Learning of pore pressure response and dynamic soil behavior from downhole array measurements

Downhole arrays are deployed to measure motions at the ground surface and within the soil profile, with some arrays instrumented to also record the pore pressure response within soft soil profiles during excitation. The measurements from these arrays have typically been used in conjunction with parametric and nonparametric inverse analysis approaches to identify soil constitutive model parameters for use in site response analysis or to identify averaged soil behavior between locations of measurement. The self-learning simulations (SelfSim) inverse analysis framework, previously developed and applied under total stress conditions, is extended to effective stress considerations and is employed to reproduce the measured motions and pore pressures from downhole arrays while extracting the underlying soil behavior and pore pressure response of individual soil layers. SelfSim is applied to the 1987 recordings from the Imperial Valley Wildlife Liquefaction Array. The extracted soil behavior suggests a new functional form for modeling the degradation of the shear modulus with respect to excess pore pressures. The extracted pore pressure response is dependent on the number and amplitude of shear strain cycles and has a functional form similar to current strain-based pore pressure generation models.     

Influence of pore size and geometry on peat unsaturated hydraulic conductivity computed from 3D computed tomography image analysis

In organic soils, hydraulic conductivity is related to the degree of decomposition and soil compression, which reduce the effective pore diameter and consequently restrict water flow. This study investigates how the size distribution and geometry of air‐filled pores control the unsaturated hydraulic conductivity of peat soils using high‐resolution (45 µm) three‐dimensional (3D) X‐ray computed tomography (CT) and digital image processing of four peat sub‐samples from varying depths under a constant soil water pressure head. Pore structure and configuration in peat were found to be irregular, with volume and cross‐sectional area showing fractal behaviour that suggests pores having smaller values of the fractal dimension in deeper, more decomposed peat, have higher tortuosity and lower connectivity, which influences hydraulic conductivity. The image analysis showed that the large reduction of unsaturated hydraulic conductivity with depth is essentially controlled by air‐filled pore hydraulic radius, tortuosity, air‐filled pore density and the fractal dimension due to degree of decomposition and compression of the organic matter. The comparisons between unsaturated hydraulic conductivity computed from the air‐filled pore size and geometric distribution showed satisfactory agreement with direct measurements using the permeameter method. This understanding is important in characterizing peat properties and its heterogeneity for monitoring the progress of complex flow processes at the field scale in peatlands. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of vegetation on soil slippage by pore pressure modification

Influences of vegetation on shallow (< 1 m) soil slip formation through modification of soil water was investigated on hillsides covered by verdant chaparral (dense shrubland), and burned vegetation in the Transverse Ranges of California. Per cent available water and hydraulic potentials were obtained from electrical resistance blocks and tensiometers for one year in soils under burned and unburned vegetation on three slopes. Soil remained moister during a dry period under burned vegetation than under unburned chaparral on two of the three slopes studied. Daily increases in per cent available water and hydraulic potential of soils were greatest for a given storm where soil was driest prior to the storm. Furthermore, water levels in soil tended to be greatest for a given storm where soil water levels had been lowest prior to the storm. These two findings were corroborated by laboratory wetting trials on undisturbed soils of vastly differing mechanical properties in that initially drier soils always absorbed water faster and became wetter than initially moister soils. In the field, soil water levels became similarly high under all vegetation after several storms and varied little throughout the remainder of the wet season. These results contradict the common assumption that depletion of soil water by vegetation would result in slower saturation rates and hence greater resistance of a soil mass to slippage.     

基于数字岩心的碳酸盐岩孔隙结构对弹性性质的影响研究(上篇):图像处理与弹性模拟

碳酸盐岩复杂的孔隙结构如何影响其弹性性质一直是地球物理研究的难点问题,在此基础上如何半定量甚至是定量地对碳酸盐岩储层预测,特别是如何有效地获取孔隙结构参数相关的地震属性体一直是油气工业界追求的目标.本研究从数字岩心角度入手,联合测井以及地震数据尝试探究这一问题的解决方案,包括如下几个方面：（1）代表性碳酸盐岩储层样品获取;（2）CT扫描数字岩心数据体获取;（3）数字岩心数据的图像处理;（4）数字岩心数据的静态弹性模拟;（5）数字岩心子数据体的孔隙结构因子提取;（6）孔隙结构因子表征与分类下的弹性性质与孔隙度的定量化量版建立;（7）数字岩心-井-地震联合的孔隙度属性提取;（8）孔隙结构因子的地震属性体获取.

