The examination of method to describe mathematically geological information observed at ou tcrops is necessary to construct outcrops database. For the purpose, we propose the structure graph and the stratigraphic graph by using the graph theory and the binary relation, and examine their theoretical background. We suppose that the geological structures have no upturned layers, and that there are no cuttings by fault and no penetrations of igneous rocks. The outcrop structure as the contact relations among beds can be expressed in the terms of binary relation xRy which means two beds x and y contact each other and y overlain x. This relation is expressed as a labeled directed graph G = (V, R), where V is a set of beds observed at an outcrop. We call this graph the structure graph. The stratigraphic sequence is the sedimentary order of beds, and this sequence is expressed in terms of binary relation xU^*y, which means x is older than y.Symbol U^* is a reflexive and transitive closure of the binary relation xRy, and the graph S = (V, U^* ) is called a strtigraphic graph. By this technique, we can make clear difference between outcrop structure and outcrop stratigraphic sequence mathematically. The stratigraphic sequence observed at an outcrop is a partial ordering and it may not necessarily be total ordering. The work to construct the local stratigrphic sequence of a certain area from structure observed at plural outcrops is formulated as the operation of the outcrop stratigraphic graphs. Thus we can mathematically express the geological structure and the stratigraphic sequence.

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Clarification of groundwater system over wide horizontal and depth ranges is indispensable to the management and maintenance of the amount and quality of groundwater resource. Electromagnetic surveys are suitable to this clarification because of their capability of detecting deep geologic structures. This study proposes a spatial modeling of resistivity by a joint inversion of MT and AMT surveys data and a 3D interpolation method Kumamoto plain covering 35 km ×32 km, which is well-known as being rich in groundwater resource, is selected as a case study. Resultant 3D resistivity model elucidates that the shallow and deep groundwater flows are similar. In addition, a hydrogeologic model of the study is constructed as the shallow groundwater system including the first and second aquifers (0 to 500 m depth range), the shallow hydrogeologic basement rocks consisting chiefly of pre-Aso volcanic rocks (500 to 1500 m depth range), the deep groundwater system containing a large aquifer composed of the Cretaceous sandstone, Mifune formation (2000 to 3500 m depth range), and the Higo metamorphic rocks forming the deep hydrogeologic basement at the bottom.

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[in Japanese]

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