237 
coincident observation. This is an exact interpolator. 
The power parameter determines how quickly weights 
fall off with distance from the grid node. As the power 
parameter approaches zero, the generated surface 
approaches a horizontal planar surface through the 
average of all observations from the data file. As the 
power parameter increases, the generated surface is a 
"nearest neighbor" interpolator and the resultant surface 
becomes polygonal. The polygons represent the nearest 
observation to the interpolated grid node. 
One of the characteristics of I.D. is the generation of 
"bull's-eyes" surrounding the position of observations 
within the gridded area. It is possible to assign a 
smoothing parameter during inverse distance gridding, 
which causes their reduction. 
2. Kriging (KR.) 
It is a geostatistical gridding method that produces 
visually appealing contour and surface plots from 
irregularly spaced data. KR. attempts to express trends 
that are suggested in the data so that, for example, high 
points might be connected along a ridge, rather than 
isolated by bull's-eye type contours. 
3. Minimum Curvature (M.C.) 
The interpolated surface generated by M.C. is analogous 
to a thin, linearly-elastic plate passing through each of the 
data values with a minimum amount of bending. It 
generates the smoothest possible surface while attempting 
to honour data as closely as possible. M.C. is not an exact 
interpolator however; this means that the residuals are not 
always small. 
4. Nearest Neighbor (N.N.) 
The N.N. gridding method assigns the value of the 
nearest datum point to each grid node. This method is 
useful when data is already on a grid, but needs to be 
converted to a Surfer grid file. Or, in cases where the data 
is nearly on a grid with only a few missing values, this 
method is effective for filling in the holes in the data. 
5. Polynomial Regression (P.R.) 
P.R. is used to define large-scale trends and patterns in 
the data. It is not really an interpolator because it does not 
attempt to predict unknown Z values. 
It is possible to select the different types of polynomials, 
among the following ones: simple planar surface, bi 
linear saddle, quadratic or cubic surface. 
It is a very fast method for any amount of data, but local 
details in the data are lost in the generated grid. 
6. Radial Basis Functions (R.B. F.) 
Radial Basis Functions are a diverse group of data 
interpolation methods. All of the R.B.F. methods are 
exact interpolators. It is possible to introduce a smoothing 
factor to all the methods in an attempt to produce a 
smoother surface and to specify some functions in order 
to define the optimal set of weights to apply to the data 
points when interpolating a grid node. 
7. Shepard's Method (SH.) 
This method uses an inverse distance weighted least 
squares method. As such it is similar to the I.D. to a 
power interpolator but the use of local least squares 
eliminates or reduces the "bull’s eye" appearance of the 
generated contours. SH.’s method can be either an exact 
or a smoothing interpolator. 
8. Triangulation with Linear Interpolation (TR.) 
It is an exact interpolator. The method works by creating 
triangles by drawing lines between data points. The 
original data points are connected in such a way that no 
triangle edges are intersected by other triangles. The 
result is a patchwork of triangular faces over the extent of 
the grid. 
Each triangle defines a plane over the grid nodes lying 
within the triangle, with the tilt and elevation of the 
triangle determined by the three original data points 
defining the triangle. All grid nodes within a given 
triangle are defined by the triangular surface. Because the 
original data points are used to define the triangles, data 
set is honoured very closely and the residuals are small. 
TR. works best when data points are evenly distributed 
over the grid area. Data sets that contain sparse areas 
result in distinct triangular facets on a surface plot or 
contour map. TR. is very effective at preserving break 
lines. 
3. DEMS INTERPOLATION 
Using the set of data obtained from the survey on the 
ground many tests of interpolation have been carried out 
with the purpose to choose those more reliable for the 
elaboration of the DEM. 
The faithfulness of the interpolated DEMs has been 
evaluated through two criteria: 
- a “statistical” criteria 
a criteria based on the “visual analysis” 
The values minimum and maximum of the residuals and 
theirs statistic parameters, i.e. the average and the 
standard deviation, have been calculated and appraised. 
Contour line maps have been outlined to verify adherence 
of the graph to the real morphology of the ground and to 
locate, within the interpolated zone, possible zones with 
anomalous characteristic elements. 
For the experimentation a computer compatible IBM 
from the following characteristics has been used: Intel 
Pentium III 450 MHz processor; 128 MB RAM. 
The first series of interpolations has been carried out with 
all the methods foreseen from the software SURFER. For 
all methods the options of default have been set, sort 
exception for the method P.R. for which as default is 
defined the plain, while a polynomial function of degree 
10 has been chosen. 
A rectangular area that includes the surveyed zone has 
been considered and the chosen grid step has always been 
equal to 2 m. 
In the table 1 the residuals and their statistic parameters 
for the three landslides are summarised, together with the 
number of sampled points and the number of points with 
residuals calculated. 
Possible difference between the two values points out the 
number of knots of the grid in correspondence of which 
some value of height has not been calculated, because of 
the lack located of an enough number of points furnished 
in input. The elaboration time for the creation of the 
DEM is also reported.