Page 111 - Carbonate Sedimentology and Sequence Stratigraphy

102 WOLFGANG SCHLAGER

A)
Andros

0.6
TWT
0 10 km
B)
Straits of Andros 12 Alabama Margin 12 New Jersey Margin 12
(carbonates) (mixed) (clastics)
log2 (number full boxes)
8 8 8

D = 1.32 D = 1.37 D = 1.48
4 4 4

-8 log2 (box size) 0 -8 -6 -4 -2 0 -8 -6 -4 -2 0

Fig. 6.19.— Trajectories of migrating shelf breaks, a pivotal feature of sequence anatomy, show fractal characteristics. Data from
Cenozoic of Great Bahama Bank (Eberli and Ginsburg, 1988) and offshore New Jersey (Greenlee, 1988). (A) Part of the migration
path of the Bahama shelf break as determined by the author using the seismic line by Western Geophysical described in Eberli and
Ginsburg (1988). (B) Fractal analysis of shelf-break migration paths box-counting (see appendix). Straight-line trends for box sizes 2 2
6
to 2 indicate a power law relationship between box size and number of boxes required to cover the curve. This in turn suggests that
the paths of shelf-break migration have fractal characteristics in these limits. The trends are somewhat irregular on the right because of
finite-size effects and break down on the left because of limited seismic resolution.
Period
6
10 y 1 y 1 day 1 hr 1 second
continental flooding
8
10 N 25 000 10
orbital
6
10 4 trend of random walk 5 Exxon/Haq SPECMAP O isotopes
sedimentation rate (m/My) 10 2 log power (m 2 /cycles/y) 0 SL spectrum O isotopes from sclerosponges

10

0
10
month
hourly tide gauge
Seattle sea level
hour
day
8
0
10
10
(Agnew)
length of observation span 2 10 4 10 6 10 y -5 2 mo to 94 y tides & waves
-10
log frequency (cycles/y) 0 4 8
Fig. 6.20.— Log-log plot ofsedimentation rates vs. length of the
time window of observation. Rates vary considerably in each time Fig. 6.21.— Power spectra of sea-level fluctuations covering 15
window but the overall trend is linear and close to that of a random orders of magnitude of frequency. In the stratigraphically relevant
8
walk. After Sadler (1981), modified. range of 10 to 10 y, the first-order trend is a power law indicating
0
that the spectrum of sea-level fluctuations is a fractal whose di-
mension is close to that of white noise. The trend breaks down for
high frequencies. Records dominated by orbital rhythms appear
as islands of order that break the trend. After Harrison (2002),
modified.