Geoinformatics

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Grouping of strata is one of the most fundamental works in geological studies. The grouping is mathematically formulated as the work to define an equivalence relation D on a set of strata B. The equivalence relation D constructs a quotient set B/D, and each group of strata corresponds to an equivalence class relative to the equivalence relation D. The grouping of strata introduces the problem how we should define relations on B/D from relations given on the original set B. As a logical approach to such a problem, this paper discusses how to define the time relation K′ on a quotient set B/D, based on Shiono and Wadatsumi (1991) 's formulation of a relation K on set B of strata such that aKb if and only if a stratum a is older than a stratum b. It is concluded that the relation K′ on B/D can be derived from the relation K given on B in such a manner that [a] K′ [b] if and only if xKy for every x ∈ [a] and y ∈ [b], where [a] and [b] are any equivalence classes in B/D, and then the relation K′∪E′ on B/D is also a partial ordering if the relation K∪E is a partial ordering.

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A commercial medical X-ray Computerized Tomography (CT) scanner has been successfully applied to analyze the internal structure of geological specimens such as unconsolidated lake sediments, specimens before and after the physical tests.
CT images are originally reconstructed as digital data. In the case of medical diagnosis, however, the CT images have been usually printed out on X-ray films with a grey scale. Output on the X-ray films has raised the difficulty of quantitative analysis of the images.
Therefore, we have developed an digital image processing system which transfer the CT images from the medical scanner to a personal computer with MS-DOS format, and which can display the detailed structure in the specimens with a pseudocolor image. Further, processed CT images provide the quantitative information which can be used to analyze numerically the geological settings of specimens.

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