Optimal systems of geoscience surveying–A preliminary discussion☆
Introduction
Geoscience exploration or survey is not a purpose by itself. Exploration is carried out to discover a new deposit of mineral or energy resources. Geological, geochemical and geophysical survey including remote sensing are carried out to get information necessary to any kind of decision in mineral and energy exploration, resource assessment, environmental assessment, site selection in construction, and so on. Various kinds of survey and exploration techniques have been developed. In order to attain the purpose of survey and exploration, each technique should be effectively applied, and also many techniques should be optimally combined.
Let us consider mineral exploration as an example to understand how the exploration is limited for attaining the purpose. Based on geoinformation obtained using mineral exploration techniques, a target area will be classified into two groups: i.e. mineralized or barren area. A result of such classification must be always modified by either the word “truly” or the words “by estimation” (Shoji, 1995). Therefore, the classification makes four possible categories (Table 1): TM-EM (truly mineralized and ‘by estimation’ mineralized), TM-EB (truly mineralized but ‘by estimation’ barren), TB-EM (truly barren but ‘by estimation’ mineralized), and TB-EB (truly barren and ‘by estimation’ barren). If numbers of areas belonging to Categories TM-EB and TB-EM are few in classification based on an exploration technique, then the technique is concluded to be effective. In an actual exploration, only the areas that are estimated to be mineralized are surveyed. We cannot classify consequently Categories TM-EB and TB-EB: i.e. the boundary between both categories is unknown. We will not be able to find sometimes any mineral deposit in an area belonging to Category TM-EM because of insufficient survey. This means that we cannot also exactly classify Categories TM-EM and TB-EM: i.e. the TM is always narrow compared with the completely clear case. It is very difficult, therefore, to know whether a technique is effective or not.
Generally, a budget in each step of survey and exploration is fixed. Simply speaking, a survey/exploration expense is product of surveyed area and unit cost (Fig. 1). Therefore, if we can reduce cost in each step without decreasing accuracy, the probability for finding a new mineral deposit surely increases, because area becomes wide (▵A in Fig. 1). An exploration program consists of many steps in each of which geoscience data are obtained and processed, and accordingly the target area is evaluated for the next step. It is very important, therefore, to optimize an exploration system as a function of expense.
In another view of point, what is the most important for survey and exploration? Many kinds of information, often geoinformation with geometric coordinates, are obtained in not only geoscience such as geology, geography, geochemistry and geophysics, but also other fields such as environmental sciences, cultural anthropology, and civil engineering. It usually involves four types of processes in dealing with the geoinformation, for example, (1) getting information, (2) storing information (data base), (3) processing information, and (4) displaying processed results. This flow of processes can be compared with that of cookery (Table 2): getting information is as baying foods, data base as refrigerator, processing information as cooking materials, and displaying processed results is dishing up. It can be seen that the most important step is getting information which determines the quality of the food materials.
Section snippets
Prize–penalty function representing purpose of getting information
Science always tries to obtain necessary data objectively. For example, statistics requires obtaining data randomly to avoid subjects of data collectors. In geological survey, an outcrop is described by not only letters but also pictures or sketches in order to guarantee objective description. A researcher, who considers strictly that pictures are not sufficient for objective description, may bring the outcrop itself, and want to paste it on his paper. Such kind of description is nonsense,
An application of prize–penalty function
Each element of a penalty matrix represents a degree of demerit of corresponding misidentification. On the other hand, the penalty coefficient represents the weighting ratio of the most demeritorious misidentification to a correct identification (Shoji and Nishioka, 1993). A value of the penalty coefficient corresponds to an amount of refund, when the identification is wrong. For instance, when the reply by a consultant is wrong, the amount of his refund to his sponsor is the same as a unit
Information-cost function
An information-cost function has been proposed for evaluation of alternative combinations of survey techniques (Shoji and Kouda, 1989). This function relates information obtained to money spent. Information in this case relates to both quality and quantity, and is assumed to be able to be evaluated. Information is clearly zero when money spent is zero. For a given technique the quality and/or quantity of information increases linearly, often very quickly, with increasing expense when
Evaluation of information by entropy
In order to combine optimally many techniques of survey using information-cost function, we have to evaluate quality or quantity of information. In this section, let us try to evaluate geoinformation based on entropy (Shoji, 1995, Shoji, 1997, Shoji, 2003).
Let us assume that a target area consists of N (=A/a) cells, where A is area of the target, and a is area of a cell. When we know whether each cell is mineralized or barren, mineralization probability of each cell is 1 or 0, respectively.
Resolution and cell entropy
The next topic is to know the relationship between the resolution of survey techniques and cell entropy (Shoji, 1997, Shoji, 2003). Let us discuss this on the basis of the relation between survey techniques and resolving powers. In the following statement, resolution power R of a technique means that we can divide a target area into R blocks using the technique. In other words, if area of a target is A, the resolvability (the smallest area to recognize close objects separately) of the applied
Conclusions
In order to optimize geoscience survey, some concepts have been proposed and discussed on the bases of getting necessary and sufficient information effectively and optimally depending on a purpose of the survey.
- (1)
A prize–penalty function defined by Eq. (1) represents quantitatively a purpose of survey giving values of prize, penalty coefficient, and matrix of penalty, and hence can suggest the best technique fitting the purpose.
- (2)
If obtained geoinformation can be evaluated, information-cost
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Partly presented at a lecture at The University of Tokyo on February 23, 2004.