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.     

Acoustic core logging in blast-damaged rock

Thill, R.E. and D' Andrea, D. V., 1975. Acoustic core logging in blast-damaged rock. Eng. Geol., 10: 13–36.The Bureau of Mines, in cooperation with the Duval Corp., conducted a blast-fragmentation experiment to determine the feasibility of preparing a porphyry copper-molybdenum deposit for in-situ leaching. The blast was designed with ten 9-inch-diameter blastholes to depths of 110 feet in an equilateral triangle configuration; spacings between blastholes were 15, 20, and 25 ft. One of the major problems in the experiment was in assessing blast damage. Acoustic core-logging equipment and methods were devised and used as one approach in solving this problem. Ultrasonic pulse travel-times were determined in four diametral directions at 2-ft intervals of depth to a final depth of 120 ft in three preblast and six postblast drill cores at the Duval test site. The acoustic logging program provided compressional wave travel-time at 0°, 45°, 90°, and 135° around the core circumference, maximum travel-time difference, mean compressional-wave velocity, and an anisotropy factor. Other acoustic parameters introduced in the analyses were stiffness modulus, seismic quality designation (SQD), and a compensated velocity to account for portions of the core that were nonrecoverable or too highly fractured to permit diametral travel-time measurements.The acoustic parameters all indicated the deterioration in structural quality from the preblast condition, in which the rock already was badly fractured and weathered, to the more highly fractured postblast condition. Because of the highly fragmented, poor structural condition of the rock after blasting, the rock was indicated to be suitable for in-situ leaching, at least at the 20- and 15-ft blasthole spacings, and even in some zones in the rock at the 25-ft blasthole spacing.     

A high-resolution geophysical investigation of sediment distribution controlled by catchment size and tides in a multi-basin turbid outwash fjord: Simpson Bay,Prince William Sound,Alaska

Surficial sediment distribution within Simpson Bay is a function of antecedent bedrock and recently deposited glacial geology, as well as active physical processes both within Simpson Bay and Prince William Sound (PWS). Simpson Bay is a turbid, outwash fjord located in northeastern PWS, Alaska. Freshwater from heavy precipitation, and the melting of high alpine glaciers enter the bay through bay head rivers and small shoreline creeks. The catchment has a high watershed/basin surface area ratio (∼8:1), and easily erodible bedrock that contribute to high sediment loads. The system can be divided into three discrete basins, each with specific morphologic and circulatory characters. Side scan sonar, swath bathymetry, and seismic profiles reveal that bathymetric highs are areas of outcropping glacial surfaces. High backscatter coupled with surface grab samples reveal these surfaces to be composed of coarse sediment and bedrock outcrops. Bathymetric lows are areas of low backscatter, and grab samples reveal these areas to be ponded deposits of organic-rich estuarine muds. The data provide evidence of terminal morainal bank systems, and glacial grounding line deposits at the mouth of the bay and rocky outcrops were identified as subsurface extensions of aerial rocky promontories. Radioisotope analyses of short cores reveal that the bay has an average accumulation rate of approx. 0.5 cm year⁻¹, but that this varies in function of the watershed/basin surface area ratios of the different basins. The interaction of tidal currents and sediment source drives sediment distribution in Simpson Bay. Hydrographic data reveal high spatial variability in surface and bottom currents throughout the bay. Subsurface currents are tide dominated, but generally weak (5–20 cm s⁻¹), while faster currents are found along shorelines, outcrops, and bathymetric highs. Bathymetric data reveal steep slopes with little to no modern sediment throughout the bay, suggesting lack of deposition due to tidal currents.     

Engineering geomorphological characterisation of the Vajont Slide,Italy, and a new interpretation of the chronology and evolution of the landslide

Although the 1963 Vajont Slide in Italy has been extensively studied for over 50 years, its regional geological and geomorphological context has been neglected. In this paper, we use field observations and remote sensing data to elucidate the interaction between endogenic and exogenic processes that brought the north slope of Monte Toc to failure. We present the first detailed pre- and post-failure engineering geomorphology maps of the slide area. The maps delineate two main landslide blocks, several sub-blocks, compressional and extensional zones, and secondary failures in the deposit. The maps provide new insights into the kinematics, dynamics and evolution of the slide. Finally, we discuss the origin of Vajont Gorge and a prehistoric failure that occurred at the same location as the 1963 slide. We propose, as part of a newly developed multi-stage landscape evolution sequence, that the prehistoric failure was a deep-seated gravitational slope deformation (sackung) that initiated during deglaciation and continued to slowly move until the catastrophic failure in 1963. We argue that the gorge was created by these deep-seated slow movements.     

