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1.
Conditional Simulation with Patterns 总被引：17，自引：0，他引：17
An entirely new approach to stochastic simulation is proposed through the direct simulation of patterns. Unlike pixel-based
(single grid cells) or object-based stochastic simulation, pattern-based simulation simulates by pasting patterns directly
onto the simulation grid. A pattern is a multi-pixel configuration identifying a meaningful entity (a puzzle piece) of the
underlying spatial continuity. The methodology relies on the use of a training image from which the pattern set (database)
is extracted. The use of training images is not new. The concept of a training image is extensively used in simulating Markov
random fields or for sequentially simulating structures using multiple-point statistics. Both these approaches rely on extracting
statistics from the training image, then reproducing these statistics in multiple stochastic realizations, at the same time
conditioning to any available data. The proposed approach does not rely, explicitly, on either a statistical or probabilistic
methodology. Instead, a sequential simulation method is proposed that borrows heavily from the pattern recognition literature
and simulates by pasting at each visited location along a random path a pattern that is compatible with the available local
data and any previously simulated patterns. This paper discusses the various implementation details to accomplish this idea.
Several 2D illustrative as well as realistic and complex 3D examples are presented to showcase the versatility of the proposed
algorithm. 相似文献
2.
Multiple-point statistics are widely used for the simulation of categorical variables because the method allows for integrating a conceptual model via a training image and then simulating complex heterogeneous fields. The multiple-point statistics inferred from the training image can be stored in several ways. The tree structure used in classical implementations has the advantage of being efficient in terms of CPU time, but is very RAM demanding and then implies limitations on the size of the template, which serves to make a proper reproduction of complex structures difficult. Another technique consists in storing the multiple-point statistics in lists. This alternative requires much less memory and allows for a straightforward parallel algorithm. Nevertheless, the list structure does not benefit from the shortcuts given by the branches of the tree for retrieving the multiple-point statistics. Hence, a serial algorithm based on list structure is generally slower than a tree-based algorithm. In this paper, a new approach using both list and tree structures is proposed. The idea is to index the lists by trees of reduced size: the leaves of the tree correspond to distinct sublists that constitute a partition of the entire list. The size of the indexing tree can be controlled, and then the resulting algorithm keeps memory requirements low while efficiency in terms of CPU time is significantly improved. Moreover, this new method benefits from the parallelization of the list approach. 相似文献
3.
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
4.
5.
Direct Multiple-Point Geostatistical Simulation of Edge Properties for Modeling Thin Irregularly Shaped Surfaces 总被引：3，自引：1，他引：2
Thin, irregularly shaped surfaces such as clay drapes often have a major control on flow and transport in heterogeneous porous
media. Clay drapes are often complex, curvilinear three-dimensional surfaces and display a very complex spatial distribution.
Variogram-based stochastic approaches are also often not able to describe the spatial distribution of clay drapes since complex,
curvilinear, continuous, and interconnected structures cannot be characterized using only two-point statistics. Multiple-point
geostatistics aims to overcome the limitations of the variogram. The premise of multiple-point geostatistics is to move beyond
two-point correlations between variables and to obtain (cross) correlation moments at three or more locations at a time using
training images to characterize the patterns of geological heterogeneity. Multiple-point geostatistics can reproduce thin
irregularly shaped surfaces such as clay drapes, but this is often computationally very intensive. This paper describes and
applies a methodology to simulate thin, irregularly shaped surfaces with a smaller CPU and RAM demand than the conventional
multiple-point statistical methods. The proposed method uses edge properties for indicating the presence of thin irregularly
shaped surfaces. Instead of pixel values, edge properties indicating the presence of irregularly shaped surfaces are simulated
using snesim. This method allows direct simulation of edge properties instead of pixel properties to make it possible to perform multiple-point
geostatistical simulations with a larger cell size and thus a smaller computation time and memory demand. This method is particularly
valuable for three-dimensional applications of multiple-point geostatistics. 相似文献
6.
本文系统地介绍了多点地质统计学的基本原理及方法，并以我国渤海湾盆地某区块新近系明化镇组河流相储层为例，进行了多点统计学随机建模的实例分析。多点地质统计学为储层随机建模的国际前沿研究方向，该方法综合了基于象元的方法易忠实条件数据以及基于目标的方法易再现目标几何形态的优点，同时克服了传统基于变差函数的二点统计学不能表达复杂空间结构和再现目标几何形态的不足。通过理论与实例研究，分析了目前多点统计学尚存在的问题(包括训练图像平稳性问题、目标连续性问题以及综合软信息的问题等)及未来发展的方向。 相似文献
7.
