Geology Reference
In-Depth Information
between variables or pairs of samples is expressed by
various similarity coefficients. Similarity measures take
two forms, quantitative or binary.
Shi (1993) lists 39 measures with the goal of mea-
suring resemblance between variable sets or all pos-
sible pairs of samples. Cluster analyses result in a group-
ing of variables (facies criteria) or samples with regard
to their similarity and correspondence. The step-wise
reduction of the most similar groups leads to a hierar-
chical classification best shown in a two-dimensional
dendrogram (Fig. 6.12).
consuming, even with the appropriate computer equip-
ment.
These drawbacks can be overcome by a method us-
ing two-state or multi-state attributes (Klovan 1964;
Bonham-Carter 1965). This method uses binary data.
These data indicate the presence or absence of attributes,
and are coded as 2 or 1; the existence of uncertain at-
tributes is coded as 0. Multistage quantitative variables
are subdivided into ranks (e.g. abundant, present, rare,
absent, uncertain) and also are coded as simple pres-
ence/absence attributes. There are no general rules as
to how the attributes should be divided and coded. Vi-
sual estimation is usually quite satisfactory.
Binary data analysis includes (a) collection and es-
tablishment of a raw data matrix; (b) calculation of mea-
sures of similarity (e.g. Jaccard coefficient) either be-
tween all possible pairs of characters (R-mode tech-
nique) or between all possible pairs of samples (Q-
mode); (c) clustering of samples, and (d) plotting of
dendrograms. This method and also the various numeri-
cal classification methods were tested using data sets
from the Bahama Bank (e.g. Ramsayer and Bonham-
Carter 1974). Binary data have been successfully ap-
plied in facies discrimination particularly with the aid
of association analyses (Gill 1993). Association analy-
sis, developed to handle binary-coded multivariate data
of plant communities, was used to discriminate mod-
ern carbonate sediments (Erez and Gill 1976), and to
recognize ancient reefal paleoenvironments of Creta-
ceous and Miocene reef complexes (Jurassic: Neuweiler
1995; Cretaceous: Ekdale et al. 1976; Miocene: Buch-
binder 1979).
Classifications based on numerical frequency dis-
tributions lead to a breakdown of continua into discrete
units, e.g. standard microfacies types. These units,
however, do not reflect compositional relays charac-
terized by overlapping compositions, caused by shift-
ing environmental gradients. These relays become evi-
dent after the binary data have been treated by using
optimized similarity matrices and correspondence tech-
niques (Hennebert and Lees 1985; Sect. 14.4).
Cluster analysis dendrograms are helpful in group-
ing samples with similar component distributions, but
should be used for facies differentiation only in the con-
text of evaluating qualitative microfacies criteria.
The question of how groupings of facies data are
related to independent factors can be approached by
factor analysis
. Factor analyses are powerful tools for
(a) determining the minimum number of causal rela-
tionships needed to explain the majority of the observed
microfacies variations, (b) to identify these causal re-
lationships, and (c) to estimate the relative importance
of microfacies variables. In facies studies, factor analy-
sis is used to derive causal factors controlling the dis-
tribution of sedimentary constituents. This technique
is used for resolving complex relationships within a
set of variables or samples by constructing hypotheti-
cal factors which reduce the overall complexity. The
factors are ranked according to the extent to which the
factor accounts for the variance observed in the data
set. An often used technique for extracting significant
factors which can be interpreted in terms of facies con-
trols, is principal component analysis. A visual inspec-
tion of factor plots indicates which objects are grouped
together and may result from the comparison process.
Different factors explain different percentages of vari-
ance observed in the data. Positive or negative factor
loadings of the variables reflect the controls in the in-
terrelationship of variables, e.g. biotic composition, hy-
drodynamic conditions and terrigenous input (Fig.
6.13).
6.3.2 Significance of Multivariate Studies:
Constituent Analysis as a Clue to Environ-
mental Conditions and Depositional Settings
Choose between quantitative numerical and binary data!
The use of quantitative methods has a few draw-
backs: Important non-quantitative attributes, e.g. rock
color, are excluded. Poorly preserved constituents, e.g.
recrystallized bioclasts, often can not be allocated to a
grain type category as would be desirable for point-
counting. Modal analysis of samples with large-sized
particles require the use of large, oversized thin sec-
tions. Last but not least: point counting is rather time
Constituent grain analysis was developed as a tool for
differentiating modern sedimentary environments. The
technique relies on the assumption that in shallow-ma-
rine environments a high proportion of carbonate sedi-
ments is produced in situ as skeletal remains of local
communities. The close correlation between spatial pat-
