共查询到10条相似文献，搜索用时 171 毫秒
1.
Michael W. Davis 《Mathematical Geosciences》1987,19(2):99-107
An algorithm for producing a nonconditional simulation by multiplying the square root of the covariance matrix by a random vector is described. First, the square root of a matrix (or a function of a matrix in general) is defined. The square root of the matrix can be approximated by a minimax matrix polynomial. The block Toeplitz structure of the covariance matrix is used to minimize storage. Finally, multiplication of the block Toeplitz matrix by the random vector can be evaluated as a convolution using the fast Fourier transform. This results in an algorithm which is not only efficient in terms of storage and computation but also easy to implement. 相似文献
2.
Chunsheng Ma 《Mathematical Geosciences》2012,44(6):765-778
This paper presents the characterization of the covariance matrix function of a Gaussian or second-order elliptically contoured vector random field on the sphere which is stationary, isotropic, and mean square continuous. This characterization involves an infinite sum of the products of positive definite matrices and Gegenbauer??s polynomials, and may not be available for other non-Gaussian vector random fields on spheres such as a ?? 2 or log-Gaussian vector random field. We also offer two simple but efficient constructing approaches, and derive some parametric covariance matrix structures on spheres. 相似文献
3.
Dean S. Oliver 《Mathematical Geology》1995,27(8):939-960
The square-root method provides a simple and computationally inexpensive way to generate multidimensional Gaussian random fields. It is applied by factoring the multidimensional covariance operator analytically, then sampling the factorization at discrete points to compute an array of weighted averages that can be convolved with an array of random normal deviates to generate a correlated random field. In many respects this is similar to the LUdecomposition method and to the one-dimensional method of moving averages. However it has been assumed that the method of moving averages could not be used in higher dimensions, whereas direct application of the matrix decomposition approach is too expensive to be practical on large grids.
In this paper, I show that it is possible to calculate the square root of many two- and three dimensional covariance operators analytically so that the method of moving averages can be applied directly to the problem of multidimensional simulation. A few numerical examples of nonconditional simulation on a 256×256 grid that show the simplicity of the method are included. The method is fast and can be applied easily to nested and anisotropic variograms. 相似文献
4.
The variogram matrix function is an important measure for the dependence of a vector random field with second-order increments, and is a useful tool for linear predication or cokriging. This paper proposes an efficient approach to construct variogram matrix functions, based on three ingredients: a univariate variogram, a conditionally negative definite matrix, and a Bernstein function, and derives three classes of variogram matrix functions for vector elliptically contoured random fields. Moreover, various dependence structures among components can be derived through appropriate mixture procedures demonstrated in this paper. We also obtain covariance matrix functions for second-order vector random fields through the Schoenberg–Lévy kernels. 相似文献
5.
Looking at kriging problems with huge numbers of estimation points and measurements, computational power and storage capacities
often pose heavy limitations to the maximum manageable problem size. In the past, a list of FFT-based algorithms for matrix
operations have been developed. They allow extremely fast convolution, superposition and inversion of covariance matrices
under certain conditions. If adequately used in kriging problems, these algorithms lead to drastic speedup and reductions
in storage requirements without changing the kriging estimator. However, they require second-order stationary covariance functions,
estimation on regular grids, and the measurements must also form a regular grid. In this study, we show how to alleviate these
rather heavy and many times unrealistic restrictions. Stationarity can be generalized to intrinsicity and beyond, if decomposing
kriging problems into the sum of a stationary problem and a formally decoupled regression task. We use universal kriging,
because it covers arbitrary forms of unknown drift and all cases of generalized covariance functions. Even more general, we
use an extension to uncertain rather than unknown drift coefficients. The sampling locations may now be irregular, but must
form a subset of the estimation grid. Finally, we present asymptotically exact but fast approximations to the estimation variance
and point out application to conditional simulation, cokriging and sequential kriging. The drastic gain in computational and
storage efficiency is demonstrated in test cases. Especially high-resolution and data-rich fields such as rainfall interpolation
from radar measurements or seismic or other geophysical inversion can benefit from these improvements. 相似文献
6.