本研究分为两篇系列文章上篇与下篇,上篇主要阐述如上提出的（1）-（4）方面,重点在于针对碳酸盐岩二值化图像处理的流程建立与验证,以及数字岩心静态弹性模拟的理论方面,这两方面是基于数字岩心获得精确的碳酸盐岩弹性性质模拟结果的关键所在;下篇主要阐述利用数字岩心数据获得孔隙结构因子的思路、理论与流程,以及为碳酸盐岩储层预测为目标而获得孔隙结构因子的地震属性体的实际应用方面.由于两篇文章共享数字岩心数据,同时所涉及的研究思路与流程形成一个有机整体,因此写成两篇系列文章而非两篇独立文章.本文为两篇系列文章的第一篇：上篇.

     

基于数字岩心的碳酸盐岩孔隙结构对弹性性质的影响研究(下篇):储层孔隙结构因子表征与反演

碳酸盐岩复杂的孔隙结构如何影响其弹性性质一直是地球物理研究的难点问题,在此基础上如何半定量甚至是定量地对碳酸盐岩储层预测,特别是如何有效地获取孔隙结构参数相关的地震属性体一直是油气工业界追求的目标,本研究从数字岩心角度入手,联合测井以及地震数据尝试探究这一问题的解决方案.首先针对代表不同孔隙结构类型的有限数目的碳酸盐岩样品获得其对应的高精度数字岩心数据体,为了获得更加可靠的具有地球物理含义的弹性性质随孔隙度变化的统计规律,我们通过子网格的技术,在有限数目的碳酸盐岩数字岩心数据体上获得了大量的数字岩心子网格样本,对于每个子网格样本可以分别获得其对应的数字岩心图像孔隙度、表征孔隙软硬程度的孔隙结构参数（γ）、以及基于有限元法模拟的弹性性质,由此基于数字岩心的研究思路,我们最终获得了基于孔隙结构因子表征与分类下的弹性性质与孔隙度的定量化解释量版.与此同时,在地震尺度上通过叠前地震资料获取的纵横波及密度属性体后,基于如上获得的定量化解释量版,我们最终获得了针对碳酸盐岩储层的新的属性体——孔隙结构参数（γ）属性体,这使得在地震尺度上预测碳酸盐岩储层的孔隙结构类型成为可能,也使利用地震数据在孔隙结构参数表征与分类下的碳酸盐岩储层反演精度的提高成为可能.

     

Tight dual models of pore spaces

The pore throats in a porous medium control permeability, drainage, and straining through their pore scale geometry and through the way they are connected via pore bodies on the macroscale. Likewise, imbibition is controlled through the geometry of the pore bodies (pore scale) and through the way the pore bodies are connected via pore throats on the macroscale. In an effort to account for both scales at the same time we recently introduced an image-based model for pore spaces that consists of two parts related by duality: (1) a decomposition of a polyhedral pore space into polyhedral pore bodies separated by polygonal pore throats and (2) a polygonal pore network that is homotopy equivalent to the pore space. In this paper we stick to the dual concept while amending the definition of the pore throats and, as a consequence, the other elements of the dual model. Formerly, the pore throats consisted of single two-dimensional Delaunay cells, while they now usually consist of more than one two-dimensional Delaunay cell and extend all the way into the narrowing ends of the pore channel cross sections. This is the first reason for naming the amended dual model “tight”. The second reason is that the formation of the pore throats is now guided by an objective function that always attains its global optimum (tight optimization). At the end of the paper we report on simulations of drainage performed on tight dual models derived from simulated sphere packings and 3D gray-level images. The C-code for the generation of the tight dual model and the simulation of drainage is publicly available at https://jshare.johnshopkins.edu/mhilper1/public_html/tdm.html.     

