ETL 1110-1-175
30 Jun 97
Chapter 1
such as kriging, lies not just in the point and block
estimates they provide, but in the information they
Introduction
provide concerning uncertainty associated with
these estimates. The uncertainty information is
usually quantified as either the standard deviation
1-1. General
(or variance) associated with kriging estimates and
is referred to as kriging standard deviation (or
a. This Engineer Technical Letter (ETL)
kriging variance) in this ETL.
addresses the use of geostatistics at hazardous,
toxic, and radioactive waste (HTRW) sites. One
c. Original geostatistical work involved
very fundamental aspect of perhaps all HTRW site
making estimates for the areal extent and concen-
investigations that deal with environmental con-
trations of economic mineral deposits, in relation to
tamination is the need to characterize the extent
mining. Today (1996), geostatistical techniques
and spatial distribution of contamination. Such a
continue to have a function in mining. However, a
characterization typically would include describ-
well-developed methodology that is capable of
ing, using a variety of statistical or analytical tools,
interpolating a given set of measured values at dis-
spatial trends and variability. A principal diffi-
crete locations into estimates for new locations or
culty in doing this is the fact that measurements
developing an individual estimate for an area
may be few, or may be sparsely scattered over
including many locations, or both, has attracted
large regions. A question that arises naturally in
users from many disciplines, and there is a trend
this situation is how one might interpolate in order
toward incorporating geostatistics as standard cur-
to make predictions (or estimates) at points where
riculum for most geo-science educational pro-
measurements of contaminant concentration are
grams. The use of geostatistical techniques as part
not available. Such interpolation will be referred
of HTRW site investigations is becoming common
to as point, or punctual, estimation in this ETL.
because of the almost routine need for data inter-
Additionally, an investigator may need to deter-
polation as part of these investigations.
mine a single representative value for an area that
is represented by several measured or estimated
d. Once investigators have established that
values or both; this will be referred to in this ETL
their data are adequate as to quality and quantity,
as block estimation. Geostatistics is a set of sta-
geostatistics can provide powerful analytical tools
tistical procedures designed to accomplish these
that result in quantitative characterization of areas
ends. Geostatistics may be applied to many prob-
of special interest within the study area or the
lems, other than contamination, that occur at
entire study area. These characterizations may
HTRW sites. Even though this document addres-
address spatial variation; for example, it may be
ses only twodimensional applications, geostatistics
determined where values for concentrations of
can be used in three dimensions as well. Indeed,
contaminants in soils are relatively high or low, are
there are many cases in which the third dimension,
less than or greater than a specified value, or even
usually stratification, is desirable to address.
have a high or low probability of exceeding a
certain value.
b. Kriging is the principal geostatistical meth-
odology described in this ETL. For introductory
purposes kriging can be defined as a technique for
1-2. Scope
determining the optimal weighting of measure-
ments at sampled locations for obtaining predic-
a. The scope of this ETL will be limited
tions, or estimates, at unsampled locations;
principally to discussions and examples of two-
additional definition of kriging is provided through-
dimensional point and block estimations using a
out this document. Kriging is well-suited for mak-
geostatistical method known as kriging. The ETL
ing point and block estimates. However, much of
will present the technical aspects of geostatistics
the advantage of using geostatistical procedures,
1-1
Previous Page
