共查询到20条相似文献，搜索用时 15 毫秒
1.
J. Mateu G. Fernández-Avilés J. M. Montero 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(2):297-309
Globally supported covariance functions are generally associated with dense covariance matrices, meaning severe numerical problems in solution feasibility. These problems can be alleviated by considering methods yielding sparse covariance matrices. Indeed, having many zero entries in the covariance matrix can both greatly reduce computer storage requirements and the number of floating point operations needed in computation. Compactly supported covariance functions considerably reduce the computational burden of kriging, and allow the use of computationally efficient sparse matrix techniques, thus becoming a core aspect in spatial prediction when dealing with massive data sets. However, most of the work done in the context of compactly supported covariance functions has been carried out in the stationary context. This assumption is not generally met in practical and real problems, and there has been a growing recognition of the need for non-stationary spatial covariance functions in a variety of disciplines. In this paper we present a new class of non-stationary, compactly supported spatial covariance functions, which adapts a class of convolution-based flexible models to non-stationary situations. Some particular examples, computational issues, and connections with existing models are considered. 相似文献
2.
Strict positive definiteness in geostatistics 总被引：1，自引：1，他引：0
Geostatistical modeling is often based on the use of covariance functions, i.e., positive definite functions. However, when interpolation problems have to be solved, it is advisable to consider the subset of strictly positive definite functions. Indeed, it will be argued that ensuring strict positive definiteness for a covariance function is convenient from a theoretical and practical point of view. In this paper, an extensive analysis on strictly positive definite covariance functions has been given. The closure of the set of strictly positive definite functions with respect to the sum and the product of covariance functions defined on the same Euclidean dimensional space or on factor spaces, as well as on partially overlapped lower dimensional spaces, has been analyzed. These results are particularly useful (a) to extend strict positive definiteness in higher dimensional spaces starting from covariance functions which are only defined on lower dimensional spaces and/or are only strictly positive definite in lower dimensional spaces, (b) to construct strictly positive definite covariance functions in space–time as well as (c) to obtain new asymmetric and strictly positive definite covariance functions. 相似文献
3.
New anisotropic covariance models and estimation of anisotropic parameters based on the covariance tensor identity 总被引：2，自引：0，他引：2
Many heterogeneous media and environmental processes are statistically anisotropic. In this paper we focus on range anisotropy,
that is, stochastic processes with variograms that have direction dependent correlation lengths and direction independent
sill. We distinguish between two classes of anisotropic covariance models: Class (A) models are reducible to isotropic after
rotation and rescaling operations. Class (B) models can be separated into a product of one-dimensional functions oriented
along the principal axes. We propose a new Class (A) model with multiscale properties that has applications in subsurface
hydrology. We also present a family of Class (B) models based on non-Euclidean distance metrics that are generated by superellipsoidal
functions. Next, we propose a new method for determining the orientation of the principal axes and the degree of anisotropy,
i.e., the ratio(s) of the correlation lengths. This information reduces the degrees of freedom of anisotropic variograms and
thus simplifies the estimation procedure. In particular, Class (A) models are reduced to isotropic and Class (B) models to
one-dimensional functions. Our method is based on an explicit relation between the second-rank slope tensor (SRST), which
can be estimated from the data, and the covariance tensor. The procedure is conceptually simple and numerically efficient.
It is more accurate for regular (on-grid) data distributions, but it can also be used for sparse (off-grid) spatial distributions.
In the case of non-differentiable random fields the method can be extended using generalized derivatives. We illustrate its
implementation with numerical simulations. 相似文献
4.
Nested covariance models, defined as linear combinations of basic covariance functions, are very popular in many branches of applied statistics, and in particular in geostatistics. A notorious limit of nested models is that the constants in the linear combination are bound to be nonnegative in order to preserve positive definiteness (admissibility). This paper studies nested models on d-dimensional spheres and spheres cross time. We show the exact interval of admissibility for the constants involved in the linear combinations. In particular, we show that at least one constant can be negative. One of the implications is that one can obtain a nested model attaining negative correlations. We provide characterization theorems for arbitrary linear combinations as well as for nonconvex combinations involving two covariance functions. We illustrate our findings through several examples involving nonconvex combinations of well-known parametric families of covariance functions. 相似文献
5.
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
6.
