Effect of grain scale alignment on seismic anisotropy and reflectivity of shales

The elastic properties and anisotropy of shales are strongly influenced by the degree of alignment of the grain scale texture. In general, an orientation distribution function (ODF) can be used to describe this alignment, which, in practice, can be characterized by two Legendre coefficients. We discuss various statistical ODFs that define the alignment by spreading from a mean value; in particular, the Gaussian, Fisher and Bingham distributions. We compare the statistical models with an ODF resulting from pure vertical compaction (no shear strain) of a sediment. The compaction ODF may be used to estimate how the elastic properties and anisotropy evolve due to burial of clayey sediments. Our study shows that the three statistical ODFs produce almost identical correspondence between the two Legendre coefficients as a function of the spreading parameter, so that the spreading parameter of one ODF can be converted to the spreading parameter of another ODF. In most cases it is then sufficient to apply the spreading parameter for the ODF instead of the two Legendre coefficients. The effect of compaction on the ODF gives a slightly different correspondence between the two Legendre coefficients from that for the other models. In principle, this opens up the possibility of distinguishing anisotropy effects due to compaction from those due to other processes. We also study reflection amplitudes versus angle of incidence (AVA) for all wave modes, where shales having various ODFs overlie an isotropic medium. The AVA responses are modelled using both exact and approximation formulae, and their intercepts and gradients are compared. The modelling shows that the S‐wave velocity is sensitive to any perturbation in the spreading parameter, while the P‐wave velocity becomes increasingly sensitive to a perturbation of a less ordered system. Similar observations are found for the AVA of the P‐P and P‐SV waves. Modelling indicates that a combined use of the amplitude versus offset of P‐P and P‐SV reflected waves may reveal certain grain scale alignment properties of shale‐like rocks.     

2D finite-difference viscoelastic wave modelling including surface topography

We have pursued two-dimensional (2D) finite-difference (FD) modelling of seismic scattering from free-surface topography. Exact free-surface boundary conditions for the particle velocities have been derived for arbitrary 2D topographies. The boundary conditions are combined with a velocity–stress formulation of the full viscoelastic wave equations. A curved grid represents the physical medium and its upper boundary represents the free-surface topography. The wave equations are numerically discretized by an eighth-order FD method on a staggered grid in space, and a leap-frog technique and the Crank–Nicholson method in time.
In order to demonstrate the capabilities of the surface topography modelling technique, we simulate incident point sources with a sinusoidal topography in seismic media of increasing complexities. We present results using parameters typical of exploration surveys with topography and heterogeneous media. Topography on homogeneous media is shown to generate significant scattering. We show additional effects of layering in the medium, with and without randomization, using a von Kármán realization of apparent anisotropy. Synthetic snapshots and seismograms indicate that prominent surface topography can cause back-scattering, wave conversions and complex wave patterns which are usually discussed in terms of inter-crust heterogeneities.     

A Bayesian hierarchical spatio-temporal model for significant wave height in the North Atlantic

Bad weather and rough seas continue to be a major cause for ship losses and is thus a significant contributor to the risk to maritime transportation. This stresses the importance of taking severe sea state conditions adequately into account in ship design and operation. Hence, there is a need for appropriate stochastic models describing the variability of sea states, taking into account long-term trends related to climate change. Various stochastic models of significant wave height are reported in the literature, but most are based on point measurements without considering spatial variations. As far as the authors are aware, no model of significant wave height to date exploits the flexible framework of Bayesian hierarchical space-time models. This framework allows modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet at the same time remains intuitive and easily interpreted. This paper presents a Bayesian hierarchical space-time model for significant wave height. The model has been fitted by significant wave height data for an area in the North Atlantic ocean. The different components of the model will be outlined, and the results from applying the model to monthly and daily data will be discussed. Different model alternatives have been tried and long-term trends in the data have been identified for all model alternatives. Overall, these trends are in reasonable agreement and also agree fairly well with previous studies. Furthermore, a discussion of possible extensions to the model, e.g. incorporating regression terms with relevant meteorological data will be presented.     

