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1.
The decomposition problem—the assignment of sample observations to component populations—is studied in a spatial context. The observations are spatially located and the assignment to component populations takes into account the value of each observation as well as the values of neighboring observations. Both parameter estimation and assignment rules use a new method that integrates a standard multivariate decomposition algorithm with nonlinear regression. The method is illustrated and tested with artificial data. The distribution of the trace component Cr2O3 in recent Lake Michigan sediments is, then, analyzed by the method. It yields a pattern of component populations that is correlated with the Lake's bottom structure and depositional environments. Study carried out as visiting scholar at the Department of Geological Sciences, Northwestern University, Evanston, Illinois U.S.A.  相似文献   

2.
Some geological events occur infrequently but still have a significant impact upon reservoir characteristics. By their very nature, however, it can be difficult to properly estimate the proportions of uncommon events because they may not appear during limited sampling. For example, even with 40 observations and an event proportion of 0.05, there is a 0.13 chance that no events will be observed. We provide some results and guidance concerning methods to estimate proportions when such events are not detected. Two cases are discussed, estimating proportions without errors in identification and estimating proportions when errors may arise. It is well-known that the distribution of possible proportions in the error-free case can be calculated using Bayesian analysis. If one assumes a standard uniform distribution as the prior for the proportion, Bayesian analysis gives a Beta distribution for the posterior. The situation becomes more complicated, however, when detection errors are included; the true proportion has a distribution consisting of several Beta distributions. The difference in results between the error-free and with-error situations can be considerable. For example, when 10 error-free observations are made and no uncommon events are detected, there is a 0.50 chance that the true proportion exceeds 0.06 and a 0.10 chance that it exceeds 0.19. Including the effects of erroneous identifications, however, increases the median proportion to 0.09 and the upper decile to 0.27. We also examine the case where there may be prior geological information, which can be incorporated by amending the prior distribution of the proportion. We find that the use of such a prior makes little difference unless there are very few observations or there are major differences between the anticipated and the observed proportions.  相似文献   

3.
Studying the mechanisms at work in waste technologies, such as waste-immobilisation, reactive barriers for waste containment, waste–waste neutralisation, etc., requires an integral characterization of materials. Materials before and after processing should be characterised in terms of (a) proportions of phases (liquids and solids), (b) composition and homogeneity of phases, (c) grain-size distribution (ideally per phase), and (d) large-scale compositional gradients within the system. Novel techniques can be applied successfully such as Rietveld-analysis of powder-XRD patterns to determine the modal proportions of fine-grained solids and laser-ablation–ICP–MS to determine trace element distributions on a ≈10-μm scale. Mathematical mass-balance and diffusion models provide checks for consistency in the characterization of materials. A case study is presented on a geochemical engineering treatment of red mud, the waste product of bauxite processing.  相似文献   

4.
Genetically meaningful decomposition (unmixing) of sediment grain-size distributions is accomplished with the end-member modelling algorithm. Unmixing of the loess grain-size distributions of a Late Quaternary loess–palaeosol succession from the north-eastern Tibetan Plateau indicates that the loess is a mixture of three end-members representing very fine sandy, coarse silty and medium silty loess. The unmixing approach potentially enables the unravelling of sediment fluxes from multiple dust sources, opening the way to significant advances in palaeoclimatic reconstructions from loess grain-size distribution data. However, as laser-diffraction size analysis is a volume-based technique, the proportional contributions of the modelled end-members might deviate (significantly) from weight proportions. Hence, calibration of the end-member volume proportions to weight proportions must be established before one can calculate the source-specific dust fluxes. This paper reports the findings of a sediment-mixing experiment which enables calibration of the modelled mixing patterns established for the Tibetan loess–palaeosol succession.  相似文献   

5.
The Austrian reconnaissance study of stream-sediment composition — more than 30000 clay-fraction samples collected over an area of 40000 km2 — is summarized in an atlas of regional maps that show the distributions of 35 elements. These maps, rich in information, reveal complicated patterns of element abundance that are difficult to compare on more than a small number of maps at one time. In such a study, multivariate procedures such as simultaneous R-Q mode components analysis may be helpful. They can compress a large number of variables into a much smaller number of independent linear combinations. These composite variables may be mapped and relationships sought between them and geological properties. As an example, R-Q mode components analysis is applied here to the Grazer Paläozoikum, a tectonic unit northeast of the city of Graz, which is composed of diverse lithologies and contains many mineral deposits.  相似文献   

