Geoscience Reference
In-Depth Information
It is perhaps due to these dii culties that
triangulation
is ot en used as
an alternative method for selecting the control points (Fig. 7.5 b). In this
technique, all control points are connected in a triangular network. Every
grid point is located within the triangular area formed by three control points.
h e
z
-value of the grid point is computed from the
z
-values of the three grid
points. A modii cation of this form of gridding also uses the three points
at the apices of the three adjoining triangles. h e
Delauney triangulation
method uses a triangular net in which the acuteness of the triangles is
minimized, i.e., the triangles are as close as possible to equilateral.
Kriging
, introduced in Section 7.11, is an alternative approach to select
control points. It is ot en regarded as the ultimate method of gridding. Some
people even use the term
geostatistics
synonymously with kriging. Kriging is
a method for quantifying the spatial autocorrelation and hence the circle's
dimension. More sophisticated versions of kriging use an elliptical area
instead of a circle.
As mentioned above, the second step in surface estimation is the actual
computation of the
z
-values for the grid points. h e
arithmetic mean
of the
measured
z
-values at the control points
provides the easiest way of computing the values at the grid points. h is is
a particularly useful method if there are only a limited number of control
points. If the study area is well covered by control points and the distance
between these points is highly variable, the
z
-values of the grid points should
be computed using a
weighted mean
. h is involves weighting the
z
-values at
the control points by the inverse of the distance
d
i
from the grid points.
Depending on the spatial scaling relationship of the variable
z
, the inverse of
the square root of the distance may be used to weight the
z
-values, rather than
simply the inverse of distance. h e i tting of 3D
splines
to the control points
of ers another method for computing the grid point values that is commonly
used in the earth sciences. Most routines used in surface estimation involve
cubic polynomial splines
, i.e., a third-degree 3D polynomial is i tted to at
