The moment of inertia, I, is an important constraint on the density variation within a body. It is defined with respect to a rotational axis. D. Measurement of the moment of inertia. Elastic veloctiies provide a constraint on the variation of density in the Earth. The seismic parameter.
Elastic velocities measure the square root of a ratio of elastic modulia over density.
The Adams-Williamson Equation for Self Compression. This equation is called the Adams-Williamson equation and is given by where r hand g and the seismic velocites on the right hand side of the equation are evaulated at the radius at which the gradient is calculated. The graviational accelaration g is calculated at a particular r is calculated by considering only the mass contained within the sphere of radius r. First assumption is violated at the inner core boundary and outer-core boundary, the second assumption at the upper mantle mineral phase transitions at 400 km and 650 km depth, the third assumption in zones having more rapid conveciton. This relation is useful in deducing the mineralogy of the mantle.