Geoscience Reference
In-Depth Information
Preliminaries
In mantle tomography the number of parame-
ters that one would like to estimate far exceeds
the information content (the number of inde-
pendent data points) of the data. It is there-
fore necessary to decide which parameters are
best resolved by the data, what is the resolu-
tion, or averaging length, which parameters to
hold constant, how to treat unsampled areas,
and how the model should be parameterized (for
example as layers or smooth functions, isotropic
or anisotropic). In addition, there are a vari-
ety of corrections that might be made (such as
crustal thickness, water depth, elevation, ellip-
ticity, attenuation). The resulting models are as
dependent on these assumptions and corrections
as they are on the quality and quantity of the
data. This is not unusual in science; data must
always be interpreted in a framework of assump-
tions, and the data are always, to some extent,
incomplete and inaccurate. In the seismologi-
cal problem the relationship between the solu-
tion, or the model, including uncertainties, and
the data can be expressed formally. The effects
of the assumptions and parameterizations, how-
ever, are more obscure, but these also influence
the solution. The hidden assumptions are the
most dangerous. For example, most seismic mod-
eling assumes perfect elasticity, isotropy, geomet-
ric or finite-frequency optics and linearity. To
some extent all of these assumptions are wrong,
and their likely effects must be kept in mind.
These artifacts and assumptions do not show up
in color tomographic cross-sections, which also
usually do not indicate which parts of the mantle
are unsampled and have been filled in by smooth-
ing. Published cross-sections are usually selected,
oriented and cropped to make a certain point.
Thus, it is easy for nonspecialists to accept these
cross-sections as data and to overinterpret them.
Tomography is best used as a hypothesis tester
rather than as a definitive and unique mapper of
heterogeneity and mantle temperature.
on the ray geometry, which is constrained by
the geometry of earthquakes and seismic stations
(Vasco
et al.
, 1995), and -- to a lesser extent -- the
details of the mathematical techniques employed
(Spakman and Nolet, 1988; Spakman
et al.
, 1989;
Shapiro and Ritzwoller, 2004). Seismic ray cov-
erage is sparse and spotty. Moreover, the visual
appearance of displayed results depends on the
color scheme, reference model, cropping and
cross-sections chosen. The resulting images con-
tain artifacts that appear convincing (Spakman
et al.
, 1989). Even further difficulties result from
the limitations of present algorithms, which
cannot correct completely for finite-frequency,
source and anisotropic effects and can certainly
not constrain regions where there are little data.
Global tomographic models have little detailed
resolution. High-frequency reflection, scattering
and coda studies paint a much more complex
picture of the mantle than is available from long-
period waves.
Visual, or intuitive, interpretations of tomo-
graphic images, qualitative chromo-tomography
(QCT) and the association of color with temper-
ature have had more crossdisciplinary impact
than quantitative and statistical analysis of the
tomographic results. To a geochemist a color
cross-section
provides overwhelming tomo-
graphic evidence that at least some of
the subducting lithospheric plates are
currently reaching the core--mantle
boundary
. The visual impressions of tomo-
graphic images, their implications regarding iso-
topic as well as major element recycling, and
the plausibility or implausibility of layering and
survival of heterogeneities in a convecting man-
tle are now at the heart of
perceived con-
flicts of geophysics and geochemistry
and mantle convection
. It has recently
become possible to quantify tomographic models,
to resolve density and to separate the effects of
temperature and composition (Ishii and Tromp,
2004; Trampert
et al.
, 2004). The basic assump-
tion in many tomographic interpretations, that
low seismic velocity is always a proxy for high
temperature and low density, is not valid. There
is no correlation in properties between the upper
mantle, midmantle and lower mantle and no
evidence
Qualitative vs. quantitative tomography
Body-wave tomography is a powerful but imper-
fect tool. Travel-time tomography, used alone, is
particularly limited. The results depend crucially
for
either
deep
slab
penetration
or
