The problem exists in which the harmonic(s) have the greatest potential for a clear, unambiguous solution upon subsequent shape analysis. In addition, shape data must be acquired economically, allowing analysis of hundreds of particles per sample and tens or hundreds of samples in any particular investigation. Amplitude spectra of a finite Fourier series in closed form are used as shape descriptors of each particle. The mixing proportions and end member compositions have proven to be of value with respect to a variety of sedimentological investigations using shape and size frequency data. The lower harmonics are a measure of gross shape while the higher harmonics measure increasingly fine-scaled surface features. The width of the intervals can be unequal and depends only on the shape of the distribution of the entire pooled data set. The lower the relative entropy of a data set, the more contrast exists between samples contained in that set.

Different users have different search goals when they submit a query to a search engine. In this paper we aim at discovering the number of diverse user's search goal for giving a query and for each goal a keyword is associated automatically. We initially derive user's search goal for a query by clustering our proposed feedback conclave. Then the feedback conclave is mapped to pseudo-documents so that the user's needs are retrieved efficiently. Finally, these pseudo documents are then clustered to deduce user search goals and depict them with some keywords. Though K means clustering is used in the existing system sometimes queries may not exactly represent user specific information needs. This method only finds whether a pair of query is belonging to the same set of goal and does not look into goal in detail. Hence we put forward a fuzzy similarity-based self-constructing algorithm for feature clustering. Our method works efficiently and will return provide better inferred properties than any other method.

This chapter provides an overview of quantitative, multivariate exploratory data analysis methods in use in environmental forensics and chemical fingerprinting. Given multiple contaminant sources and empirical chemical data from a study area, environmental scientists often wish to unravel the contributions of multiple sources with overlapping spatial and temporal distributions. Such problems may be addressed through a multivariate approach, such as principal components analysis (PCA) and self-training receptor-modeling techniques. These approaches are related in that they are exploratory data analysis methods—techniques applied when one wishes not to assume a priori knowledge of contributing sources and their fingerprints. PCA is widely used in environmental chemistry as well as many scientific disciplines, and can be implemented using commercial software packages. Four self-training receptor model methods are discussed, compared, and applied herein. There are advantages and disadvantages to each of these methods, but regardless of the method, success depends on the data analyst’s experience, sensitivity to chemical data structure, and sampling plan design. Finally, one must be aware that the compositions of original source profiles may be altered after a release (even for recalcitrant chemicals such as PCBs). In interpreting these models, the data analyst should have some knowledge of alteration, weathering, and degradation mechanisms.

The porosity exposed in a series of petrographic thin sections from a sub-arkosic sandstone reservoir of the Alwyn area (North Sea) is described by 5 morphological porous descriptors, Pore-Types, obtained by quantitative image analysis procedures and pattern recognition algorithms developed by Ehrlich et al. (1991a). By combining Pore-Type data with capillary pressure curves, we obtain preliminary results showing that in the studied reservoir, the achieved Pore-Types relate better to petrophysics when they are complemented with a sedimentological information.

Magma mixing and crystal fractionation are fundamental processes that lead to the diversity of magma compositions, but rarely are all of the major and trace element data on whole rocks used simultaneously in evaluating proposed models. Polytopic vector analysis (PVA) is an oblique factor analysis procedure designed specifically to evaluate mixing or unmixing (fractional crystallization) in geologic systems using all of the analytes (major and trace elements) simultaneously. It differs from other techniques in that it not only determines the number of end‐members and their compositions, but also partitions the relative proportions of the end‐members into each sample in the data array. These samples, expressed as proportions of end‐members, can be used as input in other multivariate analyses. The purpose of this paper is to use PVA to evaluate some examples of magma mixing and fractional crystallization and use these examples as templates for more complicated systems in order to show both the strengths and the weaknesses of the approach. Five well‐constrained examples illustrate how PVA can discriminate between these two processes and provide additional petrogenetic information. Using PVA, mixing between magma types can be easily distinguished from crystal fractionation. With fractional crystallization the end‐members, generated by PVA, are the initial and final liquids and the compositions where new phases join the crystallizing assemblage.

