Flexible spectral methods for the generation of random fields with power-law semivariograms

Random field generators serve as a tool to model heterogeneous media for applications in hydrocarbon recovery and groundwater flow. Random fields with a power-law variogram structure, also termed fractional Brownian motion (fBm) fields, are of interest to study scale dependent heterogeneity effects on one-phase and two-phase flow. We show that such fields generated by the spectral method and the Inverse Fast Fourier Transform (IFFT) have an incorrect variogram structure and variance. To illustrate this we derive the prefactor of the fBm spectral density function, which is required to generate the fBm fields. We propose a new method to generate fBm fields that introduces weighting functions into the spectral method. It leads to a flexible and efficient algorithm. The flexibility permits an optimal choice of summation points (that is points in frequency space at which the weighting function is calculated) specific for the autocovariance structure of the field. As an illustration of the method, comparisons between estimated and expected statistics of fields with an exponential variogram and of fBm fields are presented. For power-law semivariograms, the proposed spectral method with a cylindrical distribution of the summation points gives optimal results.     

Seismic Hazard Studies in the U.K.: Source Specification Problems of Intraplate Seismicity

Although the U.K. is in an area of only low to moderate seismicity, the seismic hazard is sufficient to pose a threat to sensitive structures such as chemical plants and nuclear facilities. In quantifying the level of hazard by conventional probabilistic methodology, however, some problems arise in attempting to interpret earthquake data in terms of geological structure and faults. In the U.K., not only is it impossible to identify any demonstrably active faults, but also it is extremely difficult to discern any relationship between the pattern of seismicity and local or regional geological structure.This study discusses the use of two zonation approaches which complement each other in such a way that the general character and trend of seismicity is preserved. In one approach, the zonation is informed by the structural geology, where possible; geological zonation is avoided if it produces sources with heterogeneous seismicity. In the other approach, the record of past earthquakes is divided up into very small zones around individual epicentres or groups of epicentres, the size of each zone usually being proportional to the uncertainty in the epicentral determination of the appropriate event. This zonation preserves an observed tendency of some British earthquakes to repeat themselves. It is suggested that, in intraplate areas such as the U.K., it is often inappropriate to attempt to model individual fault sources. No faults in the U.K. are provably active. Because an earthquake of moderate size can occur on a very short fault segment, it is impractical to restrict fault modelling to major features. Even the two largest U.K. faults, suspected to be active, pose problems in attributing historical seismicity to them as distinct features.     

Accretion and exhumation at a Variscan active margin, recorded in the Saxothuringian flysch

The Saxothuringian flysch basin, on the north flank of the Central European Variscides, was fed and eventually overthrust by the northwestern, active margin of the Tepla-Barrandian terrane. Clast spectra, mineral composition and isotopic ages of detrital mica and zircon have been analyzed in order to constrain accretion and exhumation of rocks in the orogenic wedge. The earliest clastic sediments preserved are of early Famennian age (ca. 370?Ma). They are exposed immediately to the NW of the suture, and belong to the par-autochthon of the foreland. Besides ultramafic (?ophiolite) material, these rocks contain clasts derived from Early Paleozoic continental slope sediments, originally deposited at the NW margin of the Saxothuringian basin. These findings, together with the paleogeographic position of the Famennian clastics debris on the northwestern passive margin, indicate that the Saxothuringian narrow ocean had been closed by that time. Microprobe analyses of detrital hornblendes suggest derivation from the “Randamphibolit” unit, now present in the middle part of the Saxothuringian allochthon (Münchberg nappes). Detrital zircons of metamorphic rocks formed a little earlier (ca. 380?Ma) indicate rapid recycling at the tectonic front. The middle part of the flysch sequence (ca. early to middle Viséan), both in the par-autochthon and in the allochthon, contains abundant clasts of Paleozoic rocks derived from the northwestern slope and rise, together with debris of Cadomian basement, 500-Ma granitoids and 380?Ma (early Variscan) crystalline rocks. All of these source rocks were still available in the youngest part of the flysch (c. middle to late Viséan), but some clasts record, in addition, accretion of the northwestern shelf. Our findings permit deduction of minimum rates of tectonic shortening well in excess of 10–30?mm per year, and rates of exhumation of ca. 3?mm/a, and possibly more.     

