Geoscience Reference
In-Depth Information
subject to constraints including preservation of known superpositional relations and
co-occurrences of taxa and events. Hammer and Harper (
2005
, p. 296) conclude
that constrained optimization is “an excellent, flexible method for biostratigraphy,
based on simple but sound theoretical concepts and potentially providing high-
resolution results”. For a recent summary of this method with an application, see
Cody et al. (
2008
).
CONOP also has been used for constructing numerical geologic time scales for
Paleozoic periods (Gradstein et al.
2004
,
2012
). In this approach, known age
determinations of rock samples for a period are plotted against the positions of
these samples along a relative geologic time-scale provided by the constrained
optimum sequence for a suitable group of fossils. When the ranges are plotted along
the vertical scale, their ordinates can be used as the abscissae in this new applica-
tion. A smoothing spline (Sect.
9.2
) then is fitted with consideration of uncertainties
in both the age determinations and the stratigraphic positions of the rock samples.
This spline curve is used to estimate the ages of stage boundaries with 95 %
confidence intervals (Agterberg
2004
; Agterberg et al.
2012
).
Other methods of quantitative stratigraphy include Appearance Event Ordina-
tion (Alroy
2000
) abbreviated to AEO, and graphic biostratigraphic correlation
using genetic algorithms (Zhang and Plotnick
2006
). Alroy uses super-positional
information on taxa as follows: If it can be established that the FO of taxon A occurs
below the LO of taxon B in a section, this can be interpreted as a definitive F/L
(First/Last) statement because the FO of A can only be extended downwards toward
its FAD and the LO of B upwards towards B's LAD. AEO attempts to honor all
F/Ls while minimizing the number of F/Ls that would be implied but are not
observed. This method is more sensitive to the possible occurrence of local
reworking than RASC. For a recent AEO application, see Crampton et al. (
2012
).
Zhang and Plotnick (
2006
) proposed to use genetic algorithms, a branch of
artificial intelligence that solves complex optimizations problems by imitating
neo-Darwinian evolution to solve the “traveling salesman” (TSM) problem. In
TSM there are
N
cities to be visited. In total, there would be 0.5 x
N
! possible
alternative trajectories. This number quickly becomes too large for the trajectories
to be investigated separately. A close-to-optimum trajectory is found by imposing
constraints so that sets of unsuitable solutions are successively eliminated. In
biostratigraphic applications the cities are replaced by biostratigraphic events and
the constraints include the super-positional (and co-existential) relations between
events. Zhang and Plotnick's method resembles CONOP.
Especially during the first 20 years of its existence, RASC has been widely
applied to last occurrences of microfossils observed in cuttings obtained at discrete,
regular intervals (e.g., every 10 m) from exploratory wells drilled by oil companies
in sedimentary basins. To some extent, this sampling procedure affects the output as
will be discussed later (Sect.
9.3.2
). Often in a sedimentary basin that is being
studied, there occur other types of stratigraphic events such as ash layers, seismic
events and gamma ray peaks, which are not subject to biostratigraphic uncertainty.
Some of these, especially ash layers, can be used for correlation without uncertainty
between stratigraphic sections that may be tens of kilometers apart. Seismic events
Search WWH ::
Custom Search