GEOPHYSICAL RESEARCHLETTERS, VOL. 22, NO. 9, PAGES 1013-1016, MAY 1, 1995 Seismic-geodynamic determination of the origin of excess ellipticity of the core-mantle boundary Alessandro M. Forte Institut de Physiquedu Globe de P•ris, D•pt. de Sismologie, P•ris, France Jerry X. Mitrovica Department of Physics, University of Toronto, Toronto, Ontario, Canada Robert L. Woodward Albuquerque Seismological Lab., U.S.G.S., Albuquerque, NM, USA Abstract We demonstrate that the excess dynamic ellipticity of the core-mantle-boundary (CMB) inferred from the period of the Earth's retrograde free core nutation (RFCN) may be explained in termsof viscous stresses generatedby mantle convective flow. The 3D elastic structure and radial viscosity profile which define the model used in the viscous flow calculations are con- strained to simultaneously reconcile a large set of seis- mic and geodynamic data. Introduction The outer surface of the Earth and the CMB are char- acterized by relatively small departures from perfectly spherical forms. In the case of the ellipticity of the CMB, a misalignmentof the rotation axes of the man- tle and fluid outer coreresultsin a pair of perturbations in the Earth's rotational dynamics:The retrogradefree corenutation(RFCN), whichcorresponds to a retro- grade motion of the figure axis in inertial space, and the related nearly diurnal free wobble (NDFW) [e.g., Wahr,1981].If oneneglects viscous, gravitational, and electro-magnetic coupling between the mantle and core, then the period of the RFCN may be used to infer the dynamical ellipticity of the CMB andits flattening [e.g., Gwinnet al., 1986]. Recent calculations suggest that other components of the CMB topography contribute a small, but potentially non-negligible, perturbation to the RFCN period[Wu and Wahr,1994]. Theoretical predictions of the period of the RFCN, based on radially stratified referenceEarth models and Poincard core flow, are summarized in Table 1 (see also Table 2 of Cummins and Wahr [1993]). The pre- dicted RFCN period for the elastic Earth models 1066A and PREM are very near 460 days. Table 1 also lists published •observational estimatesof the RFCN period based on a number of independentdata sets. These esti- Copyright 1995 by the American Geophysical Union. Papernumber95GL01065 0094-8534/95/95GL-01065503.00 mates are all obtained from observations of the (RFCN induced) resonant enhancements of the Earth's forced response to the lunisolar gravitational potential. (Di- rect detectionof the RFCN eigenmode has only recently been claimed [e.g., Herring et al., 1991].) The most accurate of the studies have consistently suggested an RFCN period near 430 days. The discrepancy between the theoretically predicted periodof the RFCN [Wahr, 1981]and the VLBI deter- mined value for this period [Herring et al., 1986]led Gwinn et al. [1986] to suggest that the CMB elliptic- ity is larger than that implied by the theoretical calcu- lation which assumeda rotating Earth in hydrostatic equilibrium. This inferenceof a nonhydrostaticor 'ex- cess'CMB elliptictry, expressed by the degree 2 zonal coefficient 50• ø- -0.52 q- 0.12 km, (1) is supported by subsequent analyses of the RFCN pe- riod (Table 1). The spherical harmonic normalization assumed in (1) and throughout this paper is that of Gwinnet al. [1986]. An explanation for the excess ellipticityof the CMB hasremained elusive. The seismically inferred radially stratified reference Earth models (and the associated hydrostatic CMB flattening) may beuncertain; however our owncalculations suggest that the changes in these reference Earth models which would be required to rec- oncile the theoretical predictions of the RFCN period with the observations would lead to significant misfits to the seismic constraints. The most viable explanation for the excess ellipticityis to be foundin the dynamic stresses exerted on the CMB by the thermal convective flow in the mantle [Forte et al., 1994a,b]. The plausibil- ity of thisexplanation was suggested by theearliest pre- dictions of mantle flow using seismic tomographic mod- els of 3D mantle structure, by Hager et al. [1985]; these calculations showed that mantle flow could readily gen- erateCMB undulations of several kilometres amplitude [see also Hagerand Clayton, 1989; Forte andPeltier, 1991; Forte et al., 1993].In this paper we will present a fullyconsistent explanation fortheexcess CMB elliptic- ity in (1) in terms of mantle flowpredicted with recent seismic tomographic modelsof 3D mantle structure. 1013