A Numerical Study on Travel Time Based Hydraulic Tomography Using the SIRT Algorithm with Cimmino Iteration

Abstract

Travel time based hydraulic tomography is a technique for reconstructing the spatial distribution of aquifer hydraulic properties (e.g., hydraulic di usivity). Simultaneous Iterative Reconstruction Technique (SIRT) is a widely used algorithm for travel time related inversions. Due to the drawbacks of SIRT implementation in practice, a modified SIRT with Cimmino iteration (SIRT-Cimmino) is proposed in this study. The incremental correction is adjusted, and an iteration-dependent relaxation parameter is introduced. These two modifications enable an appropriate speed of convergence, and the stability of the inversion process. Furthermore, a new result selection rule is suggested to determine the optimal iteration step and its corresponding result. SIRT-Cimmino and SIRT are implemented and verified by using two numerical aquifer models with di erent predefined (“true”) di usivity distributions, where high di usivity zones are embedded in a homogenous low di usivity field. Visual comparison of the reconstructions shows that the reconstruction based on SIRT-Cimmino demonstrates the aquifer’s hydraulic features better than the conventional SIRT algorithm. Root mean square errors and correlation coe cients are also used to quantitatively evaluate the performance of the inversion. The reconstructions based on SIRT-Cimmino are found to preserve the connectivity of the high di usivity zones and to provide a higher structural similarity to the “true” distribution.