Quantitative statement and general properties of solutions of cooperative inverse problems (integral geophysics)

Abstract

Sometimes geophysical methods used independently can yield no solution of a practical problem because of nonstability (either in general or because of lacking information). Cooperative data inversion of a few methods with the help of optimization procedures of summation functionals may bring about irresistible complication of problems (non-stability of solution and appearance of false extrema) due to the poor theoretical grounds of the statement of these problems. The paper proposes a quantitative (mathematical) statement of cooperative inverse problems of geophysical methods of different physical nature. Cause and effect of non-equivalence of the totality of all individual inverse problems and the unit cooperative problem have been studied. The complimentary geophysical feature of inverse problems of different methods has been formulated. Examples are presented of two or more methods, which are not able to give a unique or stable solution in an individual statement, yielding a unique and stable solution to a cooperative problem.