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1.
Environmental studies require multivariate data such as chemical concentrations with space-time coordinates. There are two
general conditions related to such data: the existence of correlations among the coregionalized variables and the differences
in numbers of data which occur because of insufficient data caused by measurement error or bad weather conditions. This study
proposes geostatistical techniques for space-time multivariate modeling that take into consideration these correlations and
data absences. These techniques consist of suitable modeling of semivariograms and cross-semivariograms for quantifying correlation
structures among multivariables and of extending standardized ordinary cokriging. The tensor product cubic smoothing surface
method is used for space-time semivariogram modeling. These methods are applied to the chemical component data of the Ariake
Sea, a typical closed sea in southwest Japan. In order to clarify environmental changes in the Ariake Sea, the concentration
data of four nutritive salts (NO2–N, NO3–N, NH4–N, and PO4–P) at 38 stations over 25 years are used as environmental indicators. For each of the kinds of data, there are spaces and
times for which there is no data available. The effectiveness of the modeling of space-time semivariograms and the high estimation
capability of the extended cokriging are demonstrated by cross-validation. Compared with ordinary kriging for a single variable,
multivariate space-time standardized ordinary cokriging can provide a more detailed concentration map of nutritive salts and
while elucidating their temporal changes over sparsely spaced data areas. In the space-time models by ordinary kriging, on
the other hand, smooth trends are obvious. 相似文献
2.
Koike Katsuaki 《地球科学》2011,36(2):209-226
Sample data in the Earth and environmental sciences are limited in quantity and sampling location and therefore, sophisticated spatial modeling techniques are indispensable for accurate imaging of complicated structures and properties of geomaterials. This paper presents several effective methods that are grouped into two categories depending on the nature of regionalized data used. Type I data originate from plural populations and type II data satisfy the prerequisite of stationarity and have distinct spatial correlations. For the type I data, three methods are shown to be effective and demonstrated to produce plausible results: (1) a spline-based method, (2) a combination of a spline-based method with a stochastic simulation, and (3) a neural network method. Geostatistics proves to be a powerful tool for type II data. Three new approaches of geostatistics are presented with case studies: an application to directional data such as fracture, multi-scale modeling that incorporates a scaling law, and space-time joint analysis for multivariate data. Methods for improving the contribution of such spatial modeling to Earth and environmental sciences are also discussed and future important problems to be solved are summarized. 相似文献
3.
Joint Consistent Mapping of High-Dimensional Geochemical Surveys 总被引：1，自引：0，他引：1
Geochemical surveys often contain several tens of components, obtained from different horizons and with different analytical techniques. These are used either to obtain elemental concentration maps or to explore links between the variables. The first task involves interpolation, the second task principal component analysis (PCA) or a related technique. Interpolation of all geochemical variables (in wt% or ppm) should guarantee consistent results: At any location, all variables must be positive and sum up to 100 %. This is not ensured by any conventional geostatistical technique. Moreover, the maps should ideally preserve any link present in the data. PCA also presents some problems, derived from the spatial dependence between the observations, and the compositional nature of the data. Log-ratio geostatistical techniques offer a consistent solution to all these problems. Variation-variograms are introduced to capture the spatial dependence structure: These are direct variograms of all possible log ratios of two components. They can be modeled with a function analogous to the linear model of coregionalization (LMC), where for each spatial structure there is an associated variation matrix describing the links between the components. Eigenvalue decompositions of these matrices provide a PCA of that particular spatial scale. The whole data set can then be interpolated by cokriging. Factorial cokriging can also be used to map a certain spatial structure, eventually projected onto those principal components (PCs) of that structure with relevant contribution to the spatial variability. If only one PC is used for a certain structure, the maps obtained represent the spatial variability of a geochemical link between the variables. These procedures and their advantages are illustrated with the horizon C Kola data set, with 25 components and 605 samples covering most of the Kola peninsula (Finland, Norway, Russia). 相似文献
4.
Geochemical samples from part of Lake Geneva were analyzed for 29oxides and trace elements. The variables and samples were subjected to R- and Q-mode analyses. The following techniques were
applied in sequence: data transformation (normalization and standardization), data reduction (principal component and factor
analysis), and automatic classification (dendrograph). The data were treated using various combinations of these techniques,
and the resulting classifications evaluated by means of several criteria. The best classification of the samples is given
by a cluster analysis performed on four principal components computed from standardized variables. The discriminatory power
of the variables also was measured and determined to depend on their degree of intercorrelation. As a final result, the 29original variables were reduced to four components and the sediment samples classified into four facies, leading to easily
interpretable geochemical maps. 相似文献
5.
