• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.835-844
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• 2003

A difficulty in spatial data analysis is to choose a suitable theoretical variogram. Generally mean squares error(MSE) is used as a criterion of selection. However researchers encounter the case that the values of MSE are almost the same whereas the estimates of parameters are different. In this case, the selection criterion based on MSE should take into account the parameter estimates. In this paper we study on the method of selecting a variogram using spatial correlation.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.317-324
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• 2003

Kriging interpolation is one of the gennerally used interpolation techniques in Geostatics field. This research refers to the contents about important experimental variogram and the study of theoretical variogram and formulation of Kriging interpolation. Kriging interpolation is applied as interpolation for stress smoothing in finite element method. Posteriori error estimation which makes use of stress smoothing from the FEM is very important part, we try to make practical application of surface regeneration ability from Kriging interpolation. This research is necessary preceding one in order to materialize adaptive FTM through posteriori error estimation. For instance, find the estimate value and estimate the propriety through various theoretical variogram models of the reference analyzed from tensional L-shape domain. It also provides possibility of the Kriging interpolation through comparing to existing Least square method as well.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.160-165
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• 2008

Kriging interpolation technique has been proposed by Danny Krige of South Africa to find the mineral distribution grade from information of geography and space. It is one of the generally used prediction technique for the mineral distribution grade and underground water level in wide scope also used in computer graphics fields by the ability for the surface regeneration This paper comprises two specific objectives. The first is to examine the applicability of Ordinary Kriging interpolation(OK) to finite element method that is based on variogram modeling in conjunction with different allowable limits of separation distance. The second is to investigate the accuracy according to theoretical variogram such as polynomial, Gauss, and spherical models.

• Korean Journal of Soil Science and Fertilizer
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• v.16 no.4
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• pp.305-310
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• 1983

Spatial variability of infiltration rates of 96 samples from Hwadong SiCL was studied by using geostatistical concepts. The measurement was made at the nodes of the regular grid consisting of 12 rows and 8 columns. Sample spacing within rows and columns was 3 and 2 meters, respectively. This study illustrated the use of variogram as a tool to identify the degree of dependency of the infiltration rate on the distance between pairs of measurements and how to take advantage of this dependency. Fractile diagram showed that the distribution of observation was approximately normal. The range of the variogram was about 7.4 meters. The minimum number of samples necessary to reproduce the results similar to the 96 measured values was 8 to 10. Coefficients of theoretical variogram function for computing kriged values and kriged varionces of nuogget effect, slope, and range were 0.444 cm/day, 0.003 cm/day, and 7.4 m, respectively.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.3
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• pp.295-304
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• 2008

This paper comprises two specific objectives. The first is to examine the applicability of Ordinary Kriging interpolation(OK) to finite element method that is based on variogram modeling in conjunction with different allowable limits of separation distance. The second is to investigate the accuracy according to theoretical variograms such as polynomial, Gauss, and spherical models. For this purpose, the weighted least square method is applied to obtain the estimated new stress field from the stress data at the Gauss points. The weight factor is determined by experimental and theoretical variograms for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. The validity of the proposed approach has been tested by analyzing two numerical examples. It is noted that the numerical results by Gauss model using 25% allowable limit of separation distance show an excellent agreement with theoretical solutions in literature.

• Journal of the Korean Society of Groundwater Environment
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• v.1 no.2
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• pp.113-120
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• 1994

One of the delicate problems in aquifer management is the identification of the spatial distribution of tile hydrological parameters. The observed data are insufficient to identify the distribution of transmissivities in LAN aquifer. To determine the distribution of the transmissivity in LAN aquifer, it would be required to transform the observed heads at the pilot points into transmissivities. Therefore, three procedures wire tackled for the identification of the spatial distribution of the hydrological parameters; geostatistical estimate of the parameter field on the basis of known well point, heads reconstructed by a numerical model, and modification of the values at pilot points by a minimization algorithm. The variogram of Kriging has been applied to a total of 258 transmissivity value in attempt to quantify their distribution of LAN aquifer. Variogram of the observed and optimized transmissivities at pilot points are adapted to the exponential form. So, it is fitted by theoretical one with coefficients of w=0.623, a=2.743. Values of head obtained through numerical analysis are adjusted to the observed values so that heads have been transformed completely into the transmissivities at the observation wells. The procedure represented contour map of the estimated transmissivities and the calculated head.

