Fractally Invariant Distributions and an Application in Geochemical Exploration

Fractal modelling has been applied extensively as a means of characterizing the spatial distribution of geological phenomena that display self-similarity at differing scales of measurement. A fractal distribution exists where the number of objects exhibiting values larger than a specified magnitude displays a power-law dependence on that magnitude, and where this relationship is scale-invariant. This paper shows that a number of distributions, including power-function, Pareto, log-normal and Zipf, display fractal properties under certain conditions and that this may be used as the mathematical basis for developing fractal models for data exhibiting such distributions. Population limits, derived from fractal modelling using a summation method, are compared with those derived from more conventional probability plot modelling of stream sediment geochemical data from north-eastern New South Wales. Despite some degree of subjectivity in determining the number of populations to use in the models, both the fractal and probability plot modelling have assisted in isolating anomalous observations in the geochemical data related to the occurrence of mineralisation or lithological differences between sub-catchments. Thresholds for the main background populations determined by the fractal model are similar to those established using probability plot modelling, however the summation method displays less capacity to separate out anomalous populations, especially where such populations display extensive overlap. This suggests, in the geochemical data example provided, that subtle differences in the population parameters may not significantly alter the fractal dimension.     

Stochastic Modelling of the Impact of Flood Protection Measures Along the River Waal in the Netherlands

River flooding is a problem of international interest. In the past few years many countries suffered from severe floods. A large part of the Netherlands is below sea level and river levels. The Dutch flood defences along the river Rhine are designed for water levels with a probability of exceedance of 1/1250 per year. These water levels are computed with a hydrodynamic model using a deterministic bed level and a deterministic design discharge. Traditionally, the safety against flooding in the Netherlands is obtained by building and reinforcing dikes. Recently, a new policy was proposed to cope with increasing design discharges in the Rhine and Meuse rivers. This policy is known as the Room for the River (RfR) policy, in which a reduction of flood levels is achieved by measures creating space for the river, such as dike replacement, side channels and floodplain lowering. As compared with dike reinforcement, these measures may have a stronger impact on flow and sediment transport fields, probably leading to stronger morphological effects. As a result of the latter the flood conveyance capacity may decrease over time. An a priori judgement of safety against flooding on the basis of an increased conveyance capacity of the river can be quite misleading. Therefore, the determination of design water levels using a fixed-bed hydrodynamic model may not be justified and the use of a mobile-bed approach may be more appropriate. This problem is addressed in this paper, using a case study of the river Waal (one of the Rhine branches in the Netherlands). The morphological response of the river Waal to a flood protection measure (floodplain lowering in combination with summer levee removal) is analysed. The effect of this measure is subject to various sources of uncertainty. Monte Carlo simulations are applied to calculate the impact of uncertainties in the river discharge on the bed levels. The impact of the “uncertain” morphological response on design flood level predictions is analysed for three phenomena, viz. the impact of the spatial morphological variation over years, the impact of the seasonal morphological variation and the impact of the morphological variability around bifurcation points. The impact of seasonal morphological variations turns out to be negligible, but the other two phenomena appear to have each an appreciable impact (order of magnitude 0.05–0.1 m) on the computed design water levels. We have to note however, that other sources of uncertainty (e.g. uncertainty in hydraulic roughness predictor), which may be of influence, are not taken into consideration. In fact, the present investigation is limited to the sensitivity of the design water levels to uncertainties in the predicted bed level.     

Detection and 2d modelling of cavities using pole–dipole array

The resistivity method is often used in cave prospecting. In this paper the pole–dipole array ability to detect cavities at different depths and with different water contents is investigated. The research was performed using analogical and numerical modelling. According to the results, empty caves at a depth less than four times its diameter can be easily detected. The ability of the pole–dipole array to detect water-filled caves reaches a minimum at filling percentages of 30–50%. Overburden effects research shows that low resistivity overburden reduces the resolution capability of the array. This study shows that equivalent results can be obtained by modelling the empty caves as infinite resistivity bodies or, alternatively, as very high resistivity ones. The analysis of field data acquired in the Maciço Calcário Estremenho (Portugal) shows the practical importance of the pole–dipole array in cavities prospecting.     

