Test of independence by repeated matching of stratigraphic sections

Two stratigraphic sections of unequal length and uncertain relative position are usually tested for nonrandom similarities by calculating the coefficient of cross-association, using several of their possible mutual alignments. A rigorous statistical test of independence between the two sections is derived, utilizing results of such a procedure. Proper distinction is made between sections consisting of a record of lithological strata (consecutive repetition of the same rock type is allowed),and the situation when adjacent identical strata are merged into an lithological unit (a record of these must contain no contiguous replicates).The presented theory is first developed under assumption of prior knowledge of the exact probabilities of possible rock types, but is extended to accommodate the case of these being unavailable.