8.
Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics 总被引：68，自引：0，他引：68
Sebastien Strebelle 《Mathematical Geology》2002,34(1):1-21
In many earth sciences applications, the geological objects or structures to be reproduced are curvilinear, e.g., sand channels in a clastic reservoir. Their modeling requires multiple-point statistics involving jointly three or more points at a time, much beyond the traditional two-point variogram statistics. Actual data from the field being modeled, particularly if it is subsurface, are rarely enough to allow inference of such multiple-point statistics. The approach proposed in this paper consists of borrowing the required multiple-point statistics from training images depicting the expected patterns of geological heterogeneities. Several training images can be used, reflecting different scales of variability and styles of heterogeneities. The multiple-point statistics inferred from these training image(s) are exported to the geostatistical numerical model where they are anchored to the actual data, both hard and soft, in a sequential simulation mode. The algorithm and code developed are tested for the simulation of a fluvial hydrocarbon reservoir with meandering channels. The methodology proposed appears to be simple (multiple-point statistics are scanned directly from training images), general (any type of random geometry can be considered), and fast enough to handle large 3D simulation grids. 相似文献
9.
Creation of a geological fracture network model conditioned to in situ geometric measurements is of great importance to geoprofessionals, as fractures dominate pathways for fluid flow, a major concern for many engineering applications. This paper introduces and applies the Stochastic Nelder Mead simplex method to automatically calibrate stochastic parameters of geometric characterisations of a discrete fracture network model. This method can overcome the non-convergence of a previous exploratory approach on the classic Nelder Mead method by others, and is an effective substitution to the manual trial-and-error method and is complementary to existing conditional simulation approaches. The procedure to integrate the Stochastic Nelder Mead with a discrete fracture network is presented in detail, and a case study was conducted. Results show that the improved model can better handle the stochastic nature of the underlying system and effectively simulates the observed number and mean trace length of these fractures, although the model results underestimate its standard deviation. Simulated distributions of trace lengths and spacings are within acceptable ranges except for some small offsets, which can be adjusted during model runs. 相似文献
10.
Fast FILTERSIM Simulation with Score-based Distance 总被引：5，自引：3，他引：2
FILTERSIM is a pattern-based multiple-point geostatistical algorithm for modeling both continuous and categorical variables.
It first groups all the patterns from a training image into a set of pattern classes using their filter scores. At each simulation
location, FILTERSIM identifies the training pattern class closest to the local conditioning data event, then samples a training
pattern from that prototype class and pastes it onto the simulation grid. In the original FILTERSIM algorithm, the selection
of the closest pattern class is based on the pixel-wise distance between the prototype of each training pattern class and
the local conditioning data event. Hence, FILTERSIM is computationally intensive for 3D simulations, especially with a large
and pattern-rich training image. In this paper, a novel approach is proposed to accelerate the simulation process by replacing
that pixel-wise distance calculation with a filter score comparison, which is the difference between the filter score of local
conditioning data event and that of each pattern prototype. This score-based distance calculation significantly reduces the
CPU consumption due to the tremendous data dimension reduction. The results show that this new score based-distance calculation
can speed up FILTERSIM simulation by a factor up to 10 in 3D applications. 相似文献
11.
Indicator Simulation Accounting for Multiple-Point Statistics 总被引：7，自引：0，他引：7
Geostatistical simulation aims at reproducing the variability of the real underlying phenomena. When nonlinear features or large-range connectivity is present, the traditional variogram-based simulation approaches do not provide good reproduction of those features. Connectivity of high and low values is often critical for grades in a mineral deposit. Multiple-point statistics can help to characterize these features. The use of multiple-point statistics in geostatistical simulation was proposed more than 10 years ago, on the basis of the use of training images to extract the statistics. This paper proposes the use of multiple-point statistics extracted from actual data. A method is developed to simulate continuous variables. The indicator kriging probabilities used in sequential indicator simulation are modified by probabilities extracted from multiple-point configurations. The correction is done under the assumption of conditional independence. The practical implementation of the method is illustrated with data from a porphyry copper mine. 相似文献
12.