Modélisation géométrique 3D des granites stéphaniens du massif du Pelvoux (Alpes,France)

The structural analysis and the 3D modelling of Stephanian granites of the Pelvoux Massif characterize an emplacement along sinistral NW–SE- and dextral NE–SW-trending shear zones in the Pelvoux and in the Aiguilles Rouges–Mont Blanc Massifs, respectively. This Carboniferous shear system is consistent with a north–south extension direction known in the whole Variscan belt at this time. To cite this article: P. Strzerzynski et al., C. R. Geoscience 337 (2005).     

Critical rainfall statistics for predicting watershed flood responses: rethinking the design storm concept

Recent advances have been made to modernize estimates of probable precipitation scenarios; however, researchers and engineers often continue to assume that rainfall events can be described by a small set of event statistics, typically average intensity and event duration. Given the easy availability of precipitation data and advances in desk‐top computational tools, we suggest that it is time to rethink the ‘design storm’ concept. Design storms should include more holistic characteristics of flood‐inducing rain events, which, in addition to describing specific hydrologic responses, may also be watershed or regionally specific. We present a sensitivity analysis of nine precipitation event statistics from observed precipitation events within a 60‐year record for Tompkins County, NY, USA. We perform a two‐sample Kolmogorov–Smirnov (KS) test to objectively identify precipitation event statistics of importance for two related hydrologic responses: (1) peak outflow from the Six Mile Creek watershed and (2) peak depth within the reservoir behind the Six Mile Creek Dam. We identify the total precipitation depth, peak hourly intensity, average intensity, event duration, interevent duration, and several statistics defining the temporal distribution of precipitation events to be important rainfall statistics to consider for predicting the watershed flood responses. We found that the two hydrologic responses had different sets of statistically significant parameters. We demonstrate through a stochastic precipitation generation analysis the effects of starting from a constrained parameter set (intensity and duration) when predicting hydrologic responses as opposed to utilizing an expanded suite of rainfall statistics. In particular, we note that the reduced precipitation parameter set may underestimate the probability of high stream flows and therefore underestimate flood hazard. Copyright © 2016 John Wiley & Sons, Ltd.     

Fluid generation and evolution during exhumation of deeply subducted UHP continental crust: Petrogenesis of composite granite–quartz veins in the Sulu belt,China

