Three-dimensional ERT imaging by the geostatistical approach

Abstract:

Electric resistivity tomography (ERT), with observations made at the surface or in boreholes, is a method of imaging the subsurface with many potential applications in areas that include hydrology and environmental engineering. The estimation of the resistivity function from observations is a classic inverse problem. One method to solve this problem is the Geostatistical Approach (GA), which is a stochastic method that allows one to explore the range of possible solutions. GA is an objective and empirical Bayes method. The emphasis of this talk is on methods to reduce the computational cost of implementing this approach. We will show examples of application of the Principal Component Geostatistical Approach (PCGA). PCGA is Jacobian-free and uses forward solvers as black boxes. It utilizes the leading principal components from the prior covariance to obtain a good approximation of the solution at a fraction of the cost.