A physical interpretation of the deterministic fractal–multifractal method as a realization of a generalized multiplicative cascade

In this study, we attempt to offer a solid physical basis for the deterministic fractal–multifractal (FM) approach in geophysics (Puente, Phys Let A 161:441–447, 1992; J Hydrol 187:65–80, 1996). We show how the geometric construction of derived measures, as Platonic projections of fractal interpolating functions transforming multinomial multifractal measures, naturally defines a non-trivial cascade process that may be interpreted as a particular realization of a random multiplicative cascade. In such a light, we argue that the FM approach is as “physical” as any other phenomenological approach based on Richardson’s eddies splitting, which indeed lead to well-accepted models of the intermittencies of nature, as it happens, for instance, when rainfall is interpreted as a quasi-passive tracer in a turbulent flow. Although neither a fractal interpolating function nor the specific multipliers of a random multiplicative cascade can be measured physically, we show how a fractal transformation “cuts through” plausible scenarios to produce a suitable realization that reflects specific arrangements of energies (masses) as seen in nature. This explains why the FM approach properly captures the spectrum of singularities and other statistical features of given data sets. As the FM approach faithfully encodes data sets with compression ratios typically exceeding 100:1, such a property further enhances its “physical simplicity.” We also provide a connection between the FM approach and advection–diffusion processes.     

Evaluating MT3DMS for Heat Transport Simulation of Closed Geothermal Systems

Owing to the mathematical similarities between heat and mass transport, the multi-species transport model MT3DMS should be able to simulate heat transport if the effects of buoyancy and changes in viscosity are small. Although in several studies solute models have been successfully applied to simulate heat transport, these studies failed to provide any rigorous test of this approach. In the current study, we carefully evaluate simulations of a single borehole ground source heat pump (GSHP) system in three scenarios: a pure conduction situation, an intermediate case, and a convection-dominated case. Two evaluation approaches are employed: first, MT3DMS heat transport results are compared with analytical solutions. Second, simulations by MT3DMS, which is finite difference, are compared with those by the finite element code FEFLOW and the finite difference code SEAWAT. Both FEFLOW and SEAWAT are designed to simulate heat flow. For each comparison, the computed results are examined based on residual errors. MT3DMS and the analytical solutions compare satisfactorily. MT3DMS and SEAWAT results show very good agreement for all cases. MT3DMS and FEFLOW two-dimensional (2D) and three-dimensional (3D) results show good to very good agreement, except that in 3D there is somewhat deteriorated agreement close to the heat source where the difference in numerical methods is thought to influence the solution. The results suggest that MT3DMS can be successfully applied to simulate GSHP systems, and likely other systems with similar temperature ranges and gradients in saturated porous media.     

Environmental Determinants of Emergent Macrophyte Vegetation in Pacific Northwest Estuarine Tidal Wetlands

We investigated whether within wetland environmental conditions or surrounding land cover measured at multiple scales were more influential in structuring regional vegetation patterns in estuarine tidal wetlands in the Pacific Northwest, USA. Surrounding land cover was characterized at the 100, 250, and 1,000 m, and watershed buffer scales. Vegetation communities were characterized by high species richness, lack of monotypic zonation, and paucity of invasive species. The number of species per site ranged between 4 and 20 (mean?±?standard deviation?=?10.2?±?3.1). Sites supported a high richness (mean richness of native species 8.7?±?2.8) and abundance of native macrophytes (mean relative abundance 85 %?±?19 %). Vegetation assemblages were dominated by a mix of grasses, sedges, and herbs with Sarcocornia pacifica and Distichlis spicata being common at sites in the oceanic zone of the estuary and Carex lyngbyei and Agrostis stolonifera being common at the fresher sites throughout the study area. The vegetation community was most strongly correlated with salinity and land cover within close proximity to the study site and less so with land cover variables at the watershed scale. Total species richness and richness of native species were negatively correlated with the amount of wetland in the buffer at all scales, while abundance of invasive species was significantly correlated to within wetland factors, including salinity and dissolved phosphorus concentrations. Landscape factors related to anthropogenic disturbances were only important at the 100-m buffer scale, with anthropogenic disturbances further from the wetland not being influential in shaping the vegetation assemblage. Our research suggests that the traditional paradigms of tidal wetland vegetation structure and environmental determinants developed in east coast US tidal wetlands might not hold true for Pacific Northwest wetlands due to their unique chemical and physical factors, necessitating further detailed study of these systems.     

