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1.
Multigaussian kriging technique has many applications in mining, soil science, environmental science and other fields. Particularly, in the local reserve estimation of a mineral deposit, multigaussian kriging is employed to derive panel-wise tonnages by predicting conditional probability of block grades. Additionally, integration of a suitable change of support model is also required to estimate the functions of the variables with larger support than that of the samples. However, under the assumption of strict stationarity, the grade distributions and important recovery functions are estimated by multigaussian kriging using samples within a supposedly spatial homogeneous domain. Conventionally, the underlying random function model is required to be stationary in order to carry out the inference on ore grade distribution and relevant statistics. In reality, conventional stationary model often fails to represent complicated geological structure. Traditionally, the simple stationary model neither considers the obvious changes in local means and variances, nor is it able to replicate spatial continuity of the deposit and hence produces unreliable outcomes. This study deals with the theoretical design of a non-stationary multigaussian kriging model allowing change of support and its application in the mineral reserve estimation scenario. Local multivariate distributions are assumed here to be strictly stationary in the neighborhood of the panels. The local cumulative distribution function and related statistics with respect to the panels are estimated using a distance kernel approach. A rigorous investigation through simulation experiments is performed to analyze the relevance of the developed model followed by a case study on a copper deposit. 相似文献
2.
Although modeling of cross-covariances by fitting the linear model of coregionalization (LMC) is considered a cumbersome task, cross-covariances are the key for integration of data for multiple attributes in environmental hydrology, aquifer and reservoir characterizations using multivariate geostatistics. This paper proposes a novel method of modeling cross-covariances in the linear model of coregionalization (LMC). The classic minimum/maximum autocorrelation factors (MAF) method is analyzed and found to be a good tool to discriminate the elementary nested structures of directional sample covariance matrices. Thus, separate modeling of the scalar sample covariance for each MAF factor may allow to obtain the complete LMC model for the original attributes after a back rotation of the diagonal model covariance matrix of directional factors. However, such a back rotation is not computable following the classic MAF formulation. This paper introduces an ambi-rotational minimum/maximum autocorrelation factors (AMAF) method that allows a back and forth double rotation of the directional diagonal model covariance matrix for factors. This approach provides a device for modeling of the full matrix of directional covariance and cross-covariance for the original attributes in the LMC without recurring to iterations. In this way, the use of multivariate geostatistics for data integration is allowed avoiding collocated approaches or rotation and modeling of data factor scores. The method is illustrated with an example for covariances for three attributes. 相似文献
3.
随机介质是描述地球介质小尺度非均匀性的有效模型,在地震散射波场分析、储层描述等领域具有广泛应用,快速准确的随机介质建模方法是开展相关研究的基础与前提.本文首次将FFT-MA（Fast Fourier Transform Moving Average）算法引入到随机介质建模研究中,分析了该方法与传统随机介质建模方法相比具有的优势,并提出了基于FFT-MA的非平稳随机介质建模方法.建模实验表明,与传统的基于谱分解定理的随机介质建模方法相比,基于FFT-MA的方法在空间域产生随机数序列,使随机数序列与结构参数分离,因此,随机数序列与所建模型存在空间上的对应关系,可以分区域建模和局部修改模型.在非平稳随机介质模型建模时,滑动窗口的大小可以根据自相关长度变化而变化,避免了每个采样点都建立一次完整大小的模型,提高了建模效率.因此,FFT-MA随机介质建模方法能准确构建满足自相关函数要求的平稳及非平稳随机介质模型,具有建模效率高、灵活、实用的优点. 相似文献
4.
A fundamental decision to make during the analysis of geostatistical data is the modeling of the spatial dependence structure as stationary or non-stationary. Although second-order stationary modeling approaches have been successfully applied in geostatistical applications for decades, there is a growing interest in second-order non-stationary modeling approaches. This paper provides a review of modeling approaches allowing to take into account the second-order non-stationarity in univariate geostatistical data. One broad distinction between these modeling approaches relies on the way that the second-order non-stationarity is captured. It seems unlikely to prove that there would be the best second-order non-stationary modeling approach for all geostatistical applications. However, some of them are distinguished by their simplicity, interpretability, and flexibility. 相似文献
5.
