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1.
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
2.
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
3.
在储层建模中利用多点地质统计学整合地质概念模型及其解释(英文) 总被引：1，自引：0，他引：1
基于三维空间中稀疏的观测数据,地质学家和储层建模人员尝试预测井间的地质沉积相的空间非均质性时,地质概念模型和先验认识在其中扮演着重要的角色。这种整合先验模型或解释的过程有时是隐蔽或不易察觉的,正如在手工绘等值线图中的情形;它也能够被显式地运用到某种算法当中,比如数字绘图中的算法。新近兴起的多点地质统计学为地质学家和储层建模人员提供了一种有力工具,它强调使用训练图像把先验模型明确而定量地引入到储层建模当中。先验地质模型包含了被研究的真实储层中确信存在的样式,而训练图像则是该模型的定量化表达。通过再现高阶统计量,多点算法能够从训练图像中捕捉复杂的(非线性)特征样式并把它们锚定到观测的井位数据。文中描述了多点地质统计学原理,以突出训练图像概念重要性为主线,描述了多点地质统计学在建立三维储层模型中的应用。 相似文献
4.
Solving Speed and Memory Issues in Multiple-Point Statistics Simulation Program SNESIM 总被引：2，自引：2，他引：0
In the last 10 years, Multiple-Point Statistics (MPS) modeling has emerged in Geostatistics as a valuable alternative to traditional variogram-based and object-based modeling. In contrast to variogram-based simulation, which is limited to two-point correlation reproduction, MPS simulation extracts and reproduces multiple-point statistics moments from training images; this allows modeling geologically realistic features, such as channels that control reservoir connectivity and flow behavior. In addition, MPS simulation works on individual pixels or small groups of pixels (patterns), thus does not suffer from the same data conditioning limitations as object-based simulation. The Single Normal Equation Simulation program SNESIM was the first implementation of MPS simulation to propose, through the introduction of search trees, an efficient solution to the extraction and storage of multiple-point statistics moments from training images. SNESIM is able to simulate three-dimensional models; however, memory and speed issues can occur when applying it to multimillion cell grids. Several other implementations of MPS simulation were proposed after SNESIM, but most of them manage to reduce memory demand or simulation time only at the expense of data conditioning exactitude and/or training pattern reproduction quality. In this paper, the original SNESIM program is revisited, and solutions are presented to eliminate both memory demand and simulation time limitations. First, we demonstrate that the time needed to simulate a grid node is a direct function of the number of uninformed locations in the conditioning data search neighborhood. Thus, two improvements are proposed to maximize the ratio of informed to uniformed locations in search neighborhoods: a new multiple-grid approach introducing additional intermediary subgrids; and a new search neighborhood designing process to preferentially include previously simulated node locations. Finally, because SNESIM memory demand and simulation time increase with the size of the data template used to extract multiple-point statistics moments from the training image and build the search tree, a simple method is described to minimize data template sizes while preserving training pattern reproduction quality. 相似文献
5.
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
6.
Modeling Combined Geological and Grade Uncertainty: Application of Multiple-Point Simulation at the Apensu Gold Deposit, Ghana 总被引：1，自引：1，他引：0
Traditionally within the mining industry, single models for both grade and geology of orebodies are created upon which all mine development decisions are based. These models provide a single interpretation of the extent and continuity of the mineralization envelope based on solids and sections interpreted from relatively widely spaced drilling. The inherent variable behavior of grade and geology cannot be understood from a single estimated resource model. To account for uncertainty in the geology and mineralization envelope, Newmont Mining Corporation uses multiple-point statistics (MPS), an emerging spatial simulation framework, which can be employed to generate multiple, geologically realistic, realizations of data representing attributes of mineral deposits that display complex non-linear features. MPS uses a conceptual model of the geology, termed a training image, to infer these high-order spatial relationships. A detailed application of the MPS algorithm at the structurally controlled Apensu gold deposit, Ghana, demonstrates the practical intricacies of the MPS framework and documents efficiency and effectiveness. Multiple realizations of the Apensu deposit allow for an assessment of the geologic and volumetric uncertainty, which is further combined with grade simulations to generate a more complete picture of the true uncertainty of the deposit. 相似文献
7.
