Uncertainty investigation of the semivariogram by means of the bootstrap method

Abstract

The uncertainty in the semivariogram has hardly been investigated in previous geostatistical studies. This paper presents an efficient methodology of uncertainty assessment based on the bootstrap. By applying this computer-intensive statistical method one can easily simulate the distribution of the empirical semivariogram estimate for each lag. The lag-wise standard errors and confidence intervals of a given level can then be easily calculated from the bootstrap replicates. These estimations are valid in any situation when classical statistics fail. The bootstrap also provides a mathematical-statistical tool to decide whether the semivariogram reaches its maximum at a given lag or not. It leads directly to a simple determination of the range of influence. Effects beyond the range, such as the hole effect, can be explored with the same approach. The empirical semivariogram, supplied by measures of uncertainty, adequately describes the true spatial behavior of the studied variable. This universal method ren...