The chemically and mineralogically zoned Topopah Spring silicic ash-flow sheet (12.8 Ma, 1200 km(3)) in the southwest Nevada volcanic field (SWNVF) contains two pumice fragment populations, a lower silica (LS) and a high-silica rhyolite (HSR) composition. Recent interpretations are that these magmas, represented by the pumice fragments, were not related by AFC processes within a single magma chamber. The emplacement of the Pah Canyon ash-flow sheet followed the Topopah Spring ash-flow sheet eruption. This smaller volume (similar to 35 km(3)) ash-flow sheet contains pumice fragments that were previously interpreted as a hybrid magma formed by mixing of residual Topopah Spring LS and HSR magmas.Pumice fragments from these ash-flow sheets were analyzed by polytopic vector analysis (PVA), a multivariate statistical program that describes each sample in a dataset in terms of some proportion of each end member generated by the program. Therefore each sample, or pumice fragment, is uniquely described by some amount of each of the end members so that graphical analysis of the dataset allows the immediate recognition of separate magma batches, as pumice fragment samples cluster in discrete groups and show different variations in end member proportions. Recognition of hybrid magmas is also immediately apparent, as pumice fragments representing mixed magmas must plot between the parent magmas (pumice fragment groups). Our results confirm the existence of independently generated magmas involved in the formation of the Topopah Spring ash flow. However, PVA of Pah Canyon pumice fragments reveals that Pah Canyon cannot be described solely as a hybrid magma derived from Topopah Spring LS and HSR magmas. Furthermore, Pah Canyon and the Topopah Spring HSR pumice fragments have identical trends in the variation of end member proportions that most likely represent crystal fractionation or accumulation in both magmas that was previously undetected. This pattern is inconsistent with simple mixing between the TS-LS and TS-HSR magmas. Rather it is consistent with magma mixing followed by fractional crystallization. (c) 2006 Elsevier B.V. All rights reserved.

SummaryIn many disciplines, binary numerical porous media are commonly generated as realizations of a random process characterized by a limited set of morphological measurements, e.g. the conditioning and truncated Gaussian random field (GRF) model or the Monte Carlo simulated annealing (SA) reconstruction. Whether the output microstructures of a model are quantitative or qualitative depends largely on the information carried by the constraints that are implemented. We focus on the standard two‐point correlation function, also referred to as the covariance. The isotropic situation has been previously extensively studied. Here, we concentrate on a vector distance‐dependent covariance. Relying on practical solutions to the phase‐retrieval problem (retrieving an object from its Fourier modulus) encountered in general imaging, we show empirically that a finite binary two‐ or three‐dimensional actual sample can be recovered systematically to within a pixel from its correlation integral (the volume average covariance to within a scale factor). In random modelling, this characteristic, describing uniquely a single sample of finite size, must be simplified, i.e. reduced to its statistical content, prior to be fitted in a random model (GRF, SA) as the characteristic of a series of realizations of a porous medium. We consider a common simplification, i.e. truncation, in which that part of the covariance relating to the small‐scale features of the observed sample is preserved only. This arbitrary simplification is empirically supported by numerous published numerical experiments showing that the small‐scale content of a volume‐averaged covariance can be fairly well reproduced in realizations of various random models: its statistical nature is thus illustrated with the GRF model. The unique solution to the phase‐retrieval problem confers an important sense to this numerical agreement: the correlation integral being the most complete descriptor, the actual sample and the model outputs are considered as true analogues over scales smaller or equal to the cutoff length attached to the truncation. Thus, awareness of the phase‐retrieval problem supports on an empirical basis the generation of synthetic binary objects from a direct measurement on an available sample.

