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In-Depth Information
1
S
4
2
S
6
surface
surface
660 km
660 km
Fig. 11.4
Sensitivity of the
frequencies of the spheroidal modes
1
S
4
and
2
S
6
to perturbations in the
radial distributions of
v
p
(dotted),
v
s
(solid) and
ρ
(dashed) away from the
1D reference Earth model ak135
(Kennett
et al.
, 1995). The peak
amplitude of the density sensitivity is
generally smaller than the sensitivity
to
v
s
. Similar to surface waves, the
normal-mode sensitivity to density is
oscillatory, which further reduces the
net effect of large-scale density
variations.
CMB
CMB
v
p
v
s
ρ
ICB
ICB
centre
centre
centre
contributions tend to cancel. While coupled
modes provide some information on odd-degree
structure, they have so far not been used in
tomographic inversions for density.
The weak sensitivities and strong trade-offs
map directly into large uncertainties, even in
the radially symmetric density structure that
is additionally constrained by the Earth's mass
and moment of inertia. Exploring the space of
one-dimensional Earth models with Monte Carlo
sampling, Kennett (1998) found that density vari-
ations of around 1% over 200 km depth inter-
vals are compatible with the frequencies of the
gravest spheroidal modes and their associated er-
rors. These uncertainties must be kept in mind
when interpreting lateral variations relative to a
one-dimensional average.
Compared to the abundance of tomographic
inversions for velocity structure, few attempts
have been made to exploit the scarce information
on density from surface observations.
By far the most common approach to infer
3D density, is to transform tomographic P and
S velocity models using a depth-dependent
scaling. This approach relies on mineral physics
modeling (e.g. Karato, 1993) and works under the
assumption that density heterogeneities are of
purely thermal origin. While being a convenient
choice in the absence of compositional infor-
mation, the resulting density models are often
inconsistent with fundamental geodynamic
observations such as free air gravity anomalies
(Forte, 2007). The neglect of compositional
contributions to density heterogeneity can fur-
thermore lead to incorrect predictions of mantle
flow and the associated surface deformation.
To overcome such inconsistencies, Tondi
et al.
(2000, 2009) jointly inverted seismic travel times
and Bouguer anomalies for lithospheric structure
by imposing linear relations between velocities
and density. The scaling links the two other-
wise independent data sets by assuming that a
given seismic velocity uniquely specifies density
and vice versa. Using inverse problem termi-
nology, the scaling reduces the number of free
model parameters, thereby alleviating the inher-
ent non-uniqueness of pure gravity inversions.
This approach produces models of the lithosphere
that explain both gravity and seismic data sets,
but it does not allow for a decorrelation of ve-
locities and density that is likely to result from
compositional heterogeneities.
