Radio waves may be used to image the electrical properties of rock for geological exploration and mining. The tomographic reconstruction of an attenuation image from radio wave survey data may be formulated as an ill-posed linear inverse problem for which two types of information are usually available: data collected by the remote sensing process and prior information on the expected form of the reconstruction image. The inversion is ill-posed since the data are incomplete and noisy and an inexact simplified linear model of radio wave propagation through rock is assumed. Such inverse problems have many 'solutions' which fit the observed data and we must choose one reconstruction as an answer. Bayesian image estimation provides a consistent framework for reconstructing an image from noisy and in- complete data. We discuss the choice of statistical distributions to represent our prior knowledge of the image to be estimated as well as the likelihood of this image relative to the measured data. We illustrate the approach by presenting rock attenuation and variance estimate images computed for a radio tomography survey in a base metal mine in Namibia.
Neil Pendock, Neil Pendock,
"Radio-wave tomography for geological mapping", Proc. SPIE 1942, Underground and Obscured Object Imaging and Detection, (15 November 1993); doi: 10.1117/12.160331; https://doi.org/10.1117/12.160331