Kerogen, the source material for petroleum, can have a long history of alteration and diagenesis before crude oil forms. A common assumption is that the bulk composition of the expressed oil reflects so much of these progressive alterations that most of the primary biological information of the original fixed carbon has been lost. Exceptions are trace constituents, the biomarkers that comprise only a fraction of the organic material in most pristine crude oils. Analysis of the alkane/acyclic isoprenoid fraction of a large number of crude oils and rock extracts from the Timan-Pechora basin (Russia) suggest that this fraction, the main constituent of most crude oils, is a direct product of liquefaction of biological debris that was preserved essentially unaltered to the point of oil generation. Therefore, the primary biological provenance of this fraction is preserved in the oil fraction.A set of gas-chromatographic analyses of 242 crude oils as well as 83 solvent extracts from upper to middle Paleozoic putative source rocks from the Timan-Pechora basin (Russia) were analyzed by a multivariate data-analytical procedure new to organic geochemistry. The distributions of n-alkanes and acyclic isoprenoids (24 in all) in the 325 samples could be reproduced by linear combinations of six end-member compositions attributed to distinct biological inputs. Four of the six are assigned to primary producers (waxes from higher plants, cyanobacteria, microalgae, and the microorganism Gloeocapsomorpha prisca). These end members account for most of the n-alkanes and acyclic isoprenoids in our samples. The other two represent the products of secondary bacterial alteration of primary organics during sedimentation and low-level bacterial alteration in the reservoir (biodegradation). Each end member is composed of a spectrum of analytes whose abundances are related to one another by fixed ratios. We surmise that each primary end member represents the breakdown of a resistant biopolymer that forms cell walls and partitions of a given biological group. The n-alkanes and acyclic isoprenoids in crude oils represent the weighted signatures of their various ancestors (i.e., their primary organic inputs). If the precursors of most oils are the products of a small set of chemically simple biopolymers, then many of our assumptions concerning the importance of total organic carbon and the nature of the oil window must be reexamined.

Macroscopic transport properties of natural porous media, such as the permeability tensor \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K} }\), are the sum of uncountable microscopic events. Understanding how these microscopic events come together to yield a descriptive property, such as \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K} }\), is facilitated if a set of porous descriptors Pii=1,N can be measured that synthesize all the critical microscopic properties of a real porous medium and that can be related to the computed \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K} }\). The main difficulty lies in choosing the correct Pii=1,N. A description of the microgeometry of a porous medium by a set of Pii=1,N will be declared adequate if synthetic numerical porous media generated from the Pii=1,N possess the same \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K} }\) as the real medium. This paper is another step for creating such synthetic porous media. The candidate geometrical descriptor P1 considered herein is the autocorrelation function (ACF) measured directly on a sample of finite size v included in a porous medium of size V; V ≫ v. Capitalizing on the phase retrieval problem (retrieving an object from knowledge of its Fourier modulus) encountered in general imaging, it is shown that there exists a one-to-one relation between a digital thin section and its ACF. This is demonstrated using an iterative procedure, the Error Reduction/Hybrid Input Output algorithm, that allows one to recover uniquely, to within a pixel, a finite image from its ACF. A theoretical implication of this is that a direct measurement on a finite image cannot characterize the geometry of a porous medium. Yet, in stochastic modeling, quasi-infinite numerical porous media are commonly generated from acquired ACF. Such quasi-infinite stochastic porous media must include a structural noise as a practical consequence of the unicity of the relation between an image and its ACF. To correctly interpret the relation between \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K} }\) and the microgeometry, it becomes necessary to verify that this nonimposed structural noise does not control the output \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K} }\) of the numerical simulations.

Environmental forensic analysis has evolved significantly from the early days of qualitative chemical fingerprint evaluations. The need for quantitative rigor has made the use of numerical methods critical in identifying and mapping contaminant sources in complex environmental systems. Given multiple contaminant sources, the environmental scientist is faced with the challenge of unraveling the contributions of multiple plumes with overlapping spatial and temporal distributions. The problem may be addressed through a multivariate statistical approach, but there is a mind-boggling array of the available "chemometric" methods. This paper provides an overview of these methods, along with a review of their advantages, disadvantages, and pitfalls. Methods discussed include principal component analysis and several receptor-modeling techniques.

