The motion of deformable ellipsoids in power-law viscous materials: Formulation and numerical implementation of a micromechanical approach applicable to flow partitioning and heterogeneous deformation in Earth’s lithosphere

Earth’s lithosphere is heterogeneous in rheology on a wide range of observation scales. When subjected to a tectonic deformation, the incurred flow field can vary significantly from one rheologically distinct element to another and the flow field in an individual element is generally different from the bulk averaged flow field. Kinematic and mechanical models for high-strain zones provide the relations between prescribed tectonic boundary conditions and the resulting bulk flow field. They do not determine how structures and fabrics observed on local and small scales form. To bridge the scale gap between the bulk flow field and minor structures, Eshelby’s formalism extended for general power-law viscous materials is shown to be a powerful means. This paper first gives a complete presentation of Eshelby’s formalism, from the classic elastic inclusion problem, to Newtonian viscous materials, and to the most general case of a power-law viscous inhomogeneity embedded in a general power-law viscous medium. The formulation is then implemented numerically. The implications and potential applications of the approach are discussed. It is concluded that the general Eshelby formalism together with the self-consistent method is a powerful and physically sound means to tackle large plastic deformation of Earth’s lithosphere.     

Multi-scale risk assessment of stream pollution by wastewater of olive oil mills in Kolymvari,Crete

In the streams of the Mediterranean island of Crete (Greece), olive mill wastewater (OMW) has been reported to reduce biodiversity up to 85 %. Mere conduction of impact assessment based on pollutant concentrations, however, cannot reveal how impacted areas may be connected to the pollution sources. In this study, we developed a new methodology which allows for a dynamic cause-effect linking of pollution sources and impacted areas through the pathways of OMW. Risk is hierarchically assessed and mapped at three different scales and more specifically, at the source scale (targeting olive mill units and their waste tanks), at the receptor scale (targeting potential impacted sites in the streams) and at the watershed scale (which is the scale of overall water management). The approach is based mainly on remote sensing data without taking account of groundwater regimes or field measurements. Involvement of local experts for recognizing spatial features of interest and selecting appropriate risk parameters was proved necessary and efficient in order to model the stream pollution risk realistically. Potential impacted sites in the stream network were occasionally verified by a field survey. The results comprise a set of risk maps at the three different scales. The constructed digital geo-database can be updated or modified and thus is considered to be a dynamic tool for future environmental management in the service of the local community.     

Short Note: Effective Hydraulic Conductivity and Transmissivity for Heterogeneous Aquifers

Regional scale models of groundwater flow and transport often employ domain discretizations with grid blocks larger than typical scales of field data. For heterogeneous formations, this difference in scales is often handled by using effective (upscaled) parameters. We investigate the problem of upscaling hydraulic conductivity and transmissivity from a small scale of measurement to a larger scale of grid blocks. Transmissivity statistics is expressed in terms of statistics of hydraulic conductivity, and expressions for the effective (upscaled) hydraulic conductivity K _eff and transmissivity T _eff for steady state flow in confined heterogeneous aquifers are derived by means of stochastic averaging and perturbation analysis. These expressions reveal that the commonly used relation T _eff = BK _eff, where B is the confined aquifer thickness, is not generally valid.     

Texture Analysis of Grey-Tone Images by Mathematical Morphology: A Nondestructive Tool for the Quantitative Assessment of Stone Decay

Both a low-cost and easily handled nondestructive methodology and its validation criterion are proposed. The methodology is based on image analysis by mathematical morphology for the assessment of decayed stone surfaces in historic limestone buildings. It is adapted to follow the evolution, at macroscopic time and space scales, of stone materials used in art pieces and monument building stones. This methodology is applied to the quantitative analysis of textures of static grey-tone CCD video camera images representative of flat stone structures that cannot be handled. These structures line the walls inside an important church, Basílica da Estrela, built in the 18th century and located in the city of Lisbon. Detailed visual/tactile observation shows that these flat vertical structures are more or less damaged depending on their position inside the church. The damage is possibly associated with different environment conditions both from the atmosphere inside the church and from contact with the walls of the church. The presence of these pathologies breaks down the order and organization of sound rock textures introducing changes in the topographical and optical characteristics of the texture of the surfaces. This new methodology is based on the granulometry and covariance analysis of grey-tone images corresponding to the structures studied. The validation criterion allows the results of the proposed methodology to be compared to the results of a previous qualitative study made by experts in the field using visual assessment and monument mapping as a valid methodology to assess the degree of decay. This procedure is based on optical and topographical characteristics and type of decay of the stone surface, and the quantity of material lost from the surface of the panels during the year. As discussed in this paper, in the context of cultural heritage, the proposed methodology was validated and its results can be considered an improvement on and complementary to expert visual analysis and also to other nondestructive techniques.     

