The Adams–Williamson equation, named after Leason H. Adams and E. D. Williamson, is an equation used to determine density as a function of radius, more commonly used to determine the relation between the velocities of seismic waves and the density of the Earth's interior.
[2] It assumes that the compression is adiabatic and that the Earth is spherically symmetric, homogeneous, and in hydrostatic equilibrium.
The dense interior cannot consist of ordinary rocks compressed to a small volume; we must therefore fall back on the only reasonable alternative, namely, the presence of a heavier material, presumably some metal, which, to judge from its abundance in the Earth's crust, in meteorites and in the Sun, is probably iron.
The definition of the bulk modulus, is equivalent to Suppose a region at a distance r from the Earth's center can be considered a fluid in hydrostatic equilibrium, it is acted on by gravitational attraction from the part of the Earth that is below it and pressure from the part above it.
Given ρ0 and profiles of the P- and S-wave speeds, the radial dependence of the density can be determined by numerical integration.