Three nonparametric techniques for the optimum discretization of quantitative geological features are proposed and demonstrated. The three methods are: isolated weight, entropy information, and rank correlation. Optimum discretization plays important roles in solutions to the following geoscience problems: (1) signal/noise separation and delineation of meaningful anomalies and other geofields related to mineral targets; (2) selection of those geological variables that explain variations in mineral resources; (3) determination of the best subintervals of values for a variable with respect to mineralization; (4) enhancement of certain complex and concealed information of a geofeature about its correlation with magnitude of mineralization; and (5) unification of diverse geodata so that these data can be integrated and analyzed. 相似文献
6.
Savithru Jayasinghe David L. Darmofal Nicholas K. Burgess Marshall C. Galbraith Steven R. Allmaras 《Computational Geosciences》2018,22(1):107-123
This paper presents a space-time adaptive framework for solving porous media flow problems, with specific application to reservoir simulation. A fully unstructured mesh discretization of space and time is used instead of a conventional time-marching approach. A space-time discontinuous Galerkin finite element method is employed to achieve a high-order discretization on the anisotropic, unstructured meshes. Anisotropic mesh adaptation is performed to reduce the error of a specified output of interest, by using a posteriori error estimates from the dual-weighted residual method to drive a metric-based mesh optimization algorithm. The space-time adaptive method is tested on a one-dimensional two-phase flow problem, and is found to be more efficient in terms of computational cost (degrees-of-freedom and total runtime) required to achieve a specified output error level, when compared to a conventional first-order time-marching finite volume method and the space-time discontinuous Galerkin method on structured meshes. 相似文献
7.
James C. Kelley 《Mathematical Geology》1971,3(1):43-50
Increasing attention in recent years has been devoted to the application of statistical techniques in the analysis and interpretation of geologic and oceanographic data. Equally important, but less well explored, are methods for efficient experimental design. The theory of linear programming provides plans for optimal sampling of geologic and oceanographic phenomena. Of particular significance are solutions to problems of multivariate sampling. Often, a single field sample may be analyzed for a number of oxides, or a number of minerals, or a number of textural parameters. In general, these variables differ in the degree to which they are diagnostic of changes in the phenomenon of interest, and thus they must be known with different levels of precision if they are to be useful. Similarly, the variables differ in the ease with which they may be measured. If a sampling plan is to be most efficient, it must provide the requisite levels of precision for the minimum expenditure of time and effort. Sampling for a single variable may be optimized directly. Sampling for several variables simultaneously usually introduces special difficulties, but if the objective function can be generalized to hold for all variables, solutions can be determined even in this situation. 相似文献
8.
Y. Zee Ma 《Mathematical Geosciences》2011,43(4):401-419
Both statistical methods and artificial neural network (ANN) have been used for lithology or facies clustering. ANN, in particular,
has increasingly gained popularity for clustering of categorical variables as well as for predictions of continuous variables.
In this article, we discuss several counter examples that show deficiencies of these techniques when used for automatic lithofacies
clustering. Our examples show that the lithofacies clustered by ANN alone or ANN in combination with principal component analysis
(PCA), as commonly used, are highly inconsistent with the benchmark charts based on laboratory results. We propose several
techniques to overcome these problems and improve the clustering of lithofacies, including (1) classification of lithofacies
using the minor or intermediate principal component(s), (2) rotation of a principal component before using ANN for clustering,
(3) cascading two or more PCAs and ANNs for clustering lithofacies or electrofacies, and (4) classifying lithofacies with
demarcated stratigraphic reference classes. 相似文献
9.
10.
