Mapping an uncertainty zone between interpolated types of a categorical variable

Yamamoto, Jorge Kazuo; Mao, X. M.; Koike, Katsuaki; Crósta, Álvaro Penteado; Landim, Paulo Milton Barbosa; Hu, He-xuan; Wang, C. Y.; Yao, Liqiang

doi:10.1016/j.cageo.2011.09.005

Cited by 22 publications

(24 citation statements)

References 11 publications

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“…This expression is equivalent to the interpolation variance formula ( [12], p. 491-493) that was proved by ( [14], p. 147). Therefore, the interpolation variance is valid for assessing uncertainties for both continuous and categorical variables.…”

Section: Indicator Kriging and Multiquadric Equationsmentioning

confidence: 68%

“…Because of the problems described above with computing horizontal indicator variograms, our technique calls for using multiquadric equations as proposed by ( [14], p. 148-150). Further details about multiquadric equations can be found in ( [14], p. 148-150).…”

Section: Indicator Kriging and Multiquadric Equationsmentioning

confidence: 99%

“…To illustrate how the reference value affects the size of the zone of uncertainty, let us consider the interpolation results of a categorical variable that is composed of five types. A sample with 81 data points was [14], p. 151) defined the zone of uncertainty for interpolation variances greater than 0.20. This reference value has been used repeatedly because the results are compatible with the sample size and the distribution of data points within the sampled area.…”

Section: Indicator Kriging and Multiquadric Equationsmentioning

confidence: 99%

“…( [14], p. 151) used the Bernoulli variance (3) to map a zone of uncertainty between interpolated types of a categorical variable (Fig. 2).…”

Section: Indicator Kriging and Multiquadric Equationsmentioning

confidence: 99%

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Post-processing of sequential indicator simulation realizations for modeling geologic bodies

et al. 2015

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Sequential indicator simulation realizations contain unavoidable artifacts that are geologically unrealistic. This happens because unlikely types can be drawn randomly from the cumulative distribution and be assigned to a cell in the simulated model. This cell may then be used as previously simulated data when a cell in its neighborhood is visited during a random walk. The sequential process sometimes results in geologically unrealistic realizations. However, different realizations can reveal hidden features. Each realization contains both reliable geological information and noise that is displayed as unlikely types. This paper proposes applying the averaging filter that is commonly used in seismic reflection data to improve the signal to noise ratio. After applying this filter, all L realizations will be condensed into a single geological model that contains certain and uncertain cells. This average model is then exhaustively sampled for the certain cells, and this new sample is used to post-process the uncertain cells to reduce the uncertainty. This resampling and post-processing procedure can be repeated until the final model is considered to be good enough. The proposed method is tested with a model of a dike that crosscuts two sedimentary units. The synthetic geologic model was sampled with 24 drill holes. The resultsshow that the final geological model with reduced uncertainty reproduces very well the sedimentary units and the orientation of the dike as well. The dike shape is not fully reproduced and still presents uncertainties because of lack of neighbor data.

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Section: Indicator Kriging and Multiquadric Equationsmentioning

confidence: 68%

Section: Indicator Kriging and Multiquadric Equationsmentioning

confidence: 99%

Section: Indicator Kriging and Multiquadric Equationsmentioning

confidence: 99%

“…( [14], p. 151) used the Bernoulli variance (3) to map a zone of uncertainty between interpolated types of a categorical variable (Fig. 2).…”

Section: Indicator Kriging and Multiquadric Equationsmentioning

confidence: 99%

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Post-processing of sequential indicator simulation realizations for modeling geologic bodies

et al. 2015

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“…IK yields a unique and smooth solution aiming at local accuracy (Isaaks and Srivastava, 1989;Journel et al, 2000) with the most probable facies category at each grid node (Yamamoto et al, 2012). Due to the smoothing by interpolation methods, variograms computed from IK output facies distributions reveal larger continuity compared with theoretical variograms fitted to the exhaustive dataset, which increase with reducing conditioning wells ( Figure 6B).…”

Section: Facies Interpolationsmentioning

confidence: 97%

Forecasting coal resources and reserves in heterogeneous coal zones using 3D facies models (As Pontes Basin, NW Spain)

