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Resolution of 3D density structure in the mantle using normal mode data

Barbara Romanowicz

Introduction

A recent study by Ishii and Tromp (1999) has revived a long-lasting controversy regarding whether or not lateral variations in density in the mantle can be constrained using normal mode data. In principle, low angular degree normal modes are sensitive to 3D structure in all three elastic parameters: $V_{s}$, $V_{p}$, and density ($\rho $). However, the sensitivity to $\rho $ is significantly smaller than that to $V_{s}$ or $V_{p}$, making it difficult to resolve even the 1D mantle density profile, and casting doubts as to the feasibility of resolving $\rho $ in 3D.

Using a collection of normal mode splitting data to test inversions for 3D elastic structure up to degree 8, Resovsky and Ritzwoller (1999) showed that the resulting density distribution depends strongly on a priori constraints on the model parametrization and regularization. Recently, Kuo and Romanowicz (2000) inverted normal mode spectral waveforms to illustrate how, depending on the parametrization and the starting models in $V_{s}$ and $V_{p}$, significantly different final density models can be obtained. In the latter study, lateral structure up to spherical harmonics degree 6 was considered.

A prominent feature of the Ishii and Tromp (1999) model is that high density regions correspond to low seismic velocities, in the central Pacific and under Africa, in the bottom 200-500 km of the mantle. If robust, this structure bears important implications for the dynamics and mineral physics of the mantle. This feature has a strong degree 2 component. Since higher order normal mode splitting coefficients are still subject to large measurement uncertainties, whereas different authors agree on the values of most degree 2 coefficients, we reanalyze the degree 2 data to try and further clarify the issue of resolution of 3D density structure in the mantle. This analysis also allows us to confirm the behavior, at the longest wavelengths, of the ratio $R_{s/p} = dlnVs/dlnVp$, which appears to increase with depth in the lower mantle (e.g. Robertson and Woodhouse, 1995; Su and Dziewonski, 1997).

Dataset and Model Parametrization

Degree 2 splitting coefficients were measured recently by various authors. We only consider mantle modes with no sensitivity in the inner core. We exclude modes for which measurements differ significantly between authors. In particular, only 13 toroidal modes are kept, for which at least two compatible measurements exist, or for which the unique measurement agrees with the predictions of the SH tomographic model SAW12D (Li and Romanowicz, 1996). Several layered parametrizations are considered. Data are corrected for crustal structure using an isostatically compensated Moho model based on Etopo5 topography and bathymetry. The details of the crustal corrections have no incidence on the lower mantle structure retrieved. Since the resolution of this low angular order splitting dataset is poor in the upper mantle, we focus the discussion on the lower mantle results.

Figure 29.1: Maps of degree 2 in $Vs$, $Vp$ and $\rho $ at representatives depths in the lower mantle, for a model obtained by inverting the 3 parameters independently. Note the low densities in the central Pacific at a depth of 2800km.
\begin{figure}\begin{center}
\epsfig{file=barbara01_1_fig1.eps, bbllx=20,bblly=100,bburx=227
,bbury=320,width=8cm}\end{center}\end{figure}

In our inversions, we consider overall norm damping parameters that can be adjusted separately for $V_{s}$, $V_{p}$ and $\rho $ as well as for topography of the 670-km discontinuity (d670) and the core-mantle boundary (CMB). No regularization scheme is applied to better assess where instabilities arise in the models. The damping parameters are adjusted so that (1) on average, the amplitudes of the depth profiles of individual degree 2 coefficients in $V_{s}$ match those of recent S tomographic models; (2) $R_{s/p}$ = $dlnV_{s}/dlnV_{p}$ matches the range of 1.5 to 2 predicted by mineral physics and obtained in previous studies in the top 1500km of the mantle; (3) when inverting independently for density, $R_{\rho /s}$ = $dln\rho/dlnV_{s}$ is on average between 0.2 and 0.3 in the mid-mantle, compatible with predictions from geodynamics and mineral physics studies (e.g. Forte and Woodward, 1997; Karato and Karki, 2000); (4) the C20 component of the CMB topography has a value comparable with that inferred from astronomical observations. Assigning the same damping parameter to $V_{s}$ and $V_{p}$ obtains (2) without further adjustments, which is an indication that $V_{p}$ can be resolved independently of $V_{s}$. However, to obtain (3), $\rho $ needs to be damped at least twice as much, and the resulting profile of $R_{\rho /s}$ is much less regular. Figure 29.1 shows an example of a model obtained by inverting independently for $V_{s}$, $V_{p}$ and $\rho $.

