Topological relations in multisystems of more than n+ 3 phases 1

Multisystems of n+k (k > 3) phases are very complicated and knowledge of them has suffered as a result. The successful solution of the topological relationships in n+ 3 phase multisystems by Zen (1966, 1967) and Zen & Roseboom (1972) has aroused much interest regarding what will happen in a multisystem of more than n+ 3 phases. Since 1979, some important research results on this topic have been published. These results have expounded the substantial rules governing the appearance of phase relations in phase diagrams of n - k (k > 3) phase multisystems. The most significant conclusions include: (1) It is impossible to incorporate all the possible phase relations in an n+k (k > 3) phase multisystem in a single closed net. Therefore, it is no longer enough to use only a single closed net to depict the topological relations involved in these types of multisystems. Instead, one or more groups of closed nets, namely the complete system(s) of closed nets are necessary for this purpose. (2) A principle called the Combination Principle has been proposed and proved. It states: Any closed net of one n+k (k > 3) phase multisystem must be a combination of two or more distinct n+ 3 order submultisystem closed nets belonging to the given n+k phase multisystem, if it is not one of the n+ 3 order submultisystem closed nets itself. The combination principle provides both a theoretical basis and a practical method for the construction of closed nets and, hence, for the derivation of the real phase diagrams for any n+k (k > 3) phase multisystem. (3) A theorem on divariant-assemblage-characteristic-stability-polygons is also important to our understanding of the n+k (k± 3) phase multisystem closed nets. This theorem can be stated as follows: A divariant assemblage of an n+k (k± 3) phase multisystem will be stable in an l-polygon lacking diagonals in an appropriate set of closed-net-diagrams, and this l-polygon may be at least a triangle, and at most a k-polygon. In addition, the closed-net-diagrams of unary and binary n+ 4 phase multisystems derived respectively by Guo (1980b, 1980c, 1981a) and by Roseboom & Zen (1982) have also been summarized. The combination principle is applied to a practical petrological problem in this paper, dealing with 7 phases in the system FeO-Fe₂O₃-SiO₂.     

Statistical treatment of experimental errors in the fission track dating method

The major stochastic elements in the fission track dating method are (i) the number of spontaneous fission tracks (N _s ) in a sample, and (ii) the number of induced tracks (N _i ) observed when the sample is irradiated with neutrons. The foundations for the statistical uncertainty in these measures are of two kinds: (i) there exists a definite probability of uranium fission by means of natural decay and by neutron activation, and (ii) within a crystal the distribution of uranium is not uniform and perhaps follows something like a Poisson law. In any event, the natural logarithm of the ratio (N _s /N _i ) is proportional to age. A plausible statistical fission track dating model should, therefore, start by considering the joint distribution of N _s and N _i . In this paper a joint bivariate normal model is described which allows the rigorous definition of the probability distributions of N_s, N _i , the ratio N _s /N _i , and age itself. A general computer program (FISSION) has been developed to perform all the necessary computations. By accounting for the correlation between N _s and N _i , the statistical model here ascribes smaller standard errors to N _s /N _i (and therefore age) than do previous methods. In addition, the error associated with neutron flux is a significant factor in the age relationships and has been incorporated into the model.     

Volcanic hazard assessment incorporating expert knowledge: Application to the yucca mountain region, Nevada, USA

Multiple-expert hazard/risk assessments have considerable precedent, particularly in the Yucca Mountain site characterization studies. A certain amount of expert knowledge is needed to interpret the geological data used in a probabilistic data analysis. As may be the situation in science, experts disagree on crucial points. Consequently, lack of consensus in some studies is a sure outcome. In this paper, we present a Bayesian approach to statistical modeling in volcanic hazard assessment for the Yucca Mountain site. Specifically, we show that the expert opinion on the site disruption parameterp is incorporated into the prior distribution, π(p), based on geological information that is available. Moreover, π(p) can combine all available geological information motivated by conflicting but realistic arguments (e.g., simulation, cluster analysis, structural control, ..., etc.). The incorporated uncertainties about the probability of repository disruptionp eventually will be averaged out by taking the expectation over π(p). We use the following priors in the analysis: (1) priors selected for mathematical convenience: Beta (r,s) for (r,s) = (2, 2), (3, 3), (5, 5), (2, 1),(2, 8), (8, 2), and (1, 1);and (2) three priors motivated by expert knowledge. Sensitivity analysis is performed for each prior distribution. Our study concludes that estimated values of hazard based on the priors selected for mathematical simplicity are uniformly higher than those obtained based on the priors motivated by expert knowledge. And, the model using the prior, Beta (8, 2), yields the highest hazard (=2.97 × 10^-2 . The minimum hazard is produced by the “three-expert prior” (i.e., values of p are equally likely for p = 10^-3, 10^-2,and 10^-1 . The estimate of the hazard is 1.39 × 10^-3, which is only about one order of magnitude smaller than the maximum value. The term, “hazard, ” is defined as the probability of at least one disruption of a repository at the Yucca Mountain site by basaltic volcanism for the next 10,000 years.     