利用三维地质模拟技术重构地质现象的三维空间分布,是实现自然资源管理和风险评估的重要基础和前提。多点统计学方法通过探寻多点间的空间结构关系,结合随机模拟方法生成具有差异性的模拟结果,较好地再现了复杂的地质现象。然而,如何构建合适、有效的训练图像一直是基于多点统计学三维地质模拟的核心问题。本文提出了一种改进的多点统计学算法。本方法结合了序贯模拟和迭代的方法,将二维剖面扩展为三维训练图像,再结合EM-Like算法,实现了三维地质结构的优化模拟。建模实例结果表明,本方法能确保训练图像对内部模拟网格的约束,准确模拟研究区的地层层序,并很好地再现二维地质剖面所反映的地层结构关系。 相似文献
8.
Tobias Lochbühler Guillaume Pirot Julien Straubhaar Niklas Linde 《Mathematical Geosciences》2014,46(5):625-645
Geophysical tomography captures the spatial distribution of the underlying geophysical property at a relatively high resolution, but the tomographic images tend to be blurred representations of reality and generally fail to reproduce sharp interfaces. Such models may cause significant bias when taken as a basis for predictive flow and transport modeling and are unsuitable for uncertainty assessment. We present a methodology in which tomograms are used to condition multiple-point statistics (MPS) simulations. A large set of geologically reasonable facies realizations and their corresponding synthetically calculated cross-hole radar tomograms are used as a training image. The training image is scanned with a direct sampling algorithm for patterns in the conditioning tomogram, while accounting for the spatially varying resolution of the tomograms. In a post-processing step, only those conditional simulations that predicted the radar traveltimes within the expected data error levels are accepted. The methodology is demonstrated on a two-facies example featuring channels and an aquifer analog of alluvial sedimentary structures with five facies. For both cases, MPS simulations exhibit the sharp interfaces and the geological patterns found in the training image. Compared to unconditioned MPS simulations, the uncertainty in transport predictions is markedly decreased for simulations conditioned to tomograms. As an improvement to other approaches relying on classical smoothness-constrained geophysical tomography, the proposed method allows for: (1) reproduction of sharp interfaces, (2) incorporation of realistic geological constraints and (3) generation of multiple realizations that enables uncertainty assessment. 相似文献
9.
The Necessity of a Multiple-Point Prior Model 总被引：9，自引：0，他引：9
Any interpolation, any hand contouring or digital drawing of a map or a numerical model necessarily calls for a prior model
of the multiple-point statistics that link together the data to the unsampled nodes, then these unsampled nodes together.
That prior model can be implicit, poorly defined as in hand contouring; it can be explicit through an algorithm as in digital
mapping. The multiple-point statistics involved go well beyond single-point histogram and two-point covariance models; the
challenge is to define algorithms that can control more of such statistics, particularly those that impact most the utilization
of the resulting maps beyond their visual appearance. The newly introduced multiple-point simulation (mps) algorithms borrow
the high order statistics from a visually and statistically explicit model, a training image. It is shown that mps can simulate
realizations with high entropy character as well as traditional Gaussian-based algorithms, while offering the flexibility
of considering alternative training images with various levels of low entropy (organized) structures. The impact on flow performance
(spatial connectivity) of choosing a wrong training image among many sharing the same histogram and variogram is demonstrated. 相似文献
10.
Training Images from Process-Imitating Methods 总被引：2，自引：2，他引：0
Alessandro Comunian Sanjeev K. Jha Beatrice M. S. Giambastiani Gregoire Mariethoz Bryce F. J. Kelly 《Mathematical Geosciences》2014,46(2):241-260
The lack of a suitable training image is one of the main limitations of the application of multiple-point statistics (MPS) for the characterization of heterogeneity in real case studies. Process-imitating facies modeling techniques can potentially provide training images. However, the parameterization of these process-imitating techniques is not straightforward. Moreover, reproducing the resulting heterogeneous patterns with standard MPS can be challenging. Here the statistical properties of the paleoclimatic data set are used to select the best parameter sets for the process-imitating methods. The data set is composed of 278 lithological logs drilled in the lower Namoi catchment, New South Wales, Australia. A good understanding of the hydrogeological connectivity of this aquifer is needed to tackle groundwater management issues. The spatial variability of the facies within the lithological logs and calculated models is measured using fractal dimension, transition probability, and vertical facies proportion. To accommodate the vertical proportions trend of the data set, four different training images are simulated. The grain size is simulated alongside the lithological codes and used as an auxiliary variable in the direct sampling implementation of MPS. In this way, one can obtain conditional MPS simulations that preserve the quality and the realism of the training images simulated with the process-imitating method. The main outcome of this study is the possibility of obtaining MPS simulations that respect the statistical properties observed in the real data set and honor the observed conditioning data, while preserving the complex heterogeneity generated by the process-imitating method. In addition, it is demonstrated that an equilibrium of good fit among all the statistical properties of the data set should be considered when selecting a suitable set of parameters for the process-imitating simulations. 相似文献
11.
