Optimized arrays for electrical resistivity tomography survey using Bayesian experimental design

Electrical resistivity tomography (ERT) is broadly used to characterize and monitor subsurface processes because of its simplicity in data acquisition and modeling. The resolution of ERT is controlled by the position of the electrodes and the measurement protocol. As a result, there has been increasing interest in optimizing ERT surveys for higher resolution. The most widely used “Compare-R” method optimizes the ERT survey by calculating the updates of possible measurement configurations to the resolution matrix. The computational burden of the Compare-R method becomes overwhelming due to the computational cost of the estimated resolution matrix with an increasing number of electrodes. We have developed a new ERT survey design methodology for a target of interest based on Bayesian experimental design. The computational challenge is alleviated through two main strategies. First, in our method, the resolution matrix is not necessary and the optimized measurements are determined using higher relative entropy, which represents the maximization of the expected information gain. Second, the simulated measurements of four-electrode configurations to calculate relative entropy are reconstructed from two-electrode configurations using the principle of superposition. Static and time-lapse ERT synthetic surveys are used to test the performance of our method. The robustness of the optimized measurement configuration is evaluated by adding different levels of noise. Results find that the Bayesian experimental design can acquire optimized measurement configurations with similar resolution compared to the Compare-R method. However, the Bayesian optimized measurement configurations are more robust to noise and the computational cost is reduced by up to 38% and 89% for 2D and 3D cases, respectively. This method has great potential in optimized ERT survey design, especially for high-resolution three dimensions or crosswell ERT surveys.