Particle trapping in stratified estuaries: Application to observations

Estuarine turbidity maxima (ETM) retain suspended particulate matter (SPM) through advection, settling, aggregation, and nonlinearities in bed processes, but the relative importance of these processes varies strongly between systems. Observations from two strongly advective systems (the Columbia and Fraser Rivers) are used to investigate seasonal cycles of SPM retention and the effects of very high flows. Results for the Fraser and Columbia plus literature values for 13 other estuaries illustrate the applicability of scaling parameters and the response of ETM phenomena to a range of river flow (U _r ) levels and tidal forcing. The most efficient trapping (represented by Trapping EfficiencyE, the ratio of maximum ETM concentration to the source SPM concentration) occurs for low ratios of river flow to tidal current amplitude (U_T), represented by low values of the Supply number S_r.E in the Columbia is found to be maximal in a null zone where advection or tidal asymmetry (represented by Advection numberA) is weak(A ∼ 0). The ratio of aggregation to disaggregation (the Floc number Θ) is maximal on neap tides, while the ratio of erosion to deposition (the Erosion number P) is maximal on spring tides. The ratio of settling velocity to vertical mixing (Rouse numberP) is relatively constant in the Columbia ETM(P ∼ 0.7), because particle settling velocity and turbulence levels adjust together. Assuming that this result applies broadly, scaling variables and data are combined to express ETM properties in terms of the friction velocity (U_*),U _r , andU _T , allowing a considerable simplification of the parameters used to describe ETM.     

Estimating and mapping snow hazard based on at-site analysis and regional approaches

The estimation of snow hazard and load faces the small sample size effect because of the short snow depth record at a station. To reduce such an effect, we propose to estimate the return period value of the annual maximum ground snow depth S, s_T, for Canada sites by applying the regional frequency analysis (RFA) and the region of influence approach (ROIA). The use of RFA and ROIA to map Canadian snow hazard is new. The comparison of their performance for snow hazard mapping has not been explored in the literature. We also consider the at-site analysis approach (ASA) for estimating s_T by using three often used probability distributions for S. A comparison of the estimated s_T by using the three approaches (ASA, RFA, ROIA) indicates that there is considerable scatter between the estimated s_T value although the identified overall spatial trends of s_T are similar. It is shown that the two-parameter lognormal distribution for S at most Canadian sites, based on the at-site analysis, is preferred; this differs from the Gumbel distribution used to develop the design snow load in Canadian structural design code. The new findings indicate that it is valuable to consider the lognormal distribution for developing design snow load for Canadian sites.

     

A low temperature X-ray single-crystal diffraction and polarised infra-red study of epidote

The effects of low-temperature on the crystal structure of a natural epidote [Ca_1.925Fe_0.745Al_2.265Ti_0.004Si_3.037O₁₂(OH), a = 8.8924(7), b = 5.6214(3), c = 10.1547(6)? and β = 115.396(8)° at room conditions, Sp. Gr. P2₁ /m] have been investigated with a series of structure refinements down to 100 K on the basis of X-ray single-crystal diffraction data. The reflection conditions confirm that the space group is maintained within the T-range investigated. Structural refinements at all temperatures show the presence of Fe³⁺ at the octahedral M(3) site only [%Fe(M3) = 70.6(4)% at 295 K]. Only one independent proton site was located and two possible H-bonds occur, with O(10) as donor and O(4) and O(2) as acceptors. The H-bonding scheme is maintained down to 100 K and is supported by single crystal room-T polarised FTIR data. FTIR Spectra over the region 4,000–2,500 cm⁻¹ are dominated by the presence of a strongly pleochroic absorption feature which can be assigned to protonation of O(10)–O(4). Previously unobserved splitting of this absorption features is consistent with a NNN influence due to the presence of Al and Fe³⁺ on the nearby M(3) site. An additional relatively minor absorption feature in FTIR spectra can be tentatively assigned to protonation of O(10)–O(2). Low-T does not affect significantly the tetrahedral and octahedral bond distances and angles, even when distances are corrected for “rigid body motions”. A more significant effect is observed for the bond distances of the distorted Ca(1)- and Ca(2)-polyhedra, especially when corrected for “non-correlated motion”. The main low-T effect is observed on the vibrational regime of the atomic sites, and in particular for the two Ca-sites. A significant reduction of the magnitude of the thermal displacement ellipsoids, with a variation of U _eq (defined as one-third of the trace of the orthogonalised U _ij tensor) by ~40% is observed for the Ca-sites between 295 and 100 K. Within the same T-range, the U _eq of the octahedral and oxygen sites decrease similarly by ~35%, whereas those of the tetrahedral cations by ~22%.     

