Inversion of ERT data including uncertainties using the FE and RB methods

The inversion process of data sets acquired with the electrical resistivity tomography can be a computational expensive calculation, because it requires a lot of forward simulations. Since computational resources are limited, the inversion for large field surveys can require immense computing times. One approach for reducing the computing times of forward simulations is the reduced basis method. It splits the problem into a parameter-dependent and parameter-independent part, which allows a precomputation of the parameter-independent part to speed up the calculation. Since the method of reduced basis has not been applied for the problem of electrical resistivity tomography so far, the question arises if and how it is applicable for this problem. Therefore, I performed forward simulations of the electrical potential distribution using the finite elements method and simulations using the reduced basis method for comparing the results. The methods give similar results, but unfortunately deviations above 1*10^4 occurred, while the error tolerance of the reduced basis method is set to 1*10^5. Since the reduced basis method has been successfully applied on other applications, I assume that the problem is in my reduced basis simulation and can be solved by more fine tuning. By comparing the computing times of the simulations, a speed-up of 109.512 is achieved by using the reduced basis method. Furthermore, the pay-off is reached after 8.803 simulations. During the project, I noticed that only considered the resistivities of the subsurface as a varying parameter in the reduced basis is not sufficient. The source position needs to be a variable parameter in simulations of the electrical resistivity tomography, as well. This is necessary to tap the full potential of the reduced basis method in the application of the electrical resistivity tomography. The reduced basis method gives significant speed-ups and therefore, it has the potential to reduce the computing times of electrical resistivity tomography inversions