Results

Our results show that degree 2 $V_{s}$ and $V_{p}$ structure is independently well resolved. The ratio $R_{s/p}$ increases significantly below 2000km depth, confirming earlier results. Additional tests, with a parameter search on $R_{s/p}$ and fixed $R_{\rho /s}$, confirm this trend, although the variance reduction achieved in such experiments is not as good as in the experiments in which $\rho $ and $V_{s}$ are allowed to vary independently, indicating that the assumption of perfect correlation of $V_{p}$, $V_{s}$ and $\rho $ is too strong.

In a study based on body wave travel times, Bolton (1997) observed that a particular region in the Pacific Ocean was primarily responsible for the anomalously large $R_{s/p}$ in the lowermost mantle. However, the global coverage was rather uneven. The fact that we observe this in degree 2 indicates that there is a global, large scale component of heterogeneity in the lowermost mantle that cannot be explained by thermal effects alone.

Structure in $\rho $, even at degree 2, is not well resolved. When $\rho $ is inverted for independently of $V_s$ and $V_p$, the sign of $R_{\rho /s}$ in the bottom 500km of the mantle trades off with topography on the CMB. Density models based on geodynamics and mineral physics inferences are compatible with the data, whereas models with amplitudes of density heterogeneity exceeding the latter by a factor of 2 or more can be ruled out (Figure 29.2). The mode splitting data alone cannot resolve the existence of high density "blobs" in the central Pacific and under Africa: models with positive correlation between $\rho $ and $V_s$ in the lowermost mantle yield slightly, but not significantly, better fits to the data (Figure 29.1), but small negative $R_{\rho /s}$ in the lowermost mantle cannot be ruled out.

The most robust feature of the degree 2 in $\rho $ is the increase in $R_{\rho /s}$ at the top of the lower mantle (Figure 29.2), reaching a maximum in the depth range 1000-1500km. Below that depth $\vert R_{\rho/s}\vert<$0.3, but its sign is not well constrained.

Figure 29.2: From left to right: $R_{p/s}$, correlations between $V_s$ and $V_p$, and $R_{\rho /s}$, as a function of depth, for the 20 best (top) and 20 worst (bottom) models obtained by inverting for $V_s$ and $V_p$ independently, and assigning separate $R_{\rho /s}$ in different depth ranges. In all cases, the layer parametrization is the same (from Romanowicz, 2001a).
\begin{figure}\begin{center}
\epsfig{file=barbara01_1_fig2.eps,bbllx=155,bblly=390,bburx=388,bbury=577, width=8cm}\end{center}\end{figure}

References

Bolton, H., Long period travel times and the structure of the Mantle, PhD Thesis, Univ. of Calif. San Diego, 1996.

Forte, A.M. and R. L. Woodward, Seismoc-geodynamic constraints on three-dimensional structure, vertical flow and heat transfer in the mantle, J. Geophys. Res.,, 102, 17981-17994, 1997.

Ishii, M., and J. Tromp, Normal-mode and free-air gravity constraints on lateral variations in velocity and density of Earth's mantle, Science, 285, 1231-1236, 1999.

Kuo, C. and B. Romanowicz, On the resolution of density anomalies in the Earth's mantle using spectral fitting of normal mode data, Geophys. J. Int, in revision, 2000.

Li, X.D. and B. Romanowicz, Global mantle shear-velocity model developed using nonlinear asymptotic coupling theory, Geophys. J. R. Astr. Soc., 101, 22,245-22,272, 1996.

Resovsky, J. S., and M. H. Ritzwoller, Regularization uncertainty in density models estimated from normal mode data, Geophys. Res. Lett., 26, 2319-2322, 1999.

Robertson, G. S. and J. H. Woodhouse, Evidence for proportionality of $P$ and $S$ heterogeneity in the lower mantle, Geophys. J. Int., 123, 85-116, 1995.

Su, W. and A.M. Dziewonski, Simultaneous inversion for 3-D variations in sehar and bulk velocity in the mantle, Phys. Earth Planet. Inter., 100, 135-156, 1997.


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