Falivene

Cabrera

Sáez

2014

International Journal of Coal Geology

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Forecasting coal resources and reserves is critical for coal mine development. Thickness maps are commonly used for assessing coal resources and reserves; however they are limited for capturing coal splitting effects in thick and heterogeneous coal zones. As an alternative, threedimensional geostatistical methods are used to populate facies distribution within a densely sampled heterogeneous coal zone in the As Pontes basin (NW Spain). Coal distribution in this zone is mainly characterized by coal-dominated areas in the central parts of the basin interfingering with terrigenousdominated alluvial fan zones at the basin margins. Resultant models are applied to forecast coal resources and reserves. Predictions using subsets of available well data are also generated to understand performance under limited data constraints. Facies interpolation methods tend to overestimate coal resources and reserves due to interpolation smoothing. Facies simulation methods yield similar resource predictions than conventional thickness map approximations. Reserves predicted by facies simulation methods are mainly influenced by: a) the specific coal proportion threshold used to determine if a block can be recovered or not, and b) the method capability to reproduce areal trends in coal proportions and splitting between coal-dominated and terrigenous-dominated areas of the basin. Reserves predictions differ between the simulation methods, even with dense conditioning datasets. Simulation methods are ranked according to the correlation of their outputs with predictions to the directly interpolated coal proportions: with lowdensity datasets sequential indicator simulation with trends yields the best correlation, with highdensity datasets sequential indicator simulation with post-processing using maximum a posteriori selection yields the best correlation. AbstractForecasting coal resources and reserves is critical for coal mine development. Thickness maps are commonly used for assessing coal resources and reserves; however they are limited for capturing coal splitting effects in thick and heterogeneous coal zones. As an alternative, three-dimensional geostatistical methods are used to populate facies distribution within a densely sampled heterogeneous coal zone in the As Pontes basin (NW Spain). Coal distribution in this zone is mainly characterized by coaldominated areas in the central parts of the basin interfingering with terrigenousdominated alluvial fan zones at the basin margins. Resultant models are applied to forecast coal resources and reserves. Predictions using subsets of available well data are also generated to understand performance under limited data constraints.Facies interpolation methods tend to overestimate coal resources and reserves due to interpolation smoothing. Facies simulation methods yield similar resource predictions than conventional thickness map approximations. Reserves predicted by facies simulation methods are mainly influenced by: a) the specific coal proportion threshold used to determine if a ...

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Reservoir history matching using constrained ensemble Kalman filtering

et al. 2017

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The high heterogeneity of petroleum reservoirs, represented by their spatially varying rock properties (porosity and permeability), greatly dictates the quantity of recoverable oil. In this work, the estimation of the spatial permeability distribution, which is crucial for predicting the future performance of a reservoir, is carried out through a history matching technique based on constrained ensemble Kalman filtering (EnKF). The main contribution in this work is the novel implementation of hard and soft constraints in the recursive EnKF estimation methodology for petroleum reservoirs. Hard data is obtained from the actual values of the reservoir parameters at discrete locations obtained by core sampling and well logging, while the soft data considered is obtained from correlograms, which characterize the spatial correlation of the rock properties in a reservoir. In each time update, the parameter estimates obtained from the unconstrained EnKF are modified by one of two novel algorithms. In the first, the correlation matrix obtained after the unconstrained EnKF update is transformed to honour the true correlation structure from the correlogram by applying a projection-based method. The second algorithm involves the use of a technique for soft constrained covariance localization. We observe that the soft data constrained localization method results in the best estimates of the permeability and also reduces the computational time significantly. We quantify the improvement in estimation performance of each of the constrained methods over unconstrained estimation. The method, while developed for estimation in petroleum reservoirs, is also generally applicable to systems with spatial heterogeneity and underlying spatial correlations.

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Mapping an uncertainty zone between interpolated types of a categorical variable

Cited by 22 publications

References 11 publications

Post-processing of sequential indicator simulation realizations for modeling geologic bodies

Post-processing of sequential indicator simulation realizations for modeling geologic bodies

Forecasting coal resources and reserves in heterogeneous coal zones using 3D facies models (As Pontes Basin, NW Spain)

Reservoir history matching using constrained ensemble Kalman filtering

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