Simultaneous Estimation of Geologic and Reservoir State Variables Within an Ensemble-Based Multiple-Point Statistic Framework

Assessment of uncertainty due to inadequate data and imperfect geological knowledge is an essential aspect of the subsurface model building process. In this work, a novel methodology for characterizing complex geological structures is presented that integrates dynamic data. The procedure results in the assessment of uncertainty associated with the predictions of flow and transport. The methodology is an extension of a previously developed pattern search-based inverse method that models the spatial variation in flow parameters by searching for patterns in an ensemble of reservoir models. More specifically, the pattern-searching algorithm is extended in two directions: (1) state values (such as piezometric head) and parameters (such as conductivities) are simultaneously and sequentially estimated, which implies that real-time assimilation of dynamic data is possible as in ensemble filtering approaches; and (2) both the estimated parameter and state variables are considered when pattern searching is implemented. The new scheme results in two main advantages—better characterization of parameters, especially for delineating small scale features, and an ensemble of head states that can be used to update the parameter field using the dynamic data at the next instant, without running expensive flow simulations. An efficient algorithm for pattern search is developed, which works with a flexible search radius and can be optimized for the estimation of either large- or small-scale structures. Synthetic examples are employed to demonstrate the effectiveness and robustness of the proposed approach.     

Generalized Coarse Graining Procedures for Flow in Porous Media

This paper focuses on heterogeneous soil conductivities and on the impact their resolution has on a solution of the piezometric head equation: owing to spatial variations of the conductivity, the flow properties at larger scales differ from those found for experiments performed at smaller scales. The method of coarse graining is proposed in order to upscale the piezometric head equation on arbitrary intermediate scales. At intermediate scales large scale fluctuations of the conductivities are resolved, whereas small scale fluctuations are smoothed by a partialy spatial filtering procedure. The filtering procedure is performed in Fourier space with the aid of a low-frequency cut-off function. We derive the partially upscaled head equations. In these equations, the impact of the small scale variability is modeled by scale dependent effective conductivities which are determined by additional differential equations. Explicit results for the scale dependent conductivity values are presented in lowest order perturbation theory. The perturbation theory contributions are summed up with using a renormalisation group analysis yielding explicit results for the effective conductivity in isotropic media. Therefore, the results are also valid for highly heterogeneous media. The results are compared with numerical simulations performed by Dykaar and Kitanidis (1992). The method of coarse graining combined by a renormalisation group analysis offers a tool to derive exact and explicit expressions for resolution dependent conductivity values. It is, e.g., relevant for the interpretation of measurement data on different scales and for reduction of grid-block resolution in numerical modeling. This revised version was published online in July 2006 with corrections to the Cover Date.     

A simple kriging method incorporating multiscale measurements in geochemical survey

In this study, we propose a kriging algorithm, multiscale kriging model, to incorporate geochemical data observed at multiscales (multiresolutions). We assume that there are a number of measurements at different scales, and that the target scale at which the parameter values are needed may be different from the measurement scales. Several synthetic examples and the vanadium geochemical data from 8402 stream sediment samples in Zhejiang Province, China, have been used to illustrate the method. These examples demonstrate that, by incorporating measurements from all scales, the estimated field is better than the field estimated using measurements from any individual scale. This method also allows us to estimate a parameter field at the scale that does not have any measurements.     

