Effective velocities in fractured media: a numerical study using the rotated staggered finite‐difference grid

The modelling of elastic waves in fractured media with an explicit finite‐difference scheme causes instability problems on a staggered grid when the medium possesses high‐contrast discontinuities (strong heterogeneities). For the present study we apply the rotated staggered grid. Using this modified grid it is possible to simulate the propagation of elastic waves in a 2D or 3D medium containing cracks, pores or free surfaces without hard‐coded boundary conditions. Therefore it allows an efficient and precise numerical study of effective velocities in fractured structures. We model the propagation of plane waves through a set of different, randomly cracked media. In these numerical experiments we vary the wavelength of the plane waves, the crack porosity and the crack density. The synthetic results are compared with several static theories that predict the effective P‐ and S‐wave velocities in fractured materials in the long wavelength limit. For randomly distributed and randomly orientated, rectilinear, non‐intersecting, thin, dry cracks, the numerical simulations of velocities of P‐, SV‐ and SH‐waves are in excellent agreement with the results of the modified (or differential) self‐consistent theory. On the other hand for intersecting cracks, the critical crack‐density (porosity) concept must be taken into account. To describe the wave velocities in media with intersecting cracks, we propose introducing the critical crack‐density concept into the modified self‐consistent theory. Numerical simulations show that this new formulation predicts effective elastic properties accurately for such a case.     

Late Holocene local vegetation dynamics in the marsh of Gravgaz(southwest Turkey)

Late Holocene local vegetation succession is reconstructed in twodifferent sites in a small-scale open marsh ecosystem in southwest Turkey.This is done by comparison of the fossil local pollen assemblage zones in twocores with the local pollen data of 40 surface samples from the marsh. Thepollen data are supplemented with sedimentological and archaeological data. Theinsertion of the mean pollen data of the local pollen zones as passive samplesinto the canonical correspondence analysis triplot of the modern samples allowsus to detect modern analogues for the fossil pollen zones. From this numericalcomparative approach it is concluded that the marsh area was relatively dryuntil ca 2500 BP. After 2500 BP the area shifts towards a wet area dominated bySparganium and/or Typha angustifolia. A diversification of the marsh vegetationstarts at ca 2400/2300 BP. The area around one core site seems to have beensituated in an area with slowly flowing source water, whereas the other coresite is likely to have been characterised by damp conditions. The steadilyincreasing dryness of the marsh area starts after ca 680 BP. The drying upappears to be associated with recent agricultural and grazing pressure.     

Policy Contestation over the Ecosystem Services Approach in Sweden

Ecosystem services (ES) is an important approach to biodiversity protection in political rhetoric and policy practice, but it is also highly contested. This paper analyzes the introduction of ES in Swedish environmental policy and how it is contested by key stakeholders and discusses its implications for biodiversity governance. The results show that although ES is widely accepted on an abstract and conceptual level, critical features and functions are highly contested. These primarily concern the valuation of nature, appropriateness of different policy instruments, and institutional structures. The paper concludes that while the controversy surrounding ES fills an important role by reinvigorating debate and stimulating reflections on biodiversity loss, it also illustrates how ES is used to further particular values and beliefs and to challenge traditional biodiversity-protecting strategies. Understanding these policy controversies is central to addressing the challenges of transforming the promises of ES into practical policies.     

Transformation of amplitudes and frequencies of precession and nutation of the earth’s rotation vector to amplitudes and frequencies of diurnal polar motion

The temporal change of the rotation vector of a rotating body is, in the first order, identical in a space-fixed system and in a body-fixed system. Therefore, if the motion of the rotation axis of the earth relative to a space-fixed system is given as a function of time, it should be possible to compute its motion relative to an earth-fixed system, and vice versa. This paper presents such a transformation. Two models of motion of the rotation axis in the space-fixed system are considered: one consisting only of a regular (i.e., strictly conical) precession and one extended by circular nutation components, which are superimposed upon the regular precession. The Euler angles describing the orientation of the earth-fixed system with respect to the space-fixed system are derived by an analytical solution of the kinematical Eulerian differential equations. In the first case (precession only), this is directly possible, and in the second case (precession and nutation), a solution is achieved by a perturbation approach, where the result of the first case serves as an approximation and nutation is regarded as a small perturbation, which is treated in a linearized form. The transformation by means of these Euler angles shows that the rotation axis performs in the earth-fixed system retrograde conical revolutions with small amplitudes, namely one revolution with a period of one sidereal day corresponding to precession and one revolution with a period which is slightly smaller or larger than one sidereal day corresponding to each (prograde or retrograde) circular nutation component. The peculiar feature of the derivation presented here is the analytical solution of the Eulerian differential equations.     

