Two notes on the modern theory of inverse problems in geophysics

On the basis of comparison of the approaches to the solution of inverse problems in information theory and geophysics, it is shown that results, obtained in information theory, are suitable to supplement the theory of geophysical inverse problems. The conditions of the existence and uniqueness of the solutions of inverse problems in their practical discrete statement are specified. The terms of ɛ-entropy H _ɛ and informational capacity C _ɛ, characterizing “volumes” of unknown and observed data, are introduced. It is shown, that the instability of the solution of the inverse problem decreases with increase in H _ɛ, (increase in the “complexity” of studied section), if the relation H _ɛ ≤ C _ɛ is maintained.