To date, an outstanding issue in hydrologic data assimilation is a proper way of dealing with forecast bias. A frequently used method to bypass this problem is to rescale the observations to the model climatology. While this approach improves the variability in the modeled soil wetness and discharge, it is not designed to correct the results for any bias. Alternatively, attempts have been made towards incorporating dynamic bias estimates into the assimilation algorithm. Persistent bias models are most often used to propagate the bias estimate, where the a priori forecast bias error covariance is calculated as a constant fraction of the unbiased a priori state error covariance. The latter approach is a simplification to the explicit propagation of the bias error covariance. The objective of this paper is to examine to which extent the choice for the propagation of the bias estimate and its error covariance influence the filter performance. An Observation System Simulation Experiment (OSSE) has been performed, in which ground water storage observations are assimilated into a biased conceptual hydrologic model. The magnitudes of the forecast bias and state error covariances are calibrated by optimizing the innovation statistics of groundwater storage. The obtained bias propagation models are found to be identical to persistent bias models. After calibration, both approaches for the estimation of the forecast bias error covariance lead to similar results, with a realistic attribution of error variances to the bias and state estimate, and significant reductions of the bias in both the estimates of groundwater storage and discharge. Overall, the results in this paper justify the use of the traditional approach for online bias estimation with a persistent bias model and a simplified forecast bias error covariance estimation. 相似文献
7.
Ben Ingram Dan Cornford David Evans 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(5):661-670
In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic
mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging
to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc
solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations
can be projected onto a representative subset of the data, without losing significant information. This allows the complexity
of the algorithm to grow as O(n
m
2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further
extend this projective method through the application of space-limited covariance functions, which can be used as an alternative
to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes
beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this
leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values
we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the
same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse
extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings.
To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques
(SIC2004) to map the levels of background ambient gamma radiation.
相似文献
| Ben IngramEmail: |
8.
J. R. Holliday J. B. Rundle K. F. Tiampo W. Klein A. Donnellan 《Pure and Applied Geophysics》2006,163(11-12):2433-2454
Recent studies in the literature have introduced a new approach to earthquake forecasting based on representing the space-time patterns of localized seismicity by a time-dependent system state vector in a real-valued Hilbert space and deducing information about future space-time fluctuations from the phase angle of the state vector. While the success rate of this Pattern Informatics (PI) method has been encouraging, the method is still in its infancy. Procedural analysis, statistical testing, parameter sensitivity investigation and optimization all still need to be performed. In this paper, we attempt to optimize the PI approach by developing quantitative values for ``predictive goodness'' and analyzing possible variations in the proposed procedure. In addition, we attempt to quantify the systematic dependence on the quality of the input catalog of historic data and develop methods for combining catalogs from regions of different seismic rates. 相似文献
9.
10.
常规协克里金方法反演重力或重力梯度数据具有抗噪性好、加入先验信息容易等优点,其反演的地下密度分布能够识别异常体中心位置,还原异常体基本形态,但反演图像光滑,分辨率低,这是由于常规方法估计的密度协方差矩阵全局发散、平稳.为了通过协克里金方法获得聚焦的密度分布需要改善密度协方差矩阵的性质.首先,本文推导了理论密度协方差公式,其性质表明,当理论模型聚焦分布时,其密度协方差矩阵是非平稳且聚焦分布的.为了打破常规协方差矩阵全局平稳、发散的特征,本文设置密度阈值处理协方差矩阵,通过不断更新协方差矩阵来迭代实现协克里金反演,最终得到相对聚焦的反演结果.用本文方法处理重力与重力梯度数据恢复两种密度模型,均得到了与正演模型匹配的反演结果;再将方法运用于文顿盐丘的实际测量重力与重力梯度数据,反演结果与已知的地质情况匹配较好. 相似文献
11.
A model for presentation of seismic pore water pressures 总被引：3，自引：0，他引：3
Tomislav Iv&#x;i&#x; 《Soil Dynamics and Earthquake Engineering》2006,26(2-4):191-199
A model for presentation of pore water pressures induced in sand samples during cyclic undrained testing is described. The proposed model belongs to a class of so-called ‘damage parameter models’, which correlate the pore pressure rise with a parameter based on an accumulated variable during testing. The concept of threshold strain is also incorporated in the model. The model has been verified on several series of published cyclic test data. Its parameters lie in a narrow band for a wide range of sand properties. The empirical functions that represent the common shape of individual curves for interpreted pore pressure data are also suggested. The proposed procedure has been adapted for presentation of other cyclic soil tests, and examples of interpretation of cyclic stress-controlled as well as cyclic drained tests are included. 相似文献
12.
E. Porcu P. Gregori J. Mateu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,21(2):113-122
Obtaining new and flexible classes of nonseparable spatio-temporal covariances and variograms has resulted a key point of research in the last years. The goal of this paper is to introduce and develop new spatio-temporal covariance models taking into account the problem of spatial anisotropy. Recent literature has focused on the problem of full symmetry and the problem of anisotropy has been overcome. Here we propose a generalization of Gneiting’s (J Am Stat Assoc 97:590–600, 2002a) approach and obtain new classes of stationary nonseparable spatio-temporal covariance functions which are spatially anisotropic. The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability.Work partially funded by grant MTM2004-06231 from the Spanish Ministry of Science and Education. 相似文献
13.
