Hidden equivalence and efficiency of gravity data interpretation

Abstract

Analytical properties of the solutions of the inverse problem of gravimetry are studied in the context of the approximative approach and method of linear integral representations. A new effect of the inheritance of specific analytical properties in the solutions, which is named the effect of hidden equivalence, is revealed and investigated. This effect significantly influences the interpretation informativity in the complex models of a medium, and it should be taken into account in the geological interpretation of gravity data. Hidden equivalence is studied for both linear and nonlinear inverse problems. As an example of a nonlinear problem, the inverse problem of structural gravimetry is analyzed. The correlation between the boundary equations and boundary values of the harmonic functions is demonstrated. Methods are suggested to allow for the effects that occur by expanding the approximative approach for complex conditions (the models of the media with spatially distributed parameters) by the dynamical and criterion principles.