https://doi.org/10.26089/NumMet.v27r442

Parallel implementation of the TRM tunnel-detection algorithm using Coarray Fortran

Authors

  • Anastasia A. Galaktionova
  • Galina V. Reshetova

Keywords:

seismic waves
numerical modeling
tunnel position
time reversal mirror
Coarray Fortran
parallelization

Abstract

The Time Reversal Mirror (TRM) method has demonstrated its effectiveness in reconstructing various objects, including earthquake sources and small-scale inhomogeneities. However, the underlying physical principle suggests its applicability to a wider range of practical problems. The aim of this study is to develop a TRM-based algorithm for reconstructing the position of anthropogenic objects, such as tunnels. The algorithm was developed using the TRM method, a finite-difference scheme on staggered grids, and perfectly matched absorbing layers (PML) to truncate the computational domain. For the parallel software implementation, the computational-domain decomposition method and Coarray Fortran technology are used for data exchange between processes. Numerical experiments demonstrate the successful reconstruction of tunnel position using the proposed 3D TRM algorithm.


Downloads

Published

2026-11-12

Issue

Vol. 27 (2026): Issue 4.

Section

Methods and algorithms of computational mathematics and their applications

Authors

Anastasia A. Galaktionova

Novosibirsk State University

• Senior Lecturer

Galina V. Reshetova

Institute of Computational Mathematics and Mathematical Geophysics SB RAS (ICM&MG SB RAS)

• Leading Researcher

References

  1. Novosibirsk Supercomputer Center of SB RAS.
  2. A. C. Gürbüz, J. H. McClellan, W. R. Scott, and G. D. Larson, “Seismic Tunnel Imaging and Detection,” in 2006 International Conference on Image Processing, Atlanta, GA, USA, October 8–11, 2006(IEEE, 2006), pp. 3229–3232.
    doi 10.1109/ICIP.2006.312911
  3. T. Counts, G. Larson, A. C. Gürbüz, et al., “Investigation of the Detection of Shallow Tunnels Using Electromagnetic and Seismic Waves,” in Detection and Remediation Technologies for Mines and Minelike Targets XII, Orlando, Florida, USA, May 7, 2007(SPIE, 2007), Vol. 6553, Article Number 65531G.
    doi 10.1117/12.722437
  4. C. S. Sherman, J. Rector, D. Dreger, and S. Glaser, “A numerical study of surface-wave-based tunnel detection at the Black Diamond Mines Regional Preserve, California,” Geophysics 83 (4), EN13–EN22 (2018).
    doi 10.1190/geo2017-0467.1
  5. S. D. Sloan, S. L. Peterie, R. D. Miller, et al., “Detecting clandestine tunnels using near-surface seismic techniques,” Geophysics 80 (5), EN127–EN135 (2015).
    doi 10.1190/geo2014-0529.1
  6. M. Junaid, S. A. Khan, and N. Ahmed, “Unsupervised Detection of Underground Tunnels in Ground-Penetrating Radar Using Depth-Restricted Reconstruction Scoring,” arXiv:2607.04882 (2026).
    doi 10.48550/arXiv.2607.04882
  7. J. T. Schwenk, S. D. Sloan, R. D. Miller, and J. Ivanov, “Correlation of the backscatter analysis of surface waves method (BASW) for anomaly detection,” in 84th SEG Annual International Meeting, Denver, Colorado, October 26–31, 2014(SEG Technical Program Expanded Abstracts, 2014), pp. 2029–2035.
    doi 10.1190/segam2014-1684.1
  8. C. Larmat, J.-P. Montagner, M. Fink, et al., “Time-reversal imaging of seismic sources and application to the great Sumatra earthquake,” Geophys. Res. Lett. 33 (19), Article Number L19312 (2006).
    doi 10.1029/2006GL026336
  9. J.-P. Montagner, C. Larmat, Y. Capdeville, et al., “Time-reversal method and cross-correlation techniques by normal mode theory: a three-point problem,” Geophys. J. Int. 191 (2), 637–652 (2012).
    doi 10.1111/j.1365-246X.2012.05619.x
  10. M. Fink and C. Prada, “Acoustic time-reversal mirrors,” Inverse Problems 17 (1), R1–R38 (2001).
    doi 10.1088/0266-5611/17/1/201
  11. B. E. Anderson, M. Griffa, C. Larmat, et al., “Time Reversal,” Acoustics Today 4 (1), 5–16 (2008).
    doi 10.1121/1.2961165
  12. M. Shustak and E. Landa, “Time reversal for wave refocusing and scatterer detection using machine learning,” Geophysics 83 (5), T257–T263 (2018).
    doi 10.1190/geo2017-0679.1
  13. G. Reshetova and A. Galaktionova, “Reconstruction of Subsurface Scattering Objects by the Time Reversal Mirror,” Siberian Electronic Mathematical Reports 19 (2), 517–527 (2022).
    doi 10.33048/semi.2022.19.043
  14. A. N. Konovalov, “The dynamic problem of elasticity theory in the &quotvelocity-stress&quot formulation,” Differ. Equations (Differencialnye Uravnenia) 35 (2), 238–245 (1999).
    https://www.mathnet.ru/links/8637fef4f555733344e181feaf5cb170/de9878.pdf Cited October 16, 2026.
  15. J. Virieux, “P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method,” Geophysics 51 (4), 889–901 (1986).
    doi 10.1190/1.1442147
  16. D. Komatitsch and R. Martin, “An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation,” Geophysics 72 (5), SM155–SM167 (2007).
    doi 10.1190/1.2757586
  17. N. E. Huang and N. O. Attoh-Okine, The Hilbert–Huang Transform in Engineering(CRC Press, 2005).
  18. G. Reshetova, V. Cheverda, and V. Koinov, “Comparative Efficiency Analysis of MPI Blocking and Non-blocking Communications with Coarray Fortran,” in Supercomputing. RuSCDays 2021. Communications in Computer and Information Science(Springer, Cham, 2021), Vol. 1510, pp. 332–336.
    doi 10.1007/978-3-030-92864-3_25
  19. H. A. Schwarz, “Ueber einige Abbildungsaufgaben,” J. für die Reine und Angew. Math. 1869 (70), 105–120 (1869).
    doi 10.1515/crll.1869.70.105
  20. S. L. Sobolev, “Schwarz’s Algorithm in Elasticity Theory,” in Selected Works of S.L. Sobolev(Springer, Boston, 2006), pp. 399–403.
    doi 10.1007/978-0-387-34149-1_12
  21. J. Dongarra, P. Beckman, T. Moore, et al., “The International Exascale Software Project roadmap,” Int. J. High Perform. Comput. Appl. 25 (1), 3–60 (2011).
    doi 10.1177/1094342010391989
  22. A. Denis and F. Trahay, “MPI Overlap: Benchmark and Analysis,” in 2016 45th International Conference on Parallel Processing (ICPP), Philadelphia, PA, USA, August 16–19, 2016(IEEE, 2016), pp. 258–267.
    doi 10.1109/ICPP.2016.37
  23. A. Sharma and I. Moulitsas, “MPI to Coarray Fortran: experiences with a CFD solver for unstructured meshes,” Scientific Programming 1–12 (2017).
    doi 10.1155/2017/3409647

License

Copyright (c) 2026 А. А. Галактионова, Г. В. Решетова

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.