3D free‐boundary conditions for coordinate‐transform finite‐difference seismic modelling

New alternative formulations of exact boundary conditions for arbitrary three-dimensional (3D) free-surface topographies on seismic media have been derived. They are shown to be equivalent to previously published formulations, thereby verifying the validity of each set of formulations. The top of a curved grid represents the free-surface topography while the interior of the grid represents the physical medium. We assume the velocity–stress version of the viscoelastic wave equations to be valid in this grid before transforming the equations to a rectangular grid. In order to perform the numerical discretization we apply the latter version of the equations for seismic wave propagation simulation in the medium. The numerical discretization of the free-surface topography boundary conditions by second-order finite differences (FDs) is shown, as well as the spatially unconditional stability of the resulting system of equations. The FD order is increased by two for each point away from the free surface up to eight, which is the order used in the interior. We use staggered grids in both space and time and the second-order leap-frog and Crank– Nicholson methods for wavefield time propagation. An application using parameters typical of teleseismic earthquakes and explosions is presented using a 200 × 100 km² area of real topography from southwestern Norway over a homogeneous medium. A dipping plane wave simulates a teleseismic P-wave incident on the surface topography. Results show conversion from P- to Rg- (short period fundamental mode Rayleigh) waves in the steepest and/or roughest topography, as well as attenuated waves in valleys and fjords. The codes are parallelized for simulation on fast supercomputers and PC-clusters to model high frequencies and/or large areas.     

Long waves in directional seas

In recent years the group-induced long waves have received an enhanced degree of attention. Especially in nearshore regions, the long waves can be of considerable height, and consequently the influence on harbour resonance, on the operation of ship terminals, on moorings of large vessels, etc. is obviously very important. It is the grouping of natural wave fields that generates the long waves, and they are proportional to the square of the short-wave height. Therefore, the expressions for the long-wave elevations can be found to include the short-wave components of the wave field and a second-order transfer function. This function is presented in a diagram with dimensionless parameters. For practical purposes a formula for rough estimate of the long-wave height is proposed.The second-order equations show that the long waves are determined by the difference of the wave-number vectors of the short waves. This is shown to imply that the spread of the long waves is larger than that of the short waves, and that the wave lengths of the long waves are dependent on the short-wave spread. Hereby it is possible to change the long-wave lengths, which seems to be a quality of great practical importance.The long waves are also expressed in spectral terms. That is, a formula for the directional long-wave spectrum is shown to comprise the transfer function squared and the short-wave amplitudes and phases.     

Decrease in Danish semi-natural grassland – a social construct or a real-world change?

During the past century, the western hemisphere has seen a general trend of agricultural expansion on the behalf of semi-natural habitat types, such as heathlands and meadows. This has been documented in numerous studies of land use change. This trend is reflected in today’s European rural landscapes, which are dominated by intensive agriculture. However, many of these studies are based on cartographical sources, such as topographical and thematic maps, and thus prone to uncertainties regarding classification systems over time, variations in definitions of land use categories and lacking documentations of land use definitions. For this study, we conducted two change detection studies, covering the same four study areas in Denmark. The first study was based on topographic maps, and indicates a strong decline in the amount of semi-natural grassland (SNG). This was contrasted by the second study, which was based on an interpretation of aerial photos, and which indicated a much less pronounced reduction of SNGs. Year to year comparisons of these two analyses also revealed large discrepancies in the coverage of SNGs. Our results indicate that change detection studies must account for uncertainties in classifications and results should be interpreted with caution.     

Stable carbon‐isotope record of shallow‐marine evaporative epicratonic basin carbonates,Ordovician Williston Basin,North America

Secular variations in stable carbon‐isotope values of marine carbonates are used widely to correlate successions that lack high‐resolution index fossils. Various environmental processes, however, commonly may affect and alter the primary marine carbon‐isotope signal in shallow epicratonic basins. This study focuses on the marine carbon‐isotope record from the carbonate–evaporite succession of the upper Katian (Upper Ordovician) Red River Formation of the shallow epicratonic Williston Basin, USA. It documents the carbon‐isotope signal between the two major Ordovician positive shifts in δ¹³C, the early Katian Guttenberg and the Hirnantian excursions. Eight δ¹³C stages are identified based on positive excursions, shifts from positive to negative values and relatively uniform δ¹³C_carb values. A correlation between carbon‐isotope trends and the relative sea‐level changes based on gross facies stacking patterns shows no clear relation. Based on the available biostratigraphy and δ¹³C trends, the studied Williston Basin curves are tied to the isotope curves from the North American Midcontinent, Québec (Anticosti Island) and Estonia, which confirm the Late Katian age (Aphelognathus divergens Conodont Zone) of the upper Red River Formation. The differences in the δ¹³C overall trend and absolute values, coupled with the petrographic and cathodoluminescence evidence, suggest that the carbon‐isotope record has been affected by the syndepositional environmental processes in the shallow and periodically isolated Williston Basin, and stabilized by later burial diagenesis under reducing conditions and the presence of isotopically more negative fluids.     

