ALBERT

Description: We study the formation of localized shear zones during the layer-parallel extension of viscous multi-layers using two-dimensional numerical simulations based on the finite-difference method. For power-law viscous layers and a linear viscous embedding medium, the extended multi-layer develops boudins due to necking. For power-law viscous layers embedded in a power-law viscous medium, the extended multi-layer develops first distributed necks, and subsequently a localized shear zone with a vertical offset (with a size of several layer thicknesses) along the multi-layer. During the extension, the deformation style switches from distributed and symmetric necking to localized and asymmetric shearing. A localized shear zone develops in the viscous multi-layer although the rheology is everywhere strain-rate-hardening (power-law stress exponent 〉1) and no material softening and/or energy feedback mechanism (e.g., shear heating combined with a temperature-dependent viscosity) is applied. The shear localization is caused by structural softening because the formation of a localized shear zone decreases the bulk resistance and hence the work required to deform the multi-layer. A localized shear zone forms in the multi-layer when the distance between the stiff layers is approximately equal to or less than the layer thickness. The shear localization was observed in multi-layers with nine and with only three stiff layers.

Description: We have modeled numerically the seismic response of a poroelastic inclusion with properties applicable to an oil reservoir that interacts with an ambient wavefield. The model includes wave-induced fluid flow caused by pressure differences between mesoscopic-scale (i.e., in the order of centimeters to meters) heterogeneities. We used a viscoelastic approximation on the macroscopic scale to implement the attenuation and dispersion resulting from this mesoscopic-scale theory in numerical simulations of wave propagation on the kilometer scale. This upscaling method includes finite-element modeling of wave-induced fluid flow to determine effective seismic properties of the poroelastic media, such as attenuation of P- and S-waves. The fitted, equivalent, viscoelastic behavior is implemented in finite-difference wave propagation simulations. With this two-stage process, we model numerically the quasi-poroelastic wave-propagation on the kilometer scale and study the impact of fluid properties and fluid saturation on the modeled seismic amplitudes. In particular, we addressed the question of whether poroelastic effects within an oil reservoir may be a plausible explanation for low-frequency ambient wavefield modifications observed at oil fields in recent years. Our results indicate that ambient wavefield modification is expected to occur for oil reservoirs exhibiting high attenuation. Whether or not such modifications can be detected in surface recordings, however, will depend on acquisition design and noise mitigation processing as well as site-specific conditions, such as the geologic complexity of the subsurface, the nature of the ambient wavefield, and the amount of surface noise.

Description: We present two-dimensional numerical simulations for shortening a viscoelastoplastic lithosphere to quantify the impact of elasticity on strain localization due to thermal softening. The model conserves energy and mechanical work is converted into heat or stored as elastic strain energy. For a shear modulus G = 10 10 Pa, a prominent lithospheric shear zone forms and elastic energy release increases the localization intensity (strain rate amplification). For G = 5 x 10 10 Pa shear zones still form but deformation is less localized. For G = 10 12 Pa, the lithosphere behaves effectively viscoplastic and no shear zones form during homogeneous thickening. Maximal shearing-related increase of surface heat flux is 15–25 mW m –2 and of temperature at lower crustal depth is ~150 °C, whereby these peak values are transient (0.1–1 My). Elasticity and related energy release can significantly contribute to strain localization and plate-like behaviour of the lithosphere required for plate tectonics.