Heat effects of assimilation,crystallization, and vesiculation in magmas

The heat balance for crystal fractionation and assimilation processes is the enthalpy difference between the initial and final states of a system. To order the calculations, the process is viewed as one of assimilation; the heat change for a crystallization process is obtained by changing the signs of the pertinent heat effects. The initial state is a mineral assemblage at T _s and P and an initial magma at T _m and P. The final state is a magma at T _m and P.The net heat change results from: (a) Unmixing of solid solutions, (b) Heating (cooling) each component to its fusion temperature, (c) Fusion of each component, (d) Cooling (heating) of each fused component to the magma temperature, (e) Mixing of each fused component in succession with the melt.The heat required to form a basaltic melt from its equilibrium mineral assemblage is approximately twice that required for a granitic melt. A zero heat balance, with the heat of crystallization from phases with which the magma is saturated supplying the energy for assimilation, necessitates that the mass crystallized be approximately twice that assimilated. The heat effects attendant on release of H₂O from silicic melts depends on the state of the H₂O in the external environment; a low fugacity could cause the magma to cool.The uncertainties in the calculations are estimated at ±10%.     

Electron-beam induced amorphization of stishovite: Silicon-coordination change observed using Si K-edge extended electron energy-loss fine structure

The analysis of the extended energy-loss fine structure (EXELFS) of the Si K-edge for sixfold-coordinated Si in synthetic stishovite and fourfold-coordinated Si in natural α-quartz is reported by using electron energy-loss spectroscopy (EELS) in combination with transmission electron microscopy (TEM). The stishovite Si K-edge EXELFS spectra were measured as a time-dependent series to document irradiation-induced amorphization. The amorphization was also investigated through the change in Si K- and O K-edge energy-loss near edge structure (ELNES). For α-quartz, in contrast to stishovite, electron irradiation-induced vitrification, verified by selected area electron diffraction (SAED), produced no detectable changes of the EXELFS. The Si K-edge EXELFS were analysed with the classical extended X-ray absorption fine structure (EXAFS) treatment and compared to ab initio curve-waved multiple-scattering (MS) calculations of EXAFS spectra for stishovite and α-quartz. Highly accurate information on the local atomic environment of the silicon atoms during the irradiation-induced amorphization of stishovite is obtained from the EXELFS structure parameters (Si−O bond distances, coordination numbers and Debye-Waller factors). The mean Si−O bond distance R and mean Si coordination number N changes from R=0.1775 nm and N=6 for stishovite through a disordered intermediate state (R≈0.172 nm and N≈5) to R≈0.167 nm and N≈4.5 for a nearly amorphous state similar to α-quartz (R=0.1609 nm and N=4). During the amorphization process, the Debye-Waller factor (DWF) passes through a maximum value of as it changes from for sixfold to for fourfold coordination of Si. This increase in Debye-Waller factor indicates an increase in mean-square relative displacement (MSRD) between the central silicon atom and its oxygen neighbours that is consistent with the presence of an intermediate structural state with fivefold coordination of Si. The distribution of coordination states can be estimated by modelling the amorphization as a decay process. Using the EXELFS data for amorphization, a new method is developed to derive the relative amounts of Si coordinations in high-pressure minerals with mixed coordination. For the radiation-induced amorphization process of stishovite the formation of a transitory structure with Si largely in fivefold coordination is deduced. Received: 18 December 1996 / Revised, accepted: 20 June 1997     

A method for modelling mass balance in partial melting and anatectic leucosome segregation

