Bayesian estimation of medium properties in wavefield downward extrapolation problems

When acoustic waves are used for nondestructive imaging of the interior of objects such as the Earth the human body, etc., the wavefield measurements recorded on the surface of the object are extrapolated according to the wave equation to give an image of the object. The extrapolation propagates backward the noise present in the measurements, so that the quality of the final image is degraded, unless statistical restoration techniques are used. Another source of degradation of the image is the insufficient knowledge of some properties of the medium such as the wave propagation velocity. Bayesian estimation techniques are proposed for the problems and are shown to be superior to known methods such as direct inversion or Wiener filtering. Their superiority comes from the fact that they utilize all the a priori information available and also provide means to estimate characteristics of the media. Most of them are iterative algorithms, which give a flexibility in the techniques but cause problems when the convergence rate is slow. In general, the algorithms are quite computationally intensive since they use two-dimensional fast Fourier transforms for their implementation