Seismic on floating ice: data acquisition versus flexural wave noise

Geophysical surveying of the Arctic will become increasingly important in future prospecting and monitoring of the terrestrial and adjacent areas in this hemisphere. Seismic data acquired on floating ice are hampered with extensive noise due to ice vibrations related to highly dispersive ice flexural waves generated by the seismic source. Several experiments have been conducted on floating ice in van Mijenfjorden in Svalbard in the Norwegian Arctic to specifically analyse the extent of flexural waves recorded with various seismic receivers and sources deployed both on top of ice and in the water below. The data show that flexural waves are severely damped at 5 m or deeper below the ice and hydrophone data suffer less from these vibrations compared with data recorded on the ice. Aliasing of single receiver hydrophone data can to some extent be suppressed using an in-line line source of detonating cord. Experiments on ice on shallow water show prominent guided wave modes often referred to as Scholte waves propagating along the seabed. In this case, both flexural and Scholte waves interfere and make a complicated pattern of coherent noise. On shallow water, the positioning and type of the seismic source must be evaluated with respect to the coherent noise generated by these waves. Geophone strings of 25 m effectively suppress both flexural and Scholte waves due to their relative short wavelengths. An airgun generates relative more low-frequency energy than a surface source of detonating cord. Accordingly, seismic mapping of deep seismic horizons seem to be best achieved using geophone strings of such length and an airgun source. For shallow targets, the use of hydrophones in combination with detonating cord is an appropriate solution. Seismic surveying in the Arctic always have to follow environmental restrictions of not disturbing or harming wildlife and not causing permanent footprints into the vulnerable tundra, which implies that the choice of seismic acquisition strategy might occur as a trade-off between optimum data quality and environmental constraints.     

Sedimentation in arctic proglacial lakes: Mittivakkat Glacier,south‐east Greenland

Several sediment cores were collected from two proglacial lakes in the vicinity of Mittivakkat Glacier, south‐east Greenland, in order to determine sedimentation rates, estimate sediment yields and identify the dominant sources of the lacustrine sediment. The presence of varves in the ice‐dammed Icefall Lake enabled sedimentation rates to be estimated using a combination of X‐ray photography and down‐core variations in ¹³⁷Cs activity. Sedimentation rates for individual cores ranged between 0·52 and 1·06 g cm⁻² year⁻¹, and the average sedimentation rate was estimated to be 0·79 g cm⁻² year⁻¹. Despite considerable down‐core variability in annual sedimentation rates, there is no significant trend over the period 1970 to 1994. After correcting for autochthonous organic matter content and trap efficiency, the mean fine‐grained minerogenic sediment yield from the 3·8 km² basin contributing to the lake was estimated to be 327 t km⁻² year⁻¹. Cores were also collected from the topset beds of two small deltas in Icefall Lake. The deposition of coarse‐grained sediment on the delta surface was estimated to total in excess of 15 cm over the last c. 40 years. In the larger Lake Kuutuaq, which is located about 5 km from the glacier front and for which the glacier represents a smaller proportion of the contributing catchment, sedimentation rates determined for six cores collected from the centre of the lake, based on their ¹³⁷Cs depth profiles, were estimated to range between 0·05 and 0·11 g cm⁻² year⁻¹, and the average was 0·08 g cm⁻² year⁻¹. The longer‐term (c. 100–150 years) average sedimentation rate for one of the cores, estimated from its unsupported ²¹⁰Pb profile, was 0·10–0·13 g cm⁻² year⁻¹, suggesting that sedimentation rates in this lake have been essentially constant over the last c. 100–150 years. The average fine‐grained sediment yield from the 32·4 km² catchment contributing to the lake was estimated to be 13 t km⁻² year⁻¹. The ¹³⁷Cs depth profiles for cores collected from the topset beds of the delta of Lake Kuutuaq indicate that in excess of 27 cm of coarse‐grained sediment had accumulated on the delta surface over the last approximately 40 years. Caesium‐137 concentrations associated with the most recently deposited (uppermost) fine‐grained sediment in both Icefall Lake and Lake Kuutuaq were similar to those measured in fine‐grained sediment collected from steep slopes in the immediate proglacial zone, suggesting that this material, rather than contemporary glacial debris, is the most likely source of the sediment deposited in the lakes. This finding is confirmed by the ¹³⁷Cs concentrations associated with suspended sediment collected from the Mittivakkat stream, which are very similar to those for proglacial material. Copyright © 2000 John Wiley & Sons, Ltd.     