Detecting and quantifying sources of non-stationarity via experimental semivariogram modeling 总被引：1，自引：0，他引：1
Miguel A. Cuba Oy Leuangthong Julian M. Ortiz 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(2):247-260
Conventional geostatistics often relies on the assumption of second order stationarity of the random function (RF). Generally,
local means and local variances of the random variables (RVs) are assumed to be constant throughout the domain. Large scale
differences in the local means and local variances of the RVs are referred to as trends. Two problems of building geostatistical
models in presence of mean trends are: (1) inflation of the conditional variances and (2) the spatial continuity is exaggerated.
Variance trends on the other hand cause conditional variances to be over-estimated in certain regions of the domain and under-estimated
in other areas. In both cases the uncertainty characterized by the geostatistical model is improperly assessed. This paper
proposes a new approach to identify the presence and contribution of mean and variance trends in the domain via calculation
of the experimental semivariogram. The traditional experimental semivariogram expression is decomposed into three components:
(1) the mean trend, (2) the variance trend and (3) the stationary component. Under stationary conditions, both the mean and
the variance trend components should be close to zero. This proposed approach is intended to be used in the early stages of
data analysis when domains are being defined or to verify the impact of detrending techniques in the conditioning dataset
for validating domains. This approach determines the source of a trend, thereby facilitating the choice of a suitable detrending
method for effective resource modeling. 相似文献
6.
Min Liang Denis Marcotte 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(3):973-987
This article describes the use of non-stationary covariance functions with compact support to estimate and simulate a random function. Based on the kernel convolution theory, the functions are derived by convolving hyperspheres in \(\mathbb{R}^n\) followed by a Radon transform. The order of the Radon transform controls the differentiability of the covariance functions. By varying spatially the hyperspheres radius one defines non-stationary isotropic versions of the spherical, the cubic and the penta-spherical models. Closed-form expressions for the non-stationary covariances are derived for the isotropic spherical, cubic, and penta-spherical models. Simulation of the different non-stationary models is easily obtained by weighted average of independent standard Gaussian variates in both the isotropic and the anisotropic case. The non-stationary spherical covariance model is applied to estimate the overburden thickness over an area composed of two different geological domains. The results are compared to the estimation with a single stationary model and the estimation with two stationary models, one for each geological domain. It is shown that the non-stationary model enables a reduction of the mean square error and a more realistic transition between the two geological domains. 相似文献
7.
Min Liang Denis Marcotte Nicolas Benoit 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(7):1733-1741
The estimation of overburden sediment thickness is important in hydrogeology, geotechnics and geophysics. Usually, thickness is known precisely at a few sparse borehole data. To improve precision of estimation, one useful complementary information is the known position of outcrops. One intuitive approach is to code the outcrops as zero thickness data. A problem with this approach is that the outcrops are preferentially observed compared to other thickness information. This introduces a strong bias in the thickness estimation that kriging is not able to remove. We consider a new approach to incorporate point or surface outcrop information based on the use of a non-stationary covariance model in kriging. The non-stationary model is defined so as to restrict the distance of influence of the outcrops. Within this distance of influence, covariance parameters are assumed simple regular functions of the distance to the nearest outcrop. Outside the distance of influence of the outcrops, the thickness covariance is assumed stationary. The distance of influence is obtained thru a cross-validation. Compared to kriging based on a stationary model with or without zero thickness at outcrop locations, the non-stationary model provides more precise estimation, especially at points close to an outcrop. Moreover, the thickness map obtained with the non-stationary covariance model is more realistic since it forces the estimates to zero close to outcrops without the bias incurred when outcrops are simply treated as zero thickness in a stationary model. 相似文献
8.
