Folding and faulting of strain-hardening sedimentary rocks

The question of whether single- or multi-layers of sedimentary rocks will fault or fold when subjected to layer-parallel shortening is investigated by means of the theory of elastic-plastic, strain-hardening materials, which should closely describe the properties of sedimentary rocks at high levels in the Earth's crust. The most attractive feature of the theory is that folding and faulting, intimately related in nature, are different responses of the same idealized material to different conditions.When single-layers of sedimentary rock behave much as strain-hardening materials they are unlikely to fold, rather they tend to fault, because contrasts in elasticity and strength properties of sedimentary rocks are low. Amplifications of folds in such materials are negligible whether contacts between layer and media are bonded or free to slip for single layers of dolomite, limestone, sandstone, or siltstone in media of shale. Multilayers of these same rocks fault rather than fold if contacts are bonded, but they fold readily if contacts between layers are frictionless, or have low yield strengths, for example due to high pore-water pressure. Faults may accompany the folds, occurring where compression is increased in cores of folds. Where there is predominant reverse faulting in sedimentary sequences, there probably were few structural units.     

Opposite senses of fold asymmetry

If the orientation of the principal compressive stress is oblique to layering, viscous multilayers fold in response to the layer-parallel shortening and develop asymmetric interfaces in response to the layer-parallel shear. A theoretical analysis of folding of viscous multilayers with different slip laws at layer contacts shows that the sense of asymmetry of folds is determined largely by the behavior of the layer contacts and the sense of layer-parallel shear during folding.

For a given sense of layer-parallel shear, the sense of asymmetry of folds can be reversed by changing only the behavior of the layer contacts. If the slip rate is linearly proportional to the shear stress at layer contacts, the resistance to slip is the same everywhere along interfaces, and the folds develop the sense of asymmetry of drag folds. If the slip rate is a nonlinear function of the shear stress at layer contacts, however, the resistance to slip varies with position along interfaces, and folds develop the sense of asymmetry of monoclinal kink folds.

For a given variable resistance to slip at layer contacts, the sense of asymmetry depends on the sense and magnitude of the layer-parallel shear and on the thickness-to-wavelength ratio of the multilayer.

For finite multilayers with variable resistance to slip at contacts, an increase in the layer-parallel shear stress decreases the dominant wavelength and increases the amplification factor for the initial perturbation of the interface.

The multilayer consists of linear viscous layers and is confined by thick, viscous media. Resistance to slip at layer contacts is modeled theoretically by a powerlaw relationship between rate of slip and contact shear stress. The equations, derived to 2nd order in the slopes of the interfaces, describe the growth of asymmetric folds from initial, symmetric perturbations.     

Kinematics of fault-bend folding

The concept of bed-duplication folding, a process of folding by stacking of duplicate beds above a thrust ramp, was introduced by John L. Rich in 1934, and such folding has been studied mechanically and geometrically during the last few years.

This paper introduces two kinematical models to bridge between geometrical and mechanical analyses, so results of the two methods of determining the deformations and geometry of bed-duplication folding can be compared. One kinematical model is required for early stages and the other for late stages of bed-duplication folding, but each involves a simple, domainal, velocity distribution. It is remarkable that such simple kinematical models can produce complex geometrical models. The kinematical models clearly produce the type of bed-duplication fold developed by graphical construction and termed “fault-bend fold”. The kinematical models provide new insights into the essence of the type.

The velocity distributions assumed in the kinematical models are similar to those predicted by a first-order, mechanical model for thrust ramps with low slopes (less than about 20 degrees) and zero drag. The fold forms computed from the two sets of models are also similar, so geometrical construction roughly reproduces a simple, low-amplitude bed-duplication fold.

The approximation is poorer for steeper thrust ramps. The upper limit of the kinematical fold. and geometrical construction is 30 degrees and, at that ramp angle, the dip of the distal limb of the fold is twice the dip of the thrust ramp. Results of the mechanical analysis of relatively steep ramps, carried to second-order accuracy, indicate that the 30-degree limit of the ramp angle is an artifact of the geometrical analysis and that the block being thrusted is subjected to general simple shearing. The simple shear is absent in the kinematical models and the geometrical construction. Nevertheless, both the kinematical and mechanical models predict asymmetry of fold limbs.     

