Effective elastic properties of randomly fractured soils: 3D numerical experiments

This paper is concerned with numerical tests of several rock physical relationships. The focus is on effective velocities and scattering attenuation in 3D fractured media. We apply the so‐called rotated staggered finite‐difference grid (RSG) technique for numerical experiments. Using this modified grid, it is possible to simulate the propagation of elastic waves in a 3D medium containing cracks, pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli. We simulate the propagation of plane waves through a set of randomly cracked 3D media. In these numerical experiments we vary the number and the distribution of cracks. The synthetic results are compared with several (most popular) theories predicting the effective elastic properties of fractured materials. We find that, for randomly distributed and randomly orientated non‐intersecting thin penny‐shaped dry cracks, the numerical simulations of P‐ and S‐wave velocities are in good agreement with the predictions of the self‐consistent approximation. We observe similar results for fluid‐filled cracks. The standard Gassmann equation cannot be applied to our 3D fractured media, although we have very low porosity in our models. This is explained by the absence of a connected porosity. There is only a slight difference in effective velocities between the cases of intersecting and non‐intersecting cracks. This can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold. For crack densities beyond this threshold, we observe that the differential effective‐medium (DEM) theory gives the best fit with numerical results for intersecting cracks. Additionally, it is shown that the scattering attenuation coefficient (of the mean field) predicted by the classical Hudson approach is in excellent agreement with our numerical results.     

Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.     

Volatile retention from cometary impacts on the Moon

Impacts of comets and asteroids play an important role in volatile delivery on the Moon. We use a novel method for tracking vapor masses that reach escape velocity in hydrocode simulations of cometary impacts to explore the effects of volatile retention. We model impacts on the Moon to find the mass of vapor plume gravitationally trapped on the Moon as a function of impact velocity. We apply this result to the impactor velocity distribution and find that the total impactor mass retained on the Moon is approximately 6.5% of the impactor mass flux. Making reasonable assumptions about water content of comets and the comet size-frequency distribution, we derive a water flux for the Moon. After accounting for migration and stability of water ice at the poles, we estimate a total 1.3×10⁸-4.3×10⁹ metric tons of water is delivered to the Moon and remains stable at the poles over 1 Ga. A factor of 30 uncertainty in the estimated cometary impact flux is primarily responsible for this large range of values. The calculated mass of water is sufficient to account for the neutron fluxes poleward of 75° observed by Lunar Prospector. A similar analysis for water delivery to the Moon via asteroid impacts shows that asteroids provide six times more water mass via impacts than comets.     

Paleoceanographic evolution of the SW Svalbard margin (76°N) since 20,000 C yr BP

Two cores from the southwestern shelf and slope of Storfjorden, Svalbard, taken at 389 m and 1485 m water depth have been analyzed for benthic and planktic foraminifera, oxygen isotopes, and ice-rafted debris. The results show that over the last 20,000 yr, Atlantic water has been continuously present on the southwestern Svalbard shelf. However, from 15,000 to 10,000 ¹⁴C yr BP, comprising the Heinrich event H1 interval, the Bølling-Allerød interstades and the Younger Dryas stade, it flowed as a subsurface water mass below a layer of polar surface water. In the benthic environment, the shift to interglacial conditions occurred at 10,000 ¹⁴C yr BP. Due to the presence of a thin upper layer of polar water, surface conditions remained cold until ca. 9000 ¹⁴C yr BP, when the warm Atlantic water finally appeared at the surface. Neither extensive sea ice cover nor large inputs of meltwater stopped the inflow of Atlantic water. Its warm core was merely submerged below the cold polar surface water.     

A local model for analysis of pump and treat systems with vertical barrier walls

We present a mathematical model of local, steady groundwater flow near a vertical barrier wall. Flow features represented in the model include an impermeable arc-shaped barrier wall and multiple wells; distant boundary conditions are not included explicitly, but their effects on the local flow field are modelled by specifying a uniform flow at infinity and a constant areal recharge within a local domain. We develop an explicit closed-form solution to the boundary-value problem using the analytic element method. The solution is an extension of a harmonic solution presented by Anderson and Mesa [Anderson EI, Mesa E. The effects of vertical barrier walls on the hydraulic control of contaminated groundwater. Adv Water Resourc 2006;29(1):89–98] which does not include the effects of recharge. We demonstrate that the general solution with recharge consists of the harmonic solution superposed on a special case of the harmonic solution along with two elementary one-dimensional flow solutions. The results are used to investigate the effects of areal recharge on the capture zone envelopes of the pumping wells and on the reduction in discharge that can be achieved by including a barrier wall in a pump and treat design. We find that the benefits of including an open barrier wall in a design, measured as a reduction in the pumping rate required to contain a plume, increase for higher recharge rates. Dimensionless plots of capture zone envelopes are presented for a practical well and barrier wall configuration.     

