Regularization uncertainty in density models estimated from normal mode data

Abstract

Abstract. Normal mode structure coefficients provide important constraints on the long-wavelength component of 3-D mantle density (ρ) structure, but inversions for independent models of vs, vp, and ρ using normal mode data alone are ill-posed even at long wavelengths. Ill-posed inversions typically are regularized by imposing a priori assumptions on the set of estimated models, but such regularization can introduce important uncertainties in the models. We characterize these uncertainties for ρ models estimated from current normal mode data using a set of 512 different "regularization schemes". These schemes sample a variety of plausible a priori assumptions about the nature and distribution of mantle heterogeneity by specifying allowable vs, vp, ρ, and boundary topography structures. The estimated ρ models are fairly robust with respect to prior constraints on vs, vp, and topography. However, the character and amplitude of the estimated ρ models depend strongly on how ρ is allowed to decorrelate from vs, and we display several models in which ρ and vs decorrelate in very different depth intervals. Because these models all result from plausible prior constraints and fit the data equally and acceptably well, inversions of current normal mode data cannot robustly locate the decorrelation of ρ from vs. It remains possible that reliable ρ models may be obtained in the future as more normal mode measurements are introduced to break the strong tradeoffs between upper and lower mantle ρ structures that characterize current inversions.

Error bars for the global seismic Q profile

“…Though this approach is computationally efficient, it has the disadvantage of requiring a priori information in the form of strong damping to compensate for the relatively poor resolution of the existing attenuation data set. If a Backus-Gilbert regularization technique [14,15] is applied, optimal use can be made of the data resolution, but model uncertainty still tends to be underestimated, and model features that come from the data rather than the regularization are best determined by performing many inversions with different regularization schemes [6,11,16].…”

Towards a quantitative interpretation of global seismic tomography

“…Ishii and Tromp [1999] were the first to identify small or negative correlations between density and shear sound speed in the lower mantle. Their model was criticized as not being robust with respect to damping [Resovsky and Ritzwoller, 1999;Romanowicz, 2001] and initial models and parameterization [Kuo and Romanowicz, 2002]. While this may be true for the amplitude of the inferred density anomalies, the pattern and sign of the anomalies proved to be correct.…”

Global Imaging of the Earth's Deep Interior: Seismic Constraints on (An)isotropy, Density and Attenuation

“…When the data constraints are weak, this subjectivity dominates the perceived resolution, expressed, for instance, in terms of the posterior covariance Cm (Equation 11.9). Based on a series of test inversions with different choices of the prior information, Resovsky & Ritzwoller 1999 concluded that a decorrelation of S velocity and density could not be detected reliably. A similar conclusion was reached by Romanowicz (2001), who found that density in the lower mantle trades off strongly with the topography of the core-mantle boundary, and that gravity data hardly discriminate between different density models.…”

“…Resovsky & Ritzwoller (1999) pointed out that the resolution analysis in a deterministic inverse problem depends on the prior knowledge, i.e. the choice of the prior model covariance σ 2 m in Equations (11.8) and (11.9).…”