### The moments of the mass anomalies in the upper layers of the Earth

#### Abstract

In this note we consider the lithospheric and asthenospheric mass distribution from a purely static point of view and ask which would be the great circle of the Earth’s surface corresponding to the *maximum moment of inertia*, *MMI*, or else the associated theoretical rotation axis. For the present-day distribution of mass at depth, we consider the most updated crustal and lithospheric models satisfying general geological and geophysical laws. In order to simulate isostatic conditions, we also test different density models of the outer 400 and 670 km of the Earth based on topography. For the numerous tested density distribution models we identify the theoretical rotation axis corresponding to the *MMI* and compare these axes to the present-day one. Numerical results considering only the lithospheric shell show theoretical rotation axes strongly inclined and hence a complete lack of equilibrium. In other terms, as well known, the lithosphere alone formally decoupled from the asthenosphere is not a realistic geodynamic model. Using conventional asthenospheric density values, the tested mass distribution models showing theoretical axes of rotation close to (but not coincident with) the present-day one are those obtained with a compensation depth of 400 km. Assuming the existence of a deep mantle mainstream inclined with respect to the present equator and the best fitting *MMIs* associated with the 400 km-thick shell, our results suggest the occurrence of a decoupling layer within the upper asthenosphere, which is only partially able to transmit the motion to the outer Earth's shell.

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