多点地质统计学建模的发展趋势 总被引：2，自引：0，他引：2
从算法研究、训练图像处理和实际应用三个方面详细解剖了国内外多点地质统计学的发展历程,在此基础上,分析了多点地质统计学主流的几种算法的核心原理、适用范围及优缺点,以此来对储层建模的发展趋势作出展望。目前,多点地质统计学虽是随机建模的一种前沿研究热点,但由于其尚未成熟,仍需对建模算法进行研究。为此,在前人研究的基础上,重点分析了多点地质统计学的发展趋势：合理处理训练图像;合理利用软信息;选择合适的相似性方法;选择合适的标准化方法;合理利用平稳性;算法间的耦合;选择合适的过滤器;拓展缝洞型碳酸盐岩模拟。最后,提出多点地质统计学在储层建模方面,应从增加储层的模拟区域、提高模拟精度、扩大储层相的模拟范围和提高计算机模拟效率等方面进行改进。 相似文献
13.
We present a fracture-only reservoir simulator for multiphase flow: the fracture geometry is modeled explicitly, while fluid
movement between fracture and matrix is accommodated using empirical transfer functions. This is a hybrid between discrete
fracture discrete matrix modeling where both the fracture and matrix are gridded and dual-porosity or dual-permeability simulation
where both fracture and matrix continua are upscaled. The advantage of this approach is that the complex fracture geometry
that controls the main flow paths is retained. The use of transfer functions, however, simplifies meshing and makes the simulation
method considerably more efficient than discrete fracture discrete matrix models. The transfer functions accommodate capillary-
and gravity-mediated flow between fracture and matrix and have been shown to be accurate for simple fracture geometries, capturing
both the early- and late-time average behavior. We verify our simulator by comparing its predictions with simulation results
where the fracture and matrix are explicitly modeled. We then show the utility of the approach by simulating multiphase flow
in a geologically realistic fracture network. Waterflooding runs reveal the fraction of the fracture–matrix interface area
that is infiltrated by water so that matrix imbibition can occur. The evolving fraction of the fracture–matrix interface area
turns out to be an important characteristic of any particular fracture system to be used as a scaling parameter for capillary
driven fracture–matrix transfer. 相似文献
14.
乌东德水电站右岸地下厂房随机块体特征研究 总被引：1，自引：0，他引：1
随机块体的几何特征和稳定性是水利水电工程中地下厂房支护设计的重要依据。对乌东德水电站右岸地下厂房随机块体的特征进行了深入研究。对研究区域内实测的裂隙参数进行了分组统计,确定了各组裂隙产状、迹长等参数的分布形式和大小。利用逆建模方法建立了三维裂隙网络模型,获取了各组裂隙的直径和三维密度。采用一般块体方法对地下厂房进行随机块体的识别和稳定性分析,利用GeneralBlock软件进行了10次随机实现,对10次计算结果进行了统计分析和讨论。研究结果表明,结构面与开挖面形成的随机块体集中在地下厂房的顶拱部位,10次随机实现中,地下厂房全长范围内平均每次形成的随机块体为414个;随机块体的平均体积为2.9 m3,最大块体的体积达152.0 m3;可移动块体中,大部分为稳定块体,不稳定块体均以坠落形式破坏;构成可移动块体的结构面多为3~4条,最多可达12条,其中倾W向的中等倾角裂隙是构成块体并可能造成块体失稳的最危险结构面;随机块体的平均深度为1.2 m,最大深度为8.8 m。建议支护锚杆应尽量穿透倾W向中等倾角的长大裂隙,且锚杆支护长度大于8.8 m。 相似文献
15.
The advent of multiple-point geostatistics (MPS) gave rise to the integration of complex subsurface geological structures
and features into the model by the concept of training images. Initial algorithms generate geologically realistic realizations
by using these training images to obtain conditional probabilities needed in a stochastic simulation framework. More recent
pattern-based geostatistical algorithms attempt to improve the accuracy of the training image pattern reproduction. In these
approaches, the training image is used to construct a pattern database. Consequently, sequential simulation will be carried
out by selecting a pattern from the database and pasting it onto the simulation grid. One of the shortcomings of the present
algorithms is the lack of a unifying framework for classifying and modeling the patterns from the training image. In this
paper, an entirely different approach will be taken toward geostatistical modeling. A novel, principled and unified technique
for pattern analysis and generation that ensures computational efficiency and enables a straightforward incorporation of domain
knowledge will be presented. 相似文献
16.
Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium) 总被引：3，自引：1，他引：2
Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport. 相似文献
17.
Sergey Oladyshkin Holger Class Rainer Helmig Wolfgang Nowak 《Computational Geosciences》2011,15(3):565-577
CO2 storage in geological formations is currently being discussed intensively as a technology with a high potential for mitigating
CO2 emissions. However, any large-scale application requires a thorough analysis of the potential risks. Current numerical simulation
models are too expensive for probabilistic risk analysis or stochastic approaches based on a brute-force approach of repeated
simulation. Even single deterministic simulations may require parallel high-performance computing. The multiphase flow processes
involved are too non-linear for quasi-linear error propagation and other simplified stochastic tools. As an alternative approach,
we propose a massive stochastic model reduction based on the probabilistic collocation method. The model response is projected
onto a higher-order orthogonal basis of polynomials to approximate dependence on uncertain parameters (porosity, permeability,
etc.) and design parameters (injection rate, depth, etc.). This allows for a non-linear propagation of model uncertainty affecting
the predicted risk, ensures fast computation, and provides a powerful tool for combining design variables and uncertain variables
into one approach based on an integrative response surface. Thus, the design task of finding optimal injection regimes explicitly
includes uncertainty, which leads to robust designs with a minimum failure probability. We validate our proposed stochastic
approach by Monte Carlo simulation using a common 3D benchmark problem (Class et al., Comput Geosci 13:451–467, 2009). A reasonable compromise between computational efforts and precision was reached already with second-order polynomials.
In our case study, the proposed approach yields a significant computational speed-up by a factor of 100 compared with the
Monte Carlo evaluation. We demonstrate that, due to the non-linearity of the flow and transport processes during CO2 injection, including uncertainty in the analysis leads to a systematic and significant shift of the predicted leakage rates
toward higher values compared with deterministic simulations, affecting both risk estimates and the design of injection scenarios. 相似文献
18.
随着社会的发展,人类对化石能源的依赖导致大量的CO2排入大气层,从而引起全球变暖、海平面上升等一系列全球性气候问题。CO2地质封存是当前CO2减排最有前景的技术,但大量的CO2注入地层易诱发相应的力学问题：地表隆起变形、盖层完整性受损、断层活化等。因此,为了降低CO2地质封存带来的安全风险,理论分析、数值模拟和响应面方法等手段被应用于此类力学问题的分析中。由于数值模拟方法能够解决大尺度范围内复杂几何模型的多场耦合问题,数值模拟成为当前在CO2地质封存力学领域中应用最广泛的方法。因此,对CO2地质封存若干力学问题的数值模拟方法进行了全面的综述。首先,简要介绍了多孔介质的温度-渗流-力学-化学（THMC）多场耦合原理,并对数值模拟解决多场耦合问题的方法进行了归类。然后,详细总结了数值模拟在解决CO2地质封存力学问题方面的国内研究进展。最后,讨论了数值模拟方法在此类力学问题方面的应用缺陷,并提出了若干建议。 相似文献
19.
Multivariate Intrinsic Random Functions for Cokriging 总被引：2，自引：0，他引：2
In multivariate geostatistics, suppose that we relax the usual second-order-stationarity assumptions and assume that the component
processes are intrinsic random functions of general orders. In this article, we introduce a generalized cross-covariance function
to describe the spatial cross-dependencies in multivariate intrinsic random functions. A nonparametric method is then proposed
for its estimation. Based on this class of generalized cross-covariance functions, we give cokriging equations for multivariate
intrinsic random functions in the presence of measurement error. A simulation is presented that demonstrates the accuracy
of the proposed nonparametric estimation method. Finally, an application is given to a dataset of plutonium and americium
concentrations collected from a region of the Nevada Test Site used for atomic-bomb testing. 相似文献
20.
This paper investigates the use of strip transect sampling to estimate object abundance when the underlying spatial distribution
is assumed to be Poisson. A design-based rather than model-based approach to estimation is investigated through computer simulation,
with both homogeneous and non-homogeneous fields representing individual realizations of spatial point processes being considered.
Of particular interest are the effects of changing the number of transects and transect width (or alternatively, coverage
percent or fraction) on the quality of the estimate. A specific application to the characterization of unexploded ordnance
(UXO) in the subsurface at former military firing ranges is discussed. The results may be extended to the investigation of
outcrop characteristics as well as subsurface geological features. 相似文献