Geoid, its Temporal Variation and Dynamic Topography as Constraints in Global Geodynamics

\textbf{Introduction} Density distributions derived from highly resolved seismic tomography and viscosity models of Earth's mantle are investigated in analytical and numerical flow models. The aim of this project is to fit the models' predicted observables to the GRACE satellite-mission's gravity and geoid measurements and the field's variation with time and to reproduce estimates of dynamic topography as an additional constraint. Advection of a given density field yields temporal variations in the geoid and dynamic topography. In order to investigate whether identifiers of such mantledynamic processes may be discerned from other signals contained in GRACE-data, these quantities will be analyzed in the spatial and spectral domain. This permits predictions for regional mantledynamic contributions and renders variations of the harmonic coefficients with time, thus providing corrective fields to apply to GRACE-data. \textbf{Modelling} Advection of mantle density distributions derived from seismic tomography drives a flow. The variables of the governing flow equations are expressed in terms of products of radial functions and scalar spherical harmonics, yielding a set of coupled first order differential equations. Spheroidal and toroidal terms decouple, the initial solutions for a set of boundary conditions are propagated through a series of shells of constant values for the sought variables by the propagator matrix [Panasyuk and Hager, 1996]. This in turn yields solutions in the form of boundary vectors that give the fluid velocities, stresses, gravitational potential and its radial derivative at any radial level in the earth. \textbf{Results} We reproduce 70 % of the observed long-wavelength geoid corrected for isostatically compensated crust and oceanic lithosphere. Gravity field measurements and estimates of dynamic topography [Panasyuk and Hager, 2000] serve to further constrain the range of acceptable models. Advection of density distributions of best-fitting models permits first estimates of the magnitude of temporal geoid variations. According to our preliminary results, the time-dependent geoid signals produced by mantle-dynamic processes may reach or exceede the expected resolution limits for temporal geoid changes of the 5 - year GRACE mission. An iterative search of the parameter space should yield models of improved fit to the observables and its variations. \textbf{References} S.V. Panasyuk and B.H. Hager. Understanding the effects of mantle compressibility on geoid kernels. \textit{Geophysical Journal International}, 124:121-133, 1996. S.V. Panasyuk and B.H. Hager. Models of isostatic and dynamic topography, geoid anomalies, and their uncertainties. \textit{Journal of Geophysical Research}, 105:28,199-28,209, 2000.