An attenuation model for distant earthquakes

Large magnitude earthquakes generated at source–site distances exceeding 100km are typified by low‐frequency (long‐period) seismic waves. Such induced ground shaking can be disproportionately destructive due to its high displacement, and possibly high velocity, shaking characteristics. Distant earthquakes represent a potentially significant safety hazard in certain low and moderate seismic regions where seismic activity is governed by major distant sources as opposed to nearby (regional) background sources. Examples are parts of the Indian sub‐continent, Eastern China and Indo‐China. The majority of ground motion attenuation relationships currently available for applications in active seismic regions may not be suitable for handling long‐distance attenuation, since the significance of distant earthquakes is mainly confined to certain low to moderate seismicity regions. Thus, the effects of distant earthquakes are often not accurately represented by conventional empirical models which were typically developed from curve‐fitting earthquake strong‐motion data from active seismic regions. Numerous well‐known existing attenuation relationships are evaluated in this paper, to highlight their limitations in long‐distance applications. In contrast, basic seismological parameters such as the Quality factor (Q‐factor) could provide a far more accurate representation for the distant attenuation behaviour of a region, but such information is seldom used by engineers in any direct manner. The aim of this paper is to develop a set of relationships that provide a convenient link between the seismological Q‐factor (amongst other factors) and response spectrum attenuation. The use of Q as an input parameter to the proposed model enables valuable local seismological information to be incorporated directly into response spectrum predictions. The application of this new modelling approach is demonstrated by examples based on the Chi‐Chi earthquake (Taiwan and South China), Gujarat earthquake (Northwest India), Nisqually earthquake (region surrounding Seattle) and Sumatran‐fault earthquake (recorded in Singapore). Field recordings have been obtained from these events for comparison with the proposed model. The accuracy of the stochastic simulations and the regression analysis have been confirmed by comparisons between the model calculations and the actual field observations. It is emphasized that obtaining representative estimates for Q for input into the model is equally important.Thus, this paper forms part of the long‐term objective of the authors to develop more effective communications across the engineering and seismological disciplines. Copyright © 2003 John Wiley & Sons, Ltd.     

Seasonal temperatures for the past ∼400 years reconstructed from diatom and chironomid assemblages in a high-altitude lake (Lej da la Tscheppa,Switzerland)

We analysed a 42 cm long sediment record from Lej da la Tscheppa, a high-altitude lake (2,616 m a.s.l.) in the Upper Engadine valley (Switzerland) for subfossil diatoms, chironomids and pollen. The chronology of the top 21 cm of the record was established using ²¹⁰Pb analysis using a constant-rate-of-supply model, and validated with ¹³⁷Cs measurements and the content of spheroidal carbonaceous particles. A tentative chronology for the lower part of the core was obtained through extrapolation of the sedimentation rates in the uppermost part of the record. Pollen assemblages in the record reflect regional changes in forestation and land-use patterns in the Upper Engadine valley and show no evidence of significant local human activity in the lake’s catchment. Diatom assemblages record a distinct increase in planktonic taxa since the early 19th century, suggesting a decrease in the duration of ice-cover. In contrast, chironomid assemblages remained stable during a large part of the record. We applied an established chironomid-based July air temperature transfer function and a newly developed diatom-based spring air temperature transfer function to reconstruct past seasonal air temperature changes at Lej da la Tscheppa. The reconstructions indicate a diatom-inferred warming trend in spring temperatures during the past ca. 400 years, whereas chironomid-inferred summer temperatures suggest a slight cooling trend. These biota-based reconstructions are in good agreement with the centennial-scale temperature trend in an independent reconstruction of regional temperatures in the Upper Engadine region based on instrumental records and documentary proxy evidence from the Alps. Our results suggest that, in high-altitude lakes, independent chironomid- and diatom-based seasonal temperature reconstruction is possible and can be successfully used to track seasonal temperature trends.     

Polycyclic aromatic hydrocarbons and their molecular diagnostic ratios in urban atmospheric respirable particulate matter

Atmospheric concentrations of polycyclic aromatic hydrocarbons (PAHs) in Santiago de Chile city were evaluated to study particulate PAHs profiles during cold and spring weather periods. Urban atmospheric particulate matter PM10 was collected using High Volume PM10 samplers. Fifteen samples of 24 h during austral winter and 20 samples of 24 h during spring, 2000 were collected at two sampling sites (North–East and Central areas of the city) whose characteristics were representative of the prevailing conditions. Seventeen PAHs were quantified and total PAHs concentration ranged from 1.39 to 59.98 ng m⁻³, with a seasonal variation (winter vs. spring ratio) from 0.5 to 12.6 ng m⁻³. Molecular diagnostic ratios were used to characterize and identify PAHs emission sources such as combustion and biogenic emissions. Results showed that the major sources of respirable organic aerosol PM10 in Santiago are mobile and stationary ones.     