Intercomparison of soil pore water extraction methods for stable isotope analysis

Measurements of δ²H and δ¹⁸O composition of pore waters in saturated and unsaturated soil samples are routinely performed in hydrological studies. A variety of in‐situ and lab‐based pore water extraction methods for the analysis of the stable isotopes of water now exist. While some have been used for decades (e.g. cryogenic vacuum extraction) others are relatively new, such as direct vapour equilibration or the microwave extraction technique. Despite their broad range of application, a formal and comprehensive intercomparison of soil water extraction methods for stable isotope analysis is lacking and long overdue. Here we present an intercomparison among five commonly used lab‐based pore water extraction techniques (high pressure mechanical squeezing, centrifugation, direct vapour equilibration, microwave extraction, and cryogenic extraction). We applied these extraction methods to two physicochemically different soil types that were dried and rewetted with water of known isotopic composition at three different water contents. Our results showed that the extraction approach can have a significant effect on pore water isotopic composition as all methods exhibited significant deviations from the spiked reference water, depending secondarily on the soil type and soil water content. Most pronounced, cryogenic water extraction showed large deviations from the spiked reference water, whereas mechanical squeezing and centrifugation provided results closest to the spiked water for both soil types. We also compared results for each extraction method – where liquid water was obtained – on both an OA‐ICOS and IRMS. Differences between these two analytical instruments were negligible for these organic compound‐free waters. We suggest that users of soil water extraction approaches carefully choose an extraction technique that is suitable for the specific research question, adapted to the dominant soil type and water content of the study. Copyright © 2016 John Wiley & Sons, Ltd.     

Poroelasticity: Finite element modelling of anomalous tilt and pore pressure caused by pumping in a sedimentary half space with fault

Extraction of groundwater or hydrocarbons causes pore pressure gradients and soil deformation due to poroelastic coupling. Recent studies show that high-resolution engineering tiltmeters installed at shallow depth between 2 and 10 m resolve this deformation. Models using poroelasticity can describe the relationship between fluid extraction, pore pressure gradients and induced tilt for homogeneous and layered sedimentary half spaces. Faults intersecting a stack of sedimentary layers, for example in the Lower-Rhine-Embayment, are of fundamental impact to the groundwater flow system of an area. However, the fault’s hydromechanical effect on pump induced tilt and the pore pressure regime is still poorly investigated. We chose a comparatively simple approach to quantify anomalous pump induced tilt and pore pressure observed near a fault and close to the surface in a sedimentary subsoil. A PC-based Finite Element software is used to model poroelastic deformation, i.e. modelling vertical tilt and excess pore pressure in response to fluid extraction through a singular well. We compare numerical solutions for models with and without faults and show that a fault can modify symmetry and amplitude of the deformation field by more than a magnitude. We conclude that tilt and pore pressure measurements also at shallow depth can thus be biased by large subsurface structures like faults. Vice versa, these measurements may provide means to quantify hydromechanical effects caused by subsurface structures. However, depending on the geological setting, i.e. if pathways are established by a fault, the anomaly caused by the fault can also be small and hard to detect. Therefore, faults and geological structures like material boundaries have to be considered in poroelastic models carefully. For tilt surveys with a limited number of instruments in geologically well constrained areas these models allow the preselection of potential positions for tiltmeters where prominent field anomalies are expected.     

Rock physics modelling of porous rocks with multiple pore types: a multiple-porosity variable critical porosity model

A critical porosity model establishes the empirical relationship between a grain matrix and a dry rock by the concept of critical porosity. The model is simple and practical and widely used. But the critical porosity in the model is a fixed value that cannot relate to pore structure. The aim of this paper is to establish the theoretical relationship between critical porosity and pore structure by combining Kuster–Toksöz theory with the critical porosity model. Different from the traditional critical porosity model, critical porosity is not an empirical value but varied with pore shape and the ratio of bulk modulus versus shear modulus of the grain matrix. The substitution of the theoretical relationship into Kuster–Toksöz theory will generate the formulae for the bulk and shear moduli of multiple-porosity dry rocks, which is named the multiple-porosity variable critical porosity model. The new model has been used to predict elastic moduli for sandstone and carbonate rock. We compare the modelling results for P- and S-wave velocities and elastic moduli with the experimental data. The comparison shows that the new model can be used to describe the elastic properties for the rocks with multiple pore types.     