The Importance of Microbial Iron Sulfide Oxidation for Nitrate Depletion in Anoxic Danish Sediments

Nitrate (NO₃ ^?) reduction processes are important for depleting the NO₃ ^? load from agricultural source areas before the discharge water reaches surface waters or groundwater aquifers. In this study, we experimentally demonstrate the co-occurrence of microbial iron sulfide oxidation by NO₃ ^? (MISON) and other NO₃ ^?-depleting processes in a range of contrasting sediment types: sandy groundwater aquifer, non-managed minerotrophic freshwater peat and two brackish muddy sediments. Approximately 1/3 of the net NO₃ ^? reduction was caused by MISON in three of the four environments despite the presence of organic carbon in the sediment. An apparent salinity limitation to MISON was observed in the most brackish environment. Addition of high surface area synthetically precipitated iron sulfide (FeS _x ) to the aquifer sediment with the lowest natural FeS _x reactivity increased both the relative fraction of NO₃ ^? reduction linked to MISON from approximately 30–100 % and the absolute rates by a factor of 17, showing that the potential for MISON-related NO₃ ^? reduction is environmentally significant and rate limited by the availability of reactive FeS _x .     

The depositional architecture and facies variability of shelf deltas in the Eocene Battfjellet Formation,Nathorst Land,Spitsbergen

Deltas are commonly classified according to their plan‐view morphology as either river‐dominated, tide‐dominated or wave‐dominated. However, most deltas form under the mixed influence of these processes, commonly with laterally varying process regimes. It has also become clear that there is a mismatch between the plan‐view morphology and internal facies composition in some deltas. Combined outcrop and subsurface data from the Eocene Battfjellet Formation, Spitsbergen, provide an example of ancient shelf deltas that formed under mixed influence. Internally, these shelf deltas are characterized by wave‐dominated facies that are normally associated with strike‐extensive, nearly linear shoreline sandstones. However, the formation comprises partially overlapping sandstone bodies of limited lateral extent (<20 km in any direction). This stacking pattern is attributed to frequent autogenic lobe switching that caused localized and rapid transgressions. Such processes typify fluvial‐dominated deltas and occur less commonly in wave‐dominated ones. Thus, there is an apparent mismatch between inferred plan‐view morphology and internal facies composition. It is argued that the Battfjellet deltas were flood‐dominated and prograded mainly during periods of high fluvial discharge. However, reworking of the fluvial‐flood facies by fair‐weather and storm waves, as well as longshore currents, resulted in a wave‐dominated facies character. Delta lobes undergoing auto‐retreat were particularly prone to reworking by basinal processes, including tidal currents. It is suggested that repeated delta progradation from inner shelf settings towards the outer shelf and shelf edge was aided by high sediment supply rather than relative falls in sea‐level as previously suggested. This interpretation is supported by: (i) the lack of major facies dislocations and extensive sub‐aerial unconformities; and (ii) an overall relative rise in sea‐level as evidenced by an overall low‐angle (0·8 to 1·2°) ascending shoreline trajectory. The latter results from the combined effect of basin subsidence, eustatic highstand and sediment compaction.     

The Emergence of an Environmental Cartography in Denmark

Within the history of cartography, relatively little attention has been devoted to the study of the growing body of maps and spatial data focusing on environmental issues. This is rather surprising, considering the importance of this type of cartography in the handling of the complex environmental problems of modern society. This paper analyses the development of thematic maps and spatial data focusing on the terrestrial environment of Danish landscapes. The paper is introduced with a review of the concept of environmental cartography, followed by a historical analysis of the development of environmental mapping in Denmark. Results suggest that there has been a change in the content and aim of environmental cartography in the twentieth century, from an initial focus on mapping potentials for land use improvement and optimization of the economic outputs from engagement with terrestrial ecosystems, to a focus on monitoring ecosystems and regulation of human intervention. Finally, the usefulness of the concept environmental cartography to frame analytical work dealing with the still increasing number of maps produced for environmental purposes within the history of cartography, is evaluated.     

By northern lights: on the making of geography in Sweden– by Anne Buttimer and Tom Mels

Statement   The Editors do not necessarily agree with the statements contained in the book reviews, and neither they nor the RGS-IBG assume responsibility for the reviewers' assessments of the books that they evaluate.     

Modelling the dynamics of snow cover, soil frost and surface ice in Norwegian grasslands

Studying the winter survival of forage grasses under a changing climate requires models that can simulate the dynamics of soil conditions at low temperatures. We developed a simple model that simulates depth of snow cover, the lower frost boundary of the soil and the freezing of surface puddles. We calibrated the model against independent data from four locations in Norway, capturing climatic variation from south to north (Arctic) and from coastal to inland areas. We parameterized the model by means of Bayesian calibration, and identified the least important model parameters using the sensitivity analysis method of Morris. Verification of the model suggests that the results are reasonable. Because of the simple model structure, some overestimation occurs in snow and frost depth. Both the calibration and the sensitivity analysis suggested that the snow cover module could be simplified with respect to snowmelt and liquid water content. The soil frost module should be kept unchanged, whereas the surface ice module should be changed when more detailed topographical data become available, such as better estimates of the fraction of the land area where puddles may form.