A method is proposed for adjusting the mass balance to characterize quantitatively the behaviour of minerals in anatexis. The method is based on an unconstrained simple mixing model that can be expressed as: where B , A ₀, and A _1-n, are compositional vectors of segregate, source rock and source minerals, respectively. The most important concepts are: (1) degree of partial fusion: F^MM= 1/a₀; (2) mineral fractionation index: and (3) plagioclase differentiation index: . For a given mineral, the MFI values have the following meaning: (a) MFI <0: residual phase originated, at least partly, as a product of incongruent melting; (b) 0 > MFI <1: preferential retention in the residue; (c) MFI= 1: identical modal fraction in source and melt; (d) a₀ > MFI > 1: preferential incorporation into the segregate, and (e) MFI > a₀: external contribution to the anatectic system defined by a₀ A ₀. To test the method and illustrate its use, it was applied to two real problems of partial melting in the Peña Negra Anatectic Complex (Central Spain). The first is a very simple case of segregation of a diktyonitic neosome from an orthogneiss through partial melting located in vertical shear zones. This process is characterized by: (1) F^MM= 0.51; (2) active incorporation of K-feldspar, plagioclase and biotite into the segregate; (3) disequilibrium melting of plagioclase; (4) residual behaviour of quartz and ilmenite. The second case concerns the formation of a cordierite-bearing granite from granodioritoid diatexites through an anatectic process, whose most salient characteristics are: (1) F^MM= 0.45; (2) incongruent melting of biotite; (3) residual behaviour of plagioclase, which melted with a PDI of 1.22; (4) preferential incorporation of quartz into the segregate; (5) total extraction of K-feldspar from the residue.     

A new method of modelling the rock micro-fracturing process in double-torsion experiments using neural networks

Microfracturing of rock is a complicated damage evolution process. Inaccurate prediction of micro-fracturing behaviours suggests a need for the development of a better modelling method. Analysis of acoustic emission (AE) measurements in double-torsion tests indicates that micro-fracturing behaviours during the loading stage have fractal time structures. This fractal behaviour can be described by C(t) ∝ t^D, where D is the correlation exponent, t is the time and C(t) is the correlation integral. Furthermore, by utilizing measured AE data, a new method has been developed to model the AE behaviours of micro-fracturing in rock, in air, and following soaking in water and in a chemical solution of DTAB. The neutral models NN (10,21,2) and NN (10,20,2) were found to describe reasonably well the AE behaviours of micro-fracturing in rock under air and DTAB conditions, and water conditions, respectively. The cumulative AE events and the cumulative AE counts predicted by the neural models agreed well with those measured in experiments. Copyright © 1999 John Wiley & Sons, Ltd.     

Assessing probability of surface manifestation of liquefaction at a given site in a given exposure time using CPTU

This paper is a follow-up to a previous paper on the subject of liquefaction potential index (LPI), a parameter that is often used to characterize the potential for surface manifestation of liquefaction at a given site subjected to a given shaking level (represented by a pair of peak ground surface acceleration a_max and moment magnitude M_w). In the previous paper by Juang and his coworkers, the LPI was re-calibrated for a piezocone penetration test (CPTU) model, and a simplified model based on LPI was created for computing the conditional probability of surface manifestation of liquefaction (P_G). In this paper, the model for this conditional probability P_G is extended into a complete framework for assessing the probability of surface manifestation of liquefaction in a given exposure time at a given site subjected to all possible ground motions at all seismic hazard levels. This new framework is formulated and demonstrated with an example site in 10 different seismic regions in the United States.     

Preconditioned IDR(s) iterative solver for non‐symmetric linear system associated with FEM analysis of shallow foundation

Non‐associated flow rule is essential when the popular Mohr–Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes non‐symmetric when this non‐associated flow rule is applied. Efficient solution of this large‐scale non‐symmetric linear system is of practical importance. The standard Krylov solver for a non‐symmetric solver is Bi‐CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s = 6) is more efficient than Bi‐CGSTAB when the preconditioner is the incomplete factorization with zero fill‐in of global stiffness matrix K_ep (ILU(0)‐K_ep). Iteration time is reduced by 40% by using IDR(s = 6) with ILU(0)‐K_ep. To further reduce computational cost, the global stiffness matrix K_ep is divided into two parts. The first part is the linear elastic stiffness matrix K_e, which is formed only once at the beginning of solution step. The second part is a low‐rank matrix Δ, which is re‐formed at each Newton–Raphson iteration. Numerical studies show that IDR(s = 6) with this ILU(0)‐K_e preconditioner is more time effective than IDR(s = 6) with ILU(0)‐K_ep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used. Copyright © 2013 John Wiley & Sons, Ltd.     

