(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

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**

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-

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