• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.340-343
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• 2003

This study presents a practical procedure for the Bayesian inversion of geophysical data by Markov chain Monte Carlo (MCMC) sampling and geostatistics. We have applied geostatistical techniques for the acquisition of prior model information, and then the MCMC method was adopted to infer the characteristics of the marginal distributions of model parameters. For the Bayesian inversion of dipole-dipole array resistivity data, we have used the indicator kriging and simulation techniques to generate cumulative density functions from Schlumberger array resistivity data and well logging data, and obtained prior information by cokriging and simulations from covariogram models. The indicator approach makes it possible to incorporate non-parametric information into the probabilistic density function. We have also adopted the MCMC approach, based on Gibbs sampling, to examine the characteristics of a posteriori probability density function and the marginal distribution of each parameter. This approach provides an effective way to treat Bayesian inversion of geophysical data and reduce the non-uniqueness by incorporating various prior information.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.6
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• pp.391-398
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• 2023

In this paper, a penalized maximum likelihood estimation (PMLE) method that applies a penalty to increase the accuracy of a basis-screening-based Kriging model (BSKM) is introduced. The maximum order and set of basis functions used in the BSKM are determined according to their importance. In this regard, the cross-validation error (CVE) for the basis functions is employed as an indicator of importance. When constructing the Kriging model (KM), the maximum order of basis functions is determined, the importance of each basis function is evaluated according to the corresponding maximum order, and finally the optimal set of basis functions is determined. This optimal set is created by adding basis functions one by one in order of importance until the CVE of the KM is minimized. In this process, the KM must be generated repeatedly. Simultaneously, hyper-parameters representing correlations between datasets must be calculated through the maximum likelihood evaluation method. Given that the optimal set of basis functions depends on such hyper-parameters, it has a significant impact on the accuracy of the KM. The PMLE method is applied to accurately calculate hyper-parameters. It was confirmed that the accuracy of a BSKM can be improved by applying it to Branin-Hoo problem.

• Geotechnical Engineering
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• v.10 no.1
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• pp.19-26
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• 1994

In this paper, the application of the rock classification method based on indicator kriging and the cost of errors, which can incorporate qualitative data, was presented. In particular, the binary classification of rock masses was considered. To this end, a simplified RMR system was used. Since most of subjectivity in this analysis occur during the estimation of loss functions, a sensitivity analysis of loss functions was performed. Through this research, it was found out that an expected cost of errors could successfully be used as an indication for how well a sampling plan was designed. In certain conditions, qualitative data can be more economical than quantitative data in terms of expected costs of errors and sampling costs. Therefore, an additional sampling should be carefully determined depending upon the surrounding geologic conditions and its sampling cost. The application method shown in this paper can be useful for more systematic rock classifications.

• Journal of the Korean Geotechnical Society
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• v.28 no.11
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• pp.5-16
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• 2012

Since geologic data are often sampled at sparse locations, it is important not only to predict attribute values at unsampled locations, but also to assess the uncertainty attached to the prediction. In this paper, the assessment of the local uncertainty of prediction for the depth to weathered soil was performed by using the indicator kriging. A conditional cumulative distribution function (ccdf) was first modeled, and then E-type estimate was computed for the spatial distribution of the depth to the weathered soil. Also, optimal estimate of spatial distribution for the depth to weathered soil was determined by using ccdf and loss function. The design procedure and method considering the minimum expected loss presented in this paper can be used in the decision-making process for geotechnical engineering design.

• Geophysics and Geophysical Exploration
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• v.10 no.4
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• pp.293-298
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• 2007

A new way to integrate various geophysical information for evaluation of RQD was developed. In this study, we does not directly define the RQD value where borehole data are not sampled. Instead, we infer the probability of RQD values with prior probability of data directly obtained from borehole, and secondary supporting probability from resistivity and seismic tomography data. First, we applied the geostatstical indicator kriging to get prior probability of RQD value, and indicator kriging with soft data to get the supporting probability from resistivity and seismic data. And we finally applied the permanence ratio rule to integrate these information. The finally obtained result was also analyzed to fully utilize the probabilistic features. For example, we showed the probability of wrongly classifying the RQD evaluation and vice versa. This kind of analytical result may be used for decision making process based on the geophysical exploration.

• The Journal of Engineering Geology
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• v.16 no.4 s.50
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• pp.393-402
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• 2006

The contamination characteristics of BTEX and TPH components in silty soils with the oil leakage event from point source were studied. The over ratios of three soil pollution standard for TPH component were $1.5{\sim}1.7$ times higher than that of BTEX component. The mean and maximum values of BTEX and TPH components with sample points were B-zone > A-zone > C-zone, and the highest concentrations were measured at $1{\sim}2m$ depth below surface. BTEX and TPH components were increased with linear distance in zone within 120 m and 80 m from point source. For the zone more than 120 m, BTEX and TPH concentrations were under soil pollution standard. The cutoff values of indicator kriging using BTEX and TPH components were defined as confirmative limit, warn- ing limit and counterplan limit. The variograms of indicator-transformed data were selected linear model. The contamination ranges of BTEX and TPH components using confirmative limit and warning limit were estimated similar, but the contamination range of those using counterplan limit was much reduced. The maximum contamination probabilities were estimated by probability maps usinB confirmative limit, warning limit and counterplan limit. The maximum contamination probabilities with three soil pollution standard were estimated 26%, 26% and 13% for BTEX component, and 44%, 38% and 26% for TPH component.

• 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 the Korean Geotechnical Society
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• v.28 no.1
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• pp.17-27
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• 2012

Since geologic data are often sampled at sparse locations, it is important not only to predict attribute values at unsampled locations but also to assess the uncertainty attached to the prediction. In this study the assessment of the local uncertainty of prediction for the thickness of the consolidation layer was performed by using the indicator approach. A conditional cumulative distribution function (ccdf) was first modeled, and then E-type estimates and the conditional variance were computed for the spatial distribution of the thickness of the consolidation layer. These results could be used to estimate the spatial distribution of secondary compression and to assess the local uncertainty of secondary compression for Songdo New City.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.399-401
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• 2003

This paper presents a geostatistical contextual classifier for the classification of remote sensing data. To obtain accurate spatial/contextual information, a simple indicator kriging algorithm with local means that allows one to estimate the probability of occurrence of certain classes on the basis of surrounding pixel information is applied. To illustrate the proposed scheme, supervised classification of multi-sensor remote sensing data is carried out. Analysis of the results indicates that the proposed method improved the classification accuracy, compared to the method based on the spectral information only.

• Geotechnical Engineering
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• v.14 no.1
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• pp.29-36
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• 1998

The application of a multiple rock classification method, which is a generalization of a binary rock classification, is studied in this paper. In particular, this paper shows how to incorporate qualitative data through a case study. The method suggested in this paper can be effectively used for a systematic multiple rock classification such as RMR system developed by Bieniawski. It will be very useful for rock classifications. In addition, it is known that the expected cost of errors can be atopted to indicate how well a investigation plan is made.