Page 109 - Carbonate Sedimentology and Sequence Stratigraphy

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point source are scale-invariant, energy-dissipation patterns 6.17 because many authors would follow Van Wagoner et
governed by the principles of thermodynamics. Posamen- al. (1988) and accept only exposure surfaces as sequence
tier and Allen (1999) offered numerous examples of charac- boundaries in the million-year domain.
teristic sequence anatomy that develop at temporal and spa- In siliciclastics, the record of exposure may have a strong
tial scales far smaller than those of stratigraphic sequences preservational bias. As lithification at the sediment surface
but nonetheless in completely analogous fashion. Finally, is largely absent, soils formed during short exposure events
the trajectories of shelf edges that prograde and move up are likely to be washed away by the subsequent transgres-
and down in step with sea level have fractal characteristics sion (ravinement surface). Long exposure frequently is pre-
(Fig. 6.19). The last example is important because it allows served in incised-valley fills.
one to estimate fractal dimensions - an important prerequi-
site for using the fractal model in subsurface prediction. Fractals and the impression of ordered hierarchy
Changes in sea-level and sediment supply were identified in
the previous section as the two fundamental controls on se- In many sequence data, the impression of a hierarchy of
quences. Both are known to have fractal characteristics. The cycles is very strong. The model does not imply that this im-
rates of sediment supply decrease systematically as the time pression is false. It is characteristic of fractals that the same
span of observation increases (Fig. 6.20). It is generally ac- pattern is repeated at finer and finer scales. Consequently,
cepted that this persistent pattern is caused by the occur- any snapshot of the fractal taken at a certain resolution will
rence of hiatuses at all scales. The fact that the decrease fol- show a superposition of coarser and finer patterns. The cru-
lows a power law strongly suggests that the distribution of cial difference to an ordered hierarchy of cycles is the lack of
hiatuses in the stratigraphic record has fractal characteristics characteristic scales. Moreover, the apparent hierarchies in
and Plotnick (1986) proposed that stratigraphic successions statistical fractals – and this is what the model entails –, will
are random Cantor sets with gaps at all scales. be different for each random sample drawn from a popula-
Sea-level fluctuations have been studied at time scales of tion.
seconds to hundreds of millions of years. For many data The fractal model proposed here predicts that the se-
sets it was found that power laws govern the relationship quence record, like many other natural time series, has the
between frequency and wave power. Harrison (2002) com- characteristics of noise with variable persistence and thus
bined data covering 12 orders of magnitude in frequency variable predictability (see Turcotte, 1997; Hergarten, 2002,
and concluded that at time scales of years to hundreds of for examples). The model also predicts that in the sequence
millions of years, – the geologically relevant range –, the first record the effect of ordered oscillations, such as the orbital
order trend of sea-level fluctuations has fractal character cycles, generally is subtle and becomes dominant only in
(Fig. 6.21). There are islands of order that break this trend, special circumstances (e.g. “orbital” data in fig. 6.21).
for instance the sea-level history of the recent past with its
strong orbital control. The trend breaks down in the domain Purpose and scope of the fractal model
of high-frequency sea waves. Hsui et al. (1993) found frac-
tal characteristics in the sea-level curve of Haq et al. (1987) The model is meant as a conceptual framework to steer fu-
using rescaled-range analysis. Fluegeman and Snow (1989) ture data analysis and to provide a basis for statistical char-
observed the same in the Neogene oxygen-isotope record (a acterization of sequences. A logical next step is to determine
proxy for sea level) of deep-sea sediments. fractal dimensions of important features of sequences and
The distribution of parasequences and standard se- explore the limits of the fractal domain. This insight, in turn,
quences in the sediment record does not support the sub- can be used for interpolating between data sets and extrap-
division into a domain of standard sequences at the million- olating beyond technical limits of observation, for instance
year scale and a domain of parasequences at shorter time beyond the resolution of seismic data.
scales. Rather, it was observed that the two types co-exist The difference between the fractal model and the orders
and often alternate. Vail et al. (1991) reported the occurrence model with regard to prediction is best illustrated by an ex-
of parasequences and standard sequences among short cy- ample. Let us assume that seismic data of a passive margin
cles. Furthermore, there is a growing number of sequences reveal systems tracts and unconformable sequence bound-
in the million-year domain that are terminated by drowning aries. Crude estimates indicate that the boundaries are
unconformities, i.e. flooding surfaces, without prior expo- spaced at intervals of a few million years. The model of Du-
sure (see chapter 7). Finally, Fig. 6.17 summarizes over 700 val et al. (1998) would predict that the seismically recogniz-
data from detailed observations on sequences boundaries in able sequences are of the third order and therefore standard
carbonates. Important criteria for data selection in Fig. 6.17 sequences bounded by exposure surfaces and lowstand sys-
were that the authors tems tracts. The building blocks of these sequences, usu-
(1) presented detailed and specific observation on the nature ally beyond seismic resolution, are predicted to be parase-
of each discontinuity surface and quences bounded by flooding surfaces. The fractal model
(2) accepted at least the possibility that a flooding surface predicts that the seismically visible sequences as well as
could be a sequence boundary. their building blocks consist of a mix of parasequences and
The last criterion was important for the long cycles in Fig. standard sequences in about equal proportions. The model