Adams–Williamson equation
Part of a series on |
Earthquakes |
---|
The Adams–Williamson equation, named after
History
Williamson and Adams first developed the theory in 1923. They concluded that "It is therefore impossible to explain the high density of the Earth on the basis of compression alone. 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."[3]
Theory
The two types of seismic body waves are compressional waves (
These two speeds can be combined in a seismic parameter
-
(1)
The definition of the bulk modulus,
is equivalent to
-
(2)
Suppose a region at a distance r from the Earth's center can be considered a fluid in
-
(3)
where g(r) is the gravitational acceleration at radius r.[3]
If Equations 1,2 and 3 are combined, we get the Adams–Williamson equation:
This equation can be integrated to obtain
where r0 is the radius at the Earth's surface and ρ0 is the density at the surface. Given ρ0 and profiles of the P- and S-wave speeds, the radial dependence of the density can be determined by numerical integration.[3]
References
- ISBN 978-0-521-89307-7.
- ISBN 978-1-4614-9090-6.
- ^ ISBN 0-521-66313-X.
- .