Composite granite–quartz veins occur in retrogressed ultrahigh pressure (UHP) eclogite enclosed in gneiss at General's Hill in the central Sulu belt, eastern China. The granite in the veins has a high‐pressure (HP) mineral assemblage of dominantly quartz+phengite+allanite/epidote+garnet that yields pressures of 2.5–2.1 GPa (Si‐in‐phengite barometry) and temperatures of 850–780°C (Ti‐in‐zircon thermometry) at 2.5 GPa (~20°C lower at 2.1 GPa). Zircon overgrowths on inherited cores and new grains of zircon from both components of the composite veins crystallized at c. 221 Ma. This age overlaps the timing of HP retrograde recrystallization dated at 225–215 Ma from multiple localities in the Sulu belt, consistent with the HP conditions retrieved from the granite. The ε_Hf(t) values of new zircon from both components of the composite veins and the Sr–Nd isotope compositions of the granite consistently lie between values for gneiss and eclogite, whereas δ¹⁸O values of new zircon are similar in the veins and the crustal rocks. These data are consistent with zircon growth from a blended fluid generated internally within the gneiss and the eclogite, without any ingress of fluid from an external source. However, at the peak metamorphic pressure, which could have reached 7 GPa, the rocks were likely fluid absent. During initial exhumation under UHP conditions, exsolution of H₂O from nominally anhydrous minerals generated a grain boundary supercritical fluid in both gneiss and eclogite. As exhumation progressed, the volume of fluid increased allowing it to migrate by diffusing porous flow from grain boundaries into channels and drain from the dominant gneiss through the subordinate eclogite. This produced a blended fluid intermediate in its isotope composition between the two end‐members, as recorded by the composite veins. During exhumation from UHP (coesite) eclogite to HP (quartz) eclogite facies conditions, the supercritical fluid evolved by dissolution of the silicate mineral matrix, becoming increasingly solute‐rich, more ‘granitic’ and more viscous until it became trapped. As crystallization began by diffusive loss of H₂O to the host eclogite concomitant with ongoing exhumation of the crust, the trapped supercritical fluid intersected the solvus for the granite–H₂O system, allowing phase separation and formation of the composite granite–quartz veins. Subsequently, during the transition from HP eclogite to amphibolite facies conditions, minor phengite breakdown melting is recorded in both the granite and the gneiss by K‐feldspar+plagioclase+biotite aggregates located around phengite and by K‐feldspar veinlets along grain boundaries. Phase equilibria modelling of the granite indicates that this late‐stage melting records P–T conditions towards the end of the exhumation, with the subsolidus assemblage yielding 0.7–1.1 GPa at <670°C. Thus, the composite granite–quartz veins represent a rare example of a natural system recording how the fluid phase evolved during exhumation of continental crust. The successive availability of different fluid phases attending retrograde metamorphism from UHP eclogite to amphibolite facies conditions will affect the transport of trace elements through the continental crust and the role of these fluids as metasomatic agents interacting with the mantle wedge in the subduction channel.     

Characterizing rainfall–groundwater dynamics in a hard‐rock aquifer system using time series,geographic information system and geostatistical modelling

The aim of this study was to investigate rainfall–groundwater dynamics over space and annual time scales in a hard‐rock aquifer system of India by employing time series, geographic information system and geostatistical modelling techniques. Trends in 43‐year (1965–2007) annual rainfall time series of ten rainfall stations and 16‐year (1991–2006) pre‐monsoon and post‐monsoon groundwater levels of 140 sites were identified by using Mann–Kendall, Spearman rank order correlation and Kendall rank correlation tests. Trends were quantified by Kendall slope method. Furthermore, the study involves novelty of examining homogeneity of pre‐monsoon and post‐monsoon groundwater levels, for the first time, by applying seven tests. Regression analysis between rainfall and post‐monsoon groundwater levels was performed. The pre‐monsoon and post‐monsoon groundwater levels for four periods – 1991–1994, 1995–1998, 1999–2002 and 2003–2006 – were subjected to geographic information system‐based geostatistical modelling. The rainfall showed considerable spatiotemporal variations, with a declining trend at the Mavli rainfall station (p‐value < 0.05). The Levene's tests revealed spatial homogeneity of rainfall at α = 0.05. Regression analyses indicated significant relationships (r² > 0.5) between groundwater level and rainfall for eight rainfall stations. Non‐homogeneity and declining trends in the groundwater level, attributed to anthropogenic and hydrologic factors, were found at 5–61 more sites in pre‐monsoon compared with post‐monsoon season. The groundwater declining rates in phyllite–schist, gneiss, schist and granite formations were found to be 0.18, 0.26, 0.21 and 0.14 m year^?1 and 0.13, 0.19, 0.16 and 0.02 m year^?1 during the pre‐monsoon and post‐monsoon seasons, respectively. The geostatistical analyses for four time periods revealed linkages between the rainfall and groundwater levels. Copyright © 2013 John Wiley & Sons, Ltd.     

