Automated data processing and numerical methods for travel-time based hydraulic tomography

Abstract

Listen

Translate article

Travel time based hydraulic tomography is a useful and promising technique for reconstructing the spatial distribution of aquifer hydraulic properties (e.g., hydraulic diffusivity). Simultaneous Iterative Reconstruction Technique algorithm (SIRT) plays the key role in travel time related inversions. Due to the drawbacks of SIRT implementation in practice, this work proposed a new algorithm, SIRT-Cimmino, which inherits the SIRT structure and embeds Cimmino iteration. Adjustment of incremental correction and introduction of an iteration-dependent relaxation parameter are two major modifications, which enable an appropriate speed of convergence, and the stability of the inversion process. Furthermore, a new result selection rule is employed to determine the optimal iteration step. SIRT-Cimmino and SIRT are implemented and verified by using three numerical aquifer models with different predefined (“true”) diffusivity distributions, where high diffusivity continua are embedded in low diffusivity fields. The first model represents an inclined stratified aquifer, the second model represents a more complex lying Y-shaped aquifer, and the third model is derived from a highly heterogeneous aquifer analogue outcrop. Equivalent porous medium approach is used to simulate pumping tests within the models, and the groundwater drawdown is analyzed to obtain hydraulic travel time. The comparison between the inversion results and the “true” distribution shows that SIRT-Cimmino can reconstruct the continua with better connectivity and more accurate diffusivities than SIRT. Consequently, travel time based hydraulic tomography is applied at a field test site in Göttingen, Germany. The test site is classified into porous-fractured aquifer by using diagnostic plot. A series of cross-well multi-level pumping tests are performed to derive the drawdown and travel time. Type curve analysis and previous thermal tracer test are used to verify the reconstructions, due to the lack of “true” distribution. The evaluation reveals that the reconstruction obtained by using SIRT-Cimmino has a higher agreement on the structural feature similarity and value accuracy with results from the type curve analysis and thermal tracer test. In overall, the numerical and field studies prove that (a) the proposed result selection rule can determine the suitable iteration step and (b) the inversion by using SIRT-Cimmino improves the reconstruction quality by showing clear aquifer features and proper diffusivities.