Wengang Zhang Anthony T. C. Goh Yanmei Zhang 《Geotechnical and Geological Engineering》2016,34(1):193-204
Despite the rapid increases in processing speed and memory of low-cost computers, the enormous computational costs of running complicated numerical analyses such as finite element simulations makes it impractical to rely exclusively on simulation for the purpose of design optimization since many geotechnical problems are highly nonlinear and multivariate. To reduce the cost, surrogate models, also known as meta-models, are constructed and then used in place of the actual numerical simulation models. To ensure the surrogate model is more reliable, the ranges of the design variables should be as wide as possible. Thus meta-modeling techniques capable of analyzing multivariate problems are desirable. This paper explores the use of a fairly simple nonparametric regression procedure known as multivariate adaptive regression splines (MARS) in approximating the relationship between the inputs and outputs with a big data. First the basis of the MARS methodology and its associated procedures are explained in detail. Then two complicated geotechnical problems are presented to demonstrate the function approximating capabilities of MARS and its efficiency in dealing with multivariate problems involving large amounts of data. This paper demonstrates that the MARS algorithm is capable of producing simple, accurate and easy-to-interpret models and estimating the contributions of the input variables. 相似文献
11.
Kriging Regionalized Positive Variables Revisited: Sample Space and Scale Considerations 总被引：1，自引：0，他引：1
Frequently, regionalized positive variables are treated by preliminarily applying a logarithm, and kriging estimates are back-transformed
using classical formulae for the expectation of a lognormal random variable. This practice has several problems (lack of robustness,
non-optimal confidence intervals, etc.), particularly when estimating block averages. Therefore, many practitioners take exponentials
of the kriging estimates, although the final estimations are deemed as non-optimal. Another approach arises when the nature
of the sample space and the scale of the data are considered. Since these concepts can be suitably captured by an Euclidean
space structure, we may define an optimal kriging estimator for positive variables, with all properties analogous to those
of linear geostatistical techniques, even for the estimation of block averages. In this particular case, no assumption on
preservation of lognormality is needed. From a practical point of view, the proposed method coincides with the median estimator
and offers theoretical ground to this extended practice. Thus, existing software and routines remain fully applicable. 相似文献
12.
应用时空变—倾角扫描叠加KL变换提高地震资料信噪比 总被引：3，自引：0，他引：3
使用KL变换可去除地震资料中随机噪声和相干噪声，提高地震资料信噪比。但常规KL变换仅能加强水平方向同相轴，对倾斜或弯曲同相轴处理效果较差，且在处理大量数据时计算成本很高，在实际生产中难以广泛应用。一些文献中针对常规KL变换的两个缺陷进行了改进，即使用倾角扫描叠加KL变换和采用数据分块技术。作者在本文中将这两个方面的改进有机地结合起来，提出应用时空变－倾角扫描叠加KL变换对地震资料进行处理，并指出使用该方法时需要注意的一些问题。理论模型和实际资料处理效果表明，使用本方法可以克服常规KL变换的缺陷，有效改进剖面处理效果。 相似文献
13.
Research on basic characteristics of 2H, 18O and 14C in geothermal fluid in Guangdong Province,China
ZENG Tu-rong 《地下水科学与工程》2019,7(1):42-52
In general, previous geothermal geochemical studies in Guangdong Province mainly involves single method to cover limited aspects and areas. In that way, various methods available cannot actually provide more convincing results of geothermal fluid's circulation system and evolution process from different dimensions, especially in terms of isotope. As a result, more comprehensive researches remain to be done on geochemistry of geothermal fluid, in particular, the space-time law of isotope's evolution pattern as well as recharge cycle. Based on data of environmental isotopes(~2H and ~(18)O) and the isotope of radiometric dating(~(14)C), geothermal geology, characteristics of groundwater flow field and types of goethermal reservior in Guangdong Province are taken into account in this paper, so as to analyze numerical rule and spatial distribution features of isotopes. Thus, corresponding main causes, mechanism and hydrogeological significance can be revealed to further study the potential of geothermal fluid to renew and recharge in the long run, which is conducive to enrich geothermal theories and solve existing hydrogeological problems. 相似文献
14.
