shoreline, together with a nonlinear three-dimensional diffusion equation for sediment movement on steep delta foresets. Three sediment sources are modeled; they are located along strike in areas of low, medium, and high subsidence. Rates of hanging-wall subsidence, eustatic sea-level variation, and sediment supply are derived from studies of active extensional basins. The resulting stratigraphy contains three fan deltas with distinct morphologies and internal stacking patterns. Sequence boundaries and offlap (forced regression) are restricted to areas of low subsidence, toward the fault tip; aggradationally stacked deltaic wedges are along strike where subsidence rates are high, near the fault center. The simulated geometries compare well to natural examples and highlight along-strike sequence variability and the importance of local controls in such settings.