Porphyroblast crystallization kinetics: the role of the nutrient production rate

The mechanisms that govern porphyroblast crystallization are investigated by comparing quantitative textural data with predictions from different crystallization models. Such numerical models use kinetic formulations of the main crystallization mechanism to predict textural characteristics, such as grain size distributions. In turn, data on porphyroblast textures for natural samples are used to infer which mechanism dominated during their formation. Whereas previous models assume that the rate‐limiting step for a porphyroblast producing reaction is either transport or growth, the model advanced in this study considers the production of nutrients for porphyroblasts as a potentially rate‐limiting factor. This production reflects the breakdown of (metastable) reactants, which at a specific pressure (P) and temperature (T) depends on the bulk composition of the sample. The production of nutrients that potentially contribute to the formation of porphyroblasts is computed based on thermodynamic models. The conceptual model assumes that these nutrients feed into some intergranular medium, and products form by nutrient consumption from that medium, with rates depending on reaction affinity. For any sequence of P–T conditions along a P–T–t path, the numerical model first computes an effective supersaturation (σ_eff) of the product phase(s), then an effective nucleation rate (J), and finally the amount of (porphyroblast) growth. As a result, the model is useful in investigating how the textural characteristics of a sample (of given bulk composition) depend on the P–T–t path followed during porphyroblast crystallization. The numerical model is tested and validated by comparing simulation results with quantitative textural data for garnet porphyroblasts measured in samples from the Swiss Central Alps.     

Process-response analysis for Hörnum tidal inlet in the German sector of the Wadden Sea

The Hörnum tidal inlet is located in the German sector of the Wadden Sea between the barrier islands Sylt and Amrum. On the basis of seven bathymetric surveys of the tidal inlet covering a 55-yr period from 1939 to 1994 and long-term records from two tide gauges, a process-response analysis for the inlet was carried out. Following the method described by Dean and Walton (1975), the volume of sediment stored in the ebb–tidal delta (V_ebd) was calculated for each survey. Furthermore, the cross-sectional area of the tidal inlet throat (A_c), and the area-height distribution (hypsographic curve) of the study area were established. Between 1939 and 1994, A_c increased by about 32%, whereas V_ebd diminished by about 18%. Earlier investigations by, e.g., O'Brien (1931), Walton and Adams (1976), Dean (1988), and Eysink and Biegel (1992) documented a strong positive correlation between these two morphological parameters and tidal currents in the inlet. In conformity with the literature, regression of the values of A_c with the corresponding fall velocities of the water level in the inlet (a direct indication of ebb–tidal currents) produced a correlation coefficient (r) of 0.87. However, V_ebd shows a weak negative correlation (r=−0.74) with fall velocities of the water level. Apparently, other factors than changes in ebb–tidal currents must have been responsible for the decrease in V_ebd. It is suggested that one factor might be the observed considerable increase in storminess, i.e. wave action, in the region since approximately 1960. Consequently, storm wave action on the ebb–tidal delta intensified and erosion was here initiated. As a result, the swash bars of the ebb–tidal delta, in particular, suffered from severe erosion between 1959 and 1994. As the ebb–tidal currents increased simultaneously, sand supply to the terminal lobe of the ebb–tidal delta increased as well, thereby balancing the loss of sediment from the terminal lobe caused by the increasing storminess. The results of this case study indicate that the ratio of ebb–tidal currents to (storm) wave action determines, in large part, the value of V_ebd.     