The reproduction of the non-stationary distribution and detailed characteristics of geological bodies is the main difficulty of reservoir modeling. Recently developed multiple-point geostatistics can represent a stationary geological body more effectively than traditional methods. When restricted to a stationary hypothesis, multiple-point geostatistical methods cannot simulate a non-stationary geological body effectively, especially when using non-stationary training images (TIs). According to geologic principles, the non-stationary distribution of geological bodies is controlled by a sedimentary model. Therefore, in this paper, we propose auxiliary variables based on the sedimentary model, namely geological vector information (GVI). GVI can characterize the non-stationary distribution of TIs and simulation domains before sequential simulation, and the precision of data event statistics will be enhanced by the sequential simulation’s data event search area limitations under the guidance of GVI. Consequently, the reproduction of non-stationary geological bodies will be improved. The key features of this method are as follows: (1) obtain TIs and geological vector information for simulated areas restricted by sedimentary models; (2) truncate TIs into a number of sub-TIs using a set of cut-off values such that each sub-TI is stationary and the adjacent sub-TIs have a certain similarity; (3) truncate the simulation domain into a number of sub-regions with the same cut-off values used in TI truncation, so that each sub-region corresponds to a number of sub-TIs; (4) use an improved method to scan the TI or TIs and construct a single search tree to restore replicates of data events located in different sub-TIs; and (5) use an improved conditional probability distribution function to perform sequential simulation. A FORTRAN program is implemented based on the SNESIM. 相似文献
12.
Snehamoy Chatterjee Hussein Mustapha Roussos Dimitrakopoulos 《Computational Geosciences》2016,20(3):399-420
Spatial uncertainty modelling is a complex and challenging job for orebody modelling in mining, reservoir characterization in petroleum, and contamination modelling in air and water. Stochastic simulation algorithms are popular methods for such modelling. In this paper, discrete wavelet transformation (DWT)-based multiple point simulation algorithm for continuous variable is proposed that handles multi-scale spatial characteristics in datasets and training images. The DWT of a training image provides multi-scale high-frequency wavelet images and one low-frequency scaling image at the coarsest scale. The simulation of the proposed approach is performed on the frequency (wavelet) domain where the scaling image and wavelet images across the scale are simulated jointly. The inverse DWT reconstructs simulated realizations of an attribute of interest in the space domain. An automatic scale-selection algorithm using dominant mode difference is applied for the selection of the optimal scale of wavelet decomposition. The proposed algorithm reduces the computational time required for simulating large domain as compared to spatial domain multi-point simulation algorithm. The algorithm is tested with an exhaustive dataset using conditional and unconditional simulation in two- and three-dimensional fluvial reservoir and mining blasted rock data. The realizations generated by the proposed algorithm perform well and reproduce the statistics of the training image. The study conducted comparing the spatial domain filtersim multiple-point simulation algorithm suggests that the proposed algorithm generates equally good realizations at lower computational cost. 相似文献
13.
