Modeling Spatial Means of Surfaces With Stratified Nonhomogeneity
Modeling Spatial Means of Surfaces With Stratified Nonhomogeneity
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DOI：
10.1109/tgrs.2009.2023326
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发表时间：
2009-12-01
影响因子：
8.2
通讯作者：
Hu, Mao-Gui
中科院分区：
文献类型：
--
作者：
Wang, Jin-Feng;Christakos, George;Hu, Mao-Gui
在地球科学中，人们经常需要估计代表物理属性的表面的空间均值。在某些条件下，这种估计通常通过随机样本的简单求和或某种克里金法（空间回归）技术来执行。例如，朴素样本均值假设样本在空间中随机分布，这是一个限制性假设，在现实世界中的适用性有限（例如，在非均匀表面的情况下，朴素样本均值是实际表面均值的有偏估计）。克里金技术可以对某些类型的均匀表面生成无偏估计，但在协方差在表面的不同层之间表现出相当大的差异时，可能不适用于分层非均匀性的情况。在本文中，我们将克里格概念扩展到研究具有分层非均匀性的表面。推导了相应的分析公式，并进行了涉及现实世界和模拟数据集的实证研究。数值比较分析表明，与通常用于估计跨空间表面平均值的其他方法相比，所提出的方法表现良好。
In geosciences, one often needs to estimate the spatial means of surfaces representing physical attributes. Under certain conditions, this kind of estimation is often performed by a simple summation of a random sample or by some kind of a Kriging (spatial regression) technique. For example, the naive sample mean assumes that the sample is randomly distributed across space, which is a restrictive assumption with limited applicability in real-world situations (e. g., in the case of nonhomogeneous surfaces, the naive sample mean is a biased estimate of the actual surface mean). Kriging techniques can generate unbiased estimates for certain kinds of homogeneous surfaces but may be not appropriate in cases of stratified nonhomogeneity when the covariances exhibit considerable differences between different strata of the surface. In this paper, we extend the Kriging concept to study surfaces with stratified nonhomogeneity. The corresponding analytical formulas are derived, and empirical studies are performed that involve real-world and simulated data sets. Numerical comparative analysis showed that the proposed method performed well compared to other methods commonly used for the purpose of estimating surface means across space.