An infinite-dimensional Bayesian framework estimates seabed topography and roughness simultaneously from acoustic data by assuming statistical isotropy and using fractional differentiability.
White Noise Representation of Gaussian Random Fields
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abstract
We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a Gaussian random field indexed by a compact measure space. As an application we show how existing theory for integration with respect to Gaussian processes indexed by $[0,1]$ can be extended to Gaussian fields indexed by compact measure spaces.
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Simultaneous Estimation of Seabed and Its Roughness With Longitudinal Waves
An infinite-dimensional Bayesian framework estimates seabed topography and roughness simultaneously from acoustic data by assuming statistical isotropy and using fractional differentiability.