Page 28 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

24 Chapter 2

boundaries, such as geochemical anomalies, which require modeling of pertinent spatial
data to represent them as geo-objects. Modeling, therefore, involves various forms of
analysis to partition or discretise pertinent spatial data in order to represent certain
geological features of interest as geo-objects. For example, a threshold for background
element concentrations must be determined in order to map geochemical anomalies.
The geometry of geo-objects can be represented based on their spatial dimensions.
Point geo-objects are without length or area and thus 0-dimensional (0-D). Geochemical
sample locations, although strictly not dimensionless, are usually depicted as points
because they are usually too small to be represented in most map scales. Linear geo-
objects (e.g., faults) are one-dimensional (1-D) and only have length as spatial measure.
Polygonal geo-objects (e.g., geochemical anomalies) are two-dimensional (2-D) and
have area and perimeter as spatial measures. Some geo-objects (e.g., geochemical
landscape) require so-called 2.5-dimensional (2.5-D) representation, because they cannot
be strictly described in two or three dimensions. Geo-objects characterised by their
volume (e.g., orebody) require three-dimensional (3-D) representation. In addition, many
geo-objects require fractal modeling to describe their geometry (Mandelbrot, 1983;
Chapter 4). A fractal geo-object is one which can be fragmented into various parts, and
each part has a similar geometry as the whole geo-object.
The geometry of geo-objects can be defined according to either amount of sampling
data or certain criteria (Raper, 1989). If the geometry of certain geo-objects is defined by
amount of sampling data, then they are called sampling-limited geo-objects. Examples of
sampling-limited geo-objects are porphyry stocks, quartz veins, lithologic contacts, etc.,
because they cannot be sampled or mapped completely if they are only partially exposed.
If the geometry of certain geo-objects is defined by certain criteria in order to delimit
their spatial extents, then they are called definition-limited geo-objects. The best example
of a definition-limited geo-object is an orebody, the spatial extents of which are defined
by cut-off grade at prevailing economic conditions. Significant geochemical anomalies
and prospective zones are both definition-limited geo-objects, although they are also
both sampling-limited geo-objects.

Vector Model
In a vector model, geo-objects are represented as components of a graph. That means
the geometric elements of point, linear and polygonal geo-objects are interpreted in 2-D
space as in a map (Fig. 2-1). Point geo-objects are nodes defined by their graph of map
(x,y) coordinates. Linear geo-objects are defined by arcs with start-nodes and end-nodes
or by a series of arcs inter-connected at nodes called vertices. Polygonal geo-objects are
defined by inter-connected arcs that form a closed loop.
The so-called spaghetti model is the simplest type of vector model (Fig. 2-2), which
represents geo-objects in spatially less structured forms. That means, intersections
between linear geo-objects are not recorded, whereas boundaries between polygonal
geo-objects are represented separately. The latter is usually not without error and could
result in so-called false or sliver polygons. The spaghetti vector model leads to
inefficient data storage and is not amenable to true GIS functions (e.g., neighbourhood