| Citation: | ZHANG Yifan，ZHANG Lulu，XU Jiabao. Bayesian methods for geostatistical variogram model selection and comparative study[J]. Bulletin of Geological Science and Technology，2025，44（2）：1-10 doi: 10.19509/j.cnki.dzkq.tb20240202
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The variogram quantifies the variability of geological attributes between two spatial points and is of crucial significance for geostatistical analysis. When geological data exhibit a trend variation along spatial coordinates, the accurate selection and estimation of the variogram become exceptionally difficult.
To realize the model selection and parameter estimation of the variogram, this paper presents a variogram selection approach based on Bayesian theory, employing the Laplace approximation method to approximate the posterior probability distribution as a Gaussian one. Firstly, the posterior probability distribution of the parameters is computed, and subsequently, the Bayesian model evidence (BME) of each alternative variogram is calculated respectively to determine the optimal model. This study investigates the applicability of two model selection methods in the selection of variograms, encompassing Bayesian model evidence (BME), Akaike information criterion (AIC), and Bayesian information criterion (BIC).
The proposed method is elucidated through the measured cone tip resistance data from static cone penetration tests, and the disparities among the three methods in the selection of variogram models are compared from the perspectives of model fitting and complexity penalty.
The research reveals that, under the given experimental data conditions, BME can rationally take into account the fitting degree and complexity of the variogram; while the AIC and BIC identification criteria can merely reflect the fitting degree differences of different variograms when the number of model parameters is the same. Consequently, in such circumstances, BME is recommended for the selection of variograms. The method proposed in this study is capable of reasonably selecting the geostatistical variogram considering the trend term parameters, and the selected optimal variogram is relatively consistent with the experimental variogram, providing an effective reference for geostatistical analysis.
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