C. R. Dietrich 《Mathematical Geology》1993,25(4):439-451
The generation over two-dimensional grids of normally distributed random fields conditioned on available data is often required in reservoir modeling and mining investigations. Such fields can be obtained from application of turning band or spectral methods. However, both methods have limitations. First, they are only asymptotically exact in that the ensemble of realizations has the correlation structure required only if enough harmonics are used in the spectral method, or enough lines are generated in the turning bands approach. Moreover, the spectral method requires fine tuning of process parameters. As for the turning bands method, it is essentially restricted to processes with stationary and radially symmetric correlation functions. Another approach, which has the advantage of being general and exact, is to use a Cholesky factorization of the covariance matrix representing grid points correlation. For fields of large size, however, the Cholesky factorization can be computationally prohibitive. In this paper, we show that if the data are stationary and generated over a grid with regular mesh, the structure of the data covariance matrix can be exploited to significantly reduce the overall computational burden of conditional simulations based on matrix factorization techniques. A feature of this approach is its computational simplicity and suitability to parallel implementation. 相似文献
7.
Simulating Large Gaussian Random Vectors Subject to Inequality Constraints by Gibbs Sampling 总被引：4，自引：2，他引：2
The Gibbs sampler is an iterative algorithm used to simulate Gaussian random vectors subject to inequality constraints. This algorithm relies on the fact that the distribution of a vector component conditioned by the other components is Gaussian, the mean and variance of which are obtained by solving a kriging system. If the number of components is large, kriging is usually applied with a moving search neighborhood, but this practice can make the simulated vector not reproduce the target correlation matrix. To avoid these problems, variations of the Gibbs sampler are presented. The conditioning to inequality constraints on the vector components can be achieved by simulated annealing or by restricting the transition matrix of the iterative algorithm. Numerical experiments indicate that both approaches provide realizations that reproduce the correlation matrix of the Gaussian random vector, but some conditioning constraints may not be satisfied when using simulated annealing. On the contrary, the restriction of the transition matrix manages to satisfy all the constraints, although at the cost of a large number of iterations. 相似文献
8.
抛物Radon变换法(Parabolic Radon Transform)在地震资料处理中有广泛的应用。PRT可对不同频率的地震数据解耦处理,这一特点使得抛物Radon变换的计算效率比双曲Radon变换有数量级上的提高。在频率域求解时,需要对每一个频率成份求解同样大小的线性方程组。求解抛物Radon正变换的计算方法主要有Levinson递推法、共轭梯度法、Cholesky分解法和直接矩阵求逆法。最小平方抛物Radon正变换所形成的矩阵具有Toeplitz结构,可采用Levinson递推法进行计算。高分辨率抛物Radon正变换所形成矩阵的Toeplitz结构被破坏,一般采用共轭梯度法或Cholesky分解法进行求解。这里详细推导了复Toeplitz矩阵的Levinson递推算法,并分别对求解方程的四种方法进行了讨论,最后给出抛物Radon正变换求解的数值算例,并对所给出的四种方程求解方法的计算效率及计算精度进行了对比。 相似文献
9.
实现稀疏反褶积的预条件双共轭梯度法 总被引：9，自引：3，他引：9
地震勘探稀疏反褶积计算一般要导出一个Toeplitz矩阵的线性系统，通常可以用矩阵求逆、Levison递推及共轭梯度等方法直接求解。当Toeplitz矩阵的条件数很大时，数值稳定性差，甚至无法求解。使用共轭梯度法，在矩阵的对角元素上加入规则化因子，可以改善这种情况，但不能彻底解决数值稳定性和精度问题。若求解最小二乘问题的原始问题，结果会好些。线性系统形式的细微改变，将导致不同的数值计算特性。在规则化策略基础上，可巧妙地构造稀疏反褶积的问题原型，引入预条件，采用双共轭梯度法求解，从而实现稀疏反褶积，获得较好结果。数值算例表明，预条件双共轭梯度法比直接稀疏反褶积方法收敛快、精度高。 相似文献
10.
Large-scale history matching with quadratic interpolation models 总被引：2，自引：0，他引：2