Page 125 - Statistics and Data Analysis in Geology

Statistics and Data Analysis in Geology- Chapter 5

search in the pattern of a square grid, the equation simplifies to

Lambie (unpublished report, 1981) has pointed out that these equations for
geometric probability are approximations of integral equations. Comparing exact
probabilities found by numerical integration with those predicted by the approxi-
mation equations, he found that significant differences occur only for very elongate
targets that are large with respect to spacing between search lines. Then, equations
such as (5.3) and (5.6) may seriously overestimate the probabilities of detection.
The probabilities of intersecting a target, as calculated by the approximating
equations, can be shown conveniently as graphs. McCammon (1977) presented such
graphs in a particularly useful dimensionless form for various combinations of tar-
get shape and size relative to the spacing between the search lines. Figure 5-2a
gives the probability of detecting an elliptical target whose shape ranges from a
circle to a line, using a search pattern of parallel lines. The relative size of the
target is found by dividing the target's maximum dimension by the search line

Figure 5-3. Probability of intersecting targets with regular search patterns ranging from
squares to parallel lines. Rectangular search patterns with different ratios of D1 /D2
fall in the shaded region. Horizontal axis is ratio fmaior dimension of targetl/fmini-
mum spacing betwe& search lines). (a) Target is'cir&lar, (b) Target is a"li<e.'After
McCammon (1977).