Investigation into the effect of fault properties on wave transmission

The estimation of wave transmission across the fractured rock masses is of great importance for rock engineers to assess the stability of rock slopes in open pit mines. Presence of fault, as a major discontinuity, in the jointed rock mass can significantly impact on the peak particle velocity and transmission of blast waves, particularly where a fault contains a thick infilling with weak mechanical properties. This paper aims to study the effect of fault properties on transmission of blasting waves using the distinct element method. First, a validation study was carried out on the wave transmission across a single joint and different rock mediums through undertaking a comparative study against analytical models. Then, the transmission of blast wave across a fault with thick infilling in the Golgohar iron mine, Iran, was numerically studied, and the results were compared with the field measurements. The blast wave was numerically simulated using a hybrid finite element and finite difference code which then the outcome was used as the input for the distinct element method analysis. The measured uplift of hanging wall, as a result of wave transmission across the fault, in the numerical model agrees well with the recorded field measurement. Finally, the validated numerical model was used to study the effect of fault properties on wave transmission. It was found that the fault inclination angle is the most effective parameter on the peak particle velocity and uplift. Copyright © 2017 John Wiley & Sons, Ltd.     

Using raw regional climate model outputs for quantifying climate change impacts on hydrology

General circulation model outputs are rarely used directly for quantifying climate change impacts on hydrology, due to their coarse resolution and inherent bias. Bias correction methods are usually applied to correct the statistical deviations of climate model outputs from the observed data. However, the use of bias correction methods for impact studies is often disputable, due to the lack of physical basis and the bias nonstationarity of climate model outputs. With the improvement in model resolution and reliability, it is now possible to investigate the direct use of regional climate model (RCM) outputs for impact studies. This study proposes an approach to use RCM simulations directly for quantifying the hydrological impacts of climate change over North America. With this method, a hydrological model (HSAMI) is specifically calibrated using the RCM simulations at the recent past period. The change in hydrological regimes for a future period (2041–2065) over the reference (1971–1995), simulated using bias‐corrected and nonbias‐corrected simulations, is compared using mean flow, spring high flow, and summer–autumn low flow as indicators. Three RCMs driven by three different general circulation models are used to investigate the uncertainty of hydrological simulations associated with the choice of a bias‐corrected or nonbias‐corrected RCM simulation. The results indicate that the uncertainty envelope is generally watershed and indicator dependent. It is difficult to draw a firm conclusion about whether one method is better than the other. In other words, the bias correction method could bring further uncertainty to future hydrological simulations, in addition to uncertainty related to the choice of a bias correction method. This implies that the nonbias‐corrected results should be provided to end users along with the bias‐corrected ones, along with a detailed explanation of the bias correction procedure. This information would be especially helpful to assist end users in making the most informed decisions.     

Soil property variation mapping through data mining of soil category maps

Spatial information on soil properties is an important input to hydrological models. In current hydrological modelling practices, soil property information is often derived from soil category maps by the linking method in which a representative soil property value is linked to each soil polygon. Limited by the area‐class nature of soil category maps, the derived soil property variation is discontinuous and less detailed than high resolution digital terrain or remote sensing data. This research proposed dmSoil, a data‐mining‐based approach to derive continuous and spatially detailed soil property information from soil category maps. First, the soil–environment relationships are extracted through data mining of a soil map. The similarity of the soil at each location to different soil types in the soil map is then estimated using the mined relationships. Prediction of soil property values at each location is made by combining the similarities of the soil at that location to different soil types and the representative soil property values of these soil types. The new approach was applied in the Raffelson Watershed and Pleasant Valley in the Driftless Area of Wisconsin, United States to map soil A horizon texture (in both areas) and depth to soil C horizon (in Pleasant Valley). The property maps from the dmSoil approach capture the spatial gradation and details of soil properties better than those from the linking method. The new approach also shows consistent accuracy improvement at validation points. In addition to the improved performances, the inputs for the dmSoil approach are easy to prepare, and the approach itself is simple to deploy. It provides an effective way to derive better soil property information from soil category maps for hydrological modelling. Copyright © 2014 John Wiley & Sons, Ltd.