The description of transport processes is practically accomplished at the macroscopic scale compatible with our ability to observe, and measure processes. The macroscopic description requires to faithfully account for the effects of the detailed inter-phase boundaries on the microscopic level (the micro-structure) in the expression for macroscopic transport coefficients such as permeability. Herein, the porous descriptors held to express macroscopic coefficients are the porosity and the autocorrelation function (ACF) measured directly on a 2-D finite digital image of the porous material. The flow-relevance of the selected porous descriptors will be eventually demonstrated if synthetic porous media generated through a random model from measured porosity and ACF yield the same transport properties than the actual media. Towards that goal, synthetic 2-D numerical porous micro-structures are generated from measured porosity and ACF on two types of natural mechanical aggregates: an Upper Shoreface and a Tidal Channel Sandstone. The achieved synthetic porous media are shown to include all the geometrical features of the real, observed, natural aggregates. Such agreement between synthetic and actual media is demonstrated to be the consequence of: (1) the richness of the structural information carried out by the ACF and, (2) a structural noise produced by the “practical use” of the random model. The requirement to account for the impact on macroscopic physics of this structural noise is emphasized. Extension of the approach to artificial aggregates such as cement, mortars or concrete is shown to be a promising avenue.

The nuances of relative permeability curves are commonly considered to be the product of variations in pore structure and wettability. Extrapolation of the results of a few flow tests into an entire reservoir for simulation purposes assumes that wettability does not change much over most of the reservoir and that the porous microstructure is relatively random and homogeneous. However, there is an increasing body of research indicating that the distribution of porosity is never random or homogeneous. Sandstone fabrics are a mixture of close-packed domains and packing flaws. This characteristic structure imparts a characteristic structure to the pore network that, in turn, defines fluid flow behavior (both single- and multiphase). Packing flaws are zones of oversized pores and pore throats with great spatial continuity. In lithified sandstones, virtually all of the single-phase flow occurs within packing flaws. The close-packed zones have much smaller pores and pore throats, and along with microporosity, tend to retain irreducible water. Results from a variety of quartz-rich sandstone reservoirs indicate that the domainal structure of porosity exerts a major influence upon Sor and Swi values observed in unsteady-state tests. The sample set is limited to quartz-rich reservoir sands with an induced water-wet condition. However, the results demonstrate the linkage between pore fabric and relative permeability end points, and may ultimately permit one to extrapolate those properties as a function of depositional fabric.

Patterns of porosity in sandstones of the Monserrate Formation (Upper Magdalena Valley) exposed in polished blocks have been digitally recorded using an image processor coupled to a scanning electron microscope operated in backscatter electron mode. Additionally, porosity, permeability and response to mercury injection-capillary pressure tests were measured on some of the imaged samples. Porosity patterns were evaluated via an erosion/dilation-differencing image-processing algorithm and then classified by the selftraining classifier, SAWVEC. Changes in the resulting pore type proportions were strongly associated with changes in the mercury porosimetry curves. From the image processing data, five pore types, sufficient to include all of the variability in size and shape of the patterns of porosity, were identified. Variations in the number of pores of each type per unit cross sectional area were related to variations in permeability. The resultant relationships with mercury porosimetry demonstrated that pores of the same type tend to form microcircuits characterized by a limited throat size range. Permeability modeling showed that intergranular Pore Types 2 and 4 (secondary porosity resulting from carbonate dissolution) are responsible for permeability in the 0,01 -0,1 0 Darcy range. Type 5 pores (large molds) slightly contribute to permeability, except in coarse grained rocks where they are efficiently connected by microfractures.