An evaluation of shape indices as palaeoenvironmental indicators using quartzite and metavolcanic clasts in Upper Cretaceous to Palaeogene beach, river and submarine fan conglomerates

The feasibility of using quantitative shape measurements to discriminate between clast populations from different depositional settings was evaluated using samples from 11 fluvial, six submarine fan and four beach conglomerates from south-west California; these origins had been established previously by facies analysis. Quartzite and metavolcanic clasts were characterized by the following indices: modified Wentworth roundness (R_w), maximum projection sphericity (δ_p), oblate-prolate index (OPI) and long (L), intermediate (I) and short (S) axial ratios. These indices were compared with those documented previously for modern gravels. The results show that certain indices are useful palaeoenvironmental indicators, despite inherited differences in shape due to texture, provided that multiple sites are sampled and a statistical approach is used. Statistically, the most effective shape indices are δ_p and S/L which give good results with the Zingg classification (I/L vs. S/I); better results are also obtained using quartzite clasts. The OPI is useful for discriminating between beach and river conglomerates, which consist largely of oblate and prolate clasts, respectively. The relative abundance of blade-shaped clasts is a useful index of sediment maturity, being greatest for river clast samples and smallest for submarine fan clast samples. The latter are dominated by spherical particles. No correlation between palaeoenvironment and R_w is observed, hence the abundance of disc-shaped clasts in the beach conglomerates studied is attributed to selective transport in suspension and sediment by passing during fluvial transport prior to deposition in the surf zone. Selective transport of rollers (spheres and rods) by traction in a shallow marine setting, prior to redeposition by mass transport, may be responsible for the dominance of spherical particles in submarine fan conglomerates.     

Resource estimation from historical data: Mercury, a test case

A simple technique based on historical records of tonnage and grade of ore produced provides a means for calculating how much of a mineral product will be available in the future at various average grades. Estimates made on this basis are independent of geologic considerations or changing economic and political factors, although they are based on mining history, which was largely determined by these factors. The relatively minor element, mercury, was used for the test case reported here, but the method has been found applicable to forecasts of resources for other mineral products. Mercury resources available in ore in which the average grade is as low as 0.1% are estimated to be 53 ×10 ⁶ kg (1.5 ×10 ⁶ flasks) for the United States and 1551 ×10 ⁶ kg (45 ×10 ⁶ flasks) for the world; this amount is more than adequate to meet predicted demand to the year 2000. The expectable price of mercury in 1978 dollars at this 0.1% grade is projected to be $58.75 per kg ($2,025 per flask), but at a 10% annual inflation rate, it would be more than $12,000 per flask. To satisfy just the projected U.S. demand for mercury by 2000, the price is calculated to be $48.96 per kg ($1,688 per flask) in 1978 dollars at an average annual grade of 0.12%.     

Modeling spatial fracture intensity as a control on flow in fractured rock

Spatial fracture intensity (P ₃₂, fracture area by volume) is an important characteristic of a jointed rock mass. Although it can hardly ever be measured, P ₃₂ can be modeled based on available geological information such as spatial data of the fracture network. Flow in a mass composed of low-permeability hard rock is controlled by joints and fractures. In this article, models were developed from a geological data set of fractured andesite in LanYu Island (Taiwan) where a site is investigated for possible disposal of low-level and intermediate-level radionuclide waste. Three different types of conceptual models of spatial fracture intensity distribution were generated, an Enhanced Baecher’s model (EBM), a Levy–Lee Fractal model (LLFM) and a Nearest Neighborhood model (NNM). Modeling was conducted on a 10 × 10 × 10 m synthetic fractured block. Simulated flow was forced by a 1% hydraulic gradient between two vertical x–z faces of the cube (from North to South) with other boundaries set to no-flow conditions. Resulting flow vectors are very sensitive to spatial fracture intensity (P ₃₂). Flow velocity increases with higher fracture intensity (P ₃₂). R-squared values of regression analysis for the variables velocity (V/V _max) and fracture intensity (P ₃₂) are 0.293, 0.353, and 0.408 in linear fit and 0.028, 0.08, and 0.084 in power fit. Higher R ² values are positively linked with structural features but the relation between velocity and fracture intensity is non-linear. Possible flow channels are identified by stream-traces in the Levy–LeeFractal model.     

Preliminary analysis of the first digital recordings obtained in the Portuguese seismographic network — Attenuation studies

