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Three-Dimensional Reverse Time Migration of Ground-Penetrating Radar Signals

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Abstract

Three-dimensional (3D) ground-penetrating radar (GPR) systems and 3D seismic imaging techniques have been developing fast and evolving rapidly in the last decade. Ray-based migration methods have been successfully applied to processing 3D GPR signals based on the similarity between electromagnetic and seismic waves. However, reverse time migration (RTM) of 3D GPR signals has not been well studied in the past. In this paper, we present a 3D RTM based on Maxwell’s equations for 3D GPR surveys. Migration recovers the true subsurface structure from a distorted and unfocused time profile and suppresses common electromagnetic clutter and noise. RTM based on Maxwell’s equations can consider conductivity directly and compensate for the attenuation within a high-conductivity zone. Compared with 2D RTM, 3D RTM back-propagates both in-line and cross-line signals simultaneously and can include complex 3D permittivity and conductivity models. We have integrated a parallel finite-difference time-domain (FDTD) algorithm based on a hybrid MPI and OpenMP scheme to reduce the computational cost of 3D problems. The 3D RTM experiments on an anomaly of “EM” shape and a realistic sand dune model demonstrate the effective recovery of 3D subsurface structures.

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Acknowledgements

This work is supported by the National Science Foundation of China (41574104, 41874082). The calculations were performed on a Tianhe-1(A) supercomputer. We are grateful to the three anonymous reviewers for their excellent reviews and constructive suggestions.

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Authors and Affiliations

  1. Department of Geophysics, School of Earth and Space Sciences, Peking University, Beijing, 100871, China

    Weiqiang Zhu, Qinghua Huang & Bowen Ma

  2. Department of Civil and Environmental Engineering, University of Connecticut, Storrs, CT, 06269, USA

    Lanbo Liu

  3. Department of Geophysics, Stanford University, Stanford, CA, 94305, USA

    Weiqiang Zhu

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  1. Weiqiang Zhu
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  2. Qinghua Huang
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Correspondence to Qinghua Huang.

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Appendix A. Hybrid MPI & OpenMP

Appendix A. Hybrid MPI & OpenMP

This appendix shows the program structure of parallel FDTD (Fig. 11) and the pseudo-code of the hybrid MPI & OpenMP scheme (Fig. 12)  inside each subdomain of Fig. 11. The entire FDTD domain is divided into several subdomains, and each subdomain is distributed to one processor. A hybrid parallelization scheme with both OpenMP and MPI (Su et al. 2004) is used here. MPI is used for communication between nodes, and OpenMP is used to carry out multi-threading parallel computing on a single shared-memory node. Combining MPI and OpenMP makes FDTD fully utilize the power of parallel systems constructed out of interconnected symmetric multiprocessing (SMP) nodes.

Fig. 11
figure 11

Structure of the parallel FDTD algorithm. The code consists of three parts: (1) Input parameters and settings for each subdomain, which include “eps” (model of dielectric permittivity), “mu” (model of magnetic permeability), “sig” (model of electric conductivity), “src” (positions of sources and input signals), “rec” (positions of receivers), etc. (2) The main part for parallel FDTD simulation. The whole computational domain is divided into several subdomains. For each subdomain, E&H components are updated using OpenMP. For each time step, the values on edges of each domain are exchanged through MPI. (3) Output of the recorded gathers, slices, and wavefields during propagation

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Fig. 12
figure 12

Pseudo-code for hybrid MPI & OpenMP

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Zhu, W., Huang, Q., Liu, L. et al. Three-Dimensional Reverse Time Migration of Ground-Penetrating Radar Signals. Pure Appl. Geophys. 177, 853–865 (2020). https://doi.org/10.1007/s00024-019-02341-x

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