6.
Mineral shapes, sizes and proportions in mica rich (M) and quartz-mica (QM) domains of an S4 metamorphic layering have been compared in two mutually perpendicular orientations with shapes, sizes and proportions in mildly crenulated S2 enclaves preserved within a rock from part of the Willyama Complex, N.S.W., Australia. The study has shown that data from two orientations are necessary to place constraints on the movement of mineral components dissolved in solution during formation of the layering. Comparison of mineral data has shown that SiO2 has been dissolved from quartz grains in both M and QM domains. The SiO2 lost from M domains has not migrated into QM domains. Measurements have also shown that biotite has undergone less solution than quartz. Most of the biotite components have probably undergone reaction to form probable syn—S4 muscovite and chlorite. The muscovite-forming reaction requíres some silica on the lefthand side of the reaction, probably more than can be supplied by the chlorite-forming reaction. Some of this extra silica was supplied from dissolved quartz grains. However, only a small amount is needed for this purpose and most of the SiO2 has left the system. Some syn—S4 muscovite may have formed in M domains where it lies within the crenulated S2. Direct evidence for its growth is hard to find.  相似文献   

7.
Ophiolite belts and the collision of island arcs in the Arabian Shield   总被引：1，自引：0，他引：1  
The Arabian Shield is divided into several segments by ophiolite zones. The segments display features of island arcs with respect to their magmatic evolution as well as their mineralization.The northern part of the “Hulayfah—Hamdah ophiolite belt” which cuts the Arabian Shield in a north—southerly direction, has been sampled and described. Serpentinized ultramafics, gabbros, doleritic dike rocks and basalts are the most important members. The ophiolite belt is marked by magnetic anomalies with amplitudes of 200–500 gammas.In conclusion, the Arabian Shield is considered to be built up of several generations of juxtaposed volcanic arcs of Late Proterozoic age. The arcs have been closely swept together squeezing out the trench-fill sediments in the case of the Hulayfah—Hamdah belt. Cratonization was completed by the end of the Precambrian.  相似文献   

8.
Data of a microfossil group, the planktonic foraminifera, have been tested to determine the conformity of various real data distributions to univariate and multivariate normality and the effects that standard transformations have upon the distributions. Studies of two bivariate samples, one trivariate sample, and two quadrivariate samples of size data indicate that distributions frequently deviate greatly from multivariate normality. Univariate distributions are generally positively skewed and show a tendency for leptokurtosis. A logarithmic transformation improved both univariate and multivariate distributions but the number of distributions conformable to normality increased only slightly—from zero to one in the multivariate case and from one to four in the univariate case (totally 15 distributions). Arcsine (p/100) 1/2 transformations of percentage data in two samples including 16 and 23 species, respectively, decreased highly significant deviations from multivariate normality but distributions remained greatly non-normal. Although markedly positively skewed and leptokurtic univariate distributions were improved in most instances, the number of normal distributions (two) did not change. It follows that neither of the transformations caused significant increases in the number of normal distributions but if it is assumed that the consequences of non-normality are less severe as the deviation from normality decreases, the transformations are justified.  相似文献   

9.
Increasing attention has been paid to the use of non-Gaussian distributions as models of heterogeneity in sedimentary formations in recent years. In particular, the Lévy-stable distribution has been shown to be a useful model of the distribution of the increments of data measured in well logs. Frequently, the width of this distribution follows a power–law type scaling with increment lag, thus suggesting a nonstationary, fractal, multivariate Lévy distribution as a useful random field model. However, in this paper we show that it is very difficult to formulate a multivariate Lévy distribution with any nontrivial spatial correlations that can be sampled from rigorously in large models. Conventional sequential simulation techniques require two properties to hold of a multivariate distribution in order to work: (1) the marginal distributions must be of relatively simple form, and (2) in the uncorrelated limit, the multivariate distribution must factor into a product of independent distributions. At least one of these properties will break down in a multivariate Lévy distribution, depending on how it is formulated. This makes a rigorous derivation of a sequential simulation algorithm impossible. Nonetheless, many of the original observations that spurred the original interest in multivariate Lévy distributions can be reproduced with a conventional normal scoring procedure. Secondly, an approximate formulation of a sequential simulation algorithm can adequately reproduce the Lévy distributions of increments and fractal scaling frequently seen in real data.  相似文献   

