共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
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
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4.
CDFSIM: Efficient Stochastic Simulation Through Decomposition of Cumulative Distribution Functions of Transformed Spatial Patterns 总被引：1，自引：1，他引：0
Hussein Mustapha Snehamoy Chatterjee Roussos Dimitrakopoulos 《Mathematical Geosciences》2014,46(1):95-123
Simulation of categorical and continuous variables is performed using a new pattern-based simulation method founded upon coding spatial patterns in one dimension. The method consists of, first, using a spatial template to extract information in the form of patterns from a training image. Patterns are grouped into a pattern database and, then, mapped to one dimension. Cumulative distribution functions of the one-dimensional patterns are built. Patterns are then classified by decomposing the cumulative distribution functions, and calculating class or cluster prototypes. During the simulation process, a conditioning data event is compared to the class prototype, and a pattern is randomly drawn from the best matched class. Several examples are presented so as to assess the performance of the proposed method, including conditional and unconditional simulations of categorical and continuous data sets. Results show that the proposed method is efficient and very well performing in both two and three dimensions. Comparison of the proposed method to the filtersim algorithm suggests that it is better at reproducing the multi-point configurations and main characteristics of the reference images, while less sensitive to the number of classes and spatial templates used in the simulations. 相似文献
5.
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
6.
We evaluate the performance and statistical accuracy of the fast Fourier transform method for unconditional and conditional simulation. The method is applied under difficult but realistic circumstances of a large field (1001 by 1001 points) with abundant conditioning criteria and a band limited, anisotropic, fractal-based statistical characterization (the von Kármán model). The simple Fourier unconditional simulation is conducted by Fourier transform of the amplitude spectrum model, sampled on a discrete grid, multiplied by a random phase spectrum. Although computationally efficient, this method failed to adequately match the intended statistical model at small scales because of sinc-function convolution. Attempts to alleviate this problem through the covariance method (computing the amplitude spectrum by taking the square root of the discrete Fourier transform of the covariance function) created artifacts and spurious high wavenumber content. A modified Fourier method, consisting of pre-aliasing the wavenumber spectrum, satisfactorily remedies sinc smoothing. Conditional simulations using Fourier-based methods require several processing stages, including a smooth interpolation of the differential between conditioning data and an unconditional simulation. Although kriging is the ideal method for this step, it can take prohibitively long where the number of conditions is large. Here we develop a fast, approximate kriging methodology, consisting of coarse kriging followed by faster methods of interpolation. Though less accurate than full kriging, this fast kriging does not produce visually evident artifacts or adversely affect the a posteriori statistics of the Fourier conditional simulation. 相似文献
7.
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
8.
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
9.
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
10.
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
11.
12.
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
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.
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
15.
Numerical simulation is an essential component of many studies of geological storage of carbon dioxide, but care must be taken to ensure the accuracy of the results. Unlike several other possible sources of simulation errors, which have previously been considered in detail and have well-understood techniques for mitigating their effects, comparatively little discussion of the spatial grid dependence of the dissolution rate of carbon dioxide into the formation water has appeared in the literature, despite its importance to simulation studies of geological storage of carbon dioxide in saline aquifers. In many instances, sufficient refinement of the computational grid can be a practical solution. However, this approach is not always feasible, especially for large-scale simulations in three dimensions requiring multiple realisations, which commonly feature a coarse grid due to constraints on available computational capabilities. A measure of the error in the amount of dissolved carbon dioxide introduced by the use of a finite grid is therefore of great interest. In this study, the use of finite-sized grid blocks is shown to overestimate the amount of dissolved carbon dioxide in short-term results by a factor of 1?+?V f/V p, where V f is the grid block volume at the saturation front and V p is the total grid block volume of the plume. This result can be used in a number of ways to correct the calculated short-term dissolution in coarse-scale simulations so that the amount dissolved agrees better with that obtained from fine-scale simulations. 相似文献
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17.
Roussos Dimitrakopoulos 《Mathematical Geosciences》1990,22(3):361-380
Conditional simulation of intrinsic random functions of orderk is a stochastic method that generates realizations which mimic the spatial fluctuation of nonstationary phenomena, reproduce their generalized covariance and honor the available data at sampled locations. The technique proposed here requires the following steps: (i) on-line simulation of Wiener-Levy processes and of their integrations; (ii) use of the turning-bands method to generate realizations in Rn; (iii) conditioning to available data; and (iv) verification of the reproduced generalized covariance using generalized variograms. The applicational aspects of the technique are demonstrated in two and three dimensions. Examples include the conditional simulation of geological variates of the Crystal Viking petroleum reservoir, Alberta, Canada. 相似文献
18.
In most multiple-point simulation algorithms, all statistical features are provided by one or several training images (TI) that serve as a substitute for a random field model. However, because in practice the TI is always of finite size, the stochastic nature of multiple-point simulation is questionable. This issue is addressed by considering the case of a sequential simulation algorithm applied to a binary TI that is a genuine realization of an underlying random field. At each step, the algorithm uses templates containing the current target point as well as all previously simulated points. The simulation is validated by checking that all statistical features of the random field (supported by the simulation domain) are retrieved as an average over a large number of outcomes. The results are as follows. It is demonstrated that multiple-point simulation performs well whenever the TI is a complete (infinitely large) realization of a stationary, ergodic random field. As soon as the TI is restricted to a limited domain, the statistical features cannot be obtained exactly, but integral range techniques make it possible to predict how much the TI should be extended to approximate them up to a prespecified precision. Moreover, one can take advantage of extending the TI to reduce the number of disruptions in the execution of the algorithm, which arise when no conditioning template can be found in the TI. 相似文献
19.
Fast direct sampling for multiple-point stochastic simulation 总被引：1，自引：0，他引：1
Multiple-point statistics simulation has recently attracted significant attention for the simulation of complex geological structures. In this paper, a fast direct sampling (FDS) algorithm is presented based on a fast gradient descent pattern matching strategy. The match is directly extracted from the training image (TI) and so the method does not require intensive preprocessing and database storage. The initial node of the search path is selected randomly but the following nodes are selected in a principled manner so that the path is conducted to the right match. Each node is selected based on the matching accuracy and the behavior of the TI in the previous node. A simple initialization strategy is presented in this paper which significantly accelerates the matching process at the expense of a very naïve preprocessing stage. The proposed simulation algorithm has several outstanding advantages: it needs no (or very limited) preprocessing, does not need any database storage, searches for the match directly in the TI, is not limited to fixed size patterns (the pattern size can be easily changed during simulation), is capable of handling both continuous and categorical data, is capable of handling multivariate data, and finally and more importantly, is a fast method while maintaining high standards for the matching quality. Experiments on different TIs reveal that the simulation results of FDS and DS are comparable in terms of pattern reproduction and connectivity while FDS is far faster than DS. 相似文献
20.
The practice of fast conditional simulations through the LU decomposition of the covariance matrix 总被引：9，自引：0，他引：9
Francois Alabert 《Mathematical Geology》1987,19(5):369-386
The LU-matrix approach to conditional simulations allows fast generation of large numbers of realizations for a given stochastic process. Simplicity, flexibility, and quality are its main advantages. Its implementation for cases where dense grids and/or large numbers of conditioning data cause computational problems is discussed. A case study is presented. 相似文献