Ocean loading effects on the prediction of Antarctic glacial isostatic uplift and gravity rates

The effect of regional ocean loading on predicted rates of crustal uplift and gravitational change due to glacial isostatic adjustment (GIA) is determined for Antarctica. The effect is found to be significant for the ICE-3G and ICE-5G loading histories (up to ?8 mm/year and ?3 mm/year change in uplift rate and ?3 cm/year and ?1 cm/year equivalent water height change (EWHC) of surface mass, respectively). The effect is smaller (+1 mm/year; +0.25 cm/year) for the IJ05 loading history. The impact of ocean loading on the rate of change of the long-wavelength zonal harmonics of the Earth’s gravitational field is also significantly smaller for IJ05 than ICE-3G. A simple analytical formula is derived that is accurate to about 3% in a root-mean-square sense that relates predicted or observed gravitational change at the surface of the Earth (r = a) to the EWHC. A fundamental difference in the definition of the load histories accounts for the differing sensitivities to ocean loading. IJ05 defines its surface load history relative to the present-day surface load, rather than specifying an absolute loading history, and thus implicitly approximates the temporal and spatial mass exchange between grounded ice and open ocean. In contrast, ICE-3G and ICE-5G specify an absolute load history and explicit regional ocean loading substantially perturbs predicted GIA rates. Conclusions of previous studies that used IJ05 predictions without ocean loading are relatively robust.     

Geophysical signature of Målingen,the minor crater of the Lockne–Målingen doublet impact structure

Målingen is the 0.7 km wide minor crater associated to the 10 times larger Lockne crater in the unique Lockne–Målingen doublet. The craters formed at 458 Ma by the impact of a binary asteroid related to the well-known 470 Ma Main Belt breakup event responsible for a large number of Ordovician craters and fossil meteorites. The binary asteroid struck a target sequence including ~500 m of sea water, ~80 m of limestone, ~30 m of dark mud, and a peneplainized Precambrian crystalline basement. Although the Lockne crater has been extensively studied by core drillings and geophysics, little is known about the subsurface morphology of Målingen. We performed magnetic susceptibility and remanence, as well as density, measurements combined with gravity, and magnetic field surveys over the crater and its close vicinity as a base for forward magnetic and gravity modeling. The interior of the crater shows a general magnetic low of 90–100 nT broken by a clustered set of high-amplitude, short wavelength anomalies caused by bodies of mafic rock in the target below the crater and as allogenic blocks in the crater infill. The gravity shows a general −1.4 mgal anomaly over the crater caused by low-density breccia infill and fractured crystalline rocks below the crater floor. The modeling also revealed a slightly asymmetrical shape of the crater that together with the irregular ejecta distribution supports an oblique impact from the east, which is consistent with the direction of impact suggested for the Lockne crater.     

Extreme storm surge modelling in the North Sea

This study shows that storm surge model performance in the North Sea is mostly unaffected by the application of temporal variations of surface drag due to changes in sea state provided the choice of a suitable constant Charnock parameter in the sea-state-independent case. Including essential meteorological features on smaller scales and minimising interpolation errors by increasing forcing data resolution are shown to be more important for the improvement of model performance particularly at the high tail of the probability distribution. This is found in a modelling study using WAQUA/DCSMv5 by evaluating the influence of a realistic air-sea momentum transfer parameterization and comparing it to the influence of changes in the spatial and temporal resolution of the applied forcing fields in an effort to support the improvement of impact and climate analysis studies. Particular attention is given to the representation of extreme water levels over the past decades based on the example of the Netherlands. For this, WAQUA/DCSMv5 is forced with ERA-Interim reanalysis data. Model results are obtained from a set of different forcing fields, which either (i) include a wave-state-dependent Charnock parameter or (ii) apply a constant Charnock parameter (α _{C h} =?0.032) tuned for young sea states in the North Sea, but differ in their spatial and/or temporal resolution. Increasing forcing field resolution from roughly 79 to 12 km through dynamically downscaling can reduce the modelled low bias, depending on coastal station, by up to 0.25 m for the modelled extreme water levels with a 1-year return period and between 0.1 m and 0.5 m for extreme surge heights.     

Surface deformation analysis of dense GPS networks based on intrinsic geometry: deterministic and stochastic aspects

In this contribution, the regularized Earth’s surface is considered as a graded 2D surface, namely a curved surface, embedded in a Euclidean space . Thus, the deformation of the surface could be completely specified by the change of the metric and curvature tensors, namely strain tensor and tensor of change of curvature (TCC). The curvature tensor, however, is responsible for the detection of vertical displacements on the surface. Dealing with eigenspace components, e.g., principal components and principal directions of 2D symmetric random tensors of second order is of central importance in this study. Namely, we introduce an eigenspace analysis or a principal component analysis of strain tensor and TCC. However, due to the intricate relations between elements of tensors on one side and eigenspace components on other side, we will convert these relations to simple equations, by simultaneous diagonalization. This will provide simple synthesis equations of eigenspace components (e.g., applicable in stochastic aspects). The last part of this research is devoted to stochastic aspects of deformation analysis. In the presence of errors in measuring a random displacement field (under the normal distribution assumption of displacement field), the stochastic behaviors of eigenspace components of strain tensor and TCC are discussed. It is applied by a numerical example with the crustal deformation field, through the Pacific Northwest Geodetic Array permanent solutions in period January 1999 to January 2004, in Cascadia Subduction Zone. Due to the earthquake which occurred on 28 February 2001 in Puget Sound (M _w > 6.8), we performed computations in two steps: the coseismic effect and the postseismic effect of this event. A comparison of patterns of eigenspace components of deformation tensors (corresponding the seismic events) reflects that: among the estimated eigenspace components, near the earthquake region, the eigenvalues have significant variations, but eigendirections have insignificant variations.