ETL 1110-1-175
30 Jun 97
(1) Geostatistics, by the construction of a vari-
modeled as described in section 4-6. Lastly, the
ogram based on preliminary sampling, can be used
model is used to perform block kriging, as
described in section 2-4 for blocks of a size com-
to determine the typical separation of sampling
parable to the daily excavation area/volume. The
points that delineate uncorrelated data. The
block-kriged values can then be used for estimating
range of the variogram is used as a basis for selec-
the treatment plant loading, etc., related to that
ting a sample spacing that minimizes costs and
block. The kriging also quantifies the possible
provides independent data for determining, for
variance in the average concentration for each
example, average exposure values for risk assess-
block that can be used to manage the risk of
ment. First, an adequate number of preliminary
operating a treatment plant.
samples are analyzed from the site (refer to sec-
tion 4-3). Second, a variogram is constructed using
(3) Exposure concentrations for risk assess-
techniques described in Chapter 4. Third, the range
ment purposes can be computed, using geostatis-
of the variogram, as defined in section 2-3 is deter-
tics, even though the site characterization data are
mined. Lastly, the range or some multiple or frac-
somewhat clustered or were collected using biased
tion of it, is chosen for future sample spacing. The
sampling strategies. Assuming the data are
variogram should be updated as new data are col-
already available and adequate in number (refer to
lected. For example, the variogram may indicate
section 4-4), the first step is to compute a sample
data spaced more than 200 ft apart are uncorrelated.
variogram, as described in Chapter 4. Second, the
Closure sampling may then be proposed to be
variogram is modeled as described in section 4-6.
spaced every 200 ft or more along an excavation.
Next, this model is used in performing a block
Smaller spacing results in unnecessary duplication
kriging operation over the inferred exposure area,
of information and unneeded expenditure of funds.
as described in section 2-3. Finally, the block
kriging value can be used, along with the kriging
(2) Geostatistics, through block kriging, can
variance, to determine the exposure point con-
yield estimates of the average concentrations to be
centration, assuming the data were normally
encountered in a typical daily excavation area/
distributed (or were transformed to be normally
volume. For applications such as excavation of near
distributed).
surface contamination, two-dimensional block
kriging could be used to estimate mean contaminant
(4) The last example describes the use of geo-
concentration for specific excavation areas.
statistics to quantify project risk for excavation
Although this document does not address three-
dimensional block kriging for estimating mean con-
or treatment volumes. Even with ample site char-
centrations within given volumes, additional guid-
acterization point data (borings or wells), the limits
ance and tools for three-dimensional kriging are
of the treatment zone are imperfectly defined.
available through references cited in Appendix A.
Geostatistics allows one to evaluate the risk that
Alternatively, one can use two-dimensional block
the size, and therefore cost, of the remediation may
kriging to estimate mean concentrations in different
be larger or smaller than expected. First, site char-
layers within a given volume. These estimates can
acterization is performed and adequate data are
then be averaged to approximate the overall average
collected (as described in section 4-4). Second, the
concentration within the entire volume. This
data are transformed by assigning a value of one or
assumes adequate data exist to perform the two-
zero, depending on whether the value is above or
dimensional block kriging at the different depths.
below, respectively, a given clean-up value or
To perform two-dimensional block kriging, adequate
other criteria. Third, the transformed data are then
site characterization data are collected (refer to
used to construct a variogram as described in
section 4-4). Second, the data gathered from the
Chapter 4. Fourth, this variogram is modeled as
areas of interest are used to construct a variogram,
described in section 4-6. Next, this model is used
as described Chapter 4. Third, the variogram is
in performing indicator kriging as described in sec-
tion 2-6. The kriging estimates essentially reflect a
2
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