Abstract
Travel time based hydraulic tomography is a technique for reconstructing the spatial distribution of aquifer hydraulic properties (e.g., hydraulic diffusivity). 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 different predefined (“true”) diffusivity distributions, where high diffusivity zones are embedded in a homogenous low diffusivity 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 coefficients 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 diffusivity zones and to provide a higher structural similarity to the “true” distribution.
Highlights
Tomography is a technique for imaging sections of objects by using penetrating waves
The concept of different travel times is generalized through the introduction of travel time diagnostic [14,36,37]
A modified Simultaneous Iterative Reconstruction Technique (SIRT) inversion algorithm with Cimmino iteration is developed for the reconstruction of hydraulic diffusivity distribution within a fluvial aquifer
Summary
Tomography is a technique for imaging sections of objects by using penetrating waves. Ray-tracing techniques can be utilized to describe the transient pressure propagation and solve the eikonal equation With this strategy, a line integral is derived, which relates the travel time of the transient pressure signals to a hydraulic diffusivity distribution [30,35,36,37,38,39,40,41]. The travel time of waves between a source and a receiver have a line integral relationship with the velocity field within the structure This is similar to CT, where the decimal percent drop in X-ray intensity is linearly related to the attenuation as a line integral [42]. Square Errors (RMSE) and correlation coefficients, based on the comparison between the inversion results and the “truth”
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