• Journal of the Korean earth science society
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• v.31 no.5
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• pp.437-447
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• 2010

Spatial estimation of environmental variables has been regarded as an important preliminary procedure for decision-making. A minimum variance criterion, which has often been adopted in traditional kriging algorithms, does not always guarantee the optimal estimates for subsequent decision-making processes. In this paper, a geostatistical framework is illustrated that consists of uncertainty modeling via stochastic simulation and risk modeling based on loss functions for the selection of optimal estimates. Loss functions that quantify the impact of choosing any estimate different from the unknown true value are linked to geostatistical simulation. A hybrid loss function is especially presented to account for the different impact of over- and underestimation of different land-use types. The loss function-specific estimates that minimize the expected loss are chosen as optimal estimates. The applicability of the geostatistical framework is demonstrated and discussed through a case study of copper mapping.

• Geomechanics and Engineering
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• v.34 no.1
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• pp.29-41
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• 2023

The 3D geospatial modeling of geotechnical information can aid in understanding the geotechnical characteristic values of the continuous subsurface at construction sites. In this study, a geostatistical optimization model for the three-dimensional (3D) mapping of subsurface stratification and the SPT-N value based on a trial-and-error rule was developed and applied to a dam emergency spillway site in South Korea. Geospatial database development for a geotechnical investigation, reconstitution of the target grid volume, and detection of outliers in the borehole dataset were implemented prior to the 3D modeling. For the site-specific subsurface stratification of the engineering geo-layer, we developed an integration method for the borehole and geophysical survey datasets based on the geostatistical optimization procedure of ordinary kriging and sequential Gaussian simulation (SGS) by comparing their cross-validation-based prediction residuals. We also developed an optimization technique based on SGS for estimating the 3D geometry of the SPT-N value. This method involves quantitatively testing the reliability of SGS and selecting the realizations with a high estimation accuracy. Boring tests were performed for validation, and the proposed method yielded more accurate prediction results and reproduced the spatial distribution of geotechnical information more effectively than the conventional geostatistical approach.

• Geotechnical Engineering
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• v.13 no.1
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• pp.85-100
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• 1997

The heterogeneity of hydraulic conductivity of Metropolitan Waste Landfill is analized by using geostatistical methods and the contaminant transport analysis is performed by using heterogeneous hydraulic conductivity. The hydraulic conductivity data are obtained from laboratory pressurized permeability tests and the insitu, Slug test. Geostatistical methods used in this analysis are Ordinary Kriging and conditional simulation. It is concluded that the heterogeneities of hydraulic conductivity obtained from conditional simulation are greater than those from Ordinary Kriging analysis. The movement of the contaminant on the hydraulic conductivity with greater heterogeneity obtained from conditional simulation is faster than that observed in Ordinary Kriging analysis.

• Tunnel and Underground Space
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• v.13 no.2
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• pp.87-99
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• 2003

Geostatistics is defined as the theory of modeling of regionalized variables and is an efficient and elegant methodology for estimation and uncertainty evaluation from limited spatial sample data. In this study, we have made a theoretical comparison between kriging estimation and geostatistical simulation methods. Kriging methods do not preserve the histogram of original data nor their spatial structure, and also provide only an incomplete measure of uncertainty when compared to the simulation methods. A practical procedure of geostatistical simulation is suggested in this study and the technique is demonstrated through an application, in which it was used to identify the spatial distribution of RMR as well as to evaluate the spatial uncertainty. It is concluded that the geostatistical simulation is the appropriate method to quantify the spatial uncertainty of geotechnical variables such as RMA. Therefore, the results from the simulation can be used as useful information for designer's considerations in decision-making under various geological conditions as well as the related terms of contract.

• Journal of Soil and Groundwater Environment
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• v.20 no.3
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• pp.51-64
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• 2015

In the present study, we develop two history matching techniques based on Markov chain Monte Carlo method where radial basis function and Gaussian distribution generated by unconditional geostatistical simulation are employed as the random walk transition kernels. The Bayesian inverse methods for aquifer characterization as the developed models can be effectively applied to the condition even when the targeted information such as hydraulic conductivity is absent and there are transient hydraulic head records due to imposed stress at observation wells. The model which uses unconditional simulation as random walk transition kernel has advantage in that spatial statistics can be directly associated with the predictions. The model using radial basis function network shares the same advantages as the model with unconditional simulation, yet the radial basis function network based the model does not require external geostatistical techniques. Also, by employing radial basis function as transition kernel, multi-scale nested structures can be rigorously addressed. In the validations of the developed models, the overall predictabilities of both models are sound by showing high correlation coefficient between the reference and the predicted. In terms of the model performance, the model with radial basis function network has higher error reduction rate and computational efficiency than with unconditional geostatistical simulation.

• Journal of the Korean earth science society
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• v.35 no.1
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• pp.69-87
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• 2014

This paper suggests a conditional simulation framework based on multiple data transformations for geostatistical simulation of compositional data. First, log-ratio transformation is applied to original compositional data in order to apply conventional statistical methodologies. As for the next transformations that follow, minimum/maximum autocorrelation factors (MAF) and indicator transformations are sequentially applied. MAF transformation is applied to generate independent new variables and as a result, an independent simulation of individual variables can be applied. Indicator transformation is also applied to non-parametric conditional cumulative distribution function modeling of variables that do not follow multi-Gaussian random function models. Finally, inverse transformations are applied in the reverse order of those transformations that are applied. A case study with surface sediment compositions in tidal flats is carried out to illustrate the applicability of the presented simulation framework. All simulation results satisfied the constraints of compositional data and reproduced well the statistical characteristics of the sample data. Through surface sediment classification based on multiple simulation results of compositions, the probabilistic evaluation of classification results was possible, an evaluation unavailable in a conventional kriging approach. Therefore, it is expected that the presented simulation framework can be effectively applied to geostatistical simulation of various compositional data.