Metamorphism of mafic dikes from the central White-Inyo Range, eastern California

Thin mafic dikes, possibly correlative with the Independence dike swarm of SE California, transect uppermost Proterozoic–Cambrian metasedimentary strata in the White-Inyo Range. Textures and bulk-rock chemistry indicate that the protoliths were diabases and microdiorites, accompanied by Ca + Mg + Fe +Ni + Cr-rich hornblende (± minor augite) cumulates. Analytical data suggest crystal settling and fractionation at shallow depths. Most of the dikes lie in the mapped aureoles of – and were metamorphosed by – voluminous Late Jurassic granitoid plutons; however, a few metadikes cut these plutons and must have been recrystallized during the emplacement of Cretaceous granitic stocks. The mafic metadikes thus include members of two or more temporally distinct suites, pre-Late Jurassic, and latest Jurassic–Cretaceous. Neoblastic mineral assemblages and element partitioning within these nonfoliated mafic metadikes reflect lower-to-upper greenschist facies overprints; metamorphic parageneses, coincident with those developed in the metasedimentary wallrocks, are defined by the production of chlorite, biotite, white mica, epidote, and actinolite, and by albitization of the igneous plagioclase. Based on analytical and mineralogic data obtained in this study, the following conclusions regarding subsolidus recrystallization of the mafic metadikes are advanced: (1) Newly grown minerals and phase assemblages are systematic in their areal distributions. (2) Metamorphic grade increases chiefly toward the north and east, toward the Late Jurassic granitoids. (3) Element fractionation among coexisting neoblastic phases is regular, and compatible with a close approach to chemical equilibrium. (4) Assemblages 3–5 km from the granitic intrusive contacts reflect lowermost greenschist facies physical conditions. (5) Investigated mafic dikes exhibit mineral parageneses isofacial with the regional/contact metamorphic assemblages previously documented for the enclosing pre-Mesozoic clastic country rocks. Clearly, mafic dikes of several ages of injection and recrystallization are present in the central White-Inyo Range, making correlation with the Independence dike swarm problematic. In any case, the dikes record localized contact metamorphism that took place sporadically over portions of an approximately 100 million year interval. Received: 13 March 1996 / Accepted: 24 December 1996     

Argillite debris converted to bauxite during karst weathering: evidence from immobile element geochemistry at the Olmedo Deposit, Sardinia

The Olmedo bauxite deposit occurs in the Nurra district of northwest Sardinia. It forms a stratiform horizon in Cretaceous limestone and marl. Uplift in mid-Cretaceous had exposed recently deposited limestone to karst weathering, and a layer of argillaceous debris accumulated on its surface and was partly converted to bauxite. Intermediate products were desiccated marl, bauxitic argillite and argillaceous bauxite. Subsidence followed, and the bauxite was preserved by the deposition of late Cretaceous limestone and other sediments. Uplift in Oligocene-Miocene time, with ensuing erosion, exposed the bauxite horizon to its present configuration. Concentrations of normative minerals illustrate chemical processes and the build-up of Al in the bauxite horizon. Plots of chemical data and correlation coefficients show that Al, Ti, Zr, Nb, Th, Cr and V were immobile during the bauxitization process. Mass changes point to large net removal of Si, Mg and K from the system, although some of this material and slightly mobile Al were reprecipitated in the underlying argillite and altered marl. Immobile element ratios trace the source of the bauxite to the underlying argillaceous limestone. Al in the bauxite was accumulated from the degradation of 25 to 50 m of the argillaceous limestone. Received: 10 June 1996 / Accepted: 15 April 1997     

Estimation of groundwater evaporation and salt flux from Owens Lake, California, USA

Groundwater evaporation and subsequent precipitation of soluble salts at Owens Lake in eastern California have created one of the single largest sources of airborne dust in the USA, yet the evaporation and salt flux have not been fully quantified. In this study, we compare eddy correlation, microlysimeters and solute profiling methods to determine their validity and sensitivity in playa environments. These techniques are often used to estimate evaporative losses, yet have not been critically compared at one field site to judge their relative effectiveness and accuracy. Results suggest that eddy correlation methods are the most widely applicable for the variety of conditions found on large playa lakes. Chloride profiling is shown to be highly sensitive to thermal and density-driven fluxes in the near surface and, as a result, appears to underestimate yearly groundwater evaporation. Yearly mean groundwater evaporation from the playa surface estimated from the three study areas was found to range from 88 to 104 mm year⁻¹, whereas mean evaporation from the brine-covered areas was 872 mm year⁻¹. Uncertainties on these mean rates were estimated to be ±25%, based on comparisons between eddy correlation and lysimeter estimates. On a yearly basis, evaporation accounts for approximately 47 × 10⁶ m³ of water loss from the playa surface and open-water areas of the lake. Over the playa area, as much as 7.5 × 10⁸ kg (7.5 × 10⁵ t) of salt are annually concentrated by evaporation at or near the playa surface, much of which appears to be lost during dust storms in area.     

