1) Attenuation is considerably more sensitive to temperature variations than
elastic velocities. While elastic velocities have a quasi-linear dependence upon
temperature variations, seismic attenuation depends exponentially on temperature
(e.g., *Jackson*, 1993; *Karato*, 1993). Therefore, attenuation
tomography is important
for studying temperature variations within the Earth, and combining elastic and
anelastic studies has the potential to separate different effects of chemical
composition, water content, partial melting, etc.

2) Attenuation causes physical dispersion of seismic velocities, and this effect needs to be corrected for in velocity models.

Comparing P-wave and S-wave velocities can offer important indications that LLSVPs involve chemical heterogeneities. One of the most important results from previous studies is that LLSVPs have a bulk-sound-velocity anomaly that is anti-correlated with the shear wave velocity anomalies (e.g. *Resovsky and Trampert*, 2003; *Trampert et al.*, 2004). Several normal modes studies *Ishii and Tromp*, 1999; *Trampert et al.*, 2004) also indicate that density heterogeneity exists at the base of the mantle, which is dominated by the two LLSVPs on a large scale. The anti-correlation between density and shear velocity anomalies that are proposed in these studies favors chemical heterogeneity. This remains a topic of controversy (e.g. *Romanowicz*, 2001; *Kuo and Romanowicz*, 2002), but at the same time, it is equally critical to better resolve the density and anelastic structure to assess the effect of thermal buoyancy and chemical negative buoyance. Nonetheless, resolving the attenuation signature of LLSVPs is quite challenging due to the contamination from the elasticity effect and strong lateral variations existing in the upper mantle. Because surface waves lose their sensitivity to such deep structures, lower mantle tomography mostly relies on deep-turning teleseismic body waves
and normal mode data. Different from body wave datasets that could be degraded by uneven distribution of events and stations, the Earth's free oscillations involve the vibration of the whole planet and thus are much less likely to be biased by source-receiver geometry. In this way, information carried by normal modes signals can serve quite well for the purpose of exploring the physics properties of the large scale lateral variations in the lowermost mantle.

For normal mode multiplets well isolated in complex frequency, the effect of even-order aspherical structure on the splitting behavior of the spectra can be quantitatively represented by a discrete set of ``splitting coefficients.'' These coefficients determine the coupling of the singlets within a multiplet. The splitting coefficients describe a radial average of three-dimensional heterogeneity, and can be related to internal properties by:

Owing to the high quality digital data set assembled in the last 20 years on the
global broadband seismic network, and owing to the occurrence of several very
large earthquakes, putting new constraints on the large-scale attenuation in
the lower mantle from normal modes is promising.

We applied the Iterative Spectral Fitting (ISF) method (*Ritzwoller et al.* 1986, 1988) in the study. In the ISF approach, the technique breaks down naturally into two parts: A discrete regression for the interaction coefficients for a number of lower mantle sensitive modes followed by a continuous inverse problem to solve for the three-dimensional structure from the splitting coefficients. Figure 2.31 shows examples of elastic splitting functions obtained from the ISF approach, and we can clearly see the dominant degree-2 pattern in all of the mantle modes shown in the figure.

We applied the same technique to resolve anelastic splitting coefficients, but due to the data noise and very limited size of the dataset used in the study, the retrieved anelastic coefficients are generally below the error level, and appear to be quite unstable and strongly rely on the elastic starting model. With more data involved in the inversion, and more optimum regularization design, we hope to improve the stability of the anelastic splitting coefficients and then go further to invert for a three-dimensional anelastic model of the lower mantle from normal modes. Even if we can
only resolve the longest wavelengths (degrees 2 or possibly up to 4),
this will be important for the understanding of the nature of the two low
velocity regions at the base of the mantle, commonly referred
to as ``superplumes,'' whose thermo-chemical nature is still under debate
(e.g. *Masters et al.*, 1982; *Romanowicz*, 1998;
*Bijwaard and Spakman*, 1999;
*Ishii and Tromp*, 1999; *Romanowicz, 2001*;
*Trampert et al.*, 2004; *Gung and Romanowicz*, 2004; *Anderson*, 2005 ).

Ritzwoller M, Masters G, and Gilbert F, Observations of anomalous splitting
and their interpretation in terms of aspherical structure with low frequency
interaction coefficients: Application to uncoupled multiplets, *Journal of
Geophysical Research*, *91*, 10203-10228, 1986.

Ritzwoller M, Masters G, and Gilbert F, Constraining aspherical structure
with low frequency interaction coefficients: Application to uncoupled multiplets,
*Journal of Geophysical Research*, *93*, 6369-6396, 1988.

Romanowicz B and Mitchell B, Deep Earth Structure -- Q of the
Earth from Crust to Core, *Treatise on Geophysics*, *Volume 1*,
775-803, 2007.

Widmer-Schnidrig R and Laske G, Theory and Observations --
Normal Modes and Surface Wave Measurements, *Treatise on Geophysics*,
*Volume 1*, 67-125, 2007.

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