Lagrange multiplier-based domain decomposition methods for a non-linear sedimentary basin problem

We present two Lagrange multiplier-based domain decomposition methods for solving iteratively a non-linear sedimentary basin problem. Both methods are Uzawa-type algorithms derived from saddle point equations of Lagrangian and augmented Lagrangian functionals. Numerical experiments show that both methods are scalable with respect to the mesh size.     

Holocene vegetation change in northernmost Fennoscandia and the impact on prehistoric foragers 12 000–2000 cal. a BP – A review

While single pollen records are widely used in reconstructing the environment for nearby prehistoric settlements, they are less helpful when addressing large‐scale issues of variation in human settlement patterns. In order to assess the impact of vegetation change on regional prehistoric settlement and subsistence patterns in an ecotone sensitive area, we inferred the general change in main vegetation types based on palaeobotanical investigations from across northernmost Fennoscandia. Tundra vegetation was predominant during the Lateglacial and earliest parts of the Holocene. Maritime birch forests rich in ferns started to expand c. 11 000 cal. a BP and became dominant from 10 000 cal. a BP. Pine expanded from the NE of the investigation area and pine‐birch forest dominated in the inland around 8000 cal. a BP. A gradual degeneration of forest towards more open birch woodland started c. 6000 cal. a BP with the most marked change around 3500 cal. a BP. Along the northern outer coast, this eventually led to open heathland. Comparison with the archaeological setting suggests a general correlation between low forest cover and extensive mobility patterns, while widespread and varied forest cover appear to have led to a more sedentary way of life. The background for this is arguably that the forested landscapes hosted a larger diversity of resources within a shorter foraging distance, while areas and periods with low forest cover required longer travels to obtain the desired prey and materials.     

Submarine landslides caused by seamounts entering accretionary wedge systems

Seamounts entering active subduction zone trenches initially collide with the frontal sedimentary accretionary wedges resulting in severe deformation of the overriding plate. A typical feature of this deformation is the occurrence of submarine landslides due to gravitational instabilities. Such landslides have been reported from the Middle America and Hikurangi trenches and potentially generate tsunami waves. Yet, the dynamics of accretionary wedges during seamount indentation, and landsliding as a mechanical response in particular, have not been investigated qualitatively. Here, I use 3D high‐resolution numerical experiments to model the collision of conical and flat‐topped seamounts into accreting sedimentary sequences. Results show that the topographical evolution of an accretionary wedge mainly depends on the volume of the entering seamount and not on its height. Submarine landslides occur only if seamounts are not completely buried by the sedimentary sequence, and the volume of the avalanche is roughly correlated with the seamount volume overtopping the incoming sediments.     

Allogenic and autogenic processes combined in the formation of shallow-water carbonate sequences (Middle Berriasian,Swiss and French Jura Mountains)

Sediment production and accumulation on shallow carbonate platforms are controlled by allogenic, externally controlled processes (such as sea level, climate, and/or platform-wide subsidence patterns) as well as by autogenic factors that are inherent to the sedimentary system (such as lateral migration of sediment bodies). The challenge is to determine how and in which proportion these processes interacted to create the observed sedimentary record. Here, a case study of Middle Berriasian, shallow-marine carbonates of the Swiss and French Jura Mountains is presented. Based on vertical facies evolution and bedding surfaces, different orders of depositional sequences (elementary, small-scale, medium-scale) have been identified in the studied sections. The hierarchical stacking pattern of these sequences and the time span represented by the investigated interval imply that eustatic sea-level fluctuations in the Milankovitch frequency band were an important controlling factor. The small-scale and medium-scale sequences relate to the 100 and 400-kyr orbital eccentricity cycles, respectively. The elementary sequences are attributed to the 20-kyr precession cycle. Differential subsidence additionally produced accommodation changes. The present study focuses on one specific small-scale sequence situated at the base of the transgressive systems tract of large-scale sequence Be4, which is identified also in other European basins. This small-scale sequence has been logged in detail at eight different outcrops in the Jura Mountains. Detailed facies analysis reveals that different depositional environments (tidal flats, internal lagoons, open lagoons, carbonate sand shoals) were juxtaposed and evolved through time, often shifting position on the platform. The boundaries of the small-scale (100-kyr) sequence can be followed over the entire study area and thus must have formed through predominantly allogenic processes (eustatic sea-level fall, the effect of which was locally modified by differential subsidence). In two sections, five well-developed elementary sequences constitute the small-scale sequence. In the other sections, the identification of elementary sequences often is difficult because sedimentation was dominated by autogenic processes that overruled the influence of sea-level fluctuations. In low-energy, tidal-flat and internal-lagoonal settings, orbitally induced sea-level changes were recorded more faithfully, while high-energy shoals were mainly submitted to autogenic processes and the allogenic signal is masked. Consequently, the studied Jura platform experienced a combination of auto- and allogenic processes, which created a complex facies mosaic and a complex stacking of depositional sequences. Nevertheless, the 100-kyr orbital signal was strong enough to create correlatable sequence boundaries. Within a 100-kyr sequence, however, the unambiguous definition of sequences related to the 20-kyr orbital cycle is often difficult and the prediction of their lateral or vertical facies evolution impossible.     