10.
In the prediction of ore deposits, a series of geological, geochemical, and geophysical characters are used to describe the model of ore deposits. The problem is how to use the characters of known ore deposits to establish the model and to look for the target areas with similar geological environments. This can be done with a powerful mathematical tool—discriminant analysis. Nevertheless, there generally are too many geological variables to describe a class of ore deposits. Some of them are discrete, and the others are continuous. It is also difficult to know their distributions. A satisfactory method of discrimination has not been developed for such a complicated case. For this reason, we introduce a new method of orthogonally stepwise discrimination. We used this method to predict copper ore deposits of Dongchuan type in central Yunnan, China, with satisfactory results.  相似文献   

11.
The two-dimensional spatial distribution of precious stones, such as diamonds in alluvial and coastal deposits, shows a high degree of clustering. Usually, stones tend to gather in relatively small clusters or traps, made by potholes, gullies, or small depressions in the rough bedcock. Therefore, when taking samples of such deposits, discrete distributions of the number of stones counted in each sample yield an extreme skewness. Most samples have no stones, whereas samples containing a few hundred stones are not unusual. This paper constructs a model and a method for fitting a new and general family of counting distributions based on the Neyman-Scott cluster model and the mixed Poisson process, which can be used to model a differing degree of clustering. General recursion equations for the discrete probabilities of these distributions are derived. Application of this model to simulated data shows that information such as cluster size, number of point events per cluster, and number of clusters per measurement unit can be extracted easily from this model. Fitting the model to data of two real diamond deposits of a totally different nature—small rich clusters of Namibia versus larger but less rich clusters of Guinea—demonstrates its flexibility.  相似文献   

12.
The fulfillment of a scaling law for earthquake recurrence–time distributions is a clear indication of the importance of correlations in the structure of seismicity. In order to characterize these correlations we measure conditional recurrence–time and magnitude distributions for worldwide seismicity as well as for Southern California during stationary periods. Disregarding the spatial structure, we conclude that the relevant correlations in seismicity are those of the recurrence time with previous recurrence times and magnitudes; in the latter case, the conditional distribution verifies a scaling relation depending on the difference between the magnitudes of the two events defining the recurrence time. In contrast, with our present resolution, magnitude seems to be independent on the history contained in the seismic catalogs (except perhaps for Southern California for very short time scales, less than about 30 min for the magnitude ranges analyzed).  相似文献   

13.
Stochastic simulation techniques which do not depend on a back transform step to reproduce a prior marginal cumulative distribution function (cdf)may lead to deviations from that distribution which are deemed unacceptable. This paper presents an algorithm to post process simulated realizations or any spatial distribution to reproduce the target cdfin the case of continuous variables or target proportions in the case of categorical variables, yet honoring the conditioning data. Validations conducted for both continuous and categorical cases show that. by adjusting the value of a correction level parameter , the target cdfor proportions can be well reproduced without significant modification of the spatial correlation patterns of the original simulated realizations.  相似文献   

14.
TORE P°SSE 《Sedimentology》1997,44(6):1011-1014
The grain size distribution within a unimodal sediment can be described as a lognormal distribution when the distribution is formed by only one process. However, most sediments are formed by more than one process giving polymodal sediments. Polymodal sediments have to be described as the sum of several normal distributions, one for each process involved within the formation. Grain size distributions are usually interpreted with the help of graphical methods. Interpretations of polymodal sediments require mathematical methods. In mathematical terms a unimodal sediment can be described as a tangential hyperbolic function (tanh) and a polymodal sediment can generally be described by the sum of two or three tanh-functions. The tanh-method is a tool for identifying and estimating the number of modes within a grain size distribution and helps interpret the processes involved within the formation of a deposit. The mathematical method can also be used to computerize sediment data, allowing storage with just a few numbers. Different samples can easily be compared and classified. Also, this method could be a valuable tool for calculations of various sediment parameters both in geotechnology and hydrogeology.  相似文献   

