Robin Thibaut , Nicolas Compaire, Nolwenn Lesparre, Maximilian Ramgraber, Eric Laloy, Thomas Hermans

Temperature logs are an important tool in the geothermal industry. Temperature measurements from boreholes are used for exploration, system design, and monitoring. The number of observations, however, is not always sufficient to fully determine the temperature field or explore the entire parameter space of interest. Drilling in the best locations is still difficult and expensive. It is therefore critical to optimize the number and location of boreholes. Due to its higher spatial resolution and lower cost, four-dimensional (4D) temperature field monitoring via time-lapse Electrical Resistivity Tomography (ERT) has been investigated as a potential alternative. We use Bayesian Evidential Learning (BEL), a Monte Carlo-based training approach, to optimize the design of a 4D temperature field monitoring experiment. We demonstrate how BEL can take into account various data source combinations (temperature logs combined with geophysical data) in the experimental design (ED). To optimize the ED and determine the best data source combination, we use the Root Mean Squared Error (RMSE) of the predicted target in the low dimensional latent space where BEL is solving the prediction problem. The generated models agree well with the true models and are accurate enough to be used in optimal ED.
Furthermore, the method is not limited to monitoring temperature fields and can be applied to other similar experimental problems.
The method is computationally efficient and requires little training data. A training set of only 200 is sufficient for the considered optimal design problem.