During experiments with digital stations in the period 1985–1987, twenty five earthquakes with magnitudes m _b in the range 2.9 to 4.8 and epicentres located within the area 36°–42.3° (N) and 4.5°–13.6° (W) were recorded at Montemor (MOE) and Montachique (MTH). The three-component recordings were obtained by Geotech S13 instruments with 1 second period. A preliminary analysis of the recordings consisted in the determination of amplitudes and spectral contents of P and S waves, and led to the following observations: (1) The attenuation of waves is expressed by the equation V = exp(C ₂).R ^C ₁. exp(C ₃.M), where V stands for acceleration, velocity or displacement; M-magnitude; R-focal distance; C ₁, C ₂ and C ₃ are constants to be obtained by least square fitting. The application of this equation led to C ₁ of the order 1.7 for displacement, 1.8 for velocity and 2.0 for acceleration, with an average mean square error 0.8. (2) The ratios L/T (longitudinal/transversal amplitudes), for velocity and displacement, showed a tendency to reduce with increasing focal distance, being 2 for short distances (<50 km) and 1 for long distances (400 km). (3) The ratios S/P (S-wave/P-wave amplitudes), although with a large dispersion, showed a slight tendency for increasing with focal distance. (4) The predominant frequencies also showed a slight tendency to decrease with increasing focal distance and with magnitude. (5) The dependence of C ₁ with frequency (3 to 12 Hz) is well behaved from 0.95 to 1.75 (for the velocity trace).     

Computation of surface energies in an electrostatic point charge model: II. Application to zircon (ZrSiO4)

The attachment energies, the slice energies and the specific surface energies can be calculated in an electrostatic point charge model using the formula derived by Madelung for the potential introduced by an infinite row of equally spaced point charges. Power series are given for the Hankel function iH ₍₀₎ ⁽¹⁾ (iy) and (x)=d ln x!/dx. The logarithmic expression in the Madelung formula converges rapidly when applying a power series, which combines equally charged cations and anions. Besides the specific surface energy ( ^hkl), the slice energy (E _s ^hkl ) and the attachment energy (E _a ^hkl ) can be considered as special categories of surface energies as they depend on surface configurations as well. The specific surface energy is the energy per unit area of surface needed to split the crystal parallel to a face (hkl). The attachment energy (E _a) is the energy released per mole, when a new slice of thickness d _hkl crystallizes on an already existing crystal face (hkl). The growth rate of the crystal face (hkl) is a function of its attachment energy. The slice energy (E _s) is the energy released per mole, when a new slice d _hkl is formed from the vapour neglecting the influence of edge energies. The lattice energy (E _c) which is the energy released per mole of a crystal crystallizing from the vapour, is given by the following relation: E _c=E _a+E _s.     

Impact of polychaetes (Nereis spp. and Arenicola marina) on carbon biogeochemistry in coastal marine sediments

Known effects of bioturbation by common polychaetes (Nereis spp. and Arenicola marina) in Northern European coastal waters on sediment carbon diagenesis is summarized and assessed. The physical impact of irrigation and reworking activity of the involved polychaete species is evaluated and related to their basic biology. Based on past and present experimental work, it is concluded that effects of bioturbation on carbon diagenesis from manipulated laboratory experiments cannot be directly extrapolated to in situ conditions. The 45–260% flux (e.g., CO₂ release) enhancement found in the laboratory is much higher than usually observed in the field (10–25%). Thus, the faunal induced enhancement of microbial carbon oxidation in natural sediments instead causes a reduction of the organic matter inventory rather than an increased release of CO₂ across the sediment/water interface. The relative decrease in organic inventory (G _b /G _u) is inversely related to the relative increase in microbial capacity for organic matter decay (k _b /k _u). The equilibrium is controlled by the balance between organic input (deposition of organic matter at the sediment surface) and the intensity of bioturbation. Introduction of oxygen to subsurface sediment and removal of metabolites are considered the two most important underlying mechanisms for the stimulation of carbon oxidation by burrowing fauna. Introduction of oxygen to deep sediment layers of low microbial activity, either by downward irrigation transport of overlying oxic water or by upward reworking transport of sediment to the oxic water column will increase carbon oxidation of anaerobically refractory organic matter. It appears that the irrigation effect is larger than and to a higher degree dependent on animal density than the reworking effect. Enhancement of anaerobic carbon oxidation by removal of metabolites (reduced diffusion scale) may cause a significant increase in total sediment metabolism. This is caused by three possible mechanisms: (i) combined mineralization and biological uptake; (ii) combined mineralization and abiogenic precipitation; and (iii) alleviation of metabolite inhibition. Finally, some suggestions for future work on bioturbation effects are presented, including: (i) experimental verification of metabolite inhibition in bioturbated sediments; (ii) mapping and quantification of the role of metals as electron acceptors in bioturbated sediments; and (iii) identification of microbial community composition by the use of new molecular biological techniques. These three topics are not intended to cover all unresolved aspects of bioturbation, but should rather be considered a list of obvious gaps in our knowledge and present new and appealing approaches.