Bayesian inversion of Electrical resistivity data at Gondar waste disposal site, Gondar, Ethiopia

Abstract

This thesis presents a practical and objective procedure for a Bayesian inversion of geophysical data. Inverse problems in geophysics allow us to gauge parameters we cannot directly observe. A desire to quantify uncertainty of the inverted parameters requires formulating the problem as a statistical inversion. The aim of statistical inversion is to estimate parameters of interest together with corresponding uncertainties conditioning on the measurement and some prior information about the parameters. This approach requires specifying the measurement and prior information on the model parameters in probability to compute the solution as a conditional posterior density. The conditional posterior probability of the model parameters, given the measured data is considered as a solution in this approach. Markov chain Monte Carlo (MCMC) simulation from the posterior is used to estimate conditional means and to quantify corresponding uncertainties. For the measurement, we used geophysical data that was collected in a survey from solid waste disposal site of Gondar, Ethiopia. The resistivity data were inverted using Bayesian inversion technique and layer thicknesses were obtained from the field data and provide information on subsurface properties. This means to map weak and fracture zones that may be used as pathways for percolating wastes, depth to bedrock, location and distribution of conductive fluids, and location and orientation of bedrock fractures, fracture zones and faults. Then the eastern part of the disposal site is fracture and a weak zone of amygdaloidal basalt