• Tunnel and Underground Space
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• v.19 no.5
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• pp.407-420
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• 2009

In this study geostatistical technique using indicator kriging was performed to evaluate the optimal rock mass classification by integrating the various geophysical information such as borehole data and geophysical data. To get the optimal kriging result, it is necessary to devise the suitable technique to integrate the hard (borehole) and soft (geophysical) data effectively. Also, the model parameters of the variogram must be determined as a priori procedure. Iterative non-linear inversion method was implemented to determine the model parameters of theoretical variogram. To verify the algorithm, behaviour of object function and precision of convergence were investigated, revealing that gradient of the range is extremely small. This algorithm for the field data was applied to a mountainous area planned for a large-scale tunneling construction. As for a soft data, resistivity information from AMT survey is incorporated with RMR information from borehole data, a sort of hard data. Finally, RMR profiles were constructed and attempted to be interpreted at the tunnel elevation and the upper 1D level.

• Journal of the Korean Geotechnical Society
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• v.26 no.1
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• pp.5-19
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• 2010

Geo-layer information is important to determine pile length and estimate residual settlement in the construction site. An overall spatial distribution of geo-layers in the entire construction site can be predicted using drill-log information. In this study, the geo-layer distribution at Song-do area was estimated by kriging and inverse distance weighting methods, and a cross validation was adopted to verify the reliability of estimation results. The analysis results indicate that the best fitted theoretical variogram model to the experimental variogram does not always provide the most reliable estimation in the kriging method. The proper $\alpha$ value of inverse distance weighting method must be determined by types of geo-layer, because the $\alpha$ value is affected by types of geo-layer. Results of the kriging method show more reliable results than those of inverse distance weighting method, and the structure of geo-layer distribution could be evaluated by variogram in the kriging method.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.4A
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• pp.677-687
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• 2006

Kriging interpolation is one of the generally used interpolation techniques in Geostatistics field. This technique includes the experimental and theoretical variograms and the formulation of kriging interpolation. In contrast to the conventional least square method for stress recovery, kriging interpolation is based on the weighted least square method to obtain the estimated exact solution from the stress data at the Gauss points. The weight factor is determined by variogram modeling for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. In addition to this, the p-level is increased non-uniformly or selectively through a posteriori error estimation based on SPR (superconvergent patch recovery) technique, proposed by Zienkiewicz and Zhu, by auto mesh p-refinement. The cut-out plate problem under tension has been tested to validate this approach. It also provides validity of kriging interpolation through comparing to existing least square method.

• Journal of the Korean earth science society
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• v.34 no.1
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• pp.13-27
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• 2013

Quantitative precipitation estimation (QPE) is one of the most important elements in meteorological and hydrological applications. In this study, we adjusted the QPE from an S-band weather radar based on co-kriging method using the geostatistical structure function of error distribution of radar rainrate. In order to estimate the accurate quantitative precipitation, the error of radar rainrate which is a primary variable of co-kriging was determined by the difference of rain rates from rain gauge and radar. Also, the gauge rainfield, a secondary variable of co-kriging is derived from the ordinary kriging based on raingauge network. The error distribution of radar rain rate was produced by co-kriging with the derived theoretical variogram determined by experimental variogram. The error of radar rain rate was then applied to the radar estimated precipitation field. Locally heavy rainfall case during 6-7 July 2009 is chosen to verify this study. Correlation between adjusted one-hour radar rainfall accumulation and rain gauge rainfall accumulation improved from 0.55 to 0.84 when compared to prior adjustment of radar error with the adjustment of root mean square error from 7.45 to 3.93 mm.