Page 179 - MATLAB Recipes for Earth Sciences

174 7 Spatial Data

statistics. Matheron as well coined the term kriging for spatial interpolation
by geostatistical methods.

Theorical Background

A basic assumption in geostatistics is that a spatiotemporal process is com-
posed of deterministic and stochastic components (Fig. 7.10). The determin-
istic components can be global and local trends (sometimes called drifts). The
stochastic component is formed by a purely random and an autocorrelated part.
An autocorrelated component implies that on average, closer observations are
more similar than more distant observations. This behavior is described by
the variogram where squared differences between observations are plotted
against their separation distances. The fundamental idea of D. Krige was to
use the variogram for interpolation as means to determine the magnitude of

influence of neighboring observations when predicting values at unobserved
locations. Basic linear geostatistics includes two main procedures: variogra-
phy for modeling the variogram and kriging for interpolation.

Preceding Analysis

Because linear geostatistics as presented here is a parametric method, the un-
derlying assumptions have to be checked by a preceding analysis. As other
parametric methods, linear geostatistics is sensitive to outliers and deviati-
ons from normal distribution. First, after opening the data fi le geost_dat.mat
containing xyz data triplets we plot the sampling locations. Doing this, we
can check point distribution and detect gross errors on the data coordinates
x and y.
load geost_dat.mat
plot(x,y,'.')

Checking of the limits of the observations z can be done by
min(z)

ans =
3.7199
max(z)
ans =
7.8460