共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
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
3.
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
4.
Multiple-point simulation, as opposed to simulation one point at a time, operates at the pattern level using a priori structural information. To reduce the dimensionality of the space of patterns we propose a multi-point filtersim algorithm that classifies structural patterns using selected filter statistics. The pattern filter statistics are specific linear combinations of pattern pixel values that represent directional mean, gradient, and curvature properties. Simulation proceeds by sampling from pattern classes selected by conditioning data. 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.
Stochastic simulation techniques which do not depend on a back transform step to reproduce a prior marginal cumulative distribution function (cdf)may lead to deviations from that distribution which are deemed unacceptable. This paper presents an algorithm to post process simulated realizations or any spatial distribution to reproduce the target cdfin the case of continuous variables or target proportions in the case of categorical variables, yet honoring the conditioning data. Validations conducted for both continuous and categorical cases show that. by adjusting the value of a correction level parameter , the target cdfor proportions can be well reproduced without significant modification of the spatial correlation patterns of the original simulated realizations. 相似文献
7.
This work deals with the joint simulation of copper grade (as a continuous regionalized variable) and rock type (as a categorical variable) in Lince–Estefanía deposit, located in northern Chile. The region under study is heterogeneous, containing three main rock types (intrusive, andesite and breccia bodies) with different copper grade distributions. To perform joint simulation, the multi-Gaussian and pluriGaussian models are used in a combined form. To this end, three auxiliary Gaussian random fields are considered, one for simulating copper grade, up to a monotonic transformation, and two for simulating rock types according to a given truncation rule. Furthermore, the dependence between copper grade and rock types is reproduced by considering cross correlations between these Gaussian random fields. To investigate the benefits of the joint simulation algorithm, copper grade and rock types are also simulated by the traditional cascade approach and the results are compared. It is shown that the cascade approach produces hard boundaries, that is, abrupt transitions of copper grades when crossing rock-type boundaries, a condition that does not exist in the study area according to the contact analysis held on the available data. In contrast, the joint simulation approach produces gradual transitions of the copper grade near the rock-type boundaries and is more suited to the actual data. 相似文献
8.
Weidong Li 《Mathematical Geosciences》2007,39(3):321-335
Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation (or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’ theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models are nonlinear. 相似文献
9.
Weidong Li 《Mathematical Geology》2007,39(3):321-335
Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating
categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces
a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation
(or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional
probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general
solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’
theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional
simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models
are nonlinear. 相似文献
10.
Mathematical Geosciences - Modern approaches for the spatial simulation of categorical variables are largely based on multi-point statistical methods, where a training image is used to derive... 相似文献
11.
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
12.
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
13.
An important issue of using the multiple-point (MP) statistical approach for reservoir modeling concerns the integration of
auxiliary constraints derived, for instance, from seismic information. There exist two methods in the literature for these
non-stationary MP simulations. One is based on an analytical approximation (the “τ-model”) of the conditional probabilities that involve auxiliary data. The degree of approximation with this method depends
on the parameter τ, whose inference is difficult in practice. The other method is based on the inference of these conditional probabilities
directly from training images. This method classifies the auxiliary data into a few classes. This classification is in general
arbitrary and therefore inconvenient in practice, especially in the case of continuous auxiliary constraints. In this paper,
we propose an alternative method for performing non-stationary MP simulations. This method accounts for the data support in
the modeling procedure and allows, in particular, continuous auxiliary data to be integrated into MP simulations. This method
avoids the major limitations of the previous methods, namely the use of an approximate analytical model and the reduction
of the auxiliary data into a limited number of classes. This method can be easily implemented in the existing MP simulation
codes. Numerical tests show good performance of this method both in reproducing the geometrical features of the training image
and in honouring the auxiliary data. 相似文献
14.
Roussos Dimitrakopoulos 《Mathematical Geology》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
15.
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
16.
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
17.
Conditional Simulation of Random Fields by Successive Residuals 总被引：2，自引：0，他引：2
This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations. 相似文献
18.
Multiple-point geostatistics has recently attracted significant attention for characterization of environmental variables. Such methods proceed by searching a large database of patterns obtained from a training image to find a match for a given data-event. The template-matching phase is usually the most time-consuming part of a MPS method. Linear transformations like discrete cosine transform or wavelet transform are capable of representing the image patches with a few nonzero coefficients. This sparsifying capability can be employed to speed up the template-matching problem up to hundreds of times by multiplying only nonzero coefficients. This method is only applicable to rectangular data-events because it is impossible to represent an odd-shaped data-event in a transformation domain. In this paper, the method is applied to speed up the image quilting (IQ) method. The experiments show that the proposed method is capable of accelerating the IQ method tens of times without sensible degradation in simulation results. The method has the potential to be employed for accelerating optimization-based and raster-scan patch-based MPS algorithms. 相似文献
19.
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
20.
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