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Open AccessArticle

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

1
Applied Geology, Geoscience Centre, University of Goettingen, Goldschmidt Str. 3, 37077 Goettingen, Germany
2
School of Earth Science and Engineering, Hohai University, Focheng Xi Road 8, Nanjing 211100, China
3
Institute of Geosciences, University of Kiel, Ludewig-Meyn-Straße 10, 24015 Kiel, Germany
*
Author to whom correspondence should be addressed.
First author.
Water 2019, 11(5), 909; https://doi.org/10.3390/w11050909
Received: 27 March 2019 / Revised: 19 April 2019 / Accepted: 23 April 2019 / Published: 30 April 2019
(This article belongs to the Special Issue Advances in Hydrogeology: Trend, Model, Methodology and Concepts)
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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. View Full-Text
Keywords: hydraulic tomography; travel time inversion; inversion algorithm; inverse problem hydraulic tomography; travel time inversion; inversion algorithm; inverse problem
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Qiu, P.; Hu, R.; Hu, L.; Liu, Q.; Xing, Y.; Yang, H.; Qi, J.; Ptak, T. A Numerical Study on Travel Time Based Hydraulic Tomography Using the SIRT Algorithm with Cimmino Iteration. Water 2019, 11, 909.

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