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It was concluded that during coal mining, prospects for predicting sulphur
content in coal were excellent over shorter distances (up to 2,000 ft.). This recom-
mendation was accepted by DEVCO for routine planning of actual mining opera-
tions. On the other hand, prediction over longer distances from sulphur content of
mined-out areas remained speculative. No detailed hindsight studies have been
undertaken to evaluate the validity of the patterns based on Models 1 and
2 (Figs.
7.19
and
7.20
). However, from generalized production records and rela-
tively few later offshore bore-holes (Hacquebard
2002
), it can be concluded that
Model 2 worked better than Model 1, because there turned out to exist general
decline in sulphur content of the Harbour seam in the northeastern direction.
7.3 Logistic Trend Surface Analysis of Discrete Data
Previous applications of trend analysis can be regarded as applications of the general
linear model of least squares. The term “linear” in this context applies to the
coefficients
b
pq
which only occur in linear form in the polynomial equation. In
several applications (Whalesback and Lingan Mine case history studies), the general
linear model was applied to logarithmically transformed element concentration
values. Corrections had to be applied to eliminate bias arising when the fitted surfaces
were recomputed to apply to original concentration values. Further modifications of
the general linear model were used in the universal kriging applications to top of
Arbuckle Formation, base of Matinenda Formation, and sulphur in Lingan Mine coal.
One advantage of the general linear model is its simplicity in that a final solution is
obtained by matrix inversion. It is more cumbersome to obtain solutions for nonlinear
functions of the coefficients because then an iterative process with many inversions
may have to be used. An example is provided by logistic trend surface analysis.
bilities of the occurrence of a discrete event. For trend surface analysis, the logistic
model can be written in the form
Su
1
1
þe
Tu;ðÞ
where
T
(
u
,
v
) is as in our previous
applications of trend surface analysis. Although
T
(
u
,
v
) can assume any real value
depending on location and the values of the coefficients,
S
(
u
,
v
) only can assume
values in the interval between 0 and 1. It cannot be negative or greater than 1 and, for
this reason, can be used to represent the probability of occurrence of a discrete event.
Figure
7.25
shows the Island of Newfoundland subdivided into square cells
measuring 10 km on a side. Cells known to contain one or more massive sulphide
deposits are shown in black. Occurrence of massive sulphide deposits in a cell is an
event for which the probability of occurrence can be estimated. In Fig.
7.25
, the
results of two methods of trend surface analysis are shown. In both situations, the
column vector Y of observed values consisted of elements equal to 1 for the 21 cells
with deposits and elements equal to 0 for the 1,388 cells with deposits. First,
T
(
u
,
v
)
was fitted directly to the data for the second degree (
r
ðÞ¼
;
v
¼
2). The result is shown in
Fig.
7.25
(left side). Next
S
(
u
,
v
) was fitted with
T
(
u
,
v
) for the second degree
(Fig.
7.25
, right side). In some situations, the general linear model of least squares
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