Application of Markovian models for non-ergodic and non-stationary earthquake times series for the identification of seismic patterns and future projections* 
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下载免费PDF全文 Hakan Karaca 《地震科学（英文版）》2020,33(2):98-106
The current earthquake forecast algorithms are not free of shortcomings due to inherent limitations. Especially, the requirement of stationarity in the evaluation of earthquake time series as a prerequisite, significantly limits the use of forecast algorithms to areas where stationary data is not available. Another shortcoming of forecast algorithms is the ergodicity assumption, which states that certain characteristics of seismicity are spatially invariant. In this study, a new earthquake forecast approach is introduced for the locations where stationary data are not available. For this purpose, the spatial activity rate density for each spatial unit is evaluated as a parameter of a Markov chain. The temporal pattern is identified by setting the states at certain spatial activity rate densities. By using the transition patterns between the states, 1- and 5-year forecasts were computed. The method is suggested as an alternative and complementary to the existing methods by proposing a solution to the issues of ergodicity and stationarity assumptions at the same time. 相似文献
9.
Flood extremes, affected by climate change and intense human activities, exhibit non-stationary characteristics. As a result, the stationarity assumption of traditional flood frequency analysis (FFA) cannot be satisfied. Generally, the impacts of human activities, especially water conservancy projects (i.e., reservoirs), on extreme flood series are much greater than those of climate change; therefore, new FFA methods must be developed to address the non-stationary flood extremes associated with large numbers of reservoirs. In this study, a new sample reconstruction method is proposed to convert the reservoir-influenced annual maximum flow (AMF) series from non-stationary to stationary, thus warranting the feasibility of the traditional FFA approach for non-stationary cases. To be more specifically, a modified reservoir index (MRI(t)) is proposed and the original non-stationary AMF series are converted to stationary series by multiplying by a scalar factor 1/(1 ? MRI(t)), and thus traditional FFA can be adopted. Besides, Bayesian theory was applied to analyze the effect of uncertainty on the designed reconstructed AMF. As an example, the proposed method was applied to observations from Huangzhuang station located on the Hanjiang River. The original AMF observations from Huangzhuang displayed nonstationarity for the continuous construction of reservoirs in the basin. After applying the new method of sample reconstruction, the original AMF observations became stationary, and the designed AMFs were estimated using the reconstructed series and compared with those estimated based on the original observation series. In addition, Bayesian theory is adopted to quantify the uncertainty of designed reconstructed AMF and provide the expectation of the sampling distribution. 相似文献
10.
Inverse problems involving the characterization of hydraulic properties of groundwater flow systems by conditioning on observations of the state variables are mathematically ill-posed because they have multiple solutions and are sensitive to small changes in the data. In the framework of McMC methods for nonlinear optimization and under an iterative spatial resampling transition kernel, we present an algorithm for narrowing the prior and thus producing improved proposal realizations. To achieve this goal, we cosimulate the facies distribution conditionally to facies observations and normal scores transformed hydrologic response measurements, assuming a linear coregionalization model. The approach works by creating an importance sampling effect that steers the process to selected areas of the prior. The effectiveness of our approach is demonstrated by an example application on a synthetic underdetermined inverse problem in aquifer characterization. 相似文献
11.
An extended Kalman filter algorithm with local iteration is presented for the identification of non-linear and non-stationary soil properties. Borehole-array strong motions were recorded at a liquefied site during the 1995 Hyogoken-nanbu earthquake. In this study, a modified Kalman filtering method in which the extended Kalman filter is iteratively used at every local time-step to track rapid parameter changes is proposed. The method is then applied to the instrumented soil layer, which is modeled by an equivalent linear model. An identification of non-linear and non-stationary soil properties was conducted successfully; and non-linear restoring force–displacement relationships including progression with time were obtained. 相似文献
12.
R. J. WANG 《Geophysical Prospecting》1977,25(2):342-381
The Wiener prediction filter has been an effective tool for accomplishing dereverberation when the input data are stationary. For non-stationary data, however, the performance of the Wiener filter is often unsatisfactory. This is not surprising since it is derived under the stationarity assumption. Dereverberation of nonstationary seismic data is here accomplished with a difference equation model having time-varying coefficients. These time-varying coefficients are in turn expanded in terms of orthogonal functions. The kernels of these orthogonal functions are then determined according to the adaptive algorithm of Nagumo and Noda. It is demonstrated that the present adaptive predictive deconvolution method, which combines the time-varying difference equation model with the adaptive method of Nagumo and Noda, is a powerful tool for removing both the long- and short-period reverberations. Several examples using both synthetic and field data illustrate the application of adaptive predictive deconvolution. The results of applying the Wiener prediction filter and the adaptive predictive deconvolution on nonstationary data indicate that the adaptive method is much more effective in removing multiples. Furthermore, the criteria for selecting various input parameters are discussed. It has been found that the output trace from the adaptive predictive deconvolution is rather sensitive to some input parameters, and that the prediction distance is by far the most influential parameter. 相似文献
13.