15.
Modeling statistical distributions of phenomena can be compromised by the choice of goodness-of-fit statistics. The Pearson chi-square test is the most commonly used test in the geosciences, but the lesser known empirical distribution function (EDF) statistics should be preferred in many test situations. Using a data set from geomorphology, the Anderson–Darling test for grouped exponential distributions is employed to illustrate ease of use and statistical advantages of this EDF test. Attention to the issues discussed will result in more informed statistic selection and increased rigor in the identification of distribution functions that describe random variables.  相似文献   

16.
S. Santini  M. Dragoni  G. Spada 《Tectonophysics》2003,367(3-4):219-233
The 1964 Alaska earthquake was the second largest seismic events in the 20th century. The aim of this work is the use of surface deformation data to determine asperity and slip distributions on the fault plane of the Alaska earthquake: these distributions are calculated by a Monte Carlo method. To this aim, we decompose the fault plane in a large number of small square asperity units with a side of 25 km; this allows us to obtain plane surfaces with an irregular shape. In the first stage, each asperity unit is allowed to slip a constant amount or not to slip at all, providing the geometry of the dislocation surface that best reproduces the observed displacements. To this purpose, a large number of slip distributions have been tried by the use of the Monte Carlo method. The slip amplitude is the same for all the asperities and is equal to the average fault slip inferred from the seismic moment. In the second stage, we evaluate the slip distribution in the dislocation area determined by the Monte Carlo inversion: in this case, we allow unit cells to undergo different values of slip in order to refine the initial dislocation model. The results confirm the previous finding that the slip distribution of the great Alaska earthquake was essentially made of two dislocation areas with a higher slip, the Prince William Sound and the Kodiak asperities. Analysis of the post-1964 seismicity in the rupture region shows a strong correlation between the larger earthquakes (Mw≥6) and the distribution of locked asperities following the 1964 event, which can be considered as an independent test of the validity of the model. We do not find slip values higher than 25 m for any of the patches, and we determine two separate high-slip zones: one correspondent to the Prince William Sound asperity, and one (18 m slip) to the Kodiak asperity. The slip distribution connected with the 1964 shock appears to be consistent with the following seismicity in the region.  相似文献   

17.
The rate of a high-pressure phase transition increases exponentially with temperature (T) and overpressure or pressure beyond equilibrium (ΔP). It is also greatly promoted by introducing shear stress, diminishing grain size, and adding water or other catalysts to the reactants. For an isothermal and isobaric transition with no compositional change, if steady state of nucleation on grain surfaces is attained, the rate equation can be expressed: (1) before site saturation by: X = 1 − exp(−Kt4), where
Full-size image (2K)
and (2) after site saturation by: X = 1 − exp(−K′T), where
Full-size image (1K)
, where X is volume fraction of completion of transformation, t is time, and the C's are characteristic constants. C1 and C9 are functions of grain size, C3 and C6 are functions of shear stress. All the C's are almost independent of temperature and pressure. Thus, if X as a function of T, ΔP, and t over a narrow P-T range can be experimentally determined, the C's can be calculated and the effect of grain size and shear stress on the rate of transformation can be evaluated. The isothermal and isobaric rate equations for a given composition, shear stress, and grain size are then experimentally determinable. The non-isothermal and non-isobaric rate equation can be calculated from the isothermal and isobaric ones if the rate of penetration into the metastability field is known. The important feature of the kinetics of high-pressure phase transitions predicted by these rate equations is that for a given rate of penetration into the metastability field, there can be defined a characteristic temperature, Tch, below which the rate of the transition is virtually zero no matter how metastable the material is. For the olivine → spinel transition in the mantle, this characteristic temperature may be as high as 700° C. Thus, in a fast moving downgoing slab, the temperature at its cold center may remain below Tch even down to depths in excess of 600 km, thereby greatly depressing the olivine—spinel phase boundary.At an early stage in the development of a downgoing slab, the plunging speed is slow. This allows the interior of the slab to heat up and the olivine → spinel transition to proceed rapidly and near equilibrium. As a result, the olivine—spinel phase boundary in the slab will be distorted upwards. The rising of the denser spinel phase then provides an additional driving force which accelerates the plate. Since the upper portion of the slab is pulled from below and the lower portion pushed from above, earthquakes of down-dip extension will occur in the upper mantle while those of down-dip compression will originate in the transition zone. Because the transformation occurs close to equilibrium, there will be an aseismic region separating the two seismic zones. When the plate velocity exceeds a certain limit, the temperature in the cold interior becomes low enough to depress the olivine → spinel transition. The phase boundary is then distorted downwards. The buoyant force thereby created will reduce the driving force, and the plunging speed of the plate will approach a steady state. In addition, the buoyant force will compress the slab from below and result in earthquakes of down-dip compression throughout the length of the slab. Now the olivine → spinel transition is so far from equilibrium that the reaction becomes implosive. A rise in frequency of deep earthquakes towards the implosion region in the lower transition zone is thus predicted. Therefore, as well as stabilizing the plate velocity, the olivine → spinel transition may also control earthquake distributions throughout the downgoing slab.  相似文献   

