地质统计学变异函数贝叶斯模型选择方法与比较

张一凡; 张璐璐; 徐加宝

doi:10.19509/j.cnki.dzkq.tb20240202

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地质统计学变异函数贝叶斯模型选择方法与比较

专栏·地质灾害风险定量评价 | 更新时间：2026-11-05

- 地质统计学变异函数贝叶斯模型选择方法与比较
- 地质统计学变异函数贝叶斯模型选择方法与比较
- 地质科技通报 2025年44卷第2期页码：38-47
- 作者机构：
  
  上海交通大学海洋工程国家重点实验室
- 作者简介：
- 基金信息：
  
  中国长江三峡集团有限公司科研项目（WWKY-2020-0741）;国家自然科学基金项目（52025094;51979158）
- DOI：10.19509/j.cnki.dzkq.tb20240202
  中图分类号： P628.2;TU413
- 网络首发：2025-03-21，
  
  纸质出版：2025
- 稿件说明：
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张一凡, 张璐璐, 徐加宝. 地质统计学变异函数贝叶斯模型选择方法与比较[J]. 地质科技通报, 2025,44(2):38-47.

张一凡, 张璐璐, 徐加宝. 地质统计学变异函数贝叶斯模型选择方法与比较[J]. Bulletin of Geological Science and Technology, 2025, 44(2): 38-47.
张一凡, 张璐璐, 徐加宝. 地质统计学变异函数贝叶斯模型选择方法与比较[J]. 地质科技通报, 2025,44(2):38-47. DOI： 10.19509/j.cnki.dzkq.tb20240202.

张一凡, 张璐璐, 徐加宝. 地质统计学变异函数贝叶斯模型选择方法与比较[J]. Bulletin of Geological Science and Technology, 2025, 44(2): 38-47. DOI： 10.19509/j.cnki.dzkq.tb20240202.

摘要

变异函数量化了空间2点地质属性的变异性，对地质统计分析至关重要。当地质数据随空间坐标呈现趋势变化时，正确选择和估计变异函数十分困难。为实现变异函数的模型选择和参数估计，提出了基于贝叶斯理论的变异函数选择方法，采用拉普拉斯近似方法将后验概率分布近似为高斯分布。首先计算出参数的后验概率分布，随后分别计算每个备选变异函数的贝叶斯模型证据，以确定最优模型。探讨了3种模型选择方法在变异函数选择中的适用性，包括贝叶斯模型证据（BME）、Akaike information criterion(AIC)识别准则和Bayesian information criterion(BIC)识别准则。通过实测静力触探试验的锥端阻力数据，说明了该方法，并从模型拟合度和复杂度罚值2个方面比较3种方法在变异函数模型选择中的差异性。研究表明，给定试验数据条件下，BME能够合理地考虑变异函数的拟合度和复杂性；而AIC和BIC识别准则在模型参数个数相同时，仅能反映不同变异函数的拟合度差异，因此，在这种情况下推荐采用BME选择变异函数。本研究方法能够在考虑趋势项参数条件下合理地选择地质统计学变异函数，所选最优变异函数与试验变异函数较一致，为地质统计学分析提供了有效的参考。

Abstract

ObjectiveThe 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. MethodsTo 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 three model selection methods in the selection of variograms

encompassing Bayesian model evidence (BME)

Akaike information criterion (AIC)

and Bayesian information criterion (BIC). ResultsThe 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.ConclusionThe 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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