Non-stationarity in statistical properties of the subsurface is often ignored. In a classical linear Bayesian inversion setting of seismic data, the prior distribution of physical parameters is often assumed to be stationary. Here we propose a new method of handling non-stationarity in the variance of physical parameters in seismic data. We propose to infer the model variance prior to inversion using maximum likelihood estimators in a sliding window approach. A traditional, and a localized shrinkage estimator is defined for inferring the prior model variance. The estimators are assessed in a synthetic base case with heterogeneous variance of the acoustic impedance in a zero-offset seismic cross section. Subsequently, this data is inverted for acoustic impedance using a non-stationary model set up with the inferred variances. Results indicate that prediction as well as posterior resolution is greatly improved using the non-stationary model compared with a common prior model with stationary variance. The localized shrinkage predictor is shown to be slightly more robust than the traditional estimator in terms of amplitude differences in the variance of acoustic impedance and size of local neighbourhood. Finally, we apply the methodology to a real data set from the North Sea basin. Inversion results show a more realistic posterior model than using a conventional approach with stationary variance. 相似文献
14.
A latent class MDS model with spatial constraints for non-stationary spatial covariance estimation 总被引：3，自引：3，他引：0
J. F. Vera R. Macías J. M. Angulo 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(6):769-779
Multidimensional scaling (MDS) has played an important role in non-stationary spatial covariance structure estimation and
in analyzing the spatiotemporal processes underlying environmental studies. A combined cluster-MDS model, including geographical
spatial constraints, has been previously proposed by the authors to address the estimation problem in oversampled domains
in a least squares framework. In this paper is formulated a general latent class model with spatial constraints that, in a
maximum likelihood framework, allows to partition the sample stations into classes and simultaneously to represent the cluster
centers in a low-dimensional space, while the stations and clusters retain their spatial relationships. A model selection
strategy is proposed to determine the number of latent classes and the dimensionality of the problem. Real and artificial
data sets are analyzed to test the performance of the model. 相似文献
15.
A recently developed seismological model of ground motion is incorporated into the non-stationary random vibration theory making use of Priestley's evolutionary power spectral density. A general method of computing the input power spectrum is proposed and shown to reduce to the classical method when the input and the output are taken as stationary. Based on the concepts of Yang's non-stationary envelopes and first-passage reliability estimates via extreme point process, a statistical response spectrum for the pseudo-velocity is developed. Comparisons made among the results of non-stationary analysis with different modulating functions, and that of the stationary approximation, on SDOF linear structures with 5 per cent damping show that the type ofmodulating function chosen has little effect on the magnitudes of mean pseudo-velocities, provided the input power spectrum is properly scaled, and that the stationary approximation produces conservative results for structures with natural periods greater than 0.5 sec. 相似文献
16.
This paper presents a theoretical nonstationary stochastic analysis scheme using pseudo-excitation method (PEM) for seismic analysis of long-span structures under tridirectional spatially varying ground motions, based on which the local site effects on structural seismic response are studied for a high-pier railway bridge. An absolute-response-oriented scheme of PEM in nonstationary stochastic analysis of structure under tridirectional spatial seismic motions, in conjunction with the derived mathematical scheme in modeling tridirectional nonstationary spatially correlated ground motions, is proposed to resolve the drawbacks of conventional indirect approach. To apply the proposed theoretical approach readily in stochastic seismic analysis of complex and significant structures, this scheme is implemented and verified in a general finite element platform, and is then applied to a high-pier railway bridge under spatially varying ground motions considering the local site effect and the effect of ground motion nonstationarity. Conclusions are drawn and can be applied in the actual seismic design and analysis of high-pier railway bridges under tridirectional nonstationary multiple excitations. 相似文献
17.
