On a self-consistent representation of earth models,with an application to the computing of internal flattening

Most realistic Earth models published as yet have been given in tabulated form, with the noticeable exception of three simple parametric Earth models derived by Dziewonski et al. (1975). Simple interpolation in these tables may lead to inconsistencies, when we consider certain effects which depend crucially on detailed density structure. We establish algorithmic formulae, which may be used to compute all the mechanical properties of a model in an entirely consistent way, once the density as well asP— andS— wave velocities are known. We then use this formulation to integrate Clairaut’s equation in a very efficient way, and thus obtain the hydrostatic flattening to the first order in smallness at any point inside the model. For most geodynamic purposes, we may suffice with this approximation. Finally, we show the results of some calculations of hydrostatic flattening to the first and second order, using an iterative technique of solving the integral figure equations, for an Earth model consistent with all geophysical data available at present. We find that the hydrostatic flattening at the surface should be about 1/298.8, instead of 1/296.961 as quoted by Nakiboglu (1979) for essentially the same model. Moreover, from our results, we estimate the actual flattening of the coremantle boundary to be about 1/390.3.