Environmental geochemistry of an active Hg mine in Xunyang,Shaanxi Province,China

The Xunyang Hg mine (XMM) situated in Shaanxi Province is an active Hg mine in China. Gaseous elemental Hg (GEM) concentrations in ambient air were determined to evaluate its distribution pattern as a consequence of the active mining and retorting in the region. Total Hg (HgT) and methylmercury (MeHg) concentrations in riparian soil, sediment and rice grain samples (polished) as well as Hg speciation in surface water samples were measured to show local dispersion of Hg contamination. As expected, elevated concentrations of GEM were found, ranging from 7.4 to 410 ng m⁻³. High concentrations of HgT and MeHg were also obtained in riparian soils, ranged from 5.4 to 120 mg kg⁻¹ and 1.2 to 11 μg kg⁻¹, respectively. Concentrations of HgT and MeHg in sediment samples varied widely from 0.048 to 1600 mg kg⁻¹ and 1.0 to 39 μg kg⁻¹, respectively. Surface water samples showed elevated HgT concentrations, ranging from 6.2 to 23,500 ng L⁻¹, but low MeHg concentrations, ranging from 0.022 to 3.7 ng L⁻¹. Rice samples exhibited high concentrations of 50–200 μg kg⁻¹ in HgT and of 8.2–80 μg kg⁻¹ in MeHg. The spatial distribution patterns of Hg speciation in the local environmental compartments suggest that the XMM is the source of Hg contaminations in the study area.     

Effect of fluid pressure distribution on the structural evolution of accretionary wedges

Numerical experiments on evolving accretionary wedges usually implement predefined weak basal décollements and constant strength parameters for overlying compressed sequences, although fluid pressure ratio, and therefore brittle strength, can vary strongly in sedimentary basins. A two‐dimensional finite difference model with a visco‐elasto‐plastic rheology is used to investigate the influence of different simplified fluid pressure ratio distributions on the structural evolution of accretionary wedge systems. Results show that a linear increase in fluid pressure ratio towards the base leads to toeward‐verging thrust sheets and underplating of strata, while simulations with a predefined décollement form conjugate shear zones supporting box‐fold‐type frontal accretion. Surface tapers are in agreement with the critical wedge theory, which here is modified for cases of varying fluid pressure ratio. Furthermore, the numerical results resemble findings from natural examples of accretionary wedges.     

Probabilistic model for eruptions and associated flood events in the Katla caldera,Iceland

Eruptions in the subglacial Katla caldera, South Iceland, release catastrophic jokulhlaups (meltwater floods). The ice surface topography divides the caldera into three drainage sectors (Ko, So and En sectors) that drain onto Myrdalssandur, Solheimasandur and Markarfljot plains, respectively. In historical times, floods from the Ko sector have been dominant, with only two recorded So events. Geological records indicate that floods from the En sector occur every 500–800 years. A probabilistic model for an eruption is formulated in general terms by a stochastic parameter that simulates a series giving the time interval in years between two consecutive events. The model also contains a Markovian matrix that controls the location of the event and thereby what watercourse is hit by the flood. A record of Katla eruptions since the 8th and the 9th century a.d., and geological information of volcanogenic floods towards the west over the last 8,000 years is used to calibrate the model. The model is then used to find the probabilities for floods from the three sectors: Ko, So and En. The simulations predict that the most probable eruption interval for the En sector and the So sector is several times smaller than the average time interval, implying infrequent periods of high activity in these sectors. A correlation is found between the magnitude of eruptions and the following time intervals. Using the statistical approach and considering this magnitude–time interval correlation, the probability of an eruption in Katla volcano is considered to be 20% within the next 10 years. This compares to a probability of 93% if only a simple average is considered. These probabilities do not take account of long-term eruption precursors and should therefore be regarded as minimum values.     

Melt water driven stream and groundwater stage fluctuations on a glacier forefield (Dammagletscher,Switzerland)

In many mountain regions, large land areas with heterogeneous soils have become ice‐free with the ongoing glacier retreat. On these recently formed proglacial fields, the melt of the remaining glaciers typically drives pronounced diurnal stream level fluctuations that propagate into the riparian zone. This behaviour was measured on the Damma glacier forefield in central Switzerland with stage recorders in the stream and groundwater monitoring wells along four transects. In spite of the large groundwater stage variations, radon measurements in the near‐stream riparian zone indicate that there is little mixing between stream water and groundwater on daily time scales. At all four transects, including both losing and gaining reaches, the groundwater level fluctuations lagged the stream stage variations and were often damped with distance from the stream. Similar behaviours have been modelled using the diffusion equation in coastal regions influenced by tidal sea level variations. We thus tested the ability of such a model to predict groundwater level fluctuations in proglacial fields. The model reproduced several key features of the observed fluctuations at three of four locations, although discrepancies also arise due to non representative input data and model simplifications. Nevertheless, calibration of the model for the individual transects yielded realistic estimates of hydraulic diffusivities between the stream and groundwater monitoring wells. We conclude that studying diurnal groundwater fluctuations can provide important information about the subsurface hydrology of alpine watersheds dominated by glacier melt. Copyright © 2012 John Wiley & Sons, Ltd.     

Carbon emission trading and carbon taxes under uncertainties

The idea of market-based carbon emission trading and carbon taxes is gaining in popularity as a global climate change policy instrument. However, these mechanisms might not necessarily have a positive outcome unless their value reflects socioeconomic and environmental impacts and regulations. Moreover, the fact that they have various inherent exogenous and endogenous uncertainties raises serious concerns about their ability to reduce emissions in a cost-effective way. This paper aims to introduce a simple stochastic model that allows the robustness of economic mechanisms for emission reduction under multiple natural and human-related uncertainties to be analyzed. Unlike standard equilibrium state analysis, the model shows that the explicit introduction of uncertainties regarding emissions, abatement costs, and equilibrium states makes it almost impossible for existing market-based trading and carbon taxes to be environmentally safe and cost-effective. Here we propose a computerized multi-agent trading model. This can be viewed as a prototype to simulate an emission trading market that is regulated in a decentralized way. We argue that a market of this type is better equipped to deal with long-term emission reductions, their direct regulation, irreversibility, and “lock-in” equilibria.