Page 167 - Carbonate Sedimentology and Sequence Stratigraphy

158 WOLFGANG SCHLAGER

Fig. 9.1.— Valley-delta systems in plan view – invariant sedimentation patterns that reflect the dissipation of kinetic energy. Total
observed range of scale invariance is more than 14 orders of magnitude, shown examples cover only a very small part of this range.
The important point is: size and shape are uncorrelated in this example. After Van Wagoner et al. (2003), modified.

clinoform-fondoform discussed in chapter 4. Thorne (1995) much like sedimentation rates, have fractal characteristics.
contributed a quantitative analysis of the unda-clino-fondo The observations on the scaling of sedimentation rates and
trio under the assumption that the entire system consists sea level changes provide support for the fractal model of
of loose sediment. He found that the governing equations stratigraphic sequences in chapter 6. It is important to note,
can be applied in a wide range of scales, certainly includ- however, that the power-law scaling of sea-level changes
ing the geologically particularly relevant dimensions shown and sedimentation rates demonstrated to date pertains to
in Fig. 9.2. The governing principle for the formation of first-order trends. There are islands of order in the data and
prograding clinoforms is high sediment supply at the top, the exponents in the power laws vary – clearly there is much
gravity transport down the slope and decay of transporting additional information in the data and more work needs to
power on the flat basin floor. Carbonates are not always de- be done.
posited as loose sediment. They may include bodies that are
hard immediately upon formation such as reefs, automicrite Scaling laws in sedimentology and stratigraphy are both a
mounds or early-lithified sands. However, even the com- challenge and an opportunity. They are challenging because
plex carbonate systems produce scale-invariant anatomies the fundamental concepts lie outside our discipline, are still
in a considerable range of scales. A well-known example is evolving and are not always mathematically rigorous (see,
the repetition of the atoll structure at different scales. There for instance, the many ways of defining fractals; Falconer,
exists a continuous size spectrum that ranges from mini- 1990; Hergarten, 2002). On the other hand, scaling laws rep-
atolls, 10 m in diameter, to oceanic atolls exceeding 100 km resent opportunities because they often lead to quantifiable
in diameter. The underlying principle in the atoll example relationships among important variables. Two major bene-
seems to be the advantage of the rim position for benthic fits may arise from work in this area. First, scaling provides
growth. a basis for quantitative prediction of sediment bodies that
cannot directly be examined, such as subsurface reservoirs
Scale invariance is not limited to geometry. The relation- for hydrocarbons or water. Second, scaling laws may re-
ship of sedimentation rates to the length of the observation veal fundamental principles governing sedimentation, ero-
span is invariant under changes of scale over 11 orders of sion and formation of the stratigraphic record. Some po-
magnitude (p. 102). Wave phenomena are another example tential applications of fractals and power-law scaling have
of scale invariance. Especially relevant for sedimentology been outlined in chapter 6. In biology, the study of scaling
and sequence stratigraphy is the statistical behavior of sea- laws relating mass of organisms to metabolic rate started
level fluctuations: the power (= square of the absolute am- in the 1930’s (Fig. 9.3). It has led to important insights
plitude) of sea-level fluctuations is related to cycle period and triggered considerable discussion on the laws govern-
by a power law (p. 102). It seems that sea-level fluctuations, ing life processes (e.g. Calder, 1984; West et al., 2002; West