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Spatial Data Models, Management and Operations                        37















           Fig. 2-11. Fractures (linear features) and fracture density estimated as total length per unit area or
           pixel (A) and then smoothed via a gridding method (B).


           size is equivalent to area.
              Distance calculation is important in many GIS analyses for mineral exploration. For
           example, Seoane and De Barros Silva (1999) introduced a drainage sinuosity index to
           rank gold-anomalous catchment basins. They calculated sinuosity index as ratio of total
           length of drainages in a segment basin to distance between a sampling point represented
           by a segment basin and the most upstream  point of that segment basin.  Distance
           calculations are also important in  quantifying spatial associations between mineral
           deposits and certain geological features (see Chapter 6).
              Another form of measurement is point or line density, which is the number of points
           or the total length of lines,  respectively,  per  unit area. Fig. 2-11A shows a map of
           fractures and the corresponding  fracture density created by a simple  method  of
           measuring total length of fractures per unit area. Note the blocky character of the simple
           fracture density map, from which it is evident which pixels contain a facture segment. A
           smoother facture density map (Fig. 2-11B) could be achieved via a gridding method (see
           further below). It is clear in the example that a fracture density map, for example, is a
           form of transformation of line or point geo-objects into area or surface geo-objects. Point
           density calculation is an important concern in the analysis of spatial association between
           mineral deposits and certain geological features (Chapter 6). In such  analysis, linear
           geological objects are represented as or transformed into polygonal features.

           Transformations

              Most GIS operations  on spatial data can be considered transformations. In fact,
           calculation of density of point or linear geological features is transformation of the 0-D
           or 1-D, respectively, of these geo-objects into 2-D. Perhaps the most important type of
           transformation in a GIS is conversion of geographical coordinates, in which most spatial
           data are probably originally stored, into planar coordinates of suitable map projections
           (Maling, 1992). Geometric  corrections  of satellite imagery and transformations of
           various raster maps into a common pixel size are also important in GIS studies. Such
           transformations, known as resampling (Mather, 1987), ensure that map layers in a GIS
           are properly georeferenced.  Transformations  to derive  digitally-encoded data, such as
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