Many applications involving spatial data require several layers of informat
ion to be simultaneously analyzed in relation to underlying geography and t
opographic detail. This in turn generates a need for forms of multivariate
analysis particularly oriented to spatial problems and designed to handle s
patial structure and dependency both within and between spatially indexed m
ultivariate responses. In this paper we focus on one group of such methods
sometimes referred to as "spatial factor analysis." Use of these techniques
has so far been mostly restricted to applications in the geosciences and i
n some forms of image processing, but the methods have potential for wider
use outside these fields. They are concerned with identifying components of
a multivariate data set with a spatial covariance structure that predomina
ntly acts over a particular spatial range or zone of influence. We review t
he various forms of spatial factor analysis that have been proposed and emp
hasize links between them and with the linear model of coregionalization em
ployed in geostatistics. We then introduce extensions to such methods that
may prove useful in exploratory spatial analysis, both generally and more s
pecifically in the context of multivariate spatial prediction. Application
of our proposed exploratory techniques is demonstrated on a small but illus
trative geochemical data set involving multielement measurements from strea
m sediments.