Page 85 - Modern Spatiotemporal Geostatistics

66 Modern Spatiotemporal Geostatistics — Chapter 2

Figure 2.15. Plot of the spectral density of Equation 2.57.

which is nonnegative for all fc € P?. Hence, the exponential function of Equa-
tion 2.58 is a permissible covariance for the distance in Equation 2.54.
As the above analysis shows, the geostatistician must be extra cautious
when using a covariance or a variogram model: only those functions that are
compatible with the space/time geometry background should be selected.
Effect of spatiotemporal geometry on mapping

There are several ways in which spatiotemporal geometry can affect the out-
come of scientific mapping. A kriging map, e.g., is a function of the data
set and the correlation function (covariance, variogram, etc.] characterizing
the variability of the natural variable under consideration. Since the data are
functions of the coordinate system used, so is the map obtained from these
data. Furthermore, since the correlation function is the necessary input to
most mapping techniques, it should be expected that maps produced from
these techniques will also be affected by the metrical structure assumed. This
line of reasoning leads to the final postulate of this chapter.