Analysis of geological events

Abstract

Geological events, such as emplacement of granite or growth of slaty cleavage, may be ordered into a sequence by two methods. One is to assign each event a place in a time scale, such as years before the present, which amounts to assigning events an age designation from the set of real numbers. In ordering such a list, the algebra of real numbers applies. A second method is to determine the time relations of events in pairs, such as a fold is of type (S1, S2) or granite intrudes conglomerate. These binary relations between events may be used to order events into a sequence using the transitive properties of the relation “older than.” It is shown, however, that the binary relations between events do not follow the familiar rules for the algebra of real or integral numbers and it is necessary to erect a new system of relations called the “algebra of events.” The fundamental relation is “older than or equivalent to” and this may be used to define the relations “older than”, “younger than”, “equivalent to”, “incomparable to”, and “covers.” The essential difference from the algebra of integers is that the reflexive relation (“equal to”) is replaced by two such relations (“equivalent to” and “incomparable to”) in the algebra of events. A number of binary relations between events may be assembled into an event matrix which is basically a truth table for the relation “older than.” This may be ordered and stacked by operations termed ORDER and STACK. The relationship of each event to every other event may be determined by simple inspection of an ordered, stacked matrix, and from this a geological history may be assembled. If there are contradictions in the field data, ordering into a proper sequence is impossible and may be detected. If there are ambiguities in the field data, there are several different orders that are proper sequences so that the event matrix may be ordered. However, the ambiguities occur as voids in the stacked matrix.