Frequency Dependent Anelasticity

Joseph Durek, Barbara Romanowicz

Subsections

• References

Anelasticity, and the resulting velocity dispersion, is required in the Earth to reconcile seismic observations spanning three decades in frequency [e.g. Montagner and Kennett, 1996) and to compare high-frequency laboratory measurements with low-frequency tomographic models [e.g. Romanowicz, 1990; Karato, 1994]. Observed seismic wave attenuation is well explained by frequency independent anelasticity, which led to the concept of the mantle response as a superposition of absorption peaks with roughly constant attenuation in the seismic band.

We have performed preliminary investigations of the frequency dependence of anelasticity using the tranverse component surface (T>80s) and body (T>32s) waveforms of Li and Romanowicz [1986] as well as a compilation of published normal mode quality factors. We consider a power law dependence of attenuation, $Q^{-1} \sim \omega^{-\alpha}$. In our preliminary investigation, we conclude:

• Waveform inversion for anelasticity, an approach initiated at UC Berkeley [Romanowicz et al., 1996], leads to radial models of $Q_{\mu}$ consistent with previous surface wave studies. Compared to PREM [Dziewonski and Anderson, 1981], the new 1D model explains an additional 9% of the body waveform variance and 3% of the surface waveform variance.

• Inversions for frequency dependent absorption using normal mode observations has a clearly defined value of $\alpha$. It had previously been assumed that a strong trade-off existed between frequency dependence and depth resolution which would lead to a suite of acceptable values of $\alpha$.

• The inferred value of $\alpha$=0.05 is significantly lower than that observed in the laboratory (0.2-0.3). This difference would be consistent with the average grain size in the mantle being larger than that of laboratory samples, leading to a reduced frequency dependence (I. Jackson, personal communication).

References

Durek, J.J., and B. Romanowicz, Frequency Dependent Relaxation in the Seismic Band (invited abstract), EOS Trans. AGU, 78, 1997.

Dziewonski, A. M., and D. L. Anderson, Preliminary reference Earth model(PREM), Phys. Earth Planet. Inter., 25, 297-356, 1981.

Karato, S.,Importance of anelasticity in the interpretation of seismic tomography, Geophys. Res. Lett., 20,1623-1626, 1993.

Li, X.-D., and B. Romanowicz,Global mantle shear velocity model developed usingnonlinear asymptotic coupling theory,J. Geophys. Res., 101, 22,245-22,272, 1996.

Romanowicz, B., The upper mantle degree 2: Constraints and inferencesfrom global mantle wave attenuation measurements, J. Geophys. Res.,95, 11,051-11,071, 1990.

Romanowicz, B., C. Megnin, and X.-D. Li, Waveform inversion for global mantle elastic and anelastic structure (abstract), EOS Trans. AGU, 77, 482, 1996.

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