Milankovitch Cycles and Sequences: Two Different Stratigraphic Tools
253
(which can be 1: 2 or 1:8). Since both precession and obliquity have changed during geological time, the ratios have also changed. According to calculations by
Berger and Loutre (l994) the ratio of eccentricity to precession was approximately 1:4.8 in Upper Cretaceous time, 1:5.3 in Upper Carboniferous time and
1:5.7 during the Upper Ordovician.
5
Stratification Cycles, Bundles and Stacking Patterns
If detailed stratigraphic data are available, the best method for finding cyclicities
and ratios between cycles is power spectral analysis. Very often, however, detailed and continuous quantitative data for such an analysis are not available
and, for this reason, a study of the stratification pattern becomes important.
A particularly useful pattern of stratification is the grouping of identical beds
into repeated cycles (Schwarzacher 1947). The bedding planes and beds within
the groups are identical but the bedding plane which marks the boundary of the
group is differently developed, very often as a master bedding plane
(Schwarzacher 1958,1975). Geometrically, this pattern can be described by two
types of boundary, let us say Rand r and by sequences of the type
R,r,r,r,R,r,r,r,R, .... The number of beds in each is constant or very nearly constant. This type of bedding is very well described by the term bundling of beds
(Schwarzacher 1954) but for a precise description, the term stratification cycle
should be used (Schwarzacher 1987). The term stacking pattern, which has been
more recently used in the American literature, does not bring out the essential
cyclic nature of this sedimentation pattern, but is useful in the description of
other short cycles with definite sequences.
The reason why stratification cycles need special attention is that they are
very difficult to explain by anything else than the effect of two near-periodic
functions. To support this statement, we can use the following argument.
Assume that we have two types of events corresponding to the formation of
boundaries Rand r. There are four times as many events r as R, which means
that the events could be arranged in a regular series: R,r,r,r,r,R,r,r,r,r,R, .... representing bundles of five. The probability (p )of obtaining R = 115 and the probability (q) of obtaining r = 4/5. The probability of obtaining purely by chance a
single bundle R,r,r,r,r,R is equal to p2 q . The probability of obtaining several
such bundles by chance in succession, is astronomically small. The argument assumes complete statistical independence of every sedimentation process and
this is unlikely. A more realistic model can be found by using the transition
probabilities p{R,r) which can be written in matrix form:
p{R,R)
p{r,R)
p{r,R)
p{r,R)
p{r,R)
p{r,r) p{r,r)
p{r,r),
253
(which can be 1: 2 or 1:8). Since both precession and obliquity have changed during geological time, the ratios have also changed. According to calculations by
Berger and Loutre (l994) the ratio of eccentricity to precession was approximately 1:4.8 in Upper Cretaceous time, 1:5.3 in Upper Carboniferous time and
1:5.7 during the Upper Ordovician.
5
Stratification Cycles, Bundles and Stacking Patterns
If detailed stratigraphic data are available, the best method for finding cyclicities
and ratios between cycles is power spectral analysis. Very often, however, detailed and continuous quantitative data for such an analysis are not available
and, for this reason, a study of the stratification pattern becomes important.
A particularly useful pattern of stratification is the grouping of identical beds
into repeated cycles (Schwarzacher 1947). The bedding planes and beds within
the groups are identical but the bedding plane which marks the boundary of the
group is differently developed, very often as a master bedding plane
(Schwarzacher 1958,1975). Geometrically, this pattern can be described by two
types of boundary, let us say Rand r and by sequences of the type
R,r,r,r,R,r,r,r,R, .... The number of beds in each is constant or very nearly constant. This type of bedding is very well described by the term bundling of beds
(Schwarzacher 1954) but for a precise description, the term stratification cycle
should be used (Schwarzacher 1987). The term stacking pattern, which has been
more recently used in the American literature, does not bring out the essential
cyclic nature of this sedimentation pattern, but is useful in the description of
other short cycles with definite sequences.
The reason why stratification cycles need special attention is that they are
very difficult to explain by anything else than the effect of two near-periodic
functions. To support this statement, we can use the following argument.
Assume that we have two types of events corresponding to the formation of
boundaries Rand r. There are four times as many events r as R, which means
that the events could be arranged in a regular series: R,r,r,r,r,R,r,r,r,r,R, .... representing bundles of five. The probability (p )of obtaining R = 115 and the probability (q) of obtaining r = 4/5. The probability of obtaining purely by chance a
single bundle R,r,r,r,r,R is equal to p2 q . The probability of obtaining several
such bundles by chance in succession, is astronomically small. The argument assumes complete statistical independence of every sedimentation process and
this is unlikely. A more realistic model can be found by using the transition
probabilities p{R,r) which can be written in matrix form:
p{R,R)
p{r,R)
p{r,R)
p{r,R)
p{r,R)
p{r,r) p{r,r)
p{r,r),