• Journal of the Korean Geophysical Society
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• v.3 no.3
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• pp.161-174
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• 2000

Bayesian inversion is a stable approach to infer the subsurface structure with the limited data from geophysical explorations. In geophysical inverse process, due to the finite and discrete characteristics of field data and modeling process, some uncertainties are inherent and therefore probabilistic approach to the geophysical inversion is required. Bayesian framework provides theoretical base for the confidency and uncertainty analysis for the inference. However, most of the Bayesian inversion require the integration process of high dimension, so massive calculations like a Monte Carlo integration is demanded to solve it. This method, though, seemed suitable to apply to the geophysical problems which have the characteristics of highly non-linearity, we are faced to meet the promptness and convenience in field process. In this study, by the Gaussian approximation for the observed data and a priori information, fast Bayesian inversion scheme is developed and applied to the model problem with electric well logging and dipole-dipole resistivity data. Each covariance matrices are induced by geostatistical method and optimization technique resulted in maximum a posteriori information. Especially a priori information is evaluated by the cross-validation technique. And the uncertainty analysis was performed to interpret the resistivity structure by simulation of a posteriori covariance matrix.

• Geophysics and Geophysical Exploration
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• v.5 no.4
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• pp.262-271
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• 2002

This study presents a practical procedure for the Bayesian inversion of geophysical data. We have applied geostatistical techniques for the acquisition of prior model information, then the Markov Chain Monte Carlo (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.

• Geophysics and Geophysical Exploration
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• v.10 no.4
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• pp.252-258
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• 2007

We have studied the feasibility of geostatistics approach to enhancing analysis of sparsely obtained seismic data by combining with satellite gravity data. The shallow depth and numerous fishing nets in The Yellow Sea, west of Korea, makes it difficult to do seismic surveys in this area. Therefore, we have attempted to use geostatistics to integrate the seismic data along with gravity data. To evaluate the feasibility of this approach, we have extracted only a few seismic profile data from previous surveys in the Yellow Sea and performed integrated analysis combining with the results from gravity data under the assumption that seismic velocity and density have a high physical correlation. First, we analyzed the correlation between extracted seismic profiles and depths obtained from gravity inversion. Next, we transferred the gravity depth to travel time using non-linear indicator transform and analyze residual values by kriging with varying local means. Finally, the reconstructed time structure map was compared with the original seismic section given in the previous study. Our geostatistical approach demonstrates relatively satisfactory results and especially, in the boundary area where seismic lines are sparse, gives us more in-depth information than previously available.

• 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 Soil and Groundwater Environment
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• v.7 no.3
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• pp.3-17
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• 2002

Data analysis of groundwater monitoring wells and geostatistical methods are used to identify the local characteristics of sea water intrusion and the range of sea water intrusion at the southeastern coastal area of Busan, Korea. Rainfall and groundwater level of two monitoring wells show a linear correlation because of the direct groundwater recharge by the precipitation. However, rainfall and electric conductivity have the inverse relationship because of the increase of groundwater. Electric conductivity rapidly increased at 24m depth and exceeded 20,000$\mu\textrm{s}$/cm near 26m depth in the monitoring wells. The variations of groundwater level and electric conductivity show that the interface between sea water and fresh water tends to move upward when groundwater level goes down. In the cross correlation analysis, groundwater level versus rainfall represents the largest cross correlation coefficient in 0 time lag but the cross correlation coefficient of electric conductivity versus rainfall is the largest when the time lag is 9 days. This suggests that the fluctuations of groundwater level respond to rainfall in a short time, but the interface between sea water and fresh water respond very slow to rainfall. Horizontal extents of sea water intrusion are estimated to 14 m from the east of Line 1, and 25 m from the southeast end of Line 2 in the inversion of dipole-dipole profiling data of two survey lines. The data of VES by the Schulumberger array in May and July show lognormal distributions. In the kriged apparent resistivity and earth resistivity distributions, the resistivities of July are increased comparing to those of May. This reflects that the concentration of sea water in aquifer is reduced due to the increased groundwater recharge from the rainfall in June and July. In analyzing the vertical and horizontal apparent resistivities and earth resistivity distributions, the geostatistical methods are very useful to identify the variations of earth resistivity distributions at the coastal area.