Wavelet Analysis and Filtering to Identify Dominant Orientations of Permeability Anisotropy

An accurate representation of permeability anisotropy is needed to model the rate and direction of groundwater flow correctly. We develop a wavelet analysis technique that can be used to characterize principal directions of anisotropy in both stationary and non-stationary permeability fields. Wavelet analysis involves the integral transform of a field using a wavelet as a kernel. The wavelet is shifted, scaled, and rotated to analyze different locations, sizes, and orientations of the field. The wavelet variance is used to identify scales and orientations that dominate the field. If the field is non-stationary, such that different zones of the field are characterized by different dominant scales or orientations, the wavelet variance can identify all dominant scales and orientations if they are distinct. If the dominant scales and orientations of different zones are similar, the wavelet variance identifies only the dominant scale and orientation of the primary zone. In this paper, we present a combined wavelet analysis and filtering approach to identify all dominant scales and orientations in a non-stationary permeability field. We apply the method to permeability data obtained in the laboratory from the Massillon sandstone.     

Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics

In many earth sciences applications, the geological objects or structures to be reproduced are curvilinear, e.g., sand channels in a clastic reservoir. Their modeling requires multiple-point statistics involving jointly three or more points at a time, much beyond the traditional two-point variogram statistics. Actual data from the field being modeled, particularly if it is subsurface, are rarely enough to allow inference of such multiple-point statistics. The approach proposed in this paper consists of borrowing the required multiple-point statistics from training images depicting the expected patterns of geological heterogeneities. Several training images can be used, reflecting different scales of variability and styles of heterogeneities. The multiple-point statistics inferred from these training image(s) are exported to the geostatistical numerical model where they are anchored to the actual data, both hard and soft, in a sequential simulation mode. The algorithm and code developed are tested for the simulation of a fluvial hydrocarbon reservoir with meandering channels. The methodology proposed appears to be simple (multiple-point statistics are scanned directly from training images), general (any type of random geometry can be considered), and fast enough to handle large 3D simulation grids.     

Effect of pixel scale on evapotranspiration estimation by remote sensing over oasis areas in north-western China

One of the major uncertainties in the remote sensing estimates of regional evapotranspiration (ET) over heterogeneous landscapes is that significant estimation differences between different data scales always exist. It is necessary to predetermine the optimal remote sensing scale under such conditions. In this study, the effect of pixel scale on ET estimation over a typical oasis in north-western China was investigated. By the area-averaging and wavelet multi-resolution analysis aggregation techniques, four ??input?? up-scaling and ??output?? up-scaling procedures were implemented, respectively, to determine the optimal data scale. Validation suggested that high-resolution Landsat-based ET estimates could be used as the ground reference data when in situ measurements were not available. The differences between Landsat-based and MODIS-based ET estimates (i.e. the so-called Regional Error Distribution of the latter) showed that 1-km resolution MODIS data overestimated ET over the landscapes where NDVI was less than or equal to ~0.10; the data underestimated ET over the landscapes where NDVI was greater than or equal to ~0.40; ET could only be relatively accurately predicted by the data on the surfaces where NDVI ranged from 0.10 to 0.40. However, MODIS-based 1-km ET estimates could effectively reveal the predominant spatial distribution trend of regional ET. The results confirmed that the optimal remote sensing scale for modeling ET was approximately 480?m over the study area; land surface heterogeneity could cause significant errors in ET estimation once data scales exceeded this threshold; in addition, MODIS data at 250-m resolution were adequate for correcting the 1-km resolution ET estimates over heterogeneous landscapes.     

Scale Matching with Factorial Kriging for Improved Porosity Estimation from Seismic Data

When seismic data and porosity well logs contain information at different spatial scales, it is important to do a scale-matching of the datasets. Combining different data types with scale mismatch can lead to suboptimal results. A good correlation between seismic velocity and rock properties provides a basis for integrating seismic data in the estimation of petrophysical properties. Three-dimensional seismic data provides an unique exhaustive coverage of the interwell reservoir region not available from well data. However, because of the limitations of measurement frequency bandwidth and view angles, the seismic image can not capture the true seismic velocity at all spatial scales present in the earth. The small-scale spatial structure of heterogeneities may be absent in the measured seismic data. In order to take best advantage of the seismic data, factorial kriging is applied to separate the small and large-scale structures of both porosity and seismic data. Then the spatial structures in seismic data which are poorly correlated with porosity are filtered out prior to integrating seismic data into porosity estimation.     