Preparation and Measurement of Cassiterite for Sn Isotope Analysis

Increased interest in the fractionation of Sn isotopes has led to the development of several techniques for preparing cassiterite (SnO₂, the primary ore of Sn) for isotopic analysis. Two distinct methods have been applied in recent isotopic studies of cassiterite: (a) reduction to tin metal with potassium cyanide (KCN) at high temperature (800 °C), with subsequent dissolution in HCl, and (b) reduction to a Sn solution with hydriodic acid (HI) at low temperature (100 °C). This study compares the effectiveness and accuracy of these two methods and contributes additional methodological details. The KCN method consistently yielded more Sn (> 70% in comparison with < 5%), does not appear to fractionate Sn isotopes at high temperatures over a 2‐hour period and produced consistent Sn isotope values at flux mass ratios of ≥ 4:1 (flux to mineral) with a minimum reduction time of 40 min. By means of a distillation experiment, it was demonstrated that HI could volatilise Sn, explaining the consistently low yields by this method. Furthermore, the distillation generated Sn vapour, which is up to 0.38‰ per mass unit different from the starting material, the largest induced Sn fractionation reported to date. Accordingly, the HI method is not recommended for cassiterite preparation for Sn isotopic analysis.     

Stable carbon isotopes (δ<Superscript>13</Superscript>C) of total organic carbon and long-chain <Emphasis Type="Italic">n</Emphasis>-alkanes as proxies for climate and environmental change in a sediment core from Lake Petén-Itzá, Guatemala

Sediment core PI-6 from Lake Petén Itzá, Guatemala, possesses an ~85-ka record of climate and environmental change from lowland Central America. Variations in sediment lithology suggest large and abrupt changes in precipitation during the last glacial and deglacial periods, and into the early Holocene. We measured stable carbon isotope ratios of total organic carbon and long-chain n-alkanes from the core, the latter representing a largely allochthonous (terrestrial) source of organic matter, to reveal past shifts in the relative proportion of C₃–C₄ terrestrial biomass. We sought to test whether stable carbon isotope results were consistent with other paleoclimate proxies measured in the PI-6 core, and if extraction and isotope analysis of n-alkanes is warranted. The largest δ¹³C variations are associated with Heinrich Events. Carbon isotope values in sediments deposited during the last glacial maximum indicate moderate precipitation with little fluctuation. The deglacial was a period of pronounced climate variability, e.g. a relatively warm and moist Bølling–Allerød, but a cool and dry Younger Dryas. Arid periods of the deglacial were inferred from samples with high δ¹³C values in total organic carbon, which reflect times of greater proportions of C₄ plants. These inferences are supported by stable isotope measurements on ostracod shells and relative abundance of grass pollen from the same depths in core PI-6. Similar trends in carbon stable isotopes measured on bulk organic carbon and n-alkanes suggest that carbon isotope measures on bulk organic carbon in sediments from this lake are sufficient to infer past climate-driven shifts in local vegetation.     

Weathering of granite in Antarctica: II. Thermal stress at the grain scale

Granular disintegration has long been recognized and referred to in weathering texts from all environments, including the Antarctic. Despite this universal identification and referral, few to no data exist regarding thermal conditions at this scale and causative mechanisms remain little more than conjecture. Here, as part of a larger weathering study, thermal data of individual grains (using infrared thermometry and ultra‐fine thermocouples) composing a coarse granite, as well as the thermal gradients in the outer 10 cm (using thermistors), were collected from a north‐facing exposure. Measurements were also made regarding the surface roughness of the rock. Based on recorded temperatures, the nature of the rock surface and the properties of the minerals, an argument is made for complex stress fields that lead to granular disintegration. Mineral to mineral temperature differences found to occur were, in part, due to the changing exposure to solar radiation through the day (and through seasons). Because the thermal conductivity and the coefficient of thermal expansion of quartz are not equal in all directions, coupled with the vagaries of heating, this leads to inter‐granular stresses. Although fracture toughness increases with a decrease in temperature, it is suggested that the tensile forces resulting from falling temperatures are able to exceed this and produce granular disassociation. The lack of equality with respect to crystal axis of both thermal conductivity and expansion in quartz further exacerbates the propensity to failure. Grain size and porosity also influence the thermal stresses and may help explain why some grains are held in place despite disassociation near the surface. While the data presented here appear to beg more questions than providing answers, they do provide a basis for better, more detailed studies of this important weathering scale. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical modelling of the effects of foundation scour on the response of a bridge pier