Two optimization techniques ta predict a spatial variable from any number of related spatial variables are presented. The applicability of the two different methods for petroleum-resource assessment is tested in a mature oil province of the Midcontinent (USA). The information on petroleum productivity, usually not directly accessible, is related indirectly to geological, geophysical, petrographical, and other observable data. This paper presents two approaches based on construction of a multivariate spatial model from the available data to determine a relationship for prediction. In the first approach, the variables are combined into a spatial model by an algebraic map-comparison/integration technique. Optimal weights for the map comparison function are determined by the Nelder-Mead downhill simplex algorithm in multidimensions. Geologic knowledge is necessary to provide a first guess of weights to start the automatization, because the solution is not unique. In the second approach, active set optimization for linear prediction of the target under positivity constraints is applied. Here, the procedure seems to select one variable from each data type (structure, isopachous, and petrophysical) eliminating data redundancy. Automating the determination of optimum combinations of different variables by applying optimization techniques is a valuable extension of the algebraic map-comparison/integration approach to analyzing spatial data. Because of the capability of handling multivariate data sets and partial retention of geographical information, the approaches can be useful in mineral-resource exploration. 相似文献
15.
Local and Spatial Joint Frequency Uncertainty and its Application to Rock Mass Characterisation 总被引：1，自引：1，他引：0
Stability is a key issue in any mining or tunnelling activity. Joint frequency constitutes an important input into stability
analyses. Three techniques are used herein to quantify the local and spatial joint frequency uncertainty, or possible joint
frequencies given joint frequency data, at unsampled locations. Rock quality designation is estimated from the predicted joint
frequencies. The first method is based on kriging with subsequent Poisson sampling. The second method transforms the data
to near-Gaussian variables and uses the turning band method to generate a range of possible joint frequencies. The third method
assumes that the data are Poisson distributed and models the log-intensity of these data with a spatially smooth Gaussian
prior distribution. Intensities are obtained and Poisson variables are generated to examine the expected joint frequency and
associated variability. The joint frequency data is from an iron ore in the northern part of Norway. The methods are tested
at unsampled locations and validated at sampled locations. All three methods perform quite well when predicting sampled points.
The probability that the joint frequency exceeds 5 joints per metre is also estimated to illustrate a more realistic utilisation.
The obtained probability map highlights zones in the ore where stability problems have occurred. It is therefore concluded
that the methods work and that more emphasis should have been placed on these kinds of analyses when the mine was planned.
By using simulation instead of estimation, it is possible to obtain a clear picture of possible joint frequency values or
ranges, i.e. the uncertainty. 相似文献
16.
Andrew Skabar 《Mathematical Geology》2007,39(5):439-451
Multilayer perceptrons (MLPs) can be used to discover a function which can be used to map from a set of input variables onto
a value representing the conditional probability of mineralization. The standard approach to training MLPs is gradient descent,
in which the error between the network output and the target output is reduced in each iteration of the training algorithm.
In order to prevent overfitting, a split-sample validation procedure is used, in which the data is partitioned into two sets:
a training set, which is used for weight optimization, and a validation set, which is used to optimize various parameters
that can be used to prevent overfitting. One of the problems with this approach is that the resulting maps can display significant
variability which stems from (i) the (randomly initialized) starting weights and (ii) the particular training/validation set
partition (also determined randomly). This problem is especially pertinent on mineral potential mapping tasks, in which the
number of deposit cells is a very small proportion of the total number of cells in the study area. In contrast to gradient
descent methods, Bayesian learning techniques do not find a single weight vector; rather, they infer the posterior distribution
of the weights given the data. Predictions are then made by integrating over this distribution. An important advantage of
the Bayesian approach is that the optimization of parameters such as the weight decay regularization coefficient can be performed
using training data alone, thus avoiding the noise introduced through split-sample validation. This paper reports results
of applying Bayesian learning techniques to the production of maps representing gold mineralization potential over the Castlemaine
region of Victoria, Australia. Maps produced using the Bayesian approach display significantly less variability than those
produced using gradient descent training. They are also more reliable at predicting the presence of unknown deposits. 相似文献
17.
巨厚黄土地区煤田地震资料采集关键技术 总被引：1，自引：0，他引：1
巨厚黄土覆盖地区土层结构疏松,地震波速度低、吸收衰减严重、次生干扰发育,资料信噪比与分辨率极低,煤田地震勘探面临诸多难题,其核心是数据采集问题。提出了利用微测井约束的瑞雷波反演技术精细刻画浅表层黄土速度结构,合理选取激发层位;利用震/检联合大基距组合技术提高单炮信噪比、压制低速强规则干扰;采取低频检波器接收以适应厚黄土层中地震波传播的衰减特征;利用多线/长排列观测技术提高目的层段的有效覆盖等技术方案。实际应用表明,通过上述4项技术的集成应用,取得了良好的效果。 相似文献
18.
