Filter-Based Classification of Training Image Patterns for Spatial Simulation

Zhang, Tuanfeng; Switzer, Paul; Journel, André G.

doi:10.1007/s11004-005-9004-x

Cited by 305 publications

(182 citation statements)

References 2 publications

Supporting

Mentioning

170

Contrasting

Unclassified

Order By: Relevance

“…Similar observations are made in actual field applications where substantial available data show that although the spatial statistics of the TI are reproduced, the data statistics may not be (e.g., Volker and Dimitrakopoulos 2007). Similar remarks are generally valid for the filtersim algorithm (Zhang et al 2006), which uses a limited number of linear filters and may degenerate sample effects.…”

Section: A High Quality Approximationsupporting

confidence: 52%

“…Today's trends, developments, and applications in this area of problem solving focus on the so-called multiple-point simulation algorithms, such as the snesim (Strebelle 2002), filtersim (Zhang et al 2006;Wu et al 2008), and simpat (Arpat and Caers 2007) algorithms, and related extensions (Boucher 2009;Chugunova and Hu 2008;Mirowski et al 2008;Remy et al 2009;and others). Additional related new developments include Markov random field-based multiple-point type approaches (Daly 2004;Tjelmeland and Eidsvik 2004), kernel approaches (Scheidt and Caers 2009), and multiscale simulations based on discrete wavelet decomposition (Gloaguen and Dimitrakopoulos 2009;Chatterjee et al 2009).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High-order Stochastic Simulation of Complex Spatially Distributed Natural Phenomena

Mustapha

Dimitrakopoulos

2010

Math Geosci

View full text Add to dashboard Cite

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 pro-H. Mustapha ( ) · R. Dimitrakopoulos

show abstract

Section: A High Quality Approximationsupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

High-order Stochastic Simulation of Complex Spatially Distributed Natural Phenomena

Mustapha

Dimitrakopoulos

2010

Math Geosci

View full text Add to dashboard Cite

show abstract

“…The northeast faults created a region separated from rest of the study area, indicating compartmentalizing of degasification. In this figure, Q50 realizations of 1998-2006and 2006-2011 show that the E1-E11 panel area continued to deplete in GIP in all coals, at a slower rate. However, there was no change in GIP outside of the northeast faults because boreholes had stopped production after 1998.…”

Section: Spatial Time-lapsed Gas-in-place and Gas-in-place Change Resmentioning

confidence: 89%

“…However, most of these examples used variogram techniques, which cannot reproduce complex patterns, discontinuities, and curvilinear shapes (Zhang 2008). Multiple-point statistics (mps) proposed by Journel (1992) and extended by Guardiano and Srivastava (1992) by the use of a training image (TI), were made practical with SNESIM (Strebelle 2000) and SIMPAT (Arpat and Caers 2007) and FILTERSIM (Zhang et al 2006) algorithms (Wu et al 2008a). In this work, Stanford Geostatistical Modeling Software's (SGeMS) implementation of FILTERSIM was employed to simulate time-lapsed GIP and time-lapsed differences in GIP in the New Castle, Mary Lee/Blue Creek, and Jagger seams.…”

Section: Filter-based Multiple-point Geostatistical Simulation Of Timmentioning

confidence: 99%

Time-Lapse Analysis of Methane Quantity in the Mary Lee Group of Coal Seams Using Filter-Based Multiple-Point Geostatistical Simulation

