ETL 1110-1-175
30 Jun 97
Chapter 6
separate and brief discussion of measurement
errors will also be presented in this section.
Review of Kriging Applications
c. Many investigators will have a tendency to
focus on the amount of measured data that is avail-
This chapter will briefly treat three principal top-
able as an initial consideration. It is important for
ics; applicability of kriging techniques, important
the investigator to realize that decisions concerning
elements that need to be addressed in kriging appli-
the applicability of kriging techniques cannot be
cations, and errors in measured data. Much of the
based simply on the amount of measured data.
information presented in this section has been
However, unless the investigator is presented with
gathered from other sections of this ETL and is
a reliable variogram, the amount and spatial distri-
presented collectively here. The items identified as
bution of measured data can be a constraint. If,
important to kriging applications may be helpful in
for instance, the investigator has fewer than 25
assessing kriging applications under review.
measured values at optimal locations from the
field, there may not be enough data to confidently
estimate Gaussian variogram parameters, a smaller
6-1. Applicability of Kriging
amount of measured data may be suitable for other
variogram models.
a. In the preceding sections of this ETL, the
theory of kriging techniques has been summarized,
d. The amount of data needed to apply krig-
and examples have been given to indicate the util-
ing techniques is not easy to determine, but infor-
ity of kriging techniques in HTRW site investiga-
mation in this ETL, especially in Chapter 4, and
tions. The examples presented were selected so
the literature cited can provide some guidance.
that kriging would provide satisfactory results or
Section 4-4 points out that a good minimum for the
be applicable. Additionally, the examples were
number of pairs of locations in each variogram lag
designed so that, for the purposes of demonstra-
is 30 and the American Society for Testing and
tion, some sort of adjustment of the data was
Materials (Standard D 5922-96) has suggested that
needed; that is, drift was removed or transforma-
20 may work well also. Most investigators would
tions were made.
probably feel comfortable defining a Gaussian
form (which, because it has more inflection, is
b. Investigators are very likely to have data
more difficult to fit compared to the other standard
for which, although, in a strict sense, kriging may
variogram models) with 8 to 10 optimally located
be applicable, results may be unsatisfactory. A
sample variogram points (enough points to define
good deal of fundamental information that may be
the nugget, two areas of curvature, and the sill). In
used to establish how satisfactory application of
this ideal case, about 25 measured values would be
kriging techniques might be has been presented in
needed to fulfill the conservative minimum of
the preceding sections of this ETL. In particular,
30 pairs per lag. In this case, the relatively few
Chapter 4 includes a detailed discussion on vario-
measured data points need to be systematically
gram construction, the preliminary step in any
located so that the optimally located variogram
kriging application, and systematically describes
points can be computed. If the measured data were
many decisions in this process that need attention.
not located systematically, as is usually the case,
If the investigator cannot construct or otherwise
then more measured data would be needed.
obtain a variogram that has structure, then the
results of a kriging application may not be satis-
e. Once sample variogram points meeting the
factory. Some additional discussion designed to
required number of pairs of locations can be
guide investigators in evaluating the amount of
defined, the investigator needs to have a resulting
data that may be required for kriging applications
variogram that has structure. The variogram, for
is presented in this section. This discussion will
instance, may simply exhibit noise about a
assume that the measured data are correct; a
6-1
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