Mathematical Basis for Classification of Sedimentary Layers under the Law of Superposition

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  • SHIONO Kiyoji
    Department of Geosciences, Faculty of Science, Osaka City University

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  • 地層累重の法則を保存する層序区分の数学的基礎
  • チソウ ルイジュウ ノ ホウソク オ ホゾン スル ソウジョ クブン ノ スウガクテキ キソ

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Description

Classification of stratigraphic units in a 3D region Ω defines a partition of Ω such that each block represents the spatial distribution of a stratigraphic unit. LetOandAbe partitions corresponding to two stratigraphic classifications. If there exists a relation betweenOandAsuch thatOis a refinement of A, it is expected that some fundamental characteristics of sedimentary layers are preserved fromOtoA. What types of characteristics are preserved from an original classificationOto a new oneAcomposed of larger blocks, and what conditions are required ? In order to answer the question, the Law of Superposition is discussed as one of the most fundamental nature of sedimentary layers. The Law is formulated in terms of an inference rule; if it is observed at one outcrop that a unit xis lower than another unity, thenxis older thany. Then it is proved that the Law is preserved fromOtoAif and only ifAis generated fromOunder the condition that for everyxandyin O, ifxis lower thany, then f(x) is older thanf(y) , wheref(x) andf(y) represent blocks inAincluding xandyrespectively. Finally it is concluded that the Law of Superposition holds true throughout a sequence of classificationO, A1, A2, ..., AmifA1is generated from O, A2fromA1, ..., Am-1fromAmunder the condition mentioned above. The present study provides an important clue to establish a mathematical basis of geology in a formal system.

Journal

  • Geoinformatics

    Geoinformatics 10 (4), 213-223, 1999

    Japan Society of Geoinformatics

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