• Geophysics and Geophysical Exploration
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• v.15 no.4
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• pp.177-189
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• 2012

Evaluation of three-dimensional ore body modeling has been performed by applying the geostatistical integration technique to multiple geophysical (electrical resistivity, MT) and geological (borehole data, physical properties of core) information. It was available to analyze the resistivity range in borehole and other area through multiple geophysical data. A correlation between resistivity and density from physical properties test of core was also analyzed. In the case study results, the resistivity value of ore body is decreased contrast to increase of the density, which seems to be related to a reason that the ore body (magnetite) includes heavy conductive component (Fe) in itself. Based on the lab test of physical properties in iron mine region, various geophysical, geological and borehole data were used to provide ore body modeling, that is electrical resistivity, MT, physical properties data, borehole data and grade data obtained from borehole data. Of the various geostatistical techniques for the integrated data analysis, in this study, the SGS (sequential Gaussian simulation) method was applied to describe the varying non-homogeneity depending on region through the realization that maintains the mean and variance. With the geostatistical simulation results of geophysical, geological and grade data, the location of residual ore body and ore body which is previously reported was confirmed. In addition, another highly probable region of iron ore bodies was estimated deeper depth in study area through integrated modeling.

• Journal of the Korean earth science society
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• v.23 no.1
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• pp.15-29
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• 2002

Bayesian inversion for gravity and resistivity data was performed to investigate the cavity structure appearing as a lava tunnel in Cheju Island, Korea. Dipole-dipole DC resistivity data were proposed for a prior information of gravity data and we applied the geostatistical techniques such as kriging and simulation algorithms to provide a prior model information and covariance matrix in data domain. The inverted resistivity section gave the indicator variogram modeling for each threshold and it provided spatial uncertainty to give a prior PDF by sequential indicator simulations. We also presented a more objective way to make data covariance matrix that reflects the state of the achieved field data by geostatistical technique, cross-validation. Then Gaussian approximation was adopted for the inference of characteristics of the marginal distributions of model parameters and Broyden update for simple calculation of sensitivity matrix and SVD was applied. Generally cavity investigation by geophysical exploration is difficult and success is hard to be achieved. However, this exotic multiple interpretations showed remarkable improvement and stability for interpretation when compared to data-fit alone results, and suggested the possibility of diverse application for Bayesian inversion in geophysical inverse problem.

• Journal of Soil and Groundwater Environment
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• v.19 no.4
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• pp.31-44
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• 2014

In the present study, a few of recently developed geostatistical models are comparatively studied. The models are two-point statistics based sequential indicator simulation (SISIM) and generalized coupled Markov chain (GCMC), multi-point statistics single normal equation simulation (SNESIM), and object based model of FLUVSIM (fluvial simulation) that predicts structures of target object from the provided geometric information. Out of the models, SNESIM and FLUVSIM require additional information other than conditioning data such as training map and geometry, respectively, which generally claim demanding additional resources. For the comparative studies, three-dimensional fluvial reservoir model is developed considering the genetic information and the samples, as input data for the models, are acquired by mimicking realistic sampling (i.e. random sampling). For SNESIM and FLUVSIM, additional training map and the geometry data are synthesized based on the same information used for the objective model. For the comparisons of the predictabilities of the models, two different measures are employed. In the first measure, the ensemble probability maps of the models are developed from multiple realizations, which are compared in depth to the objective model. In the second measure, the developed realizations are converted to hydrogeologic properties and the groundwater flow simulation results are compared to that of the objective model. From the comparisons, it is found that the predictability of GCMC outperforms the other models in terms of the first measure. On the other hand, in terms of the second measure, the both predictabilities of GCMC and SNESIM are outstanding out of the considered models. The excellences of GCMC model in the comparisons may attribute to the incorporations of directional non-stationarity and the non-linear prediction structure. From the results, it is concluded that the various geostatistical models need to be comprehensively considered and comparatively analyzed for appropriate characterizations.

• Journal of Soil and Groundwater Environment
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• v.17 no.6
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• pp.69-81
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• 2012

Diverse geostatistical tools such as kriging have been used to estimate the volume and spatial coverage of contaminated soil needed for remediation. However, many approaches frequently yield estimation errors, due to inherent geostatistical uncertainties. Such errors may yield over- or under-estimation of the amounts of polluted soils, which cause an over-estimation of remediation cost as well as an incomplete clean-up of a contaminated land. Therefore, it is very important to use a better estimation tool considering uncertainties arising from incomplete field investigation (i.e., contamination survey) and mathematical spatial estimation. In the current work, as better estimation tools we propose stochastic simulation approaches which allow the remediation volume to be assessed more accurately along with uncertainty estimation. To test the efficiency of proposed methods, heavy metals (esp., Pb) contaminated soil of a shooting range area was selected. In addition, we suggest a quantitative method to delineate the confident interval of estimated volume (and spatial extent) of polluted soil based on the spatial aspect of uncertainty. The methods proposed in this work can improve a better decision making on soil remediation.