Uncertainty quantification for subsurface flow problems is typically accomplished through model-based inversion procedures in which multiple posterior (history-matched) geological models are generated and used for flow predictions. These procedures can be demanding computationally, however, and it is not always straightforward to maintain geological realism in the resulting history-matched models. In some applications, it is the flow predictions themselves (and the uncertainty associated with these predictions), rather than the posterior geological models, that are of primary interest. This is the motivation for the data-space inversion (DSI) procedure developed in this paper. In the DSI approach, an ensemble of prior model realizations, honoring prior geostatistical information and hard data at wells, are generated and then (flow) simulated. The resulting production data are assembled into data vectors that represent prior ‘realizations’ in the data space. Pattern-based mapping operations and principal component analysis are applied to transform non-Gaussian data variables into lower-dimensional variables that are closer to multivariate Gaussian. The data-space inversion is posed within a Bayesian framework, and a data-space randomized maximum likelihood method is introduced to sample the conditional distribution of data variables given observed data. Extensive numerical results are presented for two example cases involving oil–water flow in a bimodal channelized system and oil–water–gas flow in a Gaussian permeability system. For both cases, DSI results for uncertainty quantification (e.g., P10, P50, P90 posterior predictions) are compared with those obtained from a strict rejection sampling (RS) procedure. Close agreement between the DSI and RS results is consistently achieved, even when the (synthetic) true data to be matched fall near the edge of the prior distribution. Computational savings using DSI are very substantial in that RS requires \(O(10^5\)–\(10^6)\) flow simulations, in contrast to 500 for DSI, for the cases considered. 相似文献
19.
Research on basic characteristics of 2H, 18O and 14C in geothermal fluid in Guangdong Province,China
ZENG Tu-rong 《地下水科学与工程》2014,7(1):42-52
In general, previous geothermal geochemical studies in Guangdong Province mainly involves single method to cover limited aspects and areas. In that way, various methods available cannot actually provide more convincing results of geothermal fluid’s circulation system and evolution process from different dimensions, especially in terms of isotope. As a result, more comprehensive researches remain to be done on geochemistry of geothermal fluid, in particular, the space-time law of isotope’s evolution pattern as well as recharge cycle. Based on data of environmental isotopes (2H and 18O) and the isotope of radiometric dating (14C), geothermal geology, characteristics of groundwater flow field and types of goethermal reservior in Guangdong Province are taken into account in this paper, so as to analyze numerical rule and spatial distribution features of isotopes. Thus, corresponding main causes, mechanism and hydrogeological significance can be revealed to further study the potential of geothermal fluid to renew and recharge in the long run, which is conducive to enrich geothermal theories and solve existing hydrogeological problems. 相似文献
20.
Akira Murakami Takayuki Shuku Shin‐ichi Nishimura Kazunori Fujisawa Kazuyuki Nakamura 《国际地质力学数值与分析法杂志》2013,37(11):1642-1669
A computational method, incorporating the finite element model (FEM) into data assimilation using the particle filter, is presented for identifying elasto‐plastic material properties based on sequential measurements under the known changing traction boundary conditions to overcome some difficulties in identifying the parameters for elasto‐plastic problems from which the existing inverse analysis strategies have suffered. A soil–water coupled problem, which uses the elasto‐plastic constitutive model, is dealt with as the geotechnical application. Measured data on the settlement and the pore pressure are obtained from a synthetic FEM computation as the forward problem under the known parameters to be identified for both the element tests and the ground behavior during the embankment construction sequence. Parameter identification for elasto‐plastic problems, such as soil behavior, should be made by considering the measurements of deformation and/or pore pressure step by step from the initial stage of construction and throughout the deformation history under the changing traction boundary conditions because of the embankment or the excavation because the ground behavior is highly dependent on the loading history. Thus, it appears that sequential data assimilation techniques, such as the particle filter, are the preferable tools that can provide estimates of the state variables, that is, deformation, pore pressure, and unknown parameters, for the constitutive model in geotechnical practice. The present paper discusses the priority of the particle filter in its application to initial/boundary value problems for elasto‐plastic materials and demonstrates a couple of numerical examples. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献