Abstract
The stratigraphical formula expresses the contact relation of the two layers with the form (a lower layer unit)(a relation unit)(an upper layer unit),however, this formula does not express the case that one layer contact many layers. The stratigraphical graph expresses the geological structure of an outcrop, but this graph can not express as formula. The new symbol parentheses are defined as follows:
(L1##1L2##2···##n-2Lm-1)##n-1Ln ⇔ L1##n-1Ln, L2##n-1Ln, ···, Ln-1##n-1Ln, L1##1L2##2···##n-2Lm-1
L1##1 (L2##2L3···Ln-1##n-1Lm) ⇔ L1##1L2, L1##1L3, …, L1##1Lm, L2##2L3···Ln-1##n-1Lm
{(L1##1L2##2L3···##n-3Ln-2)##n-2Ln-1}##n-1Ln ⇔ {L1##1L2##2L3···##n-3Ln-2, L1##n-2Ln-1, L2##n-2Ln-1,···,Ln-3##n-2Ln-1}##n-1Ln ⇔ (L1##1L2##2L3···##n-3Ln-2) ##n-1Ln, (L1##n-2Ln-1) ##n-1Ln, (L2##n-2Ln-1) ##n-1Ln, ···, (Ln##n-2Ln-1) ##n-1Ln
L1##1 [L2##2L3···##n-2Ln-1 ] ##n-1Ln ⇔ L1##1L2##2L3···##n-2Ln-1, L2##n-1Ln, L3##n-1Ln, ···, Lm-1##n-1Ln ⇔ L1##1L2##2L3···##n-2Ln-1##n-1Ln,
L2##n-1Ln, ‚k3##n-1Ln, ···, Ln-2##n-2Ln L1##1(L2##2L3···##n-2Ln-1 ##n-1Ln ⇔ L2##2L3···##n-2Ln-1##n-1Ln,
L1##1L2, L1##1L3, ···, L1##1Ln-1 ⇔ L1##1L2##2L3···##n-2Ln-1##n-1Ln, L1##1L3, ···, L1##1Ln-1
Li is the symbol of the layer i, ##i is the symbol of the relation unit. With the formula including parentheses, we are able to express uniformly the structure that one layer contacts many layers.
The stratigraphical graph is represented by the structure matrix A=[aij]. An element of the matrix aij is the symbol of the contact relation between Li and Lj for the case that the lower layer Li and the upper layer Lj is contact directly, and aij is "0" for the other cases. We are able to construct the structure matrix C[cij] which represents the regional geological structure with the operation C[cij]=A[aij]∗[bij] using outcrop structure matrix A[aij] and B[bij]. The author propose the algorithm of this operation.
