The fractal geometry of flow paths in natural fractures in rock and the approach to percolation

The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold.     

Contemporary 14C radiocarbon levels of oxygenated polybrominated diphenyl ethers (O-PBDEs) isolated in sponge-cyanobacteria associations

Considerable debate surrounds the sources of oxygenated polybrominated diphenyl ethers (O-PBDEs) in wildlife as to whether they are naturally produced or result from anthropogenic industrial activities. Natural radiocarbon (¹⁴C) abundance has proven to be a powerful tool to address this problem as recently biosynthesized compounds contain contemporary (i.e. modern) amounts of atmospheric radiocarbon; whereas industrial chemicals, mostly produced from fossil fuels, contain no detectable ¹⁴C. However, few compounds isolated from organisms have been analyzed for their radiocarbon content. To provide a baseline, we analyzed the ¹⁴C content of four O-PBDEs. These compounds, 6-OH-BDE47, 2′-OH-BDE68, 2′,6-diOH-BDE159, and a recently identified compound, 2′-MeO-6-OH-BDE120, were isolated from the tropical marine sponges Dysidea granulosa and Lendenfeldia dendyi. The modern radiocarbon content of their chemical structures (i.e. diphenyl ethers, C₁₂H₂₂O) indicates that they are naturally produced. This adds to a growing baseline on, at least, the sources of these unusual compounds.     

Hydrochemical and isotopical tracers in the lacustrine aquifer of the Cerro Prieto area, Baja California, México

A series of patterns in the chemical and isotopic composition of the groundwater of the Cerro Prieto area have been recognized. These patterns were used to define four hydrochemical and isotopical zones in the area. One of these areas located at the east side was found to be the source of recharge, while another in the central part is where an older aquifer exist in lacustrine deposits. The low permeability of the area causes the aquifer to act as an aquitard, which at least is partly surrounded by an interface zone where mixing of waters occurs. Tritium and radiocarbon method revealed that the aquitard is an isolate system whose residence time is of 32 ka.     

The model of the depth variations in the properties and state of the rocks in the upper,middle, and lower continental crust of the Kola-Norwegian block,Kola Peninsula

Based on the experimental and calculated data, the model of depth variations in density, as well as the velocities of longitudinal (P) and transverse (S) waves, within the upper, middle, and lower crusts of the Kola-Norwegian block down to a depth of about 40 km is suggested. The variations in density and the velocities of the P- and S-waves are primarily caused by the changes in the mineral composition of the rocks. The relative reduction in the velocities of the P- and S-waves under the action of the increasing pressure and temperature in the depth interval from 5 to 37 km is estimated at ～2%.     

The analysis of drainage network composition

The Horton method of analyzing drainage network composition is reviewed, with the conclusion that it has not been very effective either in improving understanding or in developing useful methods of characterizing drainage basins. New methods which are based on the link rather than the Horton (or Strahler) stream are described. A number of detailed examples of the application of these new methods to the topologic and geometric properties of networks are provided. The results are compared with the predictions of the random model. Data used in the analysis were obtained from 1:24,000 U.S.G.S. topographic maps of eastern Kentucky. Thirty drainage basins were selected and their channel networks were outlined first by the contour-crenulation (CC) method and then by another, more objective, method (SC) in which stream sources were identified by a quantitative slope criterion. The CC and SC samples comprise about 8,700 and 1,700 links, respectively. The three most important results of the analysis are: (1) the channel networks are slightly but significantly more elongated than predicted by the random model, (2) there are fewer second magnitude links than predicted, and (3) the length distribution for interior links depends upon the kind of link (interior or exterior) joined downstream. These features are found in both CC and SC networks.     

