Adams-Williamson equation

The Adams-Williamson equation or Adams-Williamson equation is an equation from seismology , a sub-area of geophysics . It allows you to create density profiles of the earth. For the calculation of an earth profile, the density and the gravity potential of the earth's shells as well as seismic velocities taken from an earth model (for example: IASP91 ) are necessary as starting values . It is a nonlinear integro-differential equation and in general cannot be solved analytically.

the equation

${\displaystyle {\frac {d\rho }{dr}}=-{\frac {\rho (r)g(r)}{\Phi (r)}}}$

With ${\displaystyle \Phi (r)={v_{l}}^{2}(r)-{\frac {4}{3}}{v_{t}}^{2}(r)={\frac {K(r)}{\rho (r)}}}$

and ${\displaystyle g(r)={\frac {G}{r^{2}}}\int _{0}^{r}4\pi a^{2}\rho (a)da}$

Here, the radial density gradient , ρ the density , g the acceleration due to gravity , Φ the seismic parameter inside a hydrostatically stratified, spherically symmetrical earth formed from concentric spherical shells, and the phase velocities of longitudinal and transverse seismic waves (so-called P and S- Waves), G the gravitational constant and K the compression modulus . ${\displaystyle {\frac {d\rho }{dr}}}$ ${\displaystyle v_{l}}$ ${\displaystyle v_{t}}$

See also

• Inner structure of the earth

swell

• Geophysical constraints on mirror matter within the Earth, arxiv : hep-ph / 0005125
• Lexicon of Physics: Adams-Williamson equation
• Lexicon of Physics: Adams and Williamson equation