Camilla Zacché da Silva João Felipe Costa 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(8):1929-1938
There are many situations in the mining industry where grade estimation of multiple correlated variables is required. The resulting model is expected to reproduce the data correlation, but there is no guarantee that the correlation observed among data will be reproduced by the model if the variables are independently estimated by kriging, and the correlation is not explicitly taken into account. The best geostatistical approach to address this estimation problem is to use co-kriging, which requires both cross and direct covariance modeling of all variables. However, the co-kriging method is labor-intensive when the problem involves more than three attributes. An alternative is to decorrelate the variables and estimate each one independently, using, for instance, the minimum/maximum autocorrelation factors (MAF) approach. This method involves the application of a linear transformation to the correlated variables, transforming the original data into a space where they are uncorrelated. The resulting transformed data can be individually estimated using kriging, avoiding the use of the linear model of coregionalization. Once the kriging has been performed, the MAF estimates are back-transformed to the original data space, re-establishing their correlation.The methodology is illustrated in a case study where there are two variables with correlation coefficient, ρ = ?0.98. The MAF transformation was applied in combination with ordinary kriging (herein denoted as KMAF). Co-kriging was performed to provide a benchmark for comparing the results obtained through KMAF. The results obtained by co-kriging and KMAF showed less than 1 % average deviation between the two block models. 相似文献
18.
Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space–time heterogeneity of rainfall observations make space–time estimation of precipitation a challenging task. In this paper we propose a Box–Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space–time monthly precipitation in the monsoon periods during 1974–2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space–time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method. 相似文献
19.
Non-stationary frequency analysis of extreme precipitation in South Korea using peaks-over-threshold and annual maxima 总被引：2，自引：2，他引：0
Sungwook Wi Juan B. Valdés Scott Steinschneider Tae-Woong Kim 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(2):583-606
The conventional approach to the frequency analysis of extreme precipitation is complicated by non-stationarity resulting from climate variability and change. This study utilized a non-stationary frequency analysis to better understand the time-varying behavior of short-duration (1-, 6-, 12-, and 24-h) precipitation extremes at 65 weather stations scattered across South Korea. Trends in precipitation extremes were diagnosed with respect to both annual maximum precipitation (AMP) and peaks-over-threshold (POT) extremes. Non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with model parameters made a linear function of time were applied to AMP and POT respectively. Trends detected using the Mann–Kendall test revealed that the stations showing an increasing trend in AMP extremes were concentrated in the mountainous areas (the northeast and southwest regions) of South Korea. Trend tests on POT extremes provided fairly different results, with a significantly reduced number of stations showing an increasing trend and with some stations showing a decreasing trend. For most of stations showing a statistically significant trend, non-stationary GEV and GPD models significantly outperformed their stationary counterparts, particularly for precipitation extremes with shorter durations. Due to a significant-increasing trend in the POT frequency found at a considerable number of stations (about 10 stations for each rainfall duration), the performance of modeling POT extremes was further improved with a non-homogeneous Poisson model. The large differences in design storm estimates between stationary and non-stationary models (design storm estimates from stationary models were significantly lower than the estimates of non-stationary models) demonstrated the challenges in relying on the stationary assumption when planning the design and management of water facilities. This study also highlighted the need of caution when quantifying design storms from POT and AMP extremes by showing a large discrepancy between the estimates from those two approaches. 相似文献
20.
A p‐order multivariate kernel density model based on kernel density theory has been developed for synthetic generation of multivariate variables. It belongs to a kind of data‐driven approach and is able to avoid prior assumptions as to the form of probability distribution (normal or Pearson III) and the form of dependence (linear or non‐linear). The p‐order multivariate kernel density model is a non‐parametric method for synthesis of streamflow. The model is more flexible than conventional parametric models used in stochastic hydrology. The effectiveness and satisfactoriness of this model are illustrated through its application to the simultaneous synthetic generation of daily streamflow from Pingshan station and Yibin‐Pingshan region (Yi‐Ping region) of the Jinsha River in China. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献