Open-source MATLAB implementation of consistent discretisations on complex grids

Accurate geological modelling of features such as faults, fractures or erosion requires grids that are flexible with respect to geometry. Such grids generally contain polyhedral cells and complex grid-cell connectivities. The grid representation for polyhedral grids in turn affects the efficient implementation of numerical methods for subsurface flow simulations. It is well known that conventional two-point flux-approximation methods are only consistent for K-orthogonal grids and will, therefore, not converge in the general case. In recent years, there has been significant research into consistent and convergent methods, including mixed, multipoint and mimetic discretisation methods. Likewise, the so-called multiscale methods based upon hierarchically coarsened grids have received a lot of attention. The paper does not propose novel mathematical methods but instead presents an open-source Matlab? toolkit that can be used as an efficient test platform for (new) discretisation and solution methods in reservoir simulation. The aim of the toolkit is to support reproducible research and simplify the development, verification and validation and testing and comparison of new discretisation and solution methods on general unstructured grids, including in particular corner point and 2.5D PEBI grids. The toolkit consists of a set of data structures and routines for creating, manipulating and visualising petrophysical data, fluid models and (unstructured) grids, including support for industry standard input formats, as well as routines for computing single and multiphase (incompressible) flow. We review key features of the toolkit and discuss a generic mimetic formulation that includes many known discretisation methods, including both the standard two-point method as well as consistent and convergent multipoint and mimetic methods. Apart from the core routines and data structures, the toolkit contains add-on modules that implement more advanced solvers and functionality. Herein, we show examples of multiscale methods and adjoint methods for use in optimisation of rates and placement of wells.     

Materialevandringen og Sedimentationen i Karlsgårde Sø og dens tilløb

Karlsgårde Hydroelectric Power Station in SW Jylland had troubles with sedimentation in reservoir and canals. The extent of it has been measured and, throughout one year, monthly measurements were made of the bed load transport and of suspended load transport in the rivers flowing to the power station. A relation between discharge and bed load transport as well as between discharge and suspended load transport has been calculated. The amount of material transported during an “average year” has been found by means of duration curves. Some of the applied methods are described. The bed load transport was measured by various methods a.o. by measurement of the downstream advance of the bedforms. Fluorescent- coloured sand was used as tracer material. Its migration gave a qualitative impression of the intensity of the material transport which proved to be in good accordance with the other results. However, this method is too laborious for a quantitative determination of sediment transport.     

Meteorological observations 2005 and in a longer perspective at the Sermilik Station,Ammassalik Island,Southeast Greenland

Geografisk Tidsskrift, Danish Journal of Geography 107(2):59–68, 2007

Meteorological stations have been in operation since 1993 at Sermilik (65°40'N, 38°10'W), Ammassalik Island, southeast Greenland. This note presents meteorological observations for the year 2005 from the two meteorological stations: Station Nunatak (515 m a.s.l.) and Station Coast (25 m a.s.l.). The year 2005 was dominated by a temporal break down of Station Nunatak and defect instrument recordings at both stations. Average yearly measurements at both meteorological stations: Station Nunatak (1994–2004) and Station Coast (1998–2005) are presented to illustrate the climatic variability within the Mittivakkat Glacier catchment, and further compared with simultaneous standard synoptic meteorological DMI station climate observations (1994–2004) at the town Tasiilaq (Ammassalik) in order to establish transfer functions (linear regressions) and describe the spatial variability of climate variables.     