Description: The elevation of continental interiors over time is demonstrably variable. A major part of change in elevation within the continental interior is likely driven by density changes within the upper mantle and by global mantle convection. For example, upper-mantle flow has been invoked as the cause of Neogene uplift of the interior Rocky Mountains and Colorado Plateau, warping and tilting sediment transport slopes that link to the widespread deposition of gravel units within the Great Plains. These geomorphic and sedimentologic features, however, can also be generated by an increase in runoff, since erosion will promote change in elevation due to isostatic compensation and the loading of the lithosphere by the deposition of sediment. To explore the consequences of change in topography and climate, we use a general length-dependent diffusive sediment transport law to model both erosion and deposition that includes the concentrative effects of river systems. The simplicity of the approach means that we can collapse sediment transport to one dimension and couple erosion and deposition with plate flexure. We find that for a landscape that is gently tilted (slope of order of 10 –3 ), a change in runoff has a minor effect on transport gradient, as sediment transport and associated flexural response maintain topography at a similar elevation. However, there can be a significant change in depositional style when the degree of tilt is altered by, for example, a local change in upper-mantle density. An increase in buoyancy within the upper mantle, which increases slopes, leads to a transient reduction in grain sizes deposited at a fixed location. This behavior is due to a temporary retreat of the zone of erosion into the catchment and a transient increase in accommodation space relative to sediment supply. A reduction in tilt has the opposite effect, the older deposits are eroded, and the erosion-deposition transition rapidly moves down system. There is convincing evidence that the formation of thin and laterally extensive conglomeratic units of the Great Plains was due to a reduced rate of subsidence. Based on the results of our model, we suggest that the deposition of widespread conglomeratic units within continental interiors is generally a consequence of a reduction in slope, as the dynamic support for regions of high topography is reduced.

Description: We present analytical derivations and 2-D numerical simulations that quantify magnitudes of deviatoric stress and tectonic overpressure (i.e. difference between the pressure, or mean stress, and the lithostatic pressure) by relating them to lateral variations in the gravitational potential energy ( GPE ). These predictions of tectonic overpressure and deviatoric stress associated with GPE differences are independent of rock rheology (e.g. viscous or elastic) and rock strength. We consider a simple situation with lowlands and mountains (plateau). We use a numerical two-layer model consisting of a crust with higher Newtonian viscosity than that in the mantle, and also a three-layer model in which the two-layer lithosphere overlies a much less viscous asthenosphere. Our results (1) explain why estimates for the magnitude of stresses in Tibet, previously published by different authors, vary by a factor of two, (2) are applied to test the validity of the thin sheet approximation, (3) show that the magnitude of the depth-integrated tectonic overpressure is equal to the magnitude of the depth-integrated deviatoric stress if depth-integrated shear stresses on vertical and horizontal planes within the lithosphere are negligible (the thin sheet approximation) and (4) show that under thin sheet approximation tectonic overpressure is required to build and support continental plateaus, such as in Tibet or in the Andes, even if the topography and the crustal root are in isostatic equilibrium. Under thin sheet approximation, the magnitude of the depth-integrated tectonic overpressure is equal to the depth-integrated horizontal deviatoric stress, and both are approximately 3.5 x 10 12 N m –1 for Tibet. The horizontal driving force per unit length related to lateral GPE variations around Tibet is composed of the sum of both tectonic overpressure and deviatoric stress, and is approximately 7 x 10 12 N m –1 . This magnitude exceeds previously published estimates for the force per unit length required to fold the Indo-Australian Plate south of India, and hence the uplift of the Tibetan plateau could have folded the Indian Plate. We also discuss the mechanical conditions that are necessary to achieve isostasy, for which the lithostatic pressure is constant at a certain depth. The results show that tectonic overpressure can exist at a certain depth even if all deviatoric stresses are zero at this depth, because this tectonic overpressure is related to horizontal gradients of vertical shear stresses integrated across the entire depth of the lithosphere. The magnitude of the depth-integrated tectonic overpressure of 3.5 x 10 12 N m –1 implies that the pressure estimated from observed mineral assemblages in crustal rocks is likely significantly different from the lithostatic pressure, and pressure recorded by crustal rocks is not directly related to depth. In case of significant weakening of the entire lithosphere by any mechanism our analytical and numerical studies provide a simple estimation of tectonic overpressure via variations in GPE .

