### Interpretacja matematyczna następstwa osadów sylurskich w profilu Kościerzyny

#### Abstract

MATHEMATICAL INTERPRETATION OF THE SEQUENCE IN THE SILURIAN SEDIMENTS OF KOŚCIERZYNA (NORTHERN POLAND)

Summary

The thickness of the Silurian sediments encountered in the Kościerzyna IG-l borehole is 2 300 m, of which the shale-siltstone complex makes up 1 555 m. This complex occurs in the Lower Ludlovian and in the lower portion of the Upper Ludlovian. The siltstone beds were deposited by turbidity currents. Four facies have been distinguished in the shale-siltstone complex: siltstone, shale, shale-siltstone, and siltstone-shale. It has been assumed that the generating process of the sequence studied was a first-order Markov process. The deterministic component included in the facies sequence has been interpreted as a reflection of tectonic activity of alimentation areas of the siltstone material. With this approach the random component reflects local depositional conditions. The random "noise" obscuring the "ideal" facies sequence has been eliminated by simple calculations. The calculations have been based on the following formula: *m _{ij }= n_{ij} - n_{i}*n_{j }/ N - n_{i}* where:

*m*- the difference between the found number of upward transitions from facies

_{ij}*i*to facies

*j*and the number of upward transitions from facies

*i*to facies

*j*predicted if their vertical arrangement was random;

*n*- the number of upward transitions from facies

_{ij}*i*to facies

*j*found in the sequence;

*n*– the total number of occurrences of facies

_{i}*i*in the sequence;

*n*- the total number of occurrences of facies

_{j}*j*in the sequence;

*N*- the total number of all the examined transitions between different facies. The calculated

*m*values served to establish the ideal rythms of the facies sequence. The analysis of ideal rythms and siltstone beds thicknesses revealed, that the energy of tectonic impulses was the highest in the lower part of the Lower Ludlovian and that the most rapid changes of the impulse energy occurred in the Upper Ludlovian i.e. above the

_{ij}*Saetograptus leintwardinensis*zone.