Managing expert-information uncertainties for assessing collapse susceptibility of abandoned underground structures

Assessing the collapse susceptibility of abandoned cavities at a regional scale is associated with large uncertainties that are mainly related to the very nature of the phenomena, but also to the difficulty in collecting exhaustive information at such a scale on often “forgotten” structures. In this context, the expert's role is essential, because he is able to synthesize the information resulting from the inventory and from the commonly imprecise, if not vague, criteria on the basis of his experience and his knowledge of the geological, historical, economic regional context.In this article, we propose mathematical tools for representing and processing this information in order to give flexibility to this step and manage the uncertainty inherent in the expert's information. The first tool, based on the weight of evidence theory, is for managing the uncertainty due to the heterogeneous spatial distribution of the data, whereas the second tool, based on the fuzzy set theory, is for managing the imprecision and incompleteness of available data, which hinder the definition of the class boundaries of the quantitative decision criteria. Based on an appropriate representation of the uncertainty sources (related to the input data and to the expert diagnostic), we then propose a methodology that integrates the uncertainty in the final output of the collapse susceptibility assessment and provides a confidence indicator useful within the decision-making process. The proposed methodology is applied to the Arras territory in the North of France, where abandoned chalk pits (dating back to the Roman ages) and war saps located in the vicinity of the First World War front lines (i.e. covered trenches), raise both difficulties for urban planning.     

Does scale exist? An epistemological scale continuum for complex human-environment systems

Scale pervades interdisciplinary research on human-environment systems that exhibit hallmarks of complexity such as path dependence, nonlinearity, and surprise. Although scale concepts are woven through the data, methodology, and theory of human-environment research, the question remains: does scale exist? More broadly, can a single definition of scale suffice for human-environment systems? The meaning and use of scale is contested across the social, natural, and information sciences. Given that the study of human-environment systems spans many of these disciplines, specific research problems inherit a broad range of conflicting scale concepts. This paper proposes an epistemological scale continuum that arrays scale perspectives from the realist contention that there are natural scales independent of observers through to the constructionist view that scale is subjective and socially mediated. As seen in biocomplexity and human-environment research more broadly, this scale continuum establishes that scale is not a single measure or object of study, nor is any single definition of scale sufficient for human-environment systems. Viewpoints and tensions among scale epistemologies also suggest several general principles for using scale effectively in human-environment research.     

Transverse lineation and large-scale structures related to Alpine obduction in Corsica

In Alpine Corsica, the major tectonic event during the late Cretaceous was the thrusting to the west of an ophiolitic nappe and its sedimentary cover upon the Variscan basement and its Mesozoic cover. A detailed field survey shows that the basal contact of the nappe corresponds to a pluri-kilometric scale shear zone. Thus gneissified basement slices have been tectonically emplaced in the ophiolitic nappe. The thrusting was responsible for small scale structures: foliation, lineation and folds, initiated in a HP/LT metamorphic context. The deformation analysis shows that the finite strain ellipsoid lies in the constriction field close to that for plane strain. Moreover occurrences of rotational criteria in the XZ planes (sigmoidal micas, asymmetric pressure shadows, quartz C-axes fabrics) are in agreement with shear from east to west. All structural data from microscopic to kilometric scales, of which the most widespread is a transverse stretching lineation, can be interpreted by a simple shear model involving ductile synmetamorphic deformation. At the plate tectonic scale the ophiolitic obduction is due to intraoceanic subduction blocked by underthrusting of continental crust beneath oceanic lithosphere.     

Relative seismic shaking vulnerability microzonation using an adaptation of the Nakamura horizontal to vertical spectral ratio method

An alternative seismic shaking vulnerability survey method to computational intensive theoretical modelling of site response to earthquake, and time consuming test versus reference site horizontal ratio methods, is described. The methodology is suitable for small to large scale engineering investigations. Relative seismic shaking vulnerability microzonation using an adaptation of the Nakamura horizontal to vertical spectral ratio method provides many advantages over alternative methods including: low cost; rapid field phase (100 km² can easily be covered by a single operator in 5 days); low and flexible instrumentation requirements (a single seismometer and data logger of almost any type is required); field data can be collected at any time during the day or night (the results are insensitive to ambient social noise); no basement rock reference site is required (thus eliminating trigger synchronisation between reference and multiple test site seismographs); rapid software aided analysis; insensitivity to ground-shaking resonance peaks; ability to compare results obtained from non-contiguous survey fields. The methodology is described in detail, and a practical case study is provided, including mapped results. The resulting microzonation maps indicate the relative seismic shaking vulnerability for built structures of different height categories within adjacent zones, with a resolution of approximately 1 km.     