Piotr W. Mirowski Daniel M. Tetzlaff Roy C. Davies David S. McCormick Nneka Williams Claude Signer 《Mathematical Geosciences》2009,41(4):447-474
This research introduces a novel method to assess the validity of training images used as an input for Multipoint Geostatistics,
alternatively called Multiple Point Simulation (MPS). MPS are a family of spatial statistical interpolation algorithms that
are used to generate conditional simulations of property fields such as geological facies. They are able to honor absolute
“hard” constraints (e.g., borehole data) as well as “soft” constraints (e.g., probability fields derived from seismic data,
and rotation and scale). These algorithms require 2D or 3D training images or analogs whose textures represent a spatial arrangement
of geological properties that is presumed to be similar to that of a target volume to be modeled. To use the current generation
of MPS algorithms, statistically valid training image are required as input. In this context, “statistical validity” includes
a requirement of stationarity, so that one can derive from the training image an average template pattern. This research focuses
on a practical method to assess stationarity requirements for MPS algorithms, i.e., that statistical density or probability
distribution of the quantity shown on the image does not change spatially, and that the image shows repetitive shapes whose
orientation and scale are spatially constant. This method employs image-processing techniques based on measures of stationarity
of the category distribution, the directional (or orientation) property field and the scale property field of those images.
It was successfully tested on a set of two-dimensional images representing geological features and its predictions were compared
to actual realizations of MPS algorithms. An extension of the algorithms to 3D images is also proposed. As MPS algorithms
are being used increasingly in hydrocarbon reservoir modeling, the methods described should facilitate screening and selection
of the input training images. 相似文献
14.
多点地质统计学是一种建立地质模型的统计学方法,该方法比传统的两点地质统计学更适合河流相沉积体系。本文综合地震、测井、录井及生产资料,绘制了长庆油田苏里格气田苏48区块盒8下段辫状河训练图像,并在此基础上利用多点地质统计学方法,加入三维地震资料作为约束,以水平井整体开发为研究对象,建立了该区的地质模型,优化了水平井整体部署,指导水平井导向。利用多口水平井实钻效果验证了地质模型的精度,以苏19-62井为例得到:录井显示气层钻遇率为78.3%,测井显示气层钻遇率为69%。这与地震反演剖面预测相似,且与实钻效果有很好的对应性。 相似文献
15.
As additional multiple-point statistical (MPS) algorithms are developed, there is an increased need for scientific ways for comparison beyond the usual visual comparison or simple metrics, such as connectivity measures. In this paper, we start from the general observation that any (not just MPS) geostatistical simulation algorithm represents two types of variability: (1) the within-realization variability, namely, that realizations reproduce a spatial continuity model (variogram, Boolean, or training-image based), (2) the between-realization variability representing a model of spatial uncertainty. In this paper, it is argued that any comparison of algorithms needs, at a minimum, to be based on these two randomizations. In fact, for certain MPS algorithms, it is illustrated with different examples that there is often a trade-off: Increased pattern reproduction entails reduced spatial uncertainty. In this paper, the subjective choice that the best algorithm maximizes pattern reproduction is made while at the same time maximizes spatial uncertainty. The discussion is also limited to fairly standard multiple-point algorithms and that our method does not necessarily apply to more recent or possibly future developments. In order to render these fundamental principles quantitative, this paper relies on a distance-based measure for both within-realization variability (pattern reproduction) and between-realization variability (spatial uncertainty). It is illustrated in this paper that this method is efficient and effective for two-dimensional, three-dimensional, continuous, and discrete training images. 相似文献
16.
Non-stationary models often capture better spatial variation of real world spatial phenomena than stationary ones. However, the construction of such models can be tedious as it requires modeling both statistical trend and stationary stochastic component. Non-stationary models are an important issue in the recent development of multiple-point geostatistical models. This new modeling paradigm, with its reliance on the training image as the source for spatial statistics or patterns, has had considerable practical appeal. However, the role and construction of the training image in the non-stationary case remains a problematic issue from both a modeling and practical point of view. In this paper, we provide an easy to use, computationally efficient methodology for creating non-stationary multiple-point geostatistical models, for both discrete and continuous variables, based on a distance-based modeling and simulation of patterns. In that regard, the paper builds on pattern-based modeling previously published by the authors, whereby a geostatistical realization is created by laying down patterns as puzzle pieces on the simulation grid, such that the simulated patterns are consistent (in terms of a similarity definition) with any previously simulated ones. In this paper we add the spatial coordinate to the pattern similarity calculation, thereby only borrowing patterns locally from the training image instead of globally. The latter would entail a stationary assumption. Two ways of adding the geographical coordinate are presented, (1) based on a functional that decreases gradually away from the location where the pattern is simulated and (2) based on an automatic segmentation of the training image into stationary regions. Using ample two-dimensional and three-dimensional case studies we study the behavior in terms of spatial and ensemble uncertainty of the generated realizations. 相似文献
17.