Surface-wave tests are based on the solution of an inverse problem for shear-wave velocity profile identification from the experimentally measured dispersion curve. The main criticisms for these testing methodologies are related to the inverse problem solution and arise from the possible equivalence of different shear-wave velocity profiles. In this paper, some implications of solution non-uniqueness for seismic response studies are investigated using both numerical simulations and experimental data. A Monte Carlo approach for the inversion problem has been used to obtain a set of equivalent shear-wave velocity models. This selection is based on a statistical test which takes into account both data uncertainty and model parameterization. This set of solutions (i.e., soil profiles) is then used to evaluate the seismic response with a conventional one-dimensional analysis. It is shown that equivalent profiles with respect to surface-wave testing are equivalent also with respect to site amplification, thus countering the criticism related to inversion uncertainty for the engineering use of surface-wave tests. 相似文献
14.
Covariance functions and models for complex-valued random fields 总被引：1，自引：1，他引：0
In Geostatistics, primary interest often lies in the study of the spatial, or spatial-temporal, correlation of real-valued random fields, anyway complex-valued random field theory is surely a natural extension of the real domain. In such a case, it is useful to consider complex covariance functions which are composed of an even real part and an odd imaginary part. Generating complex covariance functions is not simple at all, but the procedure, developed in this paper, allows generating permissible covariance functions for complex-valued random fields in a straightforward way. In particular, by recalling the spectral representation of the covariance and translating the spectral density function by using a shifting factor, complex covariances are obtained. Some general aspects and properties of complex-valued random fields and their moments are pointed out and some examples are given. 相似文献
15.
This paper presents an algorithm for simulating Gaussian random fields with zero mean and non-stationary covariance functions. The simulated field is obtained as a weighted sum of cosine waves with random frequencies and random phases, with weights that depend on the location-specific spectral density associated with the target non-stationary covariance. The applicability and accuracy of the algorithm are illustrated through synthetic examples, in which scalar and vector random fields with non-stationary Gaussian, exponential, Matérn or compactly-supported covariance models are simulated. 相似文献
16.
M. Bohorquez J. Mateu L. Diaz 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(4):1011-1022
The differentiability of a random field has a direct relationship with the differentiability of its covariance function. We review the concept of differentiability of space–time covariance models and random fields, and its implications on predictions. We analyze the change of behavior of the covariance function at the origin and at different space–time lags away from the origin, by using the concept of smoothness which can be considered the geometrical view of the differentiability. We propose a way to measure the smoothness of any covariance function, and apply it to purely spatial and space–time covariance functions. 相似文献
17.
— Velocity evaluation is a key step in seismic analysis. The covariance of the true velocity field must be known when interpolating or simulating velocities from well measurements using geostatistical methods. In addition, inversion procedures often require information pertaining to this covariance. Traditionally it has been taken to be the covariance of stacking velocities. We present a simple example to show that this approximation can lead to significant errors. Better methods, such as those of Touati (1996) and Iooss (1998), use the variance of prestack picked travel times as a function of offset to infer that of the velocities. In this paper we extend their results on the estimation of the covariance of the reflected traveltimes, and obtain an explicit expression for the covariance of the square of the stacking slowness as a function of the covariance of the velocities. Although we are not able to invert the formula analytically to yield an explicit estimator for these parameters, the results obtained using it furnish a good and quick estimation of the velocity's covariance. This is illustrated with synthetic examples. 相似文献
18.
FRANCIS M. MUTUA 《水文科学杂志》2013,58(3):235-244
Abstract For a long time now, the hydrologist has been faced with the problem of finding which of the many possible probability distribution functions can be used most effectively in flood frequency analyses. This problem has been mainly due to the insufficiency of the conventional goodness-of-fit procedures when used with the typically skewed flood probability distributions. In this study, the Akaike Information Criterion (AIC) goodness-of-fit test is used to identify more objectively the optimum model for flood frequency analysis in Kenya from a class of competing models. The class is comprised of (a) seven three-parameter density functions, namely, log-normal, Pearson, log-Pearson, Fisher-Tippet, log-Fisher-Tippet, Walter Boughton and log-Walter Boughton; and (b) two five-parameter density functions, namely, Wakeby and log-Wakeby. The AIC is also used in this study as a method of testing for the existence of outlier peak-flow values in the peak annual data used. A modified version of the chi-square goodness-of-fit test is also used, but only for the sake of comparison with the AIC. 相似文献
19.
Nils-Otto Kitterrød Lars Gottschalk 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(6):459-482
Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function.
This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients
from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance
model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns
out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of
eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the
2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance
function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields
with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial
interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the
predefined covariance functions are evaluated. 相似文献
20.
Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function.
This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients
from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance
model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns
out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of
eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the
2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance
function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields
with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial
interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the
predefined covariance functions are evaluated. 相似文献