Arctic Climate and Water Change: Model and Observation Relevance for Assessment and Adaptation

The Arctic is subject to growing economic and political interest. Meanwhile, its climate and water systems are in rapid transformation. In this paper, we review and extend a set of studies on climate model results, hydro-climatic change, and hydrological monitoring systems. Results indicate that general circulation model (GCM) projections of drainage basin temperature and precipitation have improved between two model generations. However, some inaccuracies remain for precipitation projections. When considering geographical priorities for monitoring or adaptation efforts, our results indicate that future projections by GCMs and recent observations diverge regarding the basins where temperature and precipitation changes currently are the most pronounced and where they will be so in the future. Regarding late twentieth-century discharge changes in major Arctic rivers, data generally show excess of water relative to precipitation changes. This indicates a possible contribution to sea-level rise of river water that was previously stored in permafrost or groundwater. The river contribution to the increasing Arctic Ocean freshwater inflow is similar in magnitude to the separate contribution from glaciers, which underlines the importance of considering all possible sources of freshwater when assessing sea-level change. We further investigate monitoring systems and find a lack of harmonized water chemistry data, which limits the ability to understand the origin and transport of nutrients, carbon and sediment to the sea. To provide adequate information for research and policy, Arctic hydrological and hydrochemical monitoring needs to be extended, better integrated and made more accessible. Further water-focused data and modeling efforts are required to resolve the source of excess discharge in Arctic rivers. Finally, improvements in climate model parameterizations are needed, in particular for precipitation projections.     

An emendation of elastic rebound theory: Main rupture and adjacent belt of right-lateral distortion detected by Viaduct at Kaynaşli, Turkey 12 November 1999 Düzce Earthquake

The fault trace of the 12 November 1999 earthquake in theDüzce-Bolu region in Anatolia crossed the alignment of a 2.4 kmviaduct in Kaynali that had been carefully surveyed. The builders of theviaduct, the ASTALDI-BAYINDIR Co., resurveyed the viaduct after theearthquake. We repeated the survey for approximately one kilometre of theeastern end of the viaduct and obtained essentially identical results. Thoughit was unfortunate that the earthquake damaged the new structure, the piersdid produce a very rare record of ground deformation of an earthquake.In effect, the viaduct was a giant strain gage that yielded reliable data aboutground movement and distortion near a fault. This paper describes thesurvey data and their evaluation leading to convincing evidence that (a) thefault trace must be considered, not as a fault line or plane, but as a faultzone with a finite width and that (b) the structural damage within the zonewas caused, not primarily by ground acceleration, but by ground distortion.Along the right-lateral fault at Kaynali, the fault zone consists ofright-lateral movement at the main trace, a zone of right-lateral distortionnear the trace, bounded by left-lateral distortion. The 12 November 1999event in Turkey, like the ground deformation and fracturing at Landers,California (Johnson et al., 1994, 1996), thus affirmed a forgottenconclusion from the studies by Lawson (1908), Gilbert and Reid (1910)of the 1906 San Francisco earthquake that earthquake ruptures typicallyoccur throughout zones or belts, rather than along linear traces or planes.     

Analysis of faulting in porous sandstones

Faults in porous sandstones occur in three forms: deformation bands about 1-mm thick and tens of m long and across which offsets are a few mm; zones of deformation bands constituted of many closely spaced deformation bands across which offsets are a few cm or dm; and slip surfaces, that is, distinct surfaces within zones of deformation bands across which offsets are a few m to a few tens of m. Deformation bands represent highly localized deformation; analogous localization within a field of homogeneous deformation is theoretically possible in inelastic materials with certain ranges of constitutive parameters. Crushing and consolidation of sandstone within a band cause the material there to become stiffer than the surrounding porous sandstone. A zone of deformation bands behaves mesoscopically much as a stiff inclusion in a soft matrix. According to the constitutive model assumed to investigate the formation of deformation bands, an instability can develop, and strain increments within the zone of deformation bands can become boundlessly large when the far-field stresses reach critical values. This instability is here associated with the formation of slip surfaces.