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Accurate location of all surface wave modes for Green’s functions of a layered medium by consecutive perturbations

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Abstract

In this paper, an efficient method is proposed to quickly and accurately locate all the surface wave modes of spectral Green’s functions of a layered medium. This method consists of two parts. In the first part, all the surface wave poles without considering the medium loss are located by a modified dichotomy on the real axis in the complex plane. In the second part, consecutive perturbations with respect to the medium loss are performed, which means that the medium loss is increased step by step from zero to the given value, and at each step, the Newton-Raphson algorithm is employed to find all the current poles, with the poles at the previous step as initial values. The residues of the surface wave poles are analytically calculated without any contour integral. The whole procedure is based on the recursively rational forms of spectral Green’s functions. As an application, all the surface wave poles and their residues obtained by the method proposed in this paper are applied in evaluation of the spatial Green’s functions by the discrete complex image method. Some numerical examples are provided to validate the correctness and efficiency of the proposed method.

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Authors and Affiliations

  1. State Key Laboratory of Millimeter Waves, School of Information Science and Engineering, Southeast University, Nanjing, 210096, China

    Zhe Song, HouXing Zhou, Jun Hu, WeiDong Li & Wei Hong

Authors
  1. Zhe Song
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  2. HouXing Zhou
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  3. Jun Hu
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  4. WeiDong Li
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  5. Wei Hong
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Correspondence to Zhe Song or HouXing Zhou.

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Song, Z., Zhou, H., Hu, J. et al. Accurate location of all surface wave modes for Green’s functions of a layered medium by consecutive perturbations. Sci. China Inf. Sci. 53, 2363–2376 (2010). https://doi.org/10.1007/s11432-010-4093-7

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  • DOI: https://doi.org/10.1007/s11432-010-4093-7

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