Likelihood distributions for radio wave tomography

Radio wave tomography is a remote sensing technique for imaging a block of rock between two or more boreholes using radio waves. The visualization of the attenuation or slowness [inverse velocity] properties of the rock is a signal estimation problem of estimating an image of physical parameters from one-dimensional projection data. The Bayesian paradigm consists of decomposing the posterior signal estimate into a product of prior and likelihood probability distributions. We examine the choice of likelihood distribution on the final signal reconstruction. In particular, Gaussian and exponential likelihood distributions are investigated and their performance is compared for reconstructing an image of rock attenuation from a radio tomography survey conducted in a base metal mine in the northern Cape