Karacan

Olea²

2013

Math Geosci

View full text Add to dashboard Cite

Coal seam degasification and its success are important for controlling methane, and thus for the health and safety of coal miners. During the course of degasification, properties of coal seams change. Thus, the changes in coal reservoir conditions and in-place gas content as well as methane emission potential into mines should be evaluated by examining time-dependent changes and the presence of major heterogeneities and geological discontinuities in the field. In this work, timelapsed reservoir and fluid storage properties of the New Castle coal seam, Mary Lee/Blue Creek seam, and Jagger seam of Black Warrior Basin, Alabama, were determined from gas and water production history matching and production forecasting of vertical degasification wellbores. These properties were combined with isotherm and other important data to compute gas-in-place (GIP) and its change with time at borehole locations. Time-lapsed training images (TIs) of GIP and GIP difference corresponding to each coal and date were generated by using these point-wise data and Voronoi decomposition on the TI grid, which included faults as discontinuities for expansion of Voronoi regions. Filter-based multiple-point geostatistical simulations, which were preferred in this study due to anisotropies and discontinuities in the area, were used to predict time-lapsed GIP distributions within the study area. Performed simulations were used for mapping spatial timelapsed methane quantities as well as their uncertainties within the study area.The systematic approach presented in this paper is the first time in literature that history matching, TIs of GIPs and filter simulations are used for degasification performance evaluation and for assessing GIP for mining safety. Results from this study showed that using production history matching of coalbed methane wells to determine time-lapsed reservoir data could be used to compute spatial GIP and representative GIP TIs generated through Voronoi decomposition. Furthermore, performing filter simulations using point-wise data and TIs could be used to predict methane quantity in coal seams subjected to degasification. During the course of the study, it was shown that the material balance of gas produced by wellbores and the GIP reductions in coal seams predicted using filter simulations compared very well, showing the success of filter simulations for continuous variables in this case study. Quantitative results from filter simulations Correspondence to: C. Özgen Karacan, cok6@cdc.gov. HHS Public Access Author Manuscript Author ManuscriptAuthor ManuscriptAuthor Manuscript of GIP within the studied area briefly showed that GIP was reduced from an initial ~73 Bcf (median) to ~46 Bcf (2011), representing a 37 % decrease and varying spatially through degasification. It is forecasted that there will be an additional ~2 Bcf reduction in methane quantity between 2011 and 2015. This study and presented results showed that the applied methodology and utilized techniques can be used to map GIP and its change within coal...

show abstract

“…Such ineffectiveness is especially severe in geological or environmental studies, as discussed by , Strebelle (2002) and Tjelmeland and Besag (1998). In the past decade, various techniques have been developed to improve the reliability of characterizing random fields, such as bootstrapping (Kleijnen et al, 2012;Schelin and Luna, 2010;Stein, 2008, 2004;Mukul et al, 2004), copula-based methods (Kazianka, 2013;Pilz et al, 2012;Kazianka andPilz, 2010a, 2010b;Bárdossy and Li, 2008;Bárdossy, 2006), kernel-based methods (Honarkhah and Caers, 2010;Scheidt and Caers, 2010, 2009a, 2009b), Bayesian (Nieto-Barajas and Sinha, 2014Troldborg et al, 2012;Pilz et al, 2012;Kazianka andPilz, 2011, 2012), multi-point simulation methods (De Iaco, 2013;Boucher, 2009;Chugunova and Hu, 2008;Wu et al, 2008;Mirowski et al, 2008;Arpat and Caers, 2007;Zhang et al, 2006;Strebelle, 2002), multi-scale simulations using wavelets (Chatterjee and Dimitrakopoulos, 2012;Dimitrakopoulos, 2009, 2008), and spatial-cumulant-based simulation methods (Goodfellow et al, 2012;MachucaMory and Dimitrakopoulos, 2012;, Dimitrakopoulos et al, 2010.…”

Section: Introductionmentioning

confidence: 99%

A new approach to spatial data interpolation using higher-order statistics

Liu

Anh

McGree

et al. 2014

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

Abstract:Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first-and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting nonGaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility.Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function (CPDF) is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

show abstract

Filter-Based Classification of Training Image Patterns for Spatial Simulation

Cited by 305 publications

References 2 publications

High-order Stochastic Simulation of Complex Spatially Distributed Natural Phenomena

High-order Stochastic Simulation of Complex Spatially Distributed Natural Phenomena

Time-Lapse Analysis of Methane Quantity in the Mary Lee Group of Coal Seams Using Filter-Based Multiple-Point Geostatistical Simulation

A new approach to spatial data interpolation using higher-order statistics

Contact Info

Product

Resources

About