Inverse Problems of Seismology (Structural Review)

The inverse problem of seismology is formulated as the determination of the set of cross-sections fitting all given observations. The schemes of solution of this problem by the trial-and-error method and the inversion method are described. Mathematical and computational problems involved in the solution are outlined. Not all these problems are solved at the present time. Among them optimal parametrization of cross-section and the determination of a probability distribution function for cross-section are the most urgent problems. But with certain limitations the described scheme of a trial-and-error method for joint interpretation of surface and body waves is in routine operation now. Results obtained are described in papers [2, 4, 6, 15, 22, 23]. Usually it is the non-uniqueness that strikes us when we see the solution of the inverse problem. But there is another side to the matter: if we do not look for an excessively detailed cross-section we may obtain quite definite conclusions even from very rough observations which are commonly regarded as useless.