254
w. Schwarzacher
and this will lead to a periodic chain, if it takes the form:
o pI 0 0... 0
o 0 p2 0
o
pj,
in which pI to pj are either unity or square matrices with unity row sums
(Schwarzacher 1975). In order to generate a period of j, the matrix must be at
least of the dimension j >I- j. This also applies if the series is not strictly periodic
but has a recurrence probability maximum of length j.
The probability matrix provides a descriptive model but it does not explain
the mechanism which can produce this situation, in which identical states have
different transition probabilities which are determined by their position in the
chain. In this respect, stratification cycles are quite different from stacking patterns such as for example, the classical coal-measure cycle or the Bouma sequence. In any of these latter developments, the sediment sequences can be explained as being the result of a definite triggering event, such as a sea level
change or a turbidity current. The triggering event can be either random or periodic, but unless a realistic mechanism is found to explain the constantly repeated triggering of bed formation at regular intervals (without involving periodic processes) stratification cycles are one of the best methods for recognising
periodicity, and therefore for recognizing Milankovitch cycles. An obvious advantage of stratification cycles in demonstrating periodicity is that only the
counting of beds between master bedding planes is involved and variations in
bed thicknesses are of secondary importance
In a study specifically dealing with carbonate platforms, Drummond and
Wilkinson (1993) suggest that stratification cycles can develop by the interaction
of two periodic functions, one of which is a eustatic sea level change with constant frequency. The second cycle is generated by introducing a constant threshold which switches sedimentation on and off at intervals controlled by the available accommodation space, which in this unlikely model can never exceed a critical value (one metre) for any length of time. This model is an example of a
mechanism which multiplies the frequency of the signal in the recorded sediment (see Sect. 6). Inasmuch as this mechanism leads to stratification cycles
only if both the sea level change and the consequent interruptions of sedimentation are periodic, Milankovitch cyclicity is again the most likely explanation
for this model.
A simple explanation for the formation of stratification cycles is shown diagrammatically in Fig. 6. The environmental variable is assumed to be represented by two (or more) periodic functions with different wavelengths and amplitudes but with a stable phase relationship. A bedding plane is formed whenever
the signal reaches a critical value, whereby different values of the response
thresholds can lead to the development of different stratification patterns. Obvi-
w. Schwarzacher
and this will lead to a periodic chain, if it takes the form:
o pI 0 0... 0
o 0 p2 0
o
pj,
in which pI to pj are either unity or square matrices with unity row sums
(Schwarzacher 1975). In order to generate a period of j, the matrix must be at
least of the dimension j >I- j. This also applies if the series is not strictly periodic
but has a recurrence probability maximum of length j.
The probability matrix provides a descriptive model but it does not explain
the mechanism which can produce this situation, in which identical states have
different transition probabilities which are determined by their position in the
chain. In this respect, stratification cycles are quite different from stacking patterns such as for example, the classical coal-measure cycle or the Bouma sequence. In any of these latter developments, the sediment sequences can be explained as being the result of a definite triggering event, such as a sea level
change or a turbidity current. The triggering event can be either random or periodic, but unless a realistic mechanism is found to explain the constantly repeated triggering of bed formation at regular intervals (without involving periodic processes) stratification cycles are one of the best methods for recognising
periodicity, and therefore for recognizing Milankovitch cycles. An obvious advantage of stratification cycles in demonstrating periodicity is that only the
counting of beds between master bedding planes is involved and variations in
bed thicknesses are of secondary importance
In a study specifically dealing with carbonate platforms, Drummond and
Wilkinson (1993) suggest that stratification cycles can develop by the interaction
of two periodic functions, one of which is a eustatic sea level change with constant frequency. The second cycle is generated by introducing a constant threshold which switches sedimentation on and off at intervals controlled by the available accommodation space, which in this unlikely model can never exceed a critical value (one metre) for any length of time. This model is an example of a
mechanism which multiplies the frequency of the signal in the recorded sediment (see Sect. 6). Inasmuch as this mechanism leads to stratification cycles
only if both the sea level change and the consequent interruptions of sedimentation are periodic, Milankovitch cyclicity is again the most likely explanation
for this model.
A simple explanation for the formation of stratification cycles is shown diagrammatically in Fig. 6. The environmental variable is assumed to be represented by two (or more) periodic functions with different wavelengths and amplitudes but with a stable phase relationship. A bedding plane is formed whenever
the signal reaches a critical value, whereby different values of the response
thresholds can lead to the development of different stratification patterns. Obvi-