Intercomparison of soil pore water extraction methods for stable isotope analysis and interpretation of hillslope runoff sources

Intercomparison of soil pore water extraction methods for stable isotope analysis has been a focus of recent studies in relation to plant source waters, which found a wide isotopic variance depending on the extraction method. Few studies have yet explored extraction effects for mobile pore waters that relate to hillslope runoff. This is because it is extremely difficult in natural systems to control the boundary conditions in order to assess and compare impacts of pore water extraction on resulting hillslope flow. With our new semicontrolled experiments on outdoor mini‐hillslopes, we studied mixing and runoff processes by means of stable isotopes of water and quantified relations between pore water extraction methods. We tested the null hypothesis that nondestructive and destructive pore water sampling methods sample the same soil water pool. Three hillslopes were mounted on load cells, filled with loamy sand textured soils from the Landscape Evolution Observatoryat Biosphere 2, equipped with soil moisture and temperature sensors, a bottom outflow, and a surface runoff gauge for isotope sampling. We followed the precipitation isotopic composition over and through the soil profile. One hillslope was instrumented with suction cups, on the second we installed sampling ports for in‐situ soil water vapour measurements, and the third hillslope was sampled destructively for applying the centrifugation and vapour equilibrium methods. All hillslopes were sampled at four depths (0–10, 10–20, 20–30, and 30–40 cm) at three different downslope positions. ²H and ¹⁸O analyses were performed via laser spectroscopy. We found no isotopic differences between rainfall, surface runoff, and bottom outflow. The in situ vapour ports' soil isotope data showed the widest spread over all hillslope positions and depths. Centrifugation's and suction cups' isotope results plotted closest to the local meteoric water line and within the range of hillslope runoff and bottom outflow data. Hillslope position did not influence the soil isotope results. These results suggest caution be used in the field when selecting an extraction technique for matching soil waters to runoff waters. Soil suction lysimeters and centrifugation appeared to be the most appropriate tools in this regard.     

Monitoring water transport in sandstone using flow propagators: A quantitative comparison of nuclear magnetic resonance measurement with lattice Boltzmann and pore network simulations

A comparison of advective displacement probability distributions (flow propagators) obtained by nuclear magnetic resonance (NMR) experiment with both lattice Boltzmann (LB) and pore network (PN) simulations is presented. Here, we apply all three methods to the exact same sample for the first time: we consider water transport in a Bentheimer sandstone. The LB and PN simulations are based on X-ray micro-tomography (XMT) images of a small rock sample; the NMR experiments are conducted on a much larger rock core-plug from which the small rock sample originated. Despite the limited size of the simulation domains, good agreement is achieved between all three sets of results, verified quantitatively by comparison of the low order moments of the flow propagators. We are concerned primarily with validating the simulations at high liquid flow rates (>10 ml min⁻¹) in high permeability sandstone, ultimately for future application to geological carbon sequestration studies. Under these conditions the LB simulation is found, as expected, to be more robust than the PN model due primarily to the reduced requirement to manually tune the simulation lattice to match the petro-physical properties of the rock.     

Similarity analysis and scaling: An application to soil infiltration properties

Similarity and scaling theory are applied to soil physics, specifically to several parameters of unsaturated soil water movement. Following a dimensional analysis of Richards' equation, a mechanical similarity criterion of the hydraulic parameters is developed. Dimensionless factors which conform to assumptions of kinematic and dynamic mechanical similarity in the flow system are converted to relations using the scale factor a derived under the assumption of geometric similarity. As an example, the infiltration process is assessed through scaling of the parameters in Philip's equation, using experimental data from double-ring infiltration measurements at 54 locations in a study catchment as the scaling test.     

