# 亚当–威廉姆森方程

（重定向自亚当–威廉姆斯方程

## 理论

{\displaystyle {\begin{aligned}v_{p}&={\sqrt {\frac {K+(4/3)\mu }{\rho }}}\\v_{s}&={\sqrt {\frac {\mu }{\rho }}}.\end{aligned}}}

${\displaystyle \Phi =v_{p}^{2}-{\frac {4}{3}}v_{s}^{2}={\frac {K}{\rho }}.}$

(1)

${\displaystyle K=-V{\frac {dP}{dV}},}$

${\displaystyle K=\rho {\frac {dP}{d\rho }}.}$

(2)

${\displaystyle {\frac {dP}{dr}}=-\rho (r)g(r),}$

(3)

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

${\displaystyle \ln \left({\frac {\rho }{\rho _{0}}}\right)=-\int _{r_{0}}^{r}{\frac {g(r)}{\Phi (r)}}dr,}$

## 参考来源

1. ^ C. M. R. Fowler. The Solid Earth: An Introduction to Global Geophysics. 剑桥大学出版社. 2005: 333–. ISBN 978-0-521-89307-7 （英语）.
2. ^ Eugene F. Milone; William J.F. Wilson. Solar System Astrophysics: Planetary Atmospheres and the Outer Solar System. Springer Science & Business Media. 2014-01-30: 494–. ISBN 978-1-4614-9090-6 （英语）.
3. Poirier, Jean-Paul. Introduction to the Physics of the Earth's Interior. Cambridge Topics in Mineral Physics & Chemistry. 剑桥大学出版社. 2000. ISBN 0-521-66313-X （英语）.
4. ^ Dziewonski, A. M.; Anderson, D. L. Preliminary reference Earth model. Physics of the Earth and Planetary Interiors: 297–356. Bibcode:1981PEPI...25..297D. doi:10.1016/0031-9201(81)90046-7 （英语）.