The Engel Simulator and the Search for Uranium

"One of the most useful approaches to a complex problem is to model the system which gives rise to the problem and to perform simulations through the model to find appropriate solutions. The Engel Model may be used as such a simulator to investigate the problem of the exploration for natural resources.The Engel Model is based on a two-stage search procedure in which a known area (A) which contains m prizes is subjected to search by n coverings. During the first-stage search the sensor system records signals which may be a response from prizes (that is, true signals) or may be false. Signals tend to cluster around a prize and a cluster size consists of s signals. If a circle of radius R is drawn around each signal some will overlap and the overlap from s signals contains a prize. The cost of a single covering in which each point of the area comes under observation once, is designated E1. Second-stage detailed search is expensive and is confined to areas of overlap of s circles; it leads to the location of prizes. Second-stage search of the whole area costs Ea units. The expected value, V, of a prize is known and its development cost is E3 units.The sensor system characteristics are defined by the circle of radius R around a signal, which should be small compared with the total area A and enters the model as a parameter a x R2/A. The probability of a false signal during a single covering of a circle of radius I is a known constant, A.This model was applied to the search for uranium ore bodies using two different types of occurrence. In the first, the Wyoming Basin type, the area is relatively large (A = 1 496 square miles) and a few (m = 4) large prizes occur (expected value V = $30 million). In the second area, which represents the Ambrosia Lake region of New Mexico, the area is smaller (A = 212 square miles) and contains many (m = 200) smaller prizes (expectedvalue of a prize V,$2 million). The three costs, E1, E2, E3, are adjusted to the different circumstances in the two areas.Simulations were performed using n = 1 to 40 coverings with cluster sizes s = 0 to 19; the radius R was varied from 0.52 to 3 miles (and, therefore, a = 0.002 to 0.133 0, respectively, dependent on the area of interest). The value of A was varied from 0.01 to 0.10.Profitable programs were found over a wide range of the parameters; the two areas required different strategies to achieve maximum profit. In the Ambrosia Lake region a few passes (n = 4 to 6) with small cluster sizes (s = 2 to 6) are more profitable, whereas in the Wyoming Basin region a large number of passes (n = 35 to 40) and cluster sizes of s = 5 to 10 are most profitable.As pointed out by Allais (1957) the larger prizes are the most important in deciding the successful outcomes of exploration programs, and the profit margin in the search for a few large prizes is sufficient to yield success over a wide range of programs. Such programs require very large investments if they are to be successful.To refine the Engel Simulator as a decision-maker in selecting the most profitable exploration programs it is necessary to obtain firm estimates of the sensor system characteristics, that is, of R, a and ? (lambda)."