Routine analysis of sediment pore water of high ionic strength

Pore water of sediments plays an important role in aquatic systems as mediator and as the reactive zone between the sediment and surface water. Sediment pore waters with high ionic strength from acidified pit lakes were investigated to obtain information about the influence on the lake water quality. The analysis of soluble reactive phosphorus, nitrate, ammonium, silica, dissolved organic carbon, ferrous iron, sulfate, chloride, sodium, potassium, calcium, magnesium, manganese, and total dissolved iron was predetermined as the dataset required for evaluation of water quality. The data collection procedure was optimised by designing a methodology for stabilisation, dilution of pore water samples and adaptation of analytical methods. The developed methodology was evaluated with respect to the effort required in the laboratory under routine conditions. In the first round of analyses, 72% of 638 individual analyses from a random selection of pore water profiles were found to be within the calibration ranges. Remedial actions to handle the remaining 28% of invalid analytical results are exemplified. Differences between comparative analyses of some ions by continuous flow analysis, ion chromatography, and atomic emission spectroscopy were evaluated. The majority of results measured by ion chromatography differed on a highly significant level from results measured by atomic emission spectroscopy. Possible reasons, originating from the extreme sample matrix, are discussed. Finally, the designed methodology and the results of the method comparison are used to recommend the selection of analytical methods under specific conditions.     

Computation of three-phase capillary entry pressures and arc menisci configurations in pore geometries from 2D rock images: A combinatorial approach

We present a semi-analytical, combinatorial approach to compute three-phase capillary entry pressures for gas invasion into pore throats with constant cross-sections of arbitrary shapes that are occupied by oil and/or water. For a specific set of three-phase capillary pressures, geometrically allowed gas/oil, oil/water and gas/water arc menisci are determined by moving two circles in opposite directions along the pore/solid boundary for each fluid pair such that the contact angle is defined at the front circular arcs. Intersections of the two circles determine the geometrically allowed arc menisci for each fluid pair. The resulting interfaces are combined systematically to allow for all geometrically possible three-phase configuration changes. The three-phase extension of the Mayer and Stowe – Princen method is adopted to calculate capillary entry pressures for all determined configuration candidates, from which the most favorable gas invasion configuration is determined. The model is validated by comparing computed three-phase capillary entry pressures and corresponding fluid configurations with analytical solutions in idealized triangular star-shaped pores. It is demonstrated that the model accounts for all scenarios that have been analyzed previously in these shapes. Finally, three-phase capillary entry pressures and associated fluid configurations are computed in throat cross-sections extracted from segmented SEM images of Bentheim sandstone. The computed gas/oil capillary entry pressures account for the expected dependence of oil/water capillary pressure in spreading and non-spreading fluid systems at the considered wetting conditions. Because these geometries are irregular and include constrictions, we introduce three-phase displacements that have not been identified previously in pore-network models that are based on idealized pore shapes. However, in the limited number of pore geometries considered in this work, we find that the favorable displacements are not generically different from those already encountered in network models previously, except that the size and shape of oil layers that are surrounded by gas and water are described more realistically. The significance of the results for describing oil connectivity in porous media accurately can only be evaluated by including throats with more complex cross-sections in three-phase pore-network models.     

Vent area and depositional mechanisms of the Upper Member of the Neapolitan Yellow Tuff (Campi Flegrei, Italy): new insights from directional fabric through image analysis

In order to provide new information about the source area and depositional mechanisms of the Upper Member of the Neapolitan Yellow Tuff (NYT), a prominent pyroclastic deposit of the Campi Flegrei Volcanic District (southern Italy), statistics on directional fabric, by means of computer-assisted image analysis on 32 rock samples, were compiled. Seventeen samples were collected along vertical direction on two selected exposures and fifteen were taken from outcrops widely distributed all around the Campi Flegrei Volcanic District. Fabric measurements within the investigated successions reveal a vertically homogeneous direction of the mean particle iso-orientation, with considerable variability in the strength of particle iso-orientation even at cm-scale. The existence of particle iso-orientation can be related to continuous sedimentation from a concentrated bedload region beneath suspension currents, producing massive or inversely graded beds by traction carpet sedimentation. The considerable vertical variability in the strength of iso-orientation is the result of very unstable flow regimes, up to the extreme condition of discrete depositional events, with a variable combination of traction carpet and/or direct suspension sedimentation. The vertical homogeneity in the mean orientation values, found in the investigated sections, may derive from the sequential deposition of laminae to thin beds, whose relatively flat upper surfaces were unable to significantly deflect the depositional system of the following currents. According to the observed homogeneous mean particle orientation values along the investigated vertical profiles, samples collected through areal distribution are considered representative of the local paleo-flow directions of the whole deposit. The mean directions of the samples collected areally show two different coherent patterns which point to the existence of two different source areas. The first, which includes all samples from the northern outcrops, appears to converge in a narrow area about 2 km NE of the town of Pozzuoli, largely in coincidence with the inferred area on the basis of the pumice fall distribution. The second, which includes samples from Capo Miseno and Posillipo areas, points to the central part of the Pozzuoli Bay, about 4 km offshore the town of Pozzuoli.     

