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operator is not the identity matrix and hence
trade-offs between isotropic and anisotropic
parameters are artificially introduced. Partial
derivatives for isotropic and anisotropic param-
eters are different and so are the partial inverse
operators, and hence the resolution operator
is not symmetric. This means that the trade-
off from isotropic to anisotropic parameters,
S a G i , is different from anisotropic to isotropic
parameters, S i G a . The isotropic-anisotropic
trade-off can have large consequences for our
interpretation of the inferred anisotropy. If we
construct global phase velocity maps using a
purely isotropic description, i.e. S a forced to 0 ,
the models appear blobby. Once anisotropy is
introduced, both the isotropic and anisotropic
parts of the models appear smooth, with a similar
fit to the data (Trampert & Woodhouse, 2003).
Hence, the strength of anisotropy trades off with
the roughness of isotropic velocity variations.
Another example is that significant apparent
transverse isotropy is generated if the crustal
model is inappropriate (Bozdag & Trampert,
2008), or when apparent splitting is seen on
S diff caused by isotropic velocity gradients in D''
(Komatitsch et al. , 2010).
We thus have to keep in mind, when seismol-
ogists report anisotropy, they explain the data
using a description involving the least possible
parameters. They implicitly or explicitly employ
Occam's razor. In splitting measurements, the ra-
zor is implicit as the interpretation assumes a
one- or multi-layered medium a priori (e.g., Long
& Silver, 2009). A similar situation holds when
normal-mode splitting functions are used as the
medium is parametrized with a small number
of unknowns (e.g., Beghein & Trampert, 2003;
Deuss et al. , 2010). With surface wave measure-
ments, the razor is more explicit, as we search
for a parametrization which explains the data sig-
nificantly better (e.g., Trampert & Woodhouse,
2003). Due to the wavelength and resolution op-
erator averaging, this is the best the seismologists
can do. However, the interpretation of the mod-
els evoking LPO or SPO is only meaningful if this
averaging is taken into account. There are many
studies which show that anisotropy can develop
during convection in the upper (e.g., Kaminski
et al. , 2004; Becker et al. , 2008) and lower mantle
(e.g., McNamara et al. , 2002). The comparisons
to seismology, so far, are qualitative, but can be
formulated in a quantitative way using the res-
olution operator. This is important, because the
resolution strongly influences the recovered mag-
nitude of anisotropy and properly accounts for the
trade-offs.
This leaves the burning question: is the Earth
anisotropic? As argued above, seismologists find
that given the observations and the used model
parametrization, the data are usually explained
more efficiently, i.e. with less parameters, using
anisotropy. They present mathematical equiva-
lents of the physical Earth, filtered by a limited
frequency band and a nonsymmetric resolution
operator. There is consensus that the upper few
hundred kilometres of the Earth are transversely
isotropic, with decaying amplitude and a pos-
sible sign change around 200 km (Figure 11.2).
There is also agreement that there is azimuthal
anisotropy, although there is little similarity be-
tween the inferred models (e.g., Becker et al. ,
2007). There are many reports of anisotropy in the
D'' layer, but the different models tend to have
few features in common. There is a large con-
sensus that the inner core is anisotropic, but the
details have yet to emerge. We concur with Becker
et al. (2007) that the reason for this disparity are
different strategies in the inverse modelling and
we are currently comparing models with widely
differing averaging properties. Unless the seismol-
ogists come to a similar degree of consensus as
for isotropic structures, it seems difficult to infer
any geodynamic constraints from the anisotropic
models. Anisotropy needs far more parameters
for a proper description than isotropy. A possi-
ble strategy is therefore to use implicit scalings
or fix the symmetry a priori based on mineral
physics arguments (e.g., Panning & Romanowicz,
2006; Chevrot, 2006; Long et al. 2008; Panning
& Nolet, 2008). Another strategy is to be guided
by the data and invert for parameters they are
most sensitive to (e.g. Sieminski et al. 2009). The
latter is easier to interpret because it is difficult
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