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31.
Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities. 相似文献
32.
Mathematical Geosciences - 相似文献
33.
Spatially distributed and varying natural phenomena encountered in geoscience and engineering problem solving are typically
incompatible with Gaussian models, exhibiting nonlinear spatial patterns and complex, multiple-point connectivity of extreme
values. Stochastic simulation of such phenomena is historically founded on second-order spatial statistical approaches, which
are limited in their capacity to model complex spatial uncertainty. The newer multiple-point (MP) simulation framework addresses
past limits by establishing the concept of a training image, and, arguably, has its own drawbacks. An alternative to current
MP approaches is founded upon new high-order measures of spatial complexity, termed “high-order spatial cumulants.” These
are combinations of moments of statistical parameters that characterize non-Gaussian random fields and can describe complex
spatial information. Stochastic simulation of complex spatial processes is developed based on high-order spatial cumulants
in the high-dimensional space of Legendre polynomials. Starting with discrete Legendre polynomials, a set of discrete orthogonal
cumulants is introduced as a tool to characterize spatial shapes. Weighted orthonormal Legendre polynomials define the so-called
Legendre cumulants that are high-order conditional spatial cumulants inferred from training images and are combined with available
sparse data sets. Advantages of the high-order sequential simulation approach developed herein include the absence of any
distribution-related assumptions and pre- or post-processing steps. The method is shown to generate realizations of complex
spatial patterns, reproduce bimodal data distributions, data variograms, and high-order spatial cumulants of the data. In
addition, it is shown that the available hard data dominate the simulation process and have a definitive effect on the simulated
realizations, whereas the training images are only used to fill in high-order relations that cannot be inferred from data.
Compared to the MP framework, the proposed approach is data-driven and consistently reconstructs the lower-order spatial complexity
in the data used, in addition to high order. 相似文献
34.
Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images 总被引:2,自引:1,他引:1
Scale dependency is a critical topic when modeling spatial phenomena of complex geological patterns that interact at different
spatial scales. A two-dimensional conditional simulation based on wavelet decomposition is proposed for simulating geological
patterns at different scales. The method utilizes the wavelet transform of a training image to decompose it into wavelet coefficients
at different scales, and then quantifies their spatial dependence. Joint simulation of the wavelet coefficients is used together
with available hard and or soft conditioning data. The conditionally co-simulated wavelet coefficients are back-transformed
generating a realization of the attribute under study. Realizations generated using the proposed method reproduce the conditioning
data, the wavelet coefficients and their spatial dependence. Two examples using geological images as training images elucidate
the different aspects of the method, including hard and soft conditioning, the ability to reproduce some non-linear features
and scale dependencies of the training images. 相似文献
35.
E. Roussos M. Fränz C. Martinecz U. Motschmann R.A. Frahm R. Lundin 《Planetary and Space Science》2008,56(6):836-839
Energetic electron fluxes from more than two years of ASPERA-3 observations are organized in different coordinate systems for the investigation of asymmetries in the global dynamics of the Martian magnetosphere. A clear asymmetry is found in the distribution of high-flux events with respect to the solar wind convective electric field (Esw) direction. These events are frequently detected below the average magnetic pile-up boundary (MPB) location at the terminator region of the hemisphere to which the Esw points and extend toward the tail. A detailed investigation of the electron fluxes at the terminator region also reveals that the largest contribution to this Esw asymmetry comes from locations of moderate or strong crustal fields. These observations have implications about reconnection processes in the terminator and provide new insight on magnetic anomaly effects in the global dynamics of the Mars-solar wind interaction. 相似文献
36.
Mathematical Geosciences - 相似文献
37.
Mineral deposits frequently contain several elements of interest that are spatially correlated and require the use of joint geostatistical simulation techniques in order to generate models preserving their spatial relationships. Although joint-simulation methods have long been available, they are impractical when it comes to more than three variables and mid to large size deposits. This paper presents the application of block-support simulation of a multi-element mineral deposit using minimum/maximum autocorrelation factors to facilitate the computationally efficient joint simulation of large, multivariable deposits. The algorithm utilized, termed dbmafsim, transforms point-scale spatial attributes of a mineral deposit into uncorrelated service variables leading to the generation of simulated realizations of block-scale models of the attributes of interest of a deposit. The dbmafsim algorithm is utilized at the Yandi iron ore deposit in Western Australia to simulate five cross-correlated elements, namely Fe, SiO2, Al2O3, P and LOI, that are all critical in defining the quality of iron ore being produced. The block-scale simulations reproduce the direct- and cross-variograms of the elements even though only the direct variograms of the service variables have to be modeled. The application shows the efficiency, excellent performance and practical contribution of the dbmafsim algorithm in simulating large multi-element deposits. 相似文献
38.
Snehamoy Chatterjee Roussos Dimitrakopoulos Hussein Mustapha 《Mathematical Geosciences》2012,44(3):343-374
A pattern-based simulation technique using wavelet analysis is proposed for the simulation (wavesim) of categorical and continuous variables. Patterns are extracted by scanning a training image with a template and then storing
them in a pattern database. The dimension reduction of patterns in the pattern database is performed by wavelet decomposition
at certain scale and the approximate sub-band is used for pattern database classification. The pattern database classification
is performed by the k-means clustering algorithm and classes are represented by a class prototype. For the simulation of categorical variables,
the conditional cumulative density function (ccdf) for each class is generated based on the frequency of the individual categories at the central node of the template. During
the simulation process, the similarity of the conditioning data event with the class prototypes is measured using the L
2-norm. When simulating categorical variables, the ccdf of the best matched class is used to draw a pattern from a class. When continuous variables are simulated, a random pattern
is drawn from the best matched class. Several examples of conditional and unconditional simulation with two- and three- dimensional
data sets show that the spatial continuity of geometric features and shapes is well reproduced. A comparative study with the
filtersim algorithm shows that the wavesim performs better than filtersim in all examples. A full-field case study at the Olympic Dam base metals deposit, South Australia, simulates the lithological
rock-type units as categorical variables. Results show that the proportions of various rock-type units in the hard data are
well reproduced when similar to those in the training image; when rock-type proportions between the training image and hard
data differ, the results show a compromise between the two. 相似文献
39.
40.
Mathematical Geosciences - A training image free, high-order sequential simulation method is proposed herein, which is based on the efficient inference of high-order spatial statistics from the... 相似文献