An asymptotical inversion of the eigenfrequencies for a three-dimensional problem with spherical symmetry

An asymptotical method for the inversion of the eigenfrequencies of a three-dimensional nonhomogenous body with spherical symmetry is presented. The result is based on the uniform asymptotical approximation for the solution of linear differential equations of second order with turning points. This approximation is of a higher order than the well-known Wentzel-Kramers-Brilbuin (WKB)-approximation and provides the possibility of finding both the density and the elastic parameter of the media. The WKB-approximation provides the determination of sound speed only, which is a combination of the mentioned functions. The geophysical and helioseismological applications of the method are discussed.