Multiple-point statistics (MPS) provides a flexible grid-based approach for simulating complex geologic patterns that contain high-order statistical information represented by a conceptual prior geologic model known as a training image (TI). While MPS is quite powerful for describing complex geologic facies connectivity, conditioning the simulation results on flow measurements that have a nonlinear and complex relation with the facies distribution is quite challenging. Here, an adaptive flow-conditioning method is proposed that uses a flow-data feedback mechanism to simulate facies models from a prior TI. The adaptive conditioning is implemented as a stochastic optimization algorithm that involves an initial exploration stage to find the promising regions of the search space, followed by a more focused search of the identified regions in the second stage. To guide the search strategy, a facies probability map that summarizes the common features of the accepted models in previous iterations is constructed to provide conditioning information about facies occurrence in each grid block. The constructed facies probability map is then incorporated as soft data into the single normal equation simulation (snesim) algorithm to generate a new candidate solution for the next iteration. As the optimization iterations progress, the initial facies probability map is gradually updated using the most recently accepted iterate. This conditioning process can be interpreted as a stochastic optimization algorithm with memory where the new models are proposed based on the history of the successful past iterations. The application of this adaptive conditioning approach is extended to the case where multiple training images are proposed as alternative geologic scenarios. The advantages and limitations of the proposed adaptive conditioning scheme are discussed and numerical experiments from fluvial channel formations are used to compare its performance with non-adaptive conditioning techniques. 相似文献
18.
An Improved Parallel Multiple-point Algorithm Using a List Approach 总被引：15，自引：8，他引：7
Julien Straubhaar Philippe Renard Gr��goire Mariethoz Roland Froidevaux Olivier Besson 《Mathematical Geosciences》2011,43(3):305-328
Among the techniques used to simulate categorical variables, multiple-point statistics is becoming very popular because it allows the user to provide an explicit conceptual model via a training image. In classic implementations, the multiple-point statistics are inferred from the training image by storing all the observed patterns of a certain size in a tree structure. This type of algorithm has the advantage of being fast to apply, but it presents some critical limitations. In particular, a tree is extremely RAM demanding. For three-dimensional problems with numerous facies, large templates cannot be used. Complex structures are then difficult to simulate. In this paper, we propose to replace the tree by a list. This structure requires much less RAM. It has three main advantages. First, it allows for the use of larger templates. Second, the list structure being parsimonious, it can be extended to include additional information. Here, we show how this can be used to develop a new approach for dealing with non-stationary training images. Finally, an interesting aspect of the list is that it allows one to parallelize the part of the algorithm in which the conditional probability density function is computed. This is especially important for large problems that can be solved on clusters of PCs with distributed memory or on multicore machines with shared memory. 相似文献
19.
20.
Memory-Efficient Categorical Multi-point Statistics Algorithms Based on Compact Search Trees 总被引：1，自引：1，他引：0
Tuanfeng Zhang Stein Inge Pedersen Christen Knudby David McCormick 《Mathematical Geosciences》2012,44(7):863-879
Multi-point statistics (MPS) has emerged as an advanced geomodeling approach. A practical MPS algorithm named snesim (simple normal equations simulation), which uses categorical-variable training images, was proposed in 2001. The snesim algorithm generates a search tree to store the occurrence statistics of all patterns in the training image within a given set of search templates before the simulation proceeds. The snesim search tree concept makes MPS simulation central processing unit efficient but consumes large amounts of memory, particularly when three-dimensional training images contain complex patterns and when a large search template is required to ensure optimal reproduction of the image patterns. To crack the memory-restriction bottleneck, we have developed a compact search tree that contains the same information but reduces memory cost by one order of magnitude. Furthermore, the compact structure also accelerates MPS simulation significantly. Such remarkable improvement makes MPS a more practical tool to use in building the large and complex three-dimensional facies models required in the oil and gas industry. 相似文献