Upscaling equivalent hydrofacies simulation based on borehole data generalization and transition probability geostatistics

The heterogeneity of hydrofacies is represented as spatial variability on different scales, and it has a significant impact on the behavior of groundwater flow and pollutant transport. However, effectively characterizing hydrofacies heterogeneity on different scales remains one of the most challenging problems in hydrogeology. In this study, an upscaling hydrofacies simulation (UHS) framework is proposed by integrating the upscaling borehole generalization (UBG) approach and transition probability geostatistics (TPG). A new UBG approach for generating virtual boreholes with equivalent hydrofacies information based on relatively high-density borehole lithological data is proposed, and the TPG is used to delineate the multiscale facies distribution. The results show that the UBG approach can significantly reduce borehole data volume while retaining the key equivalent hydrofacies information on a coarser scale. The UHS method can well characterize the overall distribution of equivalent hydrofacies on coarser scales, with the minor-component hydrofacies underestimated and the major-component hydrofacies overestimated to a lesser extent, and more equivalent facies appearing in strong heterogeneous areas. These results demonstrate that the UHS method can provide valuable capacity insights and advantages in characterizing hydrofacies heterogeneity on different scales using such high-density borehole lithological data.

     

Regional fracture network permeability using outcrop scale measurements

Estimating the hydraulic properties of fractured aquifers is challenging due to the complexity of structural discontinuities that can generally be measured at a small scale, either in core or in outcrop, but influence groundwater flow over a range of scales. This modeling study uses fracture scanline data obtained from surface bedrock exposures to derive estimates of permeability that can be used to represent the fractured rock matrix within regional scale flow models. The model is developed using PETREL, which traditionally benefits from high resolution data sets obtained during oil and gas exploration, including for example seismic data, and borehole logging data (both lithological and geophysical). The technique consists of interpreting scanline fracture data, and using these data to generate representative Discrete Fracture Network (DFN) models for each field set. The DFN models are then upscaled to provide an effective hydraulic conductivity tensor that represents the fractured rock matrix. For each field site, the upscaled hydraulic conductivities are compared with estimates derived from pumping tests to validate the model. A hydraulic conductivity field is generated for the study region that captures the spatial variability of fracture networks in pseudo-three dimensions from scanline data. Hydraulic conductivities estimated using this approach compare well with those estimated from pumping test data. The study results suggest that such an approach may be feasible for taking small scale fracture data and upscaling these to represent the aquifer matrix hydraulic properties needed for regional groundwater modeling.     

断陷盆地油气汇聚体系研究

油气汇聚体系是一个不同于含油气系统和油气成藏系统的概念,它提出的目的旨在讨论层序格架中油气成藏单元与层序级次之间的关系。通过建立不同级别的层序地层格架,结合储层的分布和构造断裂等因素,预测油气的汇聚特征。油气汇聚体系由储集系统和油气输导系统构成,储集系统可以分为（1）高连通、大型毯状;（2）中连通、中型毯状;（3）低连通、小容量3种类型;油气输导系统分为单一型和综合型两种类型。油气汇聚体系分为大型、中型、小型3种类型,每种类型所对应的储集系统和油气榆导系统各不相同。该概念的提出,为研究层序格架中各种规模的油气汇聚体系与层序格架之间的关系提供了理论基础．     

Numerical Homogenization of the Rigidity Tensor in Hooke's Law Using the Node-Based Finite Element Method

Combining a geological model with a geomechanical model, it generally turns out that the geomechanical model is built from units that are at least a 100 times larger in volume than the units of the geological model. To counter this mismatch in scales, the geological data model's heterogeneous fine-scale Young's moduli and Poisson's ratios have to be “upscaled” to one “equivalent homogeneous” coarse-scale rigidity. This coarse-scale rigidity relates the volume-averaged displacement, strain, stress, and energy to each other, in such a way that the equilibrium equation, Hooke's law, and the energy equation preserve their fine-scale form on the coarse scale. Under the simplifying assumption of spatial periodicity of the heterogeneous fine-scale rigidity, homogenization theory can be applied. However, even then the spatial variability is generally so complex that exact solutions cannot be found. Therefore, numerical approximation methods have to be applied. Here the node-based finite element method for the displacement as primary variable has been used. Three numerical examples showing the upper bound character of this finite element method are presented.