18.
Different studies have already pointed out the influence of clays during the analysis of pure organic compounds (especially alkanols, alkanoic acids) as well as macromolecules (humic acids) by flash pyrolysis-gas chromatography–mass spectrometry (PyGC–MS). Especially, the occurrence of clay minerals favors the generation of aromatic units such as alkylbenzenes and polycyclic aromatic hydrocarbons. So as to better identify the nature of the organic compounds which are sensitive to the presence of clays during flash pyrolysis, a humic acid mixed in variable proportions of a Na-homoionic clay was tested. The smectite/humic acid mixtures containing from 10% to 100% humic acid allowed us to identify the progressive disappearance or appearance of specific compounds after PyGC–MS.n-Alk-1-enes disappear when the clay proportion is higher than 67%. For higher contents of Na-smectite, n-alkanes become less and less abundant with a preferential consumption of high molecular weight n-alkanes, whereas the aromatic hydrocarbon proportion increases. Moreover, the distribution of each aromatic hydrocarbon family (alkylbenzenes and alkylnaphthalenes) has been investigated. The pyrogram of pure humic acid exhibits a specific distribution of alkylbenzenes and alkylnaphthalenes reflecting the structure of the organic macromolecule. With the increase in clay proportion, these distributions are modified and lead to other distributions with a preferential predominance of thermally stable isomers.Pyrograms of humic acid and undecanoic acid in the presence of 90% of Na-smectite are similar, especially concerning alkylbenzene and alkylnaphthalene distributions. Therefore, clays (Na-smectite in our experiments) in high proportion modify initial organic products by recombination reactions and lead to the generation of new compounds of very similar distribution, whatever the nature of the initial organic matter. Such results underline the very important catalytic properties of clay minerals on functionalized organic matter during flash pyrolysis.  相似文献   

19.
The statistical prediction of mineral deposits can be described as follows:Basic Theories— (1) similarity-analogy, (2) differences and anomalies, (3) ore-forming factors, andBasic Principles— (1) comprehensive prediction, (2) relationship between the prediction scale and the parameter scale, (3) distribution of mineral parameters, (4) quantitative prediction, (5) assessment, and (6) discovery rate analysis, andBasic Methods.  相似文献   

20.
On November 30, 1967, a strong earthquake of magnitude M = 6.6 struck the Dibra region, eastern Albania, causing considerable loss of human life and grave material damage both in the territory of Albania and that of Yugoslavia.The object of this study is to describe the effects of this earthquake on landscape and buildings, as well as to define its macroseismic field. The study further deals with some features of the aftershocks of M 4.0 distributed in time and space, the aftershock activity and the focal-mechanism solution of the main event.From the study of the macroseismic field of this earthquake and its fault, which extends over 10 km in a 40° northeasterly direction, from the distribution of aftershocks in space and the focal-mechanism solution of this earthquake, the conclusion has been reached that this event is connected with the Vlora—Dibra seismogenic belt.The authors have mentioned the existence of this traverse belt as early as 1969 (Sulstarova and Koçiaj, 1969). The existence of this belt is also shown by the chronological and geographical distribution of some strong earthquakes in Albania in the period 1800–1967 (their macroseismic field and the position of their epicentres), and by the focal-mechanism solutions of some of these earthquakes. The Vlora—Elbasan—Dibra transverse seismogenic belt continues for several hundred kilometres northeast and southwest beyond the territory of Albania.  相似文献   

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