Geoscience Reference
In-Depth Information
characterize a heat flow province. Large volcanoes
and global tomography average large volumes of
the mantle.
Distributions are commonly asymmetric and
skewed. Medians of isotope data are more robust
measures than the arithmetic means, with which
they commonly disagree. Log-normal distribu-
tions are more appropriate than linear Gaussian
distributions for many geophysical and geochem-
ical datasets. These are relatively mild applica-
tions of bayesian reasoning. Stronger bayesian
priors would involve placing a low prior probabil-
ity on certain ranges of values of the parameter
being estimated, or on external parameters.
Basaltic volcanism is by nature an integrator
of the underlying source. All volcanoes average,
to a greater or lesser extent, the underlying het-
erogeneities. To determine the true heterogeneity
of the mantle, samples from a large variety of
environments are required, including fast and
slow spreading ridges, small off-axis seamounts,
fracture zones, new and dying ridges, various
ridge depths, overlapping spreading centers,
melt-starved regions, unstable ridge systems such
as back-arc ridges, and so on. These regions
are often avoided, as being
anomalous
. Various
materials enter subduction zones, including sed-
iments, altered oceanic crust and peridotite, and
some of these are incorporated into the upper
mantle. To the extent that anomalous mate-
rials are excluded, or anomalous regions left
unsampled, the degree of true intrinsic het-
erogeneity of the mantle will be unknown. In
essence, one must sample widely, collecting speci-
mens that represent different degrees of melting
and different source volumes. The data can be
weighted or given low probability in the bayesian
approach.
The main distinguishing feature of the
bayesian approach is that it makes use of
more information than the standard statistical
approach. Whereas the latter is based on analy-
sis of 'hard data', i.e. data derived from a well-
defined observation process, bayesian statistics
accommodates 'prior information' which is usu-
ally less well specified and may even be subjec-
tive. This makes bayesian methods potentially
more powerful, but also imposes the require-
ment for extra care in their use. In particular,
we are no longer approaching an analysis in
an 'open-minded' manner, allowing the data to
determine the result. Instead, we input 'prior
information' about what we think the answer is
before we analyse the data! The danger of subjec-
tive bayesian priors, if improperly applied, is that
prior beliefs become immune to data.
Fallacies
Logic, argument, rhetoric and fallacies are
branches of philosophy; science started out as
a branch of philosophy.
Scientific truth
is now
treated differently from
logical truth
,or
mathemat-
ical truth
, and statistics. But in the search for sci-
entific truth it is important not to make logical
errors, and not to make arguments based on log-
ical fallacies. The rules of logical inference form
the foundation of good science.
A fallacy is an error in reasoning and dif-
fers from a factual or statistical error. A fal-
lacy is an 'argument' in which the premises
given for the conclusion do not provide the
necessary support. Many of the paradoxes in
Earth science, as discussed in the following
chapters, are the result of poor assumptions
or erroneous reasoning (
logical paradoxes
)
[
mantleplumes fallacies
].
The following chapters discuss some of the
controversies and paradoxes in Earth science.
Some of these can be traced to assumptions and
fallacies. The following are a few examples of
logical fallacies;
Midocean-ridge basalts are homogenous; therefore
their mantle source is homogenous; therefore it is
vigorously convecting, therefore it is well stirred.
(There are four logical fallacies in that sentence, and
at least one factual error.)
Midocean-ridge basalts are derived from the upper
mantle; ocean-island basalts are not midocean-ridge
basalts; they therefore are derived from the lower
mantle.
Seismic velocities and density decrease with
temperature; therefore regions of the mantle that
have low seismic velocities are hotter and less dense
than other regions.
Some other well known fallacies are catego-
rized below, with examples. The examples are