Sandstone Reservoir Assessment and Production is Fundamentally Affected by Properties of a Characteristic Porous Microfabric Robert Ehrlich, SPE, U. of Utah; Christopher Prince, U. of South Carolina; Matthew B. Carr, Amoco E & P Company Abstract All sandstones have a characteristic porous micro-fabric consisting of packing flaws and close packed domains. The packing flaws are arrayed as circuits with great areal continuity composed of oversized pores linked by oversized pore throats. The porosity involved in the packing flaws can be detected and classified by two image analytical procedures and this quantitative data can be correlated with a wide range of fluid properties (permeability, Sor, Swi, etc.). Packing flaws are preferentially preserved during compaction and chemical diagenesis. Wetting phases are preferentially segregated in the close packed domains, are relatively immobile and, in most sandstones, the porosity fraction represented by close-packed porosity is correlated with Swi. However, grain size also affects the value of Swi. In general, a coarse grained conglomerate will contain close packed domains whose throats only weakly imbibe water whereas the contrary occurs in an equivalently sorted medium or fine grained quartz-rich sandstone. For a quartz rich sandstones however, Swi is proportional to the amount of porosity in close packed domains. Mobile non wetting phases are restricted to loose packed circuits. A subset of circuits with the aspect ratio closest to unity carries the non wetting phase at highest water saturations—the remainder of the loose packed circuits account for most of the Sor. Image analytical procedures can therefore objectively define reservoir rock types and evaluate the porous microfabrics of these rock types in terms of a more relevant reservoir description and tying rock type to wireline log response. The existence of the small scale heterogeneity consisting of packing flaws and close-packed domains may explain in some part the difficulty in scaling up permeability (a sample support problem) and may require a reevaluation of the basis of relative permeability procedures. Introduction Reservoir sandstones are commonly well sorted, are assembled by the process of sedimentation and the resulting depositional fabric persists over geological time scales. This depositional fabric consists of grains of variable shape and size packed in geometries dictated by the rules of sedimentation and compaction. The porosity is arrayed in a complementary fabric and consists of a three dimensional array of pores connected by pore throats. It is well known that sandstones may be internally heterogeneous at the bed level (10 cm–10 m) but, inasmuch as grain size variation is commonly minimal at the smaller scale, it is commonly assumed that the porous microstructure is uniform and homogeneous. This tacit assumption guarantees the relevance of small cylindrical plugs taken from core for measurement of physical properties. Failure of that assumption affects the ways in which we attempt to scale up core measurements and to interpret the results of physical tests. The fundamental theory for the formation of sand and empirical evaluations of that theory, show that the assumption of homogeneity at small scale is always incorrect (figure 1). In this report we document:the existence of a universal micro-structural fabric of sandstones,the relationship of that fabric to single and multi-phase flow andsuggest ways in which present practice can be modified to take advantage of this insights. Sandstone Microstructure. Sandstones are in fact universally heterogeneous from the mm scale upwards—with variation in packing dominating the smaller scales and grain size the higher scales. Graton and Fraser proposed that a characteristic sort of heterogeneity (or "structure") exists in all sandstones over scales of mm to cm (tens of grain diameters)-and that this fine-scaled structure is physically relevant in understanding permeability. They conjectured, based on experiments using monolayers of spheres, that: P. 591^

This work is part of an attempt to quantify the relationship between the permeability tensor (K) and the micro-structure of natural porous media. A brief account is first provided of popular theories used to relate the micro-structure toK. Reasons for the lack of predictive power and restricted generality of current models are discussed. An alternative is an empirically based implicit model whereinK is expressed as a consequence of a few “pore-types” arising from the dynamics of depositional processes. The analytical form of that implicit model arises from evidence of universal association between pore-type and throat size in sandstones and carbonates. An explicit model, relying on the local change of scale technique is then addressed. That explicit model allows, from knowledge of the three-dimensional micro-geometry to calculateK explicitly without having recourse to any constitutive assumptions. The predictive and general character of the explicit model is underlined. The relevance of the change of scale technique is recalled to be contingent on the availability of rock-like three-dimensional synthetic media. A random stationary ergodic process is developed, that allows us to generate three-dimensional synthetic media from a two-dimensional autocorrelation functionr(λ x ,λ y ) and associated probability density function∈ β measured on a single binary image. The focus of this work is to ensure the rock-like character of those synthetic media. This is done first through a direct approach:n two-dimensional synthetic media, derived from single set (∈ β ,r(λ x ,λ y )) yieldn permeability tensorsK i-1,n i (calculated by the local change of scale) of the same order. This is a necessary condition to ensure thatr(λ x ,λ y ) and∈ β carry all structural information relevant toK. The limits of this direct approach, in terms of required Central Process Unit time and Memory is underlined, raising the need for an alternative. This is done by comparing the pore-type content of a sandstone sample andn synthetic media derived fromr(λ x ,λ y ) and∈ β measured on that sandstone-sample. Achievement of a good match ensures that the synthetic media comprise the fundamental structural level of all natural sandstones, that is a domainal structure of well-packed clusters of grains bounded by loose-packed pores.

