Emma Finch

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.

Influences of nodular chert rhythmites on natural fracture networks in carbonates: an outcrop and two-dimensional discrete element modelling study

Abstract Natural fractures control primary fluid flow in low-matrix-permeability carbonate hydrocarbon reservoirs, making it important to understand the factors that affect natural fracture distributions and networks. Away from the influence of folds and faults, stratigraphic controls are accepted to be the major control on fracture networks. The influence of carbonate nodular chert rhythmite successions on natural fracture networks is investigated here using a Discrete Element Modelling (DEM) technique that draws on outcrop observations of naturally fractured carbonates in the Eocene Thebes Formation, exposed in the west central Sinai of Egypt, that also form reservoir rocks in the subsurface. Stratally-bound chert nodules below bedding surfaces create lateral heterogeneities that vary over short distances. The resulting distribution of physical properties (differing stiffnesses) caused by chert rhythmites is shown to generate extra complexity in natural fracture networks in addition to that caused by bed thickness and lithological physical properties. Chert rhythmite successions need to be considered as a distinct type of carbonate fractured reservoir. Stratigraphic rules for predicting the distribution, lengths and spacing of natural fractures, and quantitative fracture indices (P11, P21, P22 and fractal dimension) are generated from the DEM outcomes. In a less-stiff carbonate medium, the presence of chert nodules reduces fracture intensity at chert horizons, and fractures per unit area are higher in chert-free vertical corridors. In a stiff carbonate medium, chert has little influence on fracture development. In a peritidal cyclic succession with constant layer thicknesses, the presence of chert in less-stiff carbonate horizons results in a reduction in fracture intensity. When chert is introduced in a subtidal cyclic sequence with constant layer thicknesses, it has little effect on fracture distribution. The study has widespread significance for characterizing naturally fractured reservoirs containing carbonate nodular chert rhythmites.

Growth and Interaction of Normal Faults and Fault Network Evolution in Rifts: Insights from Three Dimensional Discrete Element Modelling

Abstract The initiation, growth and interaction of faults within an extensional rift is an inherently four-dimensional process where connectivity with time and depth are difficult to constrain. A 3D discrete element model is employed that represents the crust as a two-layered brittle–ductile system in which faults nucleate, propagate and interact in response to local heterogeneities and resulting stresses. Faults nucleate in conjugate sets throughout the model brittle crust; they grow through a combination of tip propagation and interaction of co-linear segments to form larger normal faults. Segment linkage occurs by merging of adjacent fault segments located along strike, downdip or oblique to one another. Finally, deformation localizes onto the largest faults. Displacement distribution on faults is highly variable with marked along-strike and temporal variations in displacement rates. Displacement maxima continuously migrate as smaller fault segments interact and link to form the final fault plane. As a result, displacement maxima associated with fault nucleation sites are not coincident with the location of the maximum finite displacement on a fault where segment linkage overprints the record. The observed style of fault growth is consistent with the isolated growth model in the earliest stages which then gives way to a coherent (constant-length) fault growth model at greater strains.

Visualizing a Spherical Geological Discrete Element Model of Fault Evolution

Discrete Element Modelling (DEM) is a numerical technique that uses a system of interacting discrete bodies to simulate the movement of material being exposed to external forces. This technique is often used to simulate granular systems; however by adding further elements that inter-connect the bodies, it can be used to simulate the deformation of a large volume of material. This method has precedent for use in the Earth Sciences and recently, with the increase of available computing power, it has been put to good use simulating the evolution of extensional faults in large scale crustal experiments that involve over half a million individual spherical bodies. An interactive environment that provides high quality rendering is presented, showing that interactivity is key in allowing the intelligent application of visualization methods such as colour-mapping and visibility thresholds in order to extract fault information from a geological DEM. It is also shown that glyph representation alone is not sufficient to provide full insight into the complex three dimensional geometries of the faults found within the model. To overcome this, a novel use of the MetaBall method is described, which results in implicit surface representations of sphere sub-sets. The surfaces produced are shown to provide greater insight into the faults found within the data but also raise questions as to their meaning.

Discrete element modelling using a parallelised physics engine

Discrete Element Modelling (DEM) is a technique used widely throughout science and engineering. It offers a convenient method with which to numerically simulate a system prone to developing discontinuities within its structure. Often the technique gets overlooked as designing and implementing a model on a scale large enough to be worthwhile can be both time consuming and require specialist programming skills. Currently there are a few notable efforts to produce homogenised software to allow researchers to quickly design and run DEMs with in excess of 1 million elements. However, these applications, while open source, are still complex in nature and require significant input from their original publishers in order for them to include new features as a researcher needs them. Recently software libraries notably from the computer gaming and graphics industries, known as physics engines, have emerged. These are designed specifically to calculate the physical movement and interaction of a system of independent rigid bodies. They provide conceptual equivalents of real world constructions with which an approximation of a realistic scenario can be quickly built. This paper presents a method to utilise the most notable of these engines, NVIDIAs PhysX, to produce a parallelised geological DEM capable of supporting in excess of a million elements.

ABSTRACT: Three-Dimensional Numerical Modelling of Eustatic vs Local Controls on Depositional Sequences

A three-dimensional numerical model of sediment transport and deposition in coarsegrained deltas is used to investigate the controls on depositional sequence variability. We consider the stratigraphic response to eustatic sea-level (amplitude and rates) and local controls, such as physiography, sediment supply and local subsidence. The development of key stratal surfaces, stratal geometry and facies stacking patterns show a systematic development with respect to stages in a eustatic sea-level cycle. However, even with constant sediment supply and a simple sinusoidal eustatic sea-level variation many of the features developed in the models are, by their nature, three-dimensional and twodimensional analysis of the model results can lead to erroneous interpretations of the causes of along-strike variability. Local controls generate significant variability in depositional sequence development, including the timing and amount of fluvial incision during relative sea-level fall, and the timing and nature of transgression during rapid phases of relative sea-level rise. The model results suggest that different systems tracts may be coeval and that key stratal surfaces defining and subdividing depositional sequences may be of local extent. Furthermore, the results highlight pitfalls in sequence stratigraphic interpretation and problems in interpreting controlling processes from the preserved stratigraphic product.