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We discuss procedures for the iterative solution of an integral equation of the Fredholm type of generic kernel and provide details for two particular geophysical problems. We study the inversion of gravity data in order to retrieve the profile of the underlying topography by searching for solutions giving rise to the most compact configuration. We invert radar measurements to obtain ocean spectra: this is achieved according to a perturbation procedure by minimizing a functional of errors which also expresses the deviation of the solution from an expected spectral density. Keywords: Fredholm integral equation; Ocean bathymetry; Radar measurements; Calculus of variations; Minimization of functionals.