Climate-related cyclic deposition of carbonate and organic matter in Holocene lacustrine sediment,Lower Michigan,USA

Records from lake sediment cores are critical for assessing the relative stability of climate and ecosystems over the Holocene. Duck Lake in south-central Lower Michigan, USA, was the focus of a study that identified how changes in the geochemical variables in lake sediments relate to variations in regional climate and local land use during the Holocene. More than 8.5 m of lacustrine sediment were recovered using Livingston and freeze corers and analyzed for organic carbon, inorganic (carbonate) carbon, total nitrogen, and trace metals. Repeating packages of sediment (1–10 cm thick) that grade from light (inorganic carbon-rich) to dark (organic carbon-rich) were found from the surface to a depth of about 8 m. Variations in the high-resolution gray scale data from core X-radiographs are highly correlated to the relative amount of inorganic carbon. Geochemical analyses of the upper 8.5 m of sediment revealed a wide range of values: 0.05–10.6% for inorganic carbon (i.e. 0.5–89% calcium carbonate) and 1.1–28% for organic carbon (i.e. 2.7–70% organic matter). Organic carbon to nitrogen ratios indicate that most of the sediment organic matter is produced within the lake. A core chronology based on eight AMS radiocarbon dates shows low sediment accumulation rates (0.05 cm/year) from 10,000 to 3,800 cal year BP and higher sediment accumulation rates (0.1–0.3 cm/year) from 3,800 cal year BP to present. We suggest that carbonate accumulates during relatively dry times, whereas organic matter accumulation dominates when nutrient input to the lake is enhanced by wetter climate. The Duck Lake core records a distinct low point in inorganic carbon deposition that may be related to the 8.2 ka cooling event now documented from several sites in North America. Spectral analysis of gray scale values shows significant ~200-year periodicities over the past 8,000 years, hypothesized to result from climate changes induced by solar forcing. Concentrations of trace metals (e.g. lead, iron, copper, zinc) indicate the onset of regional anthropogenic influence about 150 cal year BP.     

Lead isotopes in sulfides from the Stillwater Complex, Montana: evidence for subsolidus remobilization

Isotopic ratios of Pb in sulfide minerals (primarily pyrrhotite, chalcopyrite, and pentlandite) from a suite of samples from the platiniferous J-M Reef of the Stillwater Complex were measured to elucidate the temporal and genetic relationship between sulfides and host silicate minerals. Results indicate that sulfides and coexisting plagioclases are generally not in isotopic equilibrium, that both sulfides and feldspars record highly radiogenic initial ratios at 2.7 Ga, and that a component of “post-emplacement” radiogenic Pb has mixed with common Pb in the sulfides. A model involving introduction of radiogenic Pb carried by fluids derived from sources external to the complex is favored. Analyses of the lead isotopic composition of sulfides in veins which cut the complex indicate that a significant fraction of the radiogenic lead which was added to the sulfides was externally derived during an extensive hydrothermal episode, associated with Proterozoic regional metamorphism around 1.7 Ga. The possibility that some fractions of the radiogenic Pb may have been derived from primary minerals altered during the low-grade metamorphism cannot be discounted. The amount of radiogenic lead added is variable and in some cases negligible. There is a good correlation between the lead isotope composition and the nature of the secondary mineral assemblage. Sulfides and plagioclases in samples that show little or no alteration of the primary minerals are generally in isotopic equilibrium and preserve isotope ratios consistent with magmatic crystallization at 2.7 Ga. Samples with the most radiogenic sulfides contain abundant secondary minerals (serpentine, talc, actinolite, chlorite and zoisite) associated with greenschist facies metamorphism. Some of the radiogenic Pb in the sulfides can be removed by progressive stepwise leaching. However, in most samples recrystallization of sulfides during metamorphism has mixed common Pb and radiogenic Pb throughout the crystal structure such that, in these samples, stepwise leaching does not recover initial Pb isotopic ratios. Plagioclases are much more resistant to low temperature recrystallization and in almost all cases, stepwise leaching reveals the initial lead isotopic composition. The reactivity of sulfides over a wide temperature range enhances their utility in understanding not only the processes involved in their formation at the time of magmatic emplacement but also postmagmatic processes which were important in the redistribution and enrichment of platinum group elements (PGE) within the ore zone. Received: 30 December 1998 / Accepted: 16 June 1999