A recurrence relation for the βn-function

A recurrence relation is presented for the smoothing function, β_n, which is used in geodesy to relate spherical harmonics to their mean values over circular areas (caps). The proposed formula does not require the computation of the Legendre's polynomials. Moreover, it is numerically more stable than the formulas ofPellinen (1969) andMeissl (1971).     

On Modelling Discrete Geological Structures as Markov Random Fields

The purpose of this paper is to extend the locally based prediction methodology of BayMar to a global one by modelling discrete spatial structures as Markov random fields. BayMar uses one-dimensional Markov-properties for estimating spatial correlation and Bayesian updating for locally integrating prior and additional information. The methodology of this paper introduces a new estimator of the field parameters based on the maximum likelihood technique for one-dimensional Markov chains. This makes the estimator straightforward to calculate also when there is a large amount of missing observations, which often is the case in geological applications. We make simulations (both unconditional and conditional on the observed data) and maximum a posteriori predictions (restorations) of the non-observed data using Markov chain Monte Carlo methods, in the restoration case by employing simulated annealing. The described method gives satisfactory predictions, while more work is needed in order to simulate, since it appears to have a tendency to overestimate strong spatial dependence. It provides an important development compared to the BayMar-methodology by facilitating global predictions and improved use of sparse data.     

Limitations of the potentiometric titration technique in determining the proton active site density of goethite surfaces

Density of proton active surface sites at mineral surfaces is a property of fundamental importance in equilibrium modeling of surface complexation reactions. In this article, methods for an experimental determination of these sites at the surface of α-FeOOH (goethite) are explored. It is shown that previously obtained saturation data of goethite with respect to protons do not yield a site density that can be considered as an intrinsic sorbent property: the results are below crystallographically expected values and values for different ionic media in terms of composition and concentration yield different numbers—for example, chloride would yield higher values than nitrate at the same concentration, and higher electrolyte concentration would favor higher apparent maxima. Although site saturation might be explained by electrostatic repulsion, which is more efficient at high electrolyte concentration or for certain ions, further independent experimental results show that no saturation occurs on goethite down to ph ≡ −log[H⁺] = 2.2 and possibly to ph = 1.0 in 0.6 M NaCl. For those very low pH values, the experimental charging curve was obtained by coulometric back titration (using the Gran plot) or titrations with tris (hydroxymethyl)-aminomethane of the supernatant of acidified goethite suspension. These experimental data are to our knowledge the first high quality data at such low pHs. However, small errors in the determination of proton concentrations (1%) are shown to strongly affect the shape of the charging curve for ph < 2. Furthermore, goethite dissolution (proton consumption and iron reduction in coulometric titrations) and liquid junction effects interfere at low ph, hampering the straightforward application of coulometric Gran titrations over the whole pH range. From these experiments, it can nonetheless be ascertained that a minimum of 2.5 protons/nm² can be adsorbed at the goethite surface from the point of zero charge (ph 9.4) to pH 0.9. Although these studies are restricted to goethite, those studies in which titrations with excess acid and base have been used for the determination of proton active site concentrations of sorbents should be reconsidered.     

Phase transitions of α-quartz at elevated temperatures under dynamic compression using a membrane-driven diamond anvil cell: Clues to impact cratering?

Coesite and stishovite are high-pressure silica polymorphs known to have been formed at several terrestrial impact structures. They have been used to assess pressure and temperature conditions that deviate from equilibrium formation conditions. Here we investigate the effects of nonhydrostatic, dynamic stresses on the formation of high-pressure polymorphs and the amorphization of α-quartz at elevated temperatures. The obtained disequilibrium states are compared with those predicted by phase diagrams derived from static experiments under equilibrium conditions. We analyzed phase transformations starting with α-quartz in situ under dynamic loading utilizing a membrane-driven diamond anvil cell. Using synchrotron powder X-ray diffraction, the phase transitions of SiO₂ are identified up to 77.2 GPa and temperatures of 1160 K at compression rates ranging between 0.10 and 0.37 GPa s⁻¹. Coesite starts forming above 760 K in the pressure range between 2 and 11 GPa. At 1000 K, coesite starts to transform to stishovite. This phase transition is not completed at 1160 K in the same pressure range. Therefore, the temperature initiates the phase transition from α-quartz to coesite, and the transition from coesite to stishovite. Below 1000 K and during compression, α-quartz becomes amorphous and partially converts to stishovite. This phase transition occurs between 25 and 35 GPa. Above 1000 K, no amorphization of α-quartz is observed. High temperature experiments reveal the strong thermal dependence of the formation of coesite and stishovite under nonhydrostatic and disequilibrium conditions.     

Meteorological effects on seasonal displacements of the ?knes rockslide, western Norway

In the alpine topography along one of the long fjords with steep and high mountain sides in western Norway the large ?knes rockslide area is defined by a distinct back scarp rising from 800 to 1,000 m a.s.l. In 2004, an extensive monitoring program started, including establishment of a meteorological station above the upper tension crack, 900 m a.s.l. This paper evaluates the significance of meteorological conditions affecting the displacements recorded by five extensometers and two laser sensors in the tension crack from November 2004 to August 2008. Meteorological factors of importance for the recorded activity in the tension crack are found to be melt water in spring and large temperature fluctuations around the freezing point in spring, autumn, and early winter. The records show less acceleration phases in the measured distance across the tension crack in the second half of the analyzed period even though annual displacements are increasing, indicating that other processes, like disintegration of irregularities along unfilled joints and disintegration of intact rock bridges in the sliding plane have become more important.     

Oxidative damage in rainbow trout caged in a polluted river

Sewage treatment works (STWs) are a common source of chemicals entering into the aquatic environment. In order to assess effects of these effluents on oxidative stress parameters in aquatic organisms, we caged rainbow trout at five sites: upstream, near an STW effluent, and three sites downstream in the river Viskan in western Sweden for 14 days during autumn, 2006. We then measured protein carbonyls in plasma as well as 20S proteosome activity and lipid peroxidation products, i.e. MDA and 4-HNE, in liver samples. Levels of both lipid and protein oxidative damage products were elevated in fish caged near the STW effluent while 20S activity showed no differences. This argues that complex mixtures of chemicals entering into the aquatic environment do have deleterious effects on fish. Additionally, oxidative stress parameters can serve as a biomarker in aquatic organisms.