Foundation scour can have a detrimental effect on the performance of bridge piers, inducing a significant reduction of the lateral capacity of the footing and accumulation of permanent settlement and rotation. Although the hydraulic processes responsible for foundation scour are nowadays well known, predicting their mechanical consequences is still challenging. Indeed, its impact on the failure mechanisms developing around the foundation has not been fully investigated. In this paper, numerical simulations are performed to study the vertical and lateral response of a scoured bridge pier founded on a cylindrical caisson foundation embedded in a layer of dense sand. The sand stress–strain behaviour is reproduced by employing the Severn-Trent model. The constitutive model is firstly calibrated on a set of soil element tests, including drained and undrained monotonic triaxial tests and resonant column tests. The calibration procedure is implemented considering the stress and strain nonuniformities within the samples, by simulating the laboratory tests as boundary value problems. The numerical model is then validated against the results of centrifuge tests. The results of the simulations are in good agreement with the experimental results in terms of foundation capacity and settlement accumulation. Moreover, the model can predict the effects of local and general scour. The numerical analyses also highlight the impact of scouring on the failure mechanisms, revealing that the soil resistance depends on the hydraulic scenario.

     

Bromine cycle in subduction zones through in situ Br monitoring in diamond anvil cells

The geochemical partitioning of bromine between hydrous haplogranitic melts, initially enriched with respect to Br and aqueous fluids, has been continuously monitored in situ during decompression. Experiments were carried out in diamond anvil cells from 890 °C to room temperature and from 1.7 GPa to room pressure, typically from high P, T conditions corresponding to total miscibility (presence of a supercritical fluid). Br contents were measured in aqueous fluids, hydrous melts and supercritical fluids. Partition coefficients of bromine were characterized at pressure and temperature between fluids, hydrous melts and/or glasses, as appropriate: D^Br_fluid/melt = (Br)_fluid/(Br)_melt, ranges from 2.18 to 9.2 ± 0.5 for conditions within the ranges 0.66-1.7 GPa, 590-890 °C; and D^Br_fluid/glass = (Br)_fluid/(Br)_glass ranges from 60 to 375 at room conditions. The results suggest that because high pressure melts and fluids are capable of accepting high concentrations of bromine, this element may be efficiently removed from the slab to the mantle source of arc magmas. We show that Br may be highly concentrated in subduction zone magmas and strongly enriched in subduction-related volcanic gases, because its mobility is strongly correlated with that of water during magma degassing. Furthermore, our experimental results suggest that a non negligible part of Br present in the subducted slab may remain in the down-going slab, being transported toward the transition zone. This indicates that the Br cycle in subduction zones is in fact divided in two related but independent parts: (1) a shallower one where recycled Br may leave the slab with a water and silica-bearing “fluid” leading to enriched arc magmas that return Br to the atmosphere. (2) A deeper cycle where Br may be recycled back to the mantle maybe to the transition zone, where it may be present in high pressure water-rich metasomatic fluids.     

Hypogeal geological survey in the “Grotta del Re Tiberio” natural cave (Apennines, Italy): a valid tool for reconstructing the structural setting

As karst systems are natural windows to the underground, speleology, combined with geological surveys, can be useful tools for helping understand the geological evolution of karst areas. In order to enhance the reconstruction of the structural setting in a gypsum karst area (Vena del Gesso, Romagna Apennines), a detailed analysis has been carried out on hypogeal data. Structural features (faults, fractures, tectonic foliations, bedding) have been mapped in the ”Grotta del Re Tiberio” cave, in the nearby gypsum quarry tunnels and open pit benches. Five fracture systems and six fault systems have been identified. The fault systems have been further analyzed through stereographic projections and geometric-kinematic evaluations in order to reconstruct the relative chronology of these structures. This analysis led to the detection of two deformation phases. The results permitted linking of the hypogeal data with the surface data both at a local and regional scale. At the local scale, fracture data collected in the underground have been compared with previous authors’ surface data coming from the quarry area. The two data sets show a very good correspondence, as every underground fracture system matches with one of the surface fracture system. Moreover, in the cave, a larger number of fractures belonging to each system could be mapped. At the regional scale, the two deformation phases detected can be integrated in the structural setting of the study area, thereby enhancing the tectonic interpretation of the area (e.g., structures belonging to a new deformation phase, not reported before, have been identified underground). The structural detailed hypogeal survey has, thus, provided very useful data, both by integrating the existing information and revealing new data not detected at the surface. In particular, some small structures (e.g., displacement markers and short fractures) are better preserved in the hypogeal environment than on the surface where the outcropping gypsum is more exposed to dissolution and recrystallization. The hypogeal geological survey, therefore, can be considered a powerful tool for integrating the surface and log data in order to enhance the reconstruction of the deformational history and to get a three-dimensional model of the bedrock in karst areas.