Description: Viscous folding in mechanically heterogeneous layers is modelled numerically in two dimensions for linear and power-law viscous fluids. Viscosity heterogeneities are expressed as circular-shaped variations of the effective viscosity inside and outside the layers. The layers are initially perfectly flat and are shortened in the layer-parallel direction. The viscosity heterogeneities cause a perturbation of the velocity field from the applied bulk pure shear, which perturb geometrically the initially flat-layer interfaces from the first numerical time step. This geometrical perturbation triggers interfacial instabilities, resulting in high-amplitude folding. We compare simulations with heterogeneities with corresponding simulations in which the heterogeneities are removed after the first time step, and, hence, only the initial small geometrical perturbations control wavelength selection and high-amplitude folding. Results for folding in heterogeneous and homogeneous layers are similar, showing that viscosity heterogeneities have a minor to moderate impact on fold wavelength selection and high-amplitude folding. Our results indicate that the interfacial instability is the controlling process for the generation of buckle folds in heterogeneous rock layers. Therefore, existing analytical and numerical solutions for folding in homogeneous layers, in which folding was triggered by geometrical perturbations, are useful and applicable to study folding in natural, heterogeneous rock layers.

Description: 〈p〉Viscous folding in mechanically heterogeneous layers is modelled numerically in two dimensions for linear and power-law viscous fluids. Viscosity heterogeneities are expressed as circular-shaped variations of the effective viscosity inside and outside the layers. The layers are initially perfectly flat and are shortened in the layer-parallel direction. The viscosity heterogeneities cause a perturbation of the velocity field from the applied bulk pure shear, which perturb geometrically the initially flat-layer interfaces from the first numerical time step. This geometrical perturbation triggers interfacial instabilities, resulting in high-amplitude folding. We compare simulations with heterogeneities with corresponding simulations in which the heterogeneities are removed after the first time step, and, hence, only the initial small geometrical perturbations control wavelength selection and high-amplitude folding. Results for folding in heterogeneous and homogeneous layers are similar, showing that viscosity heterogeneities have a minor to moderate impact on fold wavelength selection and high-amplitude folding. Our results indicate that the interfacial instability is the controlling process for the generation of buckle folds in heterogeneous rock layers. Therefore, existing analytical and numerical solutions for folding in homogeneous layers, in which folding was triggered by geometrical perturbations, are useful and applicable to study folding in natural, heterogeneous rock layers.〈/p〉

Description: The mechanisms that result in the formation of high-pressure (HP) and ultrahigh-pressure (UHP) rocks are controversial. The usual interpretation assumes that pressure is close to lithostatic, petrological pressure estimates can be transferred to depth, and (U)HP rocks have been exhumed from great depth. An alternative explanation is that pressure can be larger than lithostatic, particularly in continental collision zones, and (U)HP rocks could thus have formed at shallower depths. To better understand the mechanical feasibility of these hypotheses, we performed thermomechanical numerical simulations of a typical subduction and collision scenario. If the subducting crust is laterally homogeneous and has small effective friction angles (and is thus weak), we reproduce earlier findings that 〈20% deviation of lithostatic pressure occurs within a subduction channel. However, many orogenies involve rocks that are dry and strong, and the crust is mechanically heterogeneous. If these factors are taken into account, simulations show that pressures can be significantly larger than lithostatic within nappe-size, mechanically strong crustal units, or within a strong lower crust, as a result of tectonic deformation. Systematic simulations show that these effects are most pronounced at the base of the crust (at ~40 km), where pressures can reach 2–3 GPa (therefore within the coesite stability field) for millions of years. These pressures are often released rapidly during ongoing deformation. Relating metamorphic pressure estimates to depth might thus be problematic in mechanically heterogeneous crustal rock units that appear to have been exhumed in an ultrafast manner.

Description: We use a three-dimensional finite element model for viscous flow to investigate the lateral linkage mode of two initially isolated fold segments. Depending on the separation distance between the fold hinge lines, four different fold linkage scenarios are observed. Linear linkage yields a sub-cylindrical fold with a saddle at the location where the two initial folds linked. Oblique linkage produces a fold resembling a type II refold structure. Oblique–no linkage results in two curved folds with fold axes plunging in opposite directions. Linear–no linkage yields a fold train of two separate subcylindrical folds with fold axes plunging in opposite directions. Representative numerical models for detachment and matrix folding for both power-law and linear viscous rheologies exhibit the same four fold linkage modes. The transition from linkage to no linkage occurs when the fold separation between the initially isolated folds is slightly larger than one-half of the low-amplitude fold wavelength. We demonstrate a natural example of lateral fold linkage from the Kurdistan region of Iraq, and point out the economic interest of saddle points linking the initially isolated fold segments.