The properties of the transition frequency matrix can be expressed in a more generally comparable from by conversion to probabilities.
If there are 10 transitions from shale to something ( 10 will be the row total ), and there are three transitions from shale to limestone, the conditional probability of the next bed being limestone if we start from shale is 3/10 = 0.3; using thr notation introduced in Section 2.3.4:
Pr(limestone/shale)=0.3
The transition probability matrix is simply calculated by dividing each element in the transition frequency matrix by its row total.
The properties of this matrix can be shown by using a type of tree diagram, where we lay out the lithological succession. If there is any significant pattern in the transitions, this diagram is used to facilitate geological interpretation: the most likely cycle or rhythm becomes apparent. The probability that a series of, say, four transitions will match a specified cycle is readily calculated by multiplying the four probabilities.