Information-Driven Sequential Inversion for Transient Hydraulic Tomography

Transient hydraulic tomography (THT) is proven to be effective in representing hydraulic and storage properties in diverse hydrogeologic settings. Sequential inversion of THT is computationally efficient, however, its accuracy is constrained by the number and sequence of pumping datasets used in the inversion. While signal-to-noise ratio (SNR) is commonly used to regulate the order of pumping datasets, it often disregards the information content. We propose an alternate strategy to rank the pumping ports based on the information contained in the data for use with inversion. A non-parametric Gringorten plotting position was used to generate cumulative distribution functions (CDFs) of the transient datasets, with the CDF corresponding to the maximum drawdown port set as a reference. The Kullback-Leibler divergence (KLD) is employed to quantify variations in time-drawdown datasets by statistically measuring the divergence from the reference distribution. Pumping ports are then ranked in the decreasing order of KLD and further used in the inversion. The proposed methodology is tested under a controlled environment using a laboratory sandbox model. Discrete wavelet transform (DWT) was applied to denoise the raw pumping datasets, and PEST coupled with MODFLOW was used to perform the inversion. The performance of KLD-assisted inversion (RMSE_KLD = 0.278 ± 0.177 cm) is found to be superior to SNR-assisted inversion (RMSE_SNR = 1.075 ± 0.990 cm). Further, a reduction in THT data (by 68%) by specifying a threshold on KLD (>10) has drastically reduced the computational time (by 64%) with commensurable accuracy (RMSE_KLDF = 0.265 ± 0.121 cm). Our findings lead to the conclusion that sequential inversion of THT with information-driven datasets outperforms quality-driven datasets, even with reduced pump-test data.