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###### The Probability of Magnetic or Electromagnetic Detection of a 55-gallon Drum as a Function of Line and Station Spacing

Publisher –
Environmental and Engineering Geophysical Society (EEGS), 1996 Symposium on the Application of Geophysics to Engineering and Environmental Problems (SAGEEP) proceedings.

Authors –
David Butler, MicroGeophysics Corp., Wheat Ridge, Colorado, U.S.A.

###### Abstract
A simplified elliptical footprint of a 55-gallon drum for electromagnetic and magnetic detection as a function of depth is defined. The signal-to-noise ratio for field measurements is used to scale this ellipse. For a given ellipse, the probability of detection at various line and station spacings is calculated. Representative numbers indicate that with a line spacing equal to the major axis of the ellipse and a station spacing equal to the minor axis, the probability of detection of a 1:2 (minor: major axis) ellipse by at least one station is 0.66,
but only 0.12 for the recording of two anomalous values. Compound probability enters the problem if more than one target is present. If location rather than detection is the goal, more that one anomalous station is required. If the number of stations is proportional to cost, location or characterization will certainly increase the costs. This paper provides information to disqualify specifications tendered by procurement departments who often request badly aliased surveys.
###### Introduction
This paper offers one practical solution to the problem of survey design-i.e. the selection of line and station spacing given a hypothetical target. The near-infinite number of variants of the problem are indicated, but not solved. Some, but not all, of the philosophical questions are explored. The first section indicates the solution to a simple problem which illustrates the probability technique. The mathematical problem for ellipse detection is then formulated the solution typically includes the numerical evaluation of an elliptic integral.
The practical aspects of application of this solution are then explored. Detection, location and characterization vs. signal-to-noise are the topics of discussion in this section. The Results section gives a few, practical numbers from the application of this methodology. A discussion section then discusses some of the numerous philosophical questions innate in this analysis. The concluding section asks more questions than it answers, including those of cost-effectiveness, strategies, and areas of additional required work.