Hypolimnetic density currents traced by sulphur hexafluoride (SF6)

The artificial tracer sulphur hexafluoride (SF₆) has been used to study the density-driven deep water exchange between two sill-separated basins of Lake Lucerne, Gersauersee and Urnersee. The sources of the density gradients between the two basins are (1) salinity differences between the major inlets due to the different geology of their drainage areas, and (2) temperature differences due to spatial variation of wind forcing. Wind speeds are generally larger in Urnersee, especially in spring during the so-called Föhn events, when winds blow from the south. In contrast, Gersauersee is protected form these winds. In spring 1989, a total of 630 g of SF₆ was released at 80 to 120 m depth in the small Treib Basin located between Urnersee and Gersauersee. During about 100 days the distribution of SF₆ in the lake was determined by gaschromatography. Two models are used to quantify the exchange flow, (1) a one-box mass balance model for SF₆ in the deep part of Treib Basin, and (2) a one-dimensional diffusion/advection model describing the temporal and vertical temperature variation in Urnersee. According to the first model, the flow into the deep hypolimnion of Urnersee, decreases from 21·10⁶ m³·d^?1 at the end of March to about 8·10⁶ m³·d^?1 in late April. The second model yields similar flow rates. The decrease of the flow rate during spring, confirmed by both approaches, is consistent (1) with the decreasing strength of the density gradient above the sill during spring and early summer, and (2) with hydrographic information collected in Lake Lucerne during other years.     

A mean behavior model of aerobic biodegradation in heterogeneous formation

It has been observed that the field biodegradation rates for soluble hydrocarbon plumes are significantly smaller than the aerobic rates observed in the laboratory. It is believed that this difference is related to the fact that in the field oxygen and hydrocarbon must be mixed before the biodegradation reaction can occur, and that the effective degradation rate is controlled by the actual, not mean, concentrations of oxygen and hydrocarbon. In this work, we present a conceptual model of oxygen-mixing limited biodegradation, which indicates that the effective degradation rate should depend on the cross correlation between the oxygen and hydrocarbon concentration fluctuations. This is followed by a development of a rigorous, field-scale model.     

Testing an earthquake prediction algorithm

A test to evaluate earthquake prediction algorithms is being applied to a Russian algorithm known asM8 TheM8 algorithm makes intermediate term predictions for earthquakes to occur in a large circle, based on integral counts of transient seismicity in the circle. In a retroactive prediction for the period January 1, 1985 to July 1, 1991 the algorithm as configured for the forward test would have predicted eight of ten strong earthquakes in the test area. A null hypothesis, based on random assignment of predictions, predicts eight earthquakes in 2.87% of the trials. The forward test began July 1, 1991 and will run through December 31, 1997. As of July 1, 1995, the algorithm had forward predicted five out of nine earthquakes in the test area, which success ratio would have been achieved in 53% of random trials with the null hypothesis.     

Strengths and limitations of MST radar measurements of middle-atmosphere winds

Radars have been used successfully for many years to measure atmospheric motions over a wide range of altitudes, from ground level up to heights of several hundred kilometres into the ionosphere. In this paper we particularly wish to concentrate on the accuracy of these measurements for winds in the middle atmosphere (i.e. 10–100–km altitude). We begin by briefly reviewing the literature relating to comparisons between radar methods and other techniques. We demonstrate where the radar data are most and least reliable and then, in parallel with a discussion about the basic principles of the method, discuss why these different regimes have the different accuracies and precisions they do. This discussion is used to highlight the strengths and weaknesses of radar methods. Issues like radar volume, aspect sensitivity, gravity wave effects and scatterer intermittency in producing wind biases, and the degree by which the intermittent generation of scatterers at quasi-random points in space could skew the radar measurements, are all considered. We also investigate the possibility that MF radar techniques can be contaminated by E-region scatter to heights as low as 92–95–km altitude (i.e. up to 8–10 km below the ionospheric peak echo). Within all these comments, however, we also recognize that radar methods still represent powerful techniques which have an important future at all levels of the atmosphere.