An exact spectral representation of the wave equation for propagation over a terrain

Abstract : An exact spectral representation of the wave equation above a dielectric ground is proposed. The formulation is based on the diagonalisation of the vertical operator, takes into account the angle-dependance of the reflexion coefficient, and does not include any paraxial approximation. The expressions of the spectrum comprise two parts : a continuous part and a discrete part. The latter corresponds to a possible surface wave. The use of this result in split-step algorithms to simulate wave propagation requires a discretization of the spectrum. To render the discretization consistent, an alternative discrete spectral representation is proposed that intrinsically includes the truncation of the computation domain at a finite high.
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Alexandre Chabory, Christophe Morlaas, Rémi Douvenot, Bernard Souny. An exact spectral representation of the wave equation for propagation over a terrain. ICEAA 2012, International Conference on Electromagnetics in Advanced Applications, Sep 2012, Cape Town, South Africa. pp 717-720, ⟨10.1109/ICEAA.2012.6328722⟩. ⟨hal-01022309⟩

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