Geostatistical structural analysis: Exploring, fitting and testing semivariograms

The semivariogram is a basic tool used in geostatistics to characterize the spatial correlation present in a field or area under study. Geostatistical structural analysis, or variography, involves the estimation of the semivariogram and fitting an appropriate model to the points calculated from the data. This analysis is based on certain assumptions about the spatial data points. In this work, a set of four programs was developed to check stationarity and isotropy assumptions. Another program is suitable for modeling the spatial correlation through fitting semivariogram models to the empirical data points using two methods: Ordinary least squares (OLS) and weighted least squares (WLS). SASRTM was the platform used to develop these five custom interactive programs.;Median polish Tukey, 1977) is a technique used to detrend nonstationary spatial data providing stationary residuals to which a semivariogram model is fitted. Median polish (MP) depends on the grid orientation and it is applied in the grid (rows or columns) directions. In this research, grid rotation is done to study the directionality effects on the semivariogram of MP residuals for trends oriented in directions other than the grid directions. For experimental data, MP done after grid rotation in the anisotropy axes directions left residuals with minimum sill compared to those residuals left in the grid directions. For computer simulated data studied in four directions, an important factor was the trend shape. For trends having two slopes, MP removes the trend leaving stationary residuals only when applied after rotating the grid in the trend direction. MP consistently removed not only the trend but also part of the correlation structure of the computer simulated residuals (CSR). Thus, MP residuals had smaller sill and smaller range than these CSR. Researchers applying MP need to be aware of this result.;An exponential and a spherical semivariogram model fitted equally well two datasets: silver ore data (Clark, 1979) and soil pH data (provided by D. Bullock). Nonnested hypotheses J and P tests (Davidson and MacKinnon, 1981) provided conclusive and similar results when applied to pick the better semivariogram model. For silver ore data and clustered soil pH data the exponential model was suggested while for unclustered soil pH data the spherical model was preferred. For the datasets analyzed, the J and P tests seem to be reasonable procedures for choosing between alternative semivariogram models.;In conclusion, interactive tools and two alternative techniques (median polish with grid rotation and nonnested hypotheses tests) are available to researchers doing geostatistical structural analysis.