ETL 1110-1-175
30 Jun 97
Chapter 5
indicated in Chapter 3, both of these software
packages run on the DOS platform (Table 3-1),
Practical Aspects of Geostatistics in
which will probably be most convenient to readers.
Hazardous, Toxic, and Radioactive
The results of kriging estimates are portrayed by
Waste Site Investigations
gray-scale maps rather than by contours because
of the objective nature of the gray-scale format.
North is at the top of all maps presented in this
5-1. General
ETL, although this orientation may represent some
deviation from the real data.
a. In this chapter, several example applica-
tions are described. The applications have been
developed using hydrologic, geologic, and contami-
5-2. Water-Level Examples
nant data from established and well-studied haz-
ardous waste sites. The real nature of the data
a. The following examples are for ground-
permits discussion of some problems that can
water levels. The principal purpose of the exam-
occur during HTRW site investigations that stem
ples is to expose the reader to a kriging exercise
not only from natural field conditions, but also
using groundwater levels and to indicate how, in a
from typical problems that are associated with the
simple manner, kriging standard deviations may be
types of data involved. In addition, the real nature
useful to investigators interested in evaluating
of the example data provides an opportunity for
monitoring networks. The data come from a
comparison between kriging estimates and the real
water-table setting in unconsolidated sediments
data. In accordance with the purpose and scope of
where the local relief for the land surface is about
this ETL, these comparisons will be brief and
30 m. The data involved in this example are con-
general. This ETL does not provide the compre-
sidered virtually free of actual measurement error.
hensive analysis of data that is addressed by other
more elaborate studies.
b. The location of measured water levels is
shown in Figure 5-1a and the basic univariate
b. The principal intent of the examples is to
statistics for this data set are listed in Table 4-1;
provide systematic descriptions for a few of the
modifications to the measured data, in the form of
large number of possible types of applications that
addition and removal of measured values, are
investigators may use during HTRW site investi-
shown in Figures 5-1b and 5-1c. The techniques
gations. The examples are not intended to provide
described in Chapter 4 were used to guide the
guidance for comprehensive analysis of the
following steps for variogram construction:
included data. This ETL will, however, present
some fundamental problems that can occur in
(1) A raw variogram analysis, along with
geostatistical applications and, in some examples,
basic hydrologic knowledge of water-level behav-
indicate some possible alternatives.
ior, indicated that universal kriging would be
needed for this analysis.
c. With each example, a purpose will be
established and a general environmental setting
(2) To obtain a stable variogram of residuals,
will be given. Most aspects of variogram con-
an iterative, generalized least-squares operation
struction and calibration will be briefly described
was initially used to remove prominent linear drift
and illustrated graphically and in tabular form. A
of the form a + bu + cv, observed in the measured
comprehensive treatment of variogram construc-
water levels.
tion has been presented in Chapter 4.
(3) After drift was removed, residuals were
d. GEO-EAS software has been used when-
determined to be stationary and universal kriging
ever the example data did not need universal krig-
with a linear drift was appropriate.
ing; for those examples, STATPAC was used. As
5-1
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