Optimized Sample Schemes for Geostatistical Surveys
Optimized Sample Schemes for Geostatistical Surveys
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DOI：
10.1007/s11004-006-9069-1
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发表时间：
2007-02
期刊：
影响因子：
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通讯作者：
B. P. Marchant;R. Lark
中科院分区：
文献类型：
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作者：
B. P. Marchant;R. Lark
地质统计调查中使用的样本方案必须同时适用于变异函数估计和克里格法。以前，方案已经针对这些步骤中的一个单独进行了优化。普通的克里格法一般要求采样位置均匀地分布在该地区。变异函数估计需要更不规则的采样位置模式，因为必须在空间相关性范围之内和之外的所有滞后间隔的测量值之间进行比较。以前的研究没有考虑如何将这些优化方案组合成一次调查，以及如何确定应将多大比例的抽样精力用于变异函数估计和多大比例的克里格法。推导了考虑普通克立格法和变异函数不确定性的地质统计调查总误差的表达式。与克里格方差相同，该表达式是变异函数的函数，而不是采样的响应数据的函数。如果假设某一特定的变异函数，则可在抽样之前估计地质统计调查中的总误差。因此，对于变异函数估计和普通克立格法的组合过程，我们可以通过最小化该表达式来设计最优样本方案。通过空间模拟退火法实现最小化。由此产生的样本方案确保该区域被相当均匀地覆盖，但包括一些接近的配对，以分析短距离的空间相关性。这些最优样本方案的形式对假设的变异函数很敏感。因此，我们采用贝叶斯方法，而不是假设一个单一的变异函数，而是使可信变异函数分布上的预期总误差最小化。这在计算上是昂贵的，因此建议采用一种策略来减少所需的计算量
Sample schemes used in geostatistical surveys must be suitable for both variogram estimation and kriging. Previously schemes have been optimized for one of these steps in isolation. Ordinary kriging generally requires the sampling locations to be evenly dispersed over the region. Variogram estimation requires a more irregular pattern of sampling locations since comparisons must be made between measurements separated by all lags up to and beyond the range of spatial correlation. Previous studies have not considered how to combine these optimized schemes into a single survey and how to decide what proportion of sampling effort should be devoted to variogram estimation and what proportion devoted to krigingAn expression for the total error in a geostatistical survey accounting for uncertainty due to both ordinary kriging and variogram uncertainty is derived. In the same manner as the kriging variance, this expression is a function of the variogram but not of the sampled response data. If a particular variogram is assumed the total error in a geostatistical survey may be estimated prior to sampling. We can therefore design an optimal sample scheme for the combined processes of variogram estimation and ordinary kriging by minimizing this expression. The minimization is achieved by spatial simulated annealing. The resulting sample schemes ensure that the region is fairly evenly covered but include some close pairs to analyse the spatial correlation over short distances. The form of these optimal sample schemes is sensitive to the assumed variogram. Therefore a Bayesian approach is adopted where, rather than assuming a single variogram, we minimize the expected total error over a distribution of plausible variograms. This is computationally expensive so a strategy is suggested to reduce the number of computations required