Regularization uncertainty in density models estimated from normal mode data

Normal mode structure coefficients provide important constraints on the long-wavelength component of 3-D mantle density (rho) structure, but inversions for independent models of v(s), v(p), and rho 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 rho 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 v(s), v(p), rho, and boundary topography structures. The estimated rho models are fairly robust with respect to prior constraints on v(s), v(p), and topography. However, the character and amplitude of the estimated rho models depend strongly on how rho is allowed to decorrelate from vs, and we display several models in which rho and v(s) 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 rho from v(s). It remains possible that reliable rho models may be obtained in the future as more normal mode measurements are introduced to break the strong tradeoffs between upper and lower mantle rho structures that characterize current inversions.