256
vv. Schvvarzacher
scale. In stratigraphy, this scale is largely provided by the thickness of the accumulated sediment. We know that over long periods of time and for particular
environments, sedimentation can be regarded as being constant and thickness
therefore is proportional to stratigraphic time. However, this relationship invariably breaks down and on a microscale, sedimentation is always discontinuous, and time (vvhich is derived from thickness measurements) is unpredictable
over short intervals. To establish the absolute duration of a cycle is therefore
only possible when very good time control is available in the form of good radiometric data combined with good evidence of steady and continuous sedimentation.
It is well known that sedimentation rates are at least as sensitive to the environment as most other properties of the sediment. This means that any variation
of the stratigraphic record (lithology, or biocontent) will also induce a variation
in sedimentation rates and therefore distortions of the time scale. The relationship between environment, sediment material and sedimentation rates cannot
be expected to be linear, and indeed it seems likely that the system contains stable, bistable and unstable elements which are subjected to random noise.
When the time development of cycles is studied, particular attention has to
be paid to sedimentation gaps which may be due to sedimentation still stand or
more commonly, to erosion. Figure 7 shows a simple example of a sinusoid signal and its stratigraphic record, which was formed under the assumption that
the rate of sedimentation was directly proportional to the signal. When this signal is plotted against the cumulative sediment thickness, it forms a cycloid and
if the signal exceeds a critical maximum sedimentation, then part of the record
is missing. This is indicated by the loops in curve A of Fig. 7. The second example
(curve B) assumes that only increasing rates of sedimentation resulted in sediment accumulation. This hypothetical case illustrates that a symmetrical signal
can easily lead to an asymmetrical record. The relationship between environmental conditions and sedimentation, can not only change the shape of the signal, but it can also double or even multiply the frequency of the signal. A possible
scenario for such a case is a biotope which is sensitive to extrema and which
therefore could produce a double peak for each cycle of a sine wave. A reduction
of frequency has already been illustrated by the example of the incomplete recording of stratification cycles.
As already mentioned, stochastic processes are important in producing
stratigraphic sections. Random fluctuations are not only part of the deposition
process but also of diagenesis and postdiagenetic preservation. They may be further increased by errors of observation. The magnitude of such disturbances can
be estimated, to some extent, if data are available which represent identical timespans in different localities (Schwarzacher 1975). The actual causes of random
variations are usually too complex to be identified in detail. For the study of cycles, a knowledge of the random element is important because as before, it not
only affects the recorded signal but also the thickness-related time scale. To use
the terminology of radio communication, the stratigraphic signals are not only
amplitude modulated by noise but also phase or frequency modulated.
vv. Schvvarzacher
scale. In stratigraphy, this scale is largely provided by the thickness of the accumulated sediment. We know that over long periods of time and for particular
environments, sedimentation can be regarded as being constant and thickness
therefore is proportional to stratigraphic time. However, this relationship invariably breaks down and on a microscale, sedimentation is always discontinuous, and time (vvhich is derived from thickness measurements) is unpredictable
over short intervals. To establish the absolute duration of a cycle is therefore
only possible when very good time control is available in the form of good radiometric data combined with good evidence of steady and continuous sedimentation.
It is well known that sedimentation rates are at least as sensitive to the environment as most other properties of the sediment. This means that any variation
of the stratigraphic record (lithology, or biocontent) will also induce a variation
in sedimentation rates and therefore distortions of the time scale. The relationship between environment, sediment material and sedimentation rates cannot
be expected to be linear, and indeed it seems likely that the system contains stable, bistable and unstable elements which are subjected to random noise.
When the time development of cycles is studied, particular attention has to
be paid to sedimentation gaps which may be due to sedimentation still stand or
more commonly, to erosion. Figure 7 shows a simple example of a sinusoid signal and its stratigraphic record, which was formed under the assumption that
the rate of sedimentation was directly proportional to the signal. When this signal is plotted against the cumulative sediment thickness, it forms a cycloid and
if the signal exceeds a critical maximum sedimentation, then part of the record
is missing. This is indicated by the loops in curve A of Fig. 7. The second example
(curve B) assumes that only increasing rates of sedimentation resulted in sediment accumulation. This hypothetical case illustrates that a symmetrical signal
can easily lead to an asymmetrical record. The relationship between environmental conditions and sedimentation, can not only change the shape of the signal, but it can also double or even multiply the frequency of the signal. A possible
scenario for such a case is a biotope which is sensitive to extrema and which
therefore could produce a double peak for each cycle of a sine wave. A reduction
of frequency has already been illustrated by the example of the incomplete recording of stratification cycles.
As already mentioned, stochastic processes are important in producing
stratigraphic sections. Random fluctuations are not only part of the deposition
process but also of diagenesis and postdiagenetic preservation. They may be further increased by errors of observation. The magnitude of such disturbances can
be estimated, to some extent, if data are available which represent identical timespans in different localities (Schwarzacher 1975). The actual causes of random
variations are usually too complex to be identified in detail. For the study of cycles, a knowledge of the random element is important because as before, it not
only affects the recorded signal but also the thickness-related time scale. To use
the terminology of radio communication, the stratigraphic signals are not only
amplitude modulated by noise but also phase or frequency modulated.