Pore size frequency distributions can be derived from Nuclear Magnetic Resonance (NMR) longitudinal relaxation measurements (T1) on water saturated plugs. This paper discusses the cross validation of NMR T1 relaxation distributions of porosity and how they are related to distributions obtained from image analysis of porosity in thin section. Both sets of distributions are polymodal and decomposition of each yields porosity types. Each pore type represents a subdistribution of pores with a characteristic size and shape. The mean T1 values associated with the NMR pore types are linearly related to the mean size of pore types determined from image analysis. The constant of proportionality of this relationship represents the surface relaxivity (ρ), a parameter that represents the enhancement of relaxation caused by nuclei interacting with the pore wall. The major difference between image analysis and NMR methods is that NMR can resolve much smaller pores. The relationships between pore types and throat sizes using NMR generated pore types are the same as that using image analysis generated pore types. The existence of a strong relationship between pore type and throat size ensures the relevance of NMR data in studying the properties associated with single and multiphase flow.

Nuclear Magnetic Resonance (NMR) longitudinal relaxation (T1,) experiments on water saturated plugs can be used to derive pore size frequency distributions in naturally porous media. These distributions can be cross validated with related distributions derived from petrographic image analysis (PIA). The decomposition of both NMR and PIA polymodal distributions yields pore types. Each pore type represents a subdistribution of pores possessing a characteristic size and shape. NMR pore types and PIA pore types are linearly related with respect to size. The constant of proportionality of this relationship can be used to estimate a value for the enhancement of relaxation caused by the nuclei interacting with the pore wall, called surface relaxivity (ϱ). The nature of the NMR pore type spectra indicate that a low T1 component is associated with all the NMR pore types. The calculation of an estimated value of ϱ can be either from the linear relationship or from individual NMR/PIA pore type relationships. The various calculated values are very similar, and thus, a mean value for a given sample suite can be calculated. The estimation of ϱ is critical in the interpretation of NMR T1 data, and external calibration is essential. This study demonstrates that calibration to PIA is one method, and that it is advantageous because PIA is the best method of deriving mean pore size from thin section. Moreover, PIA is advantageous because geometry effects are directly evident from thin section and SAWVEC B (an unmixing algorithm that decomposes polymodal data), as well as the ability of inferring mineralogy. In addition, PIA is advantageous because of its direct correlation to petrophysical properties. Therefore, NMR and PIA derived pore sizes can be used to cross validate each other. Thus, the relationship that commonly exists between pore size and throat size ensures that NMR and PIA derived pore sizes will have relevance in the understanding of petrophysical properties associated with fluid flow in natural porous media.

A set of formation tops from an array of wells can be simultaneously analyzed, providing rapid quantitative insights on basin development. The structural configuration of each formation can be defined in terms of relative proportions of a small number of end-member structural states. The relative proportion of each end member as a function of time is a succinct quantitative form of basin history analysis. The procedure works with mappable, as well as unmappable, data. With mappable data, the end members can be displayed as structure contour maps. The end members can also be decomposed into trends and residuals, providing additional details about the structural history of the basin. An example employs formation tops data from 12 Cretaceous formations and 99 wells in the de p basin of Alberta, Canada.