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

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.

[1]  R. Hu,et al.  Case Study of Heat Transfer during Artificial Ground Freezing with Groundwater Flow , 2018, Water.

[2]  Peter Dietrich,et al.  A travel time based hydraulic tomographic approach , 2003 .

[3]  S. Ávila,et al.  Diagnóstico y evaluación de la severidad y de la cobertura hospitalaria en la siniestralidad vial en Bogotá , 2020 .

[4]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[5]  Cheng-Haw Lee,et al.  Why Hydraulic Tomography Works? , 2014, Ground water.

[6]  P. K. Kitanidis,et al.  Large‐scale inverse modeling with an application in hydraulic tomography , 2011 .

[7]  G. Herman,et al.  Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography. , 1970, Journal of theoretical biology.

[8]  K. Karasaki,et al.  Estimation of reservoir properties using transient pressure data: An asymptotic approach , 2000 .

[9]  Peter Dietrich,et al.  A field assessment of high‐resolution aquifer characterization based on hydraulic travel time and hydraulic attenuation tomography , 2011 .

[10]  T. Yeh,et al.  Hydraulic tomography: Development of a new aquifer test method , 2000 .

[11]  Carsten Leven,et al.  Hydraulic Tomography: Continuity and Discontinuity of High‐K and Low‐K Zones , 2016, Ground water.

[12]  W. Illman.  Lessons learned from hydraulic and pneumatic tomography in fractured rocks , 2015 .

[13]  Junfeng Zhu,et al.  Laboratory sandbox validation of transient hydraulic tomography , 2007 .

[14]  Walter A Illman,et al.  Practical Issues in Imaging Hydraulic Conductivity through Hydraulic Tomography , 2008, Ground water.

[15]  A. Datta-Gupta,et al.  Rapid inverse modeling of pressure interference tests using trajectory‐based traveltime and amplitude sensitivities , 2006 .

[16]  Qiao Ling-bo.  Accelerated SIRT Algorithm Based on Multigrid , 2013 .

[17]  Kaoru Yamaguchi,et al.  A NUMERICAL EXPERIMENT ON NONLINEAR IMAGE RECONSTRUCTION FROM FIRST-ARRIVAL TIMES FOR TWO-DIMENSIONAL ISLAND ARC STRUCTURE , 1986 .

[18]  W. Illman,et al.  Comparison of Hydraulic Tomography with Traditional Methods at a Highly Heterogeneous Site , 2015, Ground water.

[19]  P. Inderwiesen,et al.  Fundamentals of Seismic Tomography , 1994 .

[20]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[21]  Walter A Illman,et al.  Hydraulic Tomography Offers Improved Imaging of Heterogeneity in Fractured Rocks , 2013, Ground water.

[22]  Per Christian Hansen,et al.  Semi-convergence and relaxation parameters for a class of SIRT algorithms , 2010 .

[23]  Yuanyuan Zha,et al.  A Reduced‐Order Successive Linear Estimator for Geostatistical Inversion and its Application in Hydraulic Tomography , 2018 .

[24]  Peter Bayer,et al.  Hydraulic tomography analog outcrop study: Combining travel time and steady shape inversion , 2011 .

[25]  Walter A. Illman,et al.  Steady-state hydraulic tomography in a laboratory aquifer with deterministic heterogeneity: Multi-method and multiscale validation of hydraulic conductivity tomograms , 2007 .

[26]  Peter K. Kitanidis,et al.  An interactive Bayesian geostatistical inverse protocol for hydraulic tomography , 2006 .

[27]  R. Brauchler,et al.  Derivation of site‐specific relationships between hydraulic parameters and p‐wave velocities based on hydraulic and seismic tomography , 2012 .

[28]  Walter A. Illman,et al.  Three‐dimensional transient hydraulic tomography in a highly heterogeneous glaciofluvial aquifer‐aquitard system , 2011 .

[29]  T. Moser.  Shortest path calculation of seismic rays , 1991 .

[30]  G. Böhm,et al.  A laboratory study of tracer tomography , 2013, Hydrogeology Journal.

[31]  Tian-Chyi J. Yeh,et al.  Characterization of aquifer heterogeneity using transient hydraulic tomography , 2004 .

[32]  P. Bayer,et al.  Evolutionary algorithms for the optimization of advective control of contaminated aquifer zones , 2004 .

[33]  Hiromitsu Saegusa,et al.  Hydraulic tomography in fractured granite: Mizunami Underground Research site, Japan , 2009 .

[34]  P. Gilbert.  Iterative methods for the three-dimensional reconstruction of an object from projections. , 1972, Journal of theoretical biology.

[35]  T. Chai,et al.  Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature , 2014 .

[36]  M. Cardiff,et al.  3‐D transient hydraulic tomography in unconfined aquifers with fast drainage response , 2011 .

[37]  H. Scudder.  Introduction to computer aided tomography , 1978, Proceedings of the IEEE.

[38]  Peter K. Kitanidis,et al.  Large‐scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA) , 2014 .

[39]  P. Bayer,et al.  Time-lapse pressure tomography for characterizing CO2 plume evolution in a deep saline aquifer , 2015 .

[40]  Jet-Chau Wen,et al.  A simultaneous successive linear estimator and a guide for hydraulic tomography analysis , 2009 .

[41]  E Sanchez-León,et al.  Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization. , 2016, Ground water.

[42]  Tian-Chyi J. Yeh,et al.  Incorporating geologic information into hydraulic tomography: A general framework based on geostatistical approach , 2017 .

[43]  Wolfgang Nowak,et al.  Parameter Estimation by Ensemble Kalman Filters with Transformed Data , 2010 .

[44]  Yonghong Hao,et al.  A temporal sampling strategy for hydraulic tomography analysis , 2013 .

[45]  Lúcio T. Santos,et al.  A parallel subgradient projections method for the convex feasibility problem , 1987 .

[46]  Nikolaos V. Sahinidis,et al.  GPU computing with Kaczmarz's and other iterative algorithms for linear systems , 2010, Parallel Comput..