A review of mathematical models of river planform changes

Different mathematical models of river planform changes exist or are being developed. They are reviewed here by discussing a two-dimensional depth-averaged model, various meander models and a model for the braided Brahmaputra-Jamuna River in Bangladesh. Much emphasis is placed on topics where further research is needed. It is concluded that the models help in understanding the underlying processes, but cannot yet be considered generally valid and easy-to-use software packages. In the hands of experienced geomorphologists or river engineers, however, some of the models do already form valuable tools which allow better predictions of future river planforms.     

Application of the Ordered Weighted Averaging (OWA) method to the Caspian Sea conflict

This study proposes a promising allocation mechanism of the Caspian Sea natural resources, which are presently shared among five countries. To date, these nations have been unable to reach an allocation agreement. We apply a methodology to propose the most appropriate solution under different risk attitudes of the states. This research is different from other studies regarding the Caspian Sea negotiations in that it employs risk-based fuzzy multi attribute decision making methods for simulating the risk attitudes or optimism/pessimism degrees of the decision makers. The ordered weighted averaging (OWA) approach, which considers the optimism/pessimism degree quantitatively, is used to take into account the effects of different risk attitudes of the negotiators on the final outcome. We demonstrate how one could obtain a range of alternatives under different multi attribute and risk attitudes. The induced OWA (IOWA) method is also used to determine the relative power of these states bordering the Caspian Sea by considering several attributes, including different risk attitudes of agents. Results indicate that taking into account the risk attitude (prone, neutral, averse) of the states can affect the overall ranking of the proposed solutions. The findings from this study may facilitate negotiation regarding the most preferred allocation mechanism for the Caspian Sea.     

Magnetostratigraphic correlation of the Oxfordian–Kimmeridgian boundary

A magnetic polarity pattern for Boreal and Sub-Boreal ammonite zones of the Upper Oxfordian to Lower Kimmeridgian was established and confirmed in four British sections, including the proposed Global Boundary Stratotype Section and Point (GSSP) on the Isle of Skye (Scotland) to define the base of the international Kimmeridgian Stage. A coeval pattern for Sub-Mediterranean ammonite zones was compiled from seven sections in Poland, one German section and multi-section composites from France and Spain. The mean paleopole for the European Craton (excluding Spain) at the Oxfordian–Kimmeridgian boundary is 74.2°N, 181.3°E (Α₉₅ = 3.8°). The common magnetic polarity scale enables inter-correlation of ammonite subzones among these three faunal provinces and to the marine magnetic-anomaly M-Sequence. The proposed GSSP at the base of the Pictonia baylei Zone is near the base of an extended interval dominated by reversed polarity, which is interpreted to be Chron M26r. This GSSP level projects to the lower to middle part of the Epipeltoceras bimammatum Subzone, which is the middle subzone of this E. bimammatum Zone in the Sub-Mediterranean standard zonation. In contrast, the traditional placement of the Oxfordian–Kimmeridgian boundary in that Sub-Mediterranean standard zonation (base of Sutneria platynota Zone) is at the base of Chron M25r, or nearly 1 million years younger.     

Present-day and future precipitation in the Baltic Sea region as simulated in a suite of regional climate models

Here we investigate simulated changes in the precipitation climate over the Baltic Sea and surrounding land areas for the period 2071–2100 as compared to 1961–1990. We analyze precipitation in 10 regional climate models taking part in the European PRUDENCE project. Forced by the same global driving climate model, the mean of the regional climate model simulations captures the observed climatological precipitation over the Baltic Sea runoff land area to within 15% in each month, while single regional models have errors up to 25%. In the future climate, the precipitation is projected to increase in the Baltic Sea area, especially during winter. During summer increased precipitation in the north is contrasted with a decrease in the south of this region. Over the Baltic Sea itself the future change in the seasonal cycle of precipitation is markedly different in the regional climate model simulations. We show that the sea surface temperatures have a profound impact on the simulated hydrological cycle over the Baltic Sea. The driving global climate model used in the common experiment projects a very strong regional increase in summertime sea surface temperature, leading to a significant increase in precipitation. In addition to the common experiment some regional models have been forced by either a different set of Baltic Sea surface temperatures, lateral boundary conditions from another global climate model, a different emission scenario, or different initial conditions. We make use of the large number of experiments in the PRUDENCE project, providing an ensemble consisting of more than 25 realizations of climate change, to illustrate sources of uncertainties in climate change projections.