Snow-distribution and melt modelling for glaciers in Zackenberg river drainage basin,north-eastern Greenland

A physically based snow-evolution modelling system (SnowModel) that includes four sub-models: MicroMet, EnBal, SnowPack, and SnowTran-3D, was used to simulate eight full-year evolutions of snow accumulation, distribution, sublimation, and surface melt from glaciers in the Zackenberg river drainage basin, in north-east Greenland. Meteorological observations from two meteorological stations were used as model inputs, and spatial snow depth observations, snow melt depletion curves from photographic time lapse, and a satellite image were used for model testing of snow and melt simulations, which differ from previous SnowModel tests methods used on Greenland glaciers. Modelled test-period-average end-of-winter snow water equivalent (SWE) depth for the depletion area differs by a maximum of 14 mm w.eq., or ∼6%, more than the observed, and modelled test-period-average snow cover extent differs by a maximum of 5%, or 0·8 km², less than the observed. Furthermore, comparison with a satellite image indicated a 7% discrepancy between observed and modelled snow cover extent for the entire drainage basin. About 18% (31 mm w.eq.) of the solid precipitation was returned to the atmosphere by sublimation. Modelled mean annual snow melt and glacier ice melt for the glaciers in the Zackenberg river drainage basin from 1997 through 2005 (September–August) averaged 207 mm w.eq. year⁻¹ and 1198 mm w.eq. year⁻¹, respectively, yielding a total averaging 1405 mm w.eq. year⁻¹. Total modelled mean annual surface melt varied from 960 mm w.eq. year⁻¹ to 1989 mm w.eq. year⁻¹. The surface-melt period started between mid-May and the beginning of June and lasted until mid-September. Annual calculated runoff averaged 1487 mm w.eq. year⁻¹ (∼150 × 10⁶ m³) (1997–2005) with variations from 1031 mm w.eq. year⁻¹ to 2051 mm w.eq. year⁻¹. The model simulated a total glacier recession averaging − 1347 mm w.eq. year⁻¹ (∼136 × 10⁶ m³) (1997–2005), which was almost equal to previous basin average hydrological water balance storage studies − 244 mm w.eq. year⁻¹ (∼125 × 10⁶ m³) (1997–2003). Copyright © 2007 John Wiley & Sons, Ltd.     

East Greenland freshwater runoff to the Greenland‐Iceland‐Norwegian Seas 1999–2004 and 2071–2100

In this paper, we quantify the terrestrial flux of freshwater runoff from East Greenland to the Greenland‐Iceland‐Norwegian (GIN) Seas for the periods 1999–2004 and 2071–2100. Our analysis includes separate calculations of runoff from the Greenland Ice Sheet (GrIS) and the land strip area between the GrIS and the ocean. This study is based on validation and calibration of SnowModel with in situ data from the only two long‐term permanent automatic meteorological and hydrometric monitoring catchments in East Greenland: the Mittivakkat Glacier catchment (65°N) in SE Greenland, and the Zackenberg Glacier catchment (74°N) in NE Greenland. SnowModel was then used to estimate runoff from all of East Greenland to the ocean. Modelled glacier recession in both catchments for the period 1999–2004 was in accordance with observations, and dominates the annual catchment runoff by 30–90%. Average runoff from Mittivakkat, ～3·7 × 10^?2 km³ y^?1, and Zackenberg, ～21·9 × 10^?2 km³ y^?1, was dominated by the percentage of catchment glacier cover. Modelled East Greenland freshwater input to the North Atlantic Ocean was ～440 km³ y^?1 (1999–2004), dominated by contributions of ～40% from the land strip area and ～60% from the GrIS. East Greenland runoff contributes ～10% of the total annual freshwater export from the Arctic Ocean to the Greenland Sea. The future (2071–2100) climate impact assessment based on the Intergovernmental Panel on Climate Change (IPCC) A2 and B2 scenarios indicates an increase of mean annual East Greenland air temperature by 2·7 °C from today's values. For 2071–2100, the mean annual freshwater input to the North Atlantic Ocean is modelled to be ～650 km³ y^?1: ～30% from the land strip area and ～70% from the GrIS. This is an increase of approximately ～50% from today's values. The freshwater runoff from the GrIS is more than double from today's values, based largely on increasing air temperature rather than from changes in net precipitation. Copyright © 2008 John Wiley & Sons, Ltd.