Relation between the extreme angular and areal distortion in cartographic representation

Summary The paper presents the method of deriving representations, optimal from the point of view of global characteristics, for areal and extreme angular distortion (3), (7), if one is optional and the other characteristic is minimized at the same time. If a special minimization method (Section 5) is used for computer processing, the problem can be solved in the region of representation equations in the form of polynomials of the 3rd or 5th degree, while assuming symmetry relative to the equator and the central meridian. Thus, the method enables both the fundamental global characteristics to be regulated freely. Their dependence is illustrated in graphs (Figs 2 and 6) depending on the selected examples of representations of the whole globe. The latter shows that method is a contribution for cartographic practice as well.     

Acid volcanism on the south Arabian coast

Along the south coast of Arabia, between Aden and the southern entrance to the Red Sea, there are six central vent volcanoes of probable Pliocene age. All are characterised by the interstratification of basic and acidic extrusives, the formation of large central calderas at a late stage in the volcanic cycle and the subsequent infilling of these calderas with horizontal acidic ignimbrites and basic lavas. Lying 60 miles to the west of Aden and of particular interest is Jebel Khariz, the largest and best preserved of the six volcanic centres, covering a roughly circular area of about 100 square miles and rising to a height of 2,766 feet. The volcanic sequence of Jebel Khariz is broadly divisible into two suites: a) alkali-rich rhyolites and trachytes which occur as flows and pyroclastic horizons and form about 80 per cent of the volume of the cone, and b) effusives of basaltic composition that occur in the caldera, locally on the south-east and south-west flanks and in a small parasitic cone on the northern flank. The alkali-rich acidic suite includes lavas, ash-flow and ash-fall rocks as well as vent and flow breccias, Generally, all rocks of this suite have phenocrysts of anorthoclase, and may contain phenocrysts of fayalitic olivine, aegirine-augite, magnetite and/or quartz. The fine grained matrix is composed of the same minerals with skeletal riebeckite and, in some cases, cossyrite. The basaltic suite is characteristically porphyritic, the phenocrysts being of calcic plagioclase, clinopyroxene, olivine and magnetite in a fine-grained mesostasis of plagioclase, olivine, clinopyroxene and ore. The plagioclase, on initial investigation, appears to lie in the labradorite-bytownite range, the olivine is commonly replaced by iddingsite and the clinopyroxene is most commonly a pale mauve titanaugite. Near the centre of the volcanic pile, as exposed in the caldera wall, masses of rhyolitic composition can be seen to form over half of the volcanic sequence. These masses are markedly lenzoid in cross-section normal to the flow direction and display intricate flow folding; they are considered to have been extruded as viscous lava. Further from the volcanic centre, these acidic extrusives become less markedly lenzoid until in the distal areas of individual units, some 5 miles from the caldera, they have spread out to form sheet-like masses covering as much as 10 square miles to a uniform thickness rarely exceeding 25 feet. The presence of agglomeratic bases, hard compact central sections and less compact upper divisions, together with the ubiquitous presence of columnar jointing and occasional shard textures suggest that these distal parts of each extrusive unit have been formed by an ash-flow/ash-fall mechanism. It is postulated that the majority of the Jebel Khariz volcanic pile was formed by emission of acidic material, effusive in the central area, but deposited mainly by an ash-flow mechanism around the flanks of the cone. This could be due to either the synchronous eruption of viscous lava from the central vent with ash flow eruptions on the flanks; or, more probably, to the progression of an individual volcanic episode through an initial ash-flow phase followed by the effusion of viscous lava, all emanating from the central vent.     

Maximum-likelihood ambiguity resolution based on Bayesian principle

 Based on the Bayesian principle and the fact that GPS carrier-phase ambiguities are integers, the posterior distribution of the ambiguities and the position parameters is derived. This is then used to derive the maximum posterior likelihood solution of the ambiguities. The accuracy of the integer ambiguity solution and the position parameters is also studied according to the posterior distribution. It is found that the accuracy of the integer solution depends not only on the variance of the corresponding float ambiguity solution but also on its values. Received: 27 July 1999 / Accepted: 22 November 2000