Geodesic
Truncated Hadamard-Babich Ansatz and Fast Huygens Sweeping Methods for Time-Harmonic Elastic Wave Equations in Inhomogeneous Media in the Asymptotic Regime
Minimax theory and its applications, Tome 8 (2023) no. 1
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In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that a time-harmonic elastic wave equation may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, motivated by our recent work [Hadamard Babich ansatz for point-source elastic wave equations in variable media at high frequencies, Multiscale Model Simul. 19/1 (2021) 46–86], we propose a new truncated Hadamard-Babich ansatz based globally valid asymptotic method, dubbed the fast Huygens sweeping method, for computing Green’s functions of frequency-domain point-source elastic wave equations in inhomogeneous media in the high-frequency asymptotic regime and in the presence of caustics
Mots-clés : Hadamard-Babich ansatz, elastic wave, eikonal equation, fast Huygens sweeping, but terfly algorithm 
@article{MTA_2023_8_1_a7,
     author = {Jianliang Qian and Jian Song,Wangtao Lu and Robert Burridge},
     title = {Truncated {Hadamard-Babich} {Ansatz} and {Fast} {Huygens} {Sweeping} {Methods} for {Time-Harmonic} {Elastic} {Wave} {Equations} in {Inhomogeneous} {Media} in the {Asymptotic} {Regime}},
     journal = {Minimax theory and its applications},
     year = {2023},
     volume = {8},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a7/}
}
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Jianliang Qian; Jian Song,Wangtao Lu; Robert Burridge. Truncated Hadamard-Babich Ansatz and Fast Huygens Sweeping Methods for Time-Harmonic Elastic Wave Equations in Inhomogeneous Media in the Asymptotic Regime. Minimax theory and its applications, Tome 8 (2023) no. 1. http://geodesic.mathdoc.fr/item/MTA_2023_8_1_a7/