Trace metal dynamics in the water column and pore waters in a temperate tidal system: response to the fate of algae-derived organic matter

Tidal and seasonal behaviour of the redox-sensitive trace metals Mn, Fe, Mo, U, and V have been investigated in the open-water column and shallow pore waters of the backbarrier tidal flats of the island of Spiekeroog (Southern North Sea) in 2002 and 2007. The purpose was to study the response of trace metal cycles on algae blooms, which are assumed to cause significant changes in the redox state of the entire ecosystem. Trace metal data were complemented by measurements of nutrients and enumeration of algae cells in 2007. Generally, Mn and V show a tidal cyclicity in the water column with maximum values during low tide which is most pronounced in summer due to elevated microbial activity in the sediments. Mo and U behave almost conservatively throughout the year with slightly increasing levels towards high tide. Exceptions are observed for both metals after summer algae blooms. Thus, the seasonal behaviour of the trace metals appear to be significantly influenced by productivity in the water column as the occurrence of algae blooms is associated with an intense release of organic matter (e.g. transparent exopolymer particles, TEP) thereby forming larger organic-rich aggregates. Along with elevated temperatures in summer, the deposition of such aggregates favours microbial activity within the surface sediments and release of DOC, nutrients and trace metals (Mn, Mo and V) during the degradation of the aggregates. Additionally, pronounced reducing conditions lead to the reduction of Mn(IV)-oxides and Fe(III)-(oxihydr)oxides, thereby releasing formerly scavenged compounds as V and phosphate. Therefore, pore-water profiles show significant enrichments in trace metals especially from July to September. Finally, the trace metals are released to the open water column via draining pore waters (esp. Mo, Mn, and V) and/or fixed in the sediment as sulphides (Fe, Mo) and bound to organic matter (U). Non-conservative behaviour of Mo in oxygenated seawater, first observed in the investigation area by Dellwig et al. (Geochim Cosmochim Acta 71:2745–2761, 2007a), was shown to be a recurrent phenomenon which is closely coupled to bacterial activity after the breakdown of algae blooms. In addition to the postulated fixation of Mo in oxygen-depleted micro-zones of the aggregates or by freshly formed organic matter, a direct removal of Mo from the water column by reduced sediment surfaces may also play an important role.     

Beach disturbance caused by off-road vehicles (ORVs) on sandy shores: relationship with traffic volumes and a new method to quantify impacts using image-based data acquisition and analysis

Vehicles cause environmental damage on sandy beaches, including physical displacement and compaction of the sediment. Such physical habitat disturbance provides a relatively simple indicator of ORV-related impacts that is potentially useful in monitoring the efficacy of beach traffic management interventions; such interventions also require data on the relationship between traffic volumes and the resulting levels of impact. Here we determined how the extent of beach disturbance is linked to traffic volumes and tested the utility of image-based data acquisition to monitor beach surfaces. Experimental traffic application resulted in disturbance effects ranging from 15% of the intertidal zone being rutted after 10 vehicle passes to 85% after 100 passes. A new camera platform, specifically designed for beach surveys, was field tested and the resulting image-based data compared with traditional line-intercept methods and in situ measurements using quadrats. All techniques gave similar results in terms of quantifying the relationship between traffic intensity and beach disturbance. However, the physical, in situ measurements, using quadrats, generally produced higher (+4.68%) estimates than photos taken with the camera platform coupled with off-site image analysis. Image-based methods can be more costly, but in politically and socially sensitive monitoring applications, such as ORV use on sandy beaches, they are superior in providing unbiased and permanent records of environmental conditions in relation to anthropogenic pressures.     

