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This paper considers the problem of estimating a two-dimensional isotropic random field given some noisy observations of this field over a disk of finite radius. By expanding the field and observations in Fourier series, and exploiting the covariance structure of the resulting Fourier coefficient processes, some vibrating equations are obtained for estimating the random field. These equations provide a set of recursions for constructing the field estimates as the radius of the observation disk increases. In the spectral domain, these recursions take the form of Schrodinger equations which can be viewed as being associated to an inverse scattering problem. (Author)