Bernhard Steinberger $^{a}$ and Richard Holme $^{b}$
$^{a}$ Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, Colorado, USA. $^{b}$ Department of Earth Sciences, University of Liverpool, Liverpool, UK.
Core-mantle boundary topography is an important geophysical quantity for studies of core-mantle coupling (Hide, 1969) and for the dynamics of flow at the top of the core and magnetic secular variation (Kuang, 2001). There are two methods of deriving models of this topography - by seismology, and by geodynamic modelling. However, seismic models suffer from significant non-uniquness, with considerable covariance between topography and D" structure. Only P wave phases internally reflected within the core are reliable indicators of topography, which unfortunately means that data coverage is far from global (Garcia and Souriau, 2000). Here we attempt to combine both geodynamic and seismological constraints. We seek an improved model of CMB topography, using the seismological data as a constraint on the geodynamic model. In a way, we use the geodynamic modelling to "interpolate" between the seismological observations, although we do not require an exact fit to the seismological observations. Whether or not we can achieve a good fit then tells us something about the consistency of the geodynamic and the seismological method. We compute mantle flow based on a model of mantle density heterogeneities, viscosity structure and other assumptions, and represent some of the uncertainties in the model assumptions by N free model parameters. Based on the model, various quantities are computed, which can be compared to observations. We then attempt to minimize a ``misfit function'' that describes the misfit to various observations within the N-dimensional model space. Here we use geoid, heat flux profile (vs. radius), CMB excess ellipticity, long-wavelength r.m.s. CMB topography (about 600 m, when averaging over regions of > 20 degrees lateral extent; Garcia and Souriau, 2000) as well as point constraints on CMB topography where available (R. Garcia, pers. comm.) as constraints. Radial heat flux is required to remain within the bounds of the theoretical curves for internally and basally heated mantle, and a penalty is added to the misfit function wherever that is not the case. In the first set of numerical experiments, only geoid and radial heat flux profile are used as constraints. We use a viscosity structure that is based on mineral physics results (Calderwood, 1999) with three free parameters. Density heterogeneities are inferred from various s-wave tomography models. The best results were obtained based on the model smean (Becker and Boschi, 2002) which is simply an average over other published tomography models: a geoid variance reduction of 78 %, as well as a reasonable heat flux profile that implies a significant fraction (>50 %) of core heating. However, without CMB constraints, we obtain values of CMB ellipticity and r.m.s. CMB topography that are too high, but these values can be reduced if the viscosity in the lowermost mantle is reduced. In the second set of experiments, we therefore introduce an additional free parameter that allows us to vary the viscosity drop in the lowermost mantle, and in some cases also a free parameter that allows us to vary the steepness of the viscosity profiles, and we additionally use the CMB constraints described above. In this case, are were not able to simultaneously obtain a good fit to all model parameters. Essentially, if the viscosity in the lowermost mantle is sufficiently low to give appropriate values of CMB ellipticity and r.m.s. CMB topography, the predicted advected heat flux in this layer is too high, and the fit to the geoid gets considerably worse. In the third set of experiments, we therefore introduce a chemical boundary in the lowermost mantle at variable depth -- thus introducing an additional free parameter -- since it has been suggested (e.g. Christensen and Hoffmann, 1994), that the region above the core-mantle-boundary may be compositionally distinct, e.g. it may contain the remains of subducted oceanic crust. In this case, we can simultaneously obtain a good fit to the geoid (81 % variance reduction), as well as reasonable heat flux profile, CMB ellipticity and r.m.s. CMB topography. The computed stresses on the compositional boundary correspond to about 200 km peak-to-peak, if a density increase of 3 % is assumed. However, the point constraints on CMB topography are not very well fit by any of these experiments. This may be related to the fact, that the worst misfit (more than twice the formal uncertainty) occurs in regions that are usually less than 10-15 degrees of arc across. Garcia and Souriau (2000) find a much higher r.m.s CMB topography when averaging over such = smaller regions. Such small-scale topography is not present in our model predictions, and may therefore be due to density heterogeneities that are not imaged in the tomography models used. References: Becker, T. W., and L. Boschi, A comparison of tomographic and geodynamic mantle models, Geochem. Geophys. Geosyst., 3, 2001GC000168, 2002. Calderwood, A. R., Mineral Physics Constraints on the Temperature and Composition of the Earth's mantle, Ph.D. thesis, University of British Columbia, %Dept. of Earth and Ocean Sciences, 1200 pp., 1999. Christensen, U. R, and A. W. Hofmann, Segregation of subducted oceanic crust in the convecting mantle, J. Geophys. Res., 99, 19,867-19,884, 1994. Garcia, R., and A. Souriau, Amplitude of the core-mantle boundary topography estimated by stochastic analysis of core phases, Phys. Earth Planet. Inter., 117, 345-359, 2000. Hide, R., Interaction between the earth's liquid core and solid mantle, Nature, 222, 1055-1056, 1969. Kuang W. J., and Chao, B. F., Topographic core-mantle coupling in geodynamo modeling Geophys. Res. Lett., 28, 1871-1874, 2001.