Effects of compound-specific dilution on transient transport and solute breakthrough: A pore-scale analysis

This pore-scale modeling study in saturated porous media shows that compound-specific effects are important not only at steady-state and for the lateral displacement of solutes with different diffusivities but also for transient transport and solute breakthrough. We performed flow and transport simulations in two-dimensional pore-scale domains with different arrangement of the solid grains leading to distinct characteristics of flow variability and connectivity, representing mildly and highly heterogeneous porous media, respectively. The results obtained for a range of average velocities representative of groundwater flow (0.1–10 m/day), show significant effects of aqueous diffusion on solute breakthrough curves. However, the magnitude of such effects can be masked by the flux-averaging approach used to measure solute breakthrough and can hinder the correct interpretation of the true dilution of different solutes. We propose, as a metric of mixing, a transient flux-related dilution index that allows quantifying the evolution of solute dilution at a given position along the main flow direction. For the different solute transport scenarios we obtained dilution breakthrough curves that complement and add important information to traditional solute breakthrough curves. Such dilution breakthrough curves allow capturing the compound-specific mixing of the different solutes and provide useful insights on the interplay between advective and diffusive processes, mass transfer limitations, and incomplete mixing in the heterogeneous pore-scale domains. The quantification of dilution for conservative solutes is in good agreement with the outcomes of mixing-controlled reactive transport simulations, in which the mass and concentration breakthrough curves of the product of an instantaneous transformation of two initially segregated reactants were used as measures of reactive mixing.     

Image analysis and circular statistics for shape-fabric analysis: applications to lithified ignimbrites

 Computer-assisted image analysis can be successfully used to derive quantitative textural data on pyroclastic rock samples. This method provides a large number of different measurements such as grain size, particle shape and 2D orientation of particle main axes (directional- or shape-fabric) automatically and in a relatively short time. Orientation data reduction requires specific statistical tests, mainly devoted to defining the kind of particle distribution pattern, the possible occurrence of preferred particle orientation, the confidence interval of the mean direction and the degree of randomness with respect to pre-assigned theoretical frequency distributions. Data obtained from image analysis of seven lithified ignimbrite samples from the Vulsini Volcanic District (Central Italy) are used to test different statistics and to provide insight about directional fabrics. First, the possible occurrence of a significant deviation from a theoretical circular uniform distribution was evaluated by using the Rayleigh and Tukey χ ² tests. Then, the Kuiper test was performed to evaluate whether or not the observation fits with a unimodal, Von Mises-like theoretical frequency distribution. Finally, the confidence interval of mean direction was calculated. With the exception of one sample (FPD10), which showed a well-developed bimodality, all the analysed samples display significant anisotropic and unimodal distributions. The minimum number of measurements necessary to obtain reasonable variabilities of the calculated statistics and mean directions was evaluated by repeating random collections of the measured particles at increments of 100 particles for each sample. Although the observed variabilities depend largely on the pattern of distribution and an absolute minimum number cannot be stated, approximately 1500–2000 measurements are required in order to get meaningful mean directions for the analysed samples. Received: 9 April 1996 / Accepted: 26 December 1996     

Regionalization of unit hydrograph parameters: 1. Comparison of regression analysis techniques

Hydrologic regionalization is a useful tool that allows for the transfer of hydrological information from gaged sites to ungaged sites. This study developed regional regression equations that relate the two parameters in Nash's IUH model to the basin characteristics for 42 major watersheds in Taiwan. In the process of developing the regional equations, different regression procedures including the conventional univariate regression, multivariate regression, and seemingly unrelated regression were used. Multivariate regression and seeming unrelated regression were applied because there exists a rather strong correlation between the Nash's IUH parameters. Furthermore, a validation study was conducted to examine the predictability of regional equations derived by different regression procedures. The study indicates that hydrologic regionalization involving several dependent variables should consider their correlations in the process of establishing the regional equations. The consideration of such correlation will enhance the predictability of resulting regional equations as compared with the ones from the conventional univariate regression procedure.