Page 46 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

42 Chapter 2

they represent qualitative variables. Buffering is performed when one intends to
determine spatial associations between locations of mineral deposits and various
geological features (e.g., structures, anomalies). Buffering is among the most common
neighbourhood operations, which are treated briefly below and treated in more detail in
Chapter 6.

Neighbourhood operations
The general objective of a neighbourhood operation is to analyze the characteristics
and/or spatial relationships of locations surrounding some specific (control) locations.
Note that control locations are actually part of the neighbourhood to be analyzed. Thus,
in fact, spatial interpolation techniques are a type of neighbourhood operation, because
they aim to estimate values at unsampled locations based on values at sampled locations.
Most types of neighbourhood operations applied in mapping of geochemical anomalies
and mineral prospectivity are performed using a raster data model, because this ensures
spatial adjacency of control pixels to neighbouring pixels. Buffering, however, may be
performed using either vector or raster data.
Neighbourhood operations applied to raster maps are basically filtering operations.
Filtering can be performed in the time domain, frequency domain or spatial domain.
Filtering in the spatial domain is a basic function in GIS, which is further discussed here.
Filtering operations in the time domain and frequency domain are beyond the scope of
this volume; Davis (2002) provides a clear discussion of filtering operations in the time
and frequency domains as applied to geological data analysis.
Filtering of a raster map involves an equal-sided filter window, also called a “kernel”
or “template”, which moves across a raster map one pixel at a time. A filter has an odd
number of pixels on each of its sides so that it defines a symmetrical neighbourhood
about the central pixel (Fig. 2-15). The simplest filter is a square of 3x3 pixels. Each
pixel visited by a filter becomes the control location in a neighbourhood and a new value
is calculated for that pixel according to certain mathematical ‘search’ functions that are
desired to characterise that neighbourhood.
There are three basic elements in a neighbourhood operation – the control pixel, the
neighbouring pixels and the search function to be applied to the neighbourhood. Because
there are four general types of spatial data – ratio, interval, ordinal, nominal – the choice
of mathematical search functions used in filtering operations depends on the type of data
being studied. Note also that if a function can be applied to any type of data in the order
as listed above, then that function can also be applied to the preceding type of data. The
following discussion details examples of eight mathematical search functions, which are
described along with their results for data in Fig. 2-15A.
The data in Fig. 2-15A can be ratio, interval or ordinal. A MINIMUM function
returns to the central pixel the value of the pixel in the neighbourhood with the lowest
value (Fig. 2-14B). The MINIMUM function is often used in a BOOLEAN search query
(true or false) to find ‘false pits’ (single pixel depressions) in a digital elevation model
(DEM) before performing runoff simulations. A MAXIMUM function returns to the
central pixel the value of the pixel in the neighbourhood with the highest value (Fig. 2-