International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
node is 0.0, that observation is given a weight of 1.0; 
all other observations are given weights of 0.0. Thus, 
the grid node is assigned the value of the coincident 
observation. The smoothing parameter is a 
mechanism for buffering this behavior. When you 
assign a non-zero smoothing parameter, no point is 
given an overwhelming weight, meaning that no 
point is given a weighting factor equal to 1.0. One of 
the characteristics of Inverse Distance to a Power is 
the generation of "bull's-eyes" surrounding the 
observation position within the grid area. A 
smoothing parameter can be assigned during Inverse 
Distance to a Power to reduce the "bull's-eye" effect 
by smoothing the interpolated grid. 
2.2 The Kriging Method 
Kriging is a geostatistical gridding method that has 
proven useful and popular in many fields. This 
method produces visually appealing maps from 
irregularly spaced data. Kriging attempts to express 
trends suggested in your data, so that, for example, 
high points might be connected along a ridge rather 
than isolated by bull's-eye type contours. Kriging is a 
very flexible gridding method. The Kriging defaults 
can be accepted to produce an accurate grid of your 
data, or Kriging can be custom-fit to a data set, by 
specifying the appropriate variogram model. Within 
SURFER, Kriging can be either an exact or a 
smoothing interpolator, depending on the 
user-specified parameters. It incorporates anisotropy 
and underlying trends in an efficient and natural 
manner. 
2.3 The Minimum Curvature Method 
Minimum Curvature is widely used in the earth 
sciences. The interpolated surface generated by 
Minimum Curvature is analogous to a thin, linearly 
elastic plate passing through each of the data values, 
with a minimum amount of bending. Minimum 
Curvature generates the smoothest possible surface 
779 
while attempting to honor your data as closely as 
possible. Minimum Curvature is not an exact 
interpolator, however. This means that your data are 
not always honored exactly. 
2.4 The Modified Shepard's Method 
The Modified Shepard's Method uses an inverse 
distance weighted least squares method. As such, 
Modified Shepard's Method is similar to the Inverse 
Distance to a Power interpolator, but the use of local 
least squares eliminates or reduces the "bull's-eye" 
appearance of the generated contours. Modified 
Shepard's Method can be either an exact or a 
smoothing interpolator. The Surfer algorithm 
implements Franke and Nielson's (1980) Modified 
Quadratic Shepard's Method with a full sector search 
as described in Renka (1988). 
2.5 The Natural Neighbor Method 
The Natural Neighbor method is quite popular in 
some fields. What is the Natural Neighbor 
interpolation? Consider a set of Thiessen polygons 
(the dual of a Delaunay triangulation). If a new point 
(target) were added to the data set, these Thiessen 
polygons would be modified. In fact, some of the 
polygons would shrink in size, while none would 
increase in size. The area associated with the target's 
Thiessen polygon that was taken from an existing 
polygon is called the "borrowed area." The Natural 
Neighbor interpolation algorithm uses a weighted 
average of the neighboring observations, where the 
weights are proportional to the "borrowed area". The 
Natural Neighbor method does not extrapolate 
contours beyond the convex hull of the data 
locations (i.e. the outline of the Thiessen polygons). 
2.6 1 he Nearest Neighbor Method 
The Nearest Neighbor method assigns the value of 
the nearest point to each grid node. This method is