Geodesic
Tube wave from a point source, placed outside the borehole
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 99-122

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Tube wave excitation by a point source, situated inside surrounding elastic medium is considered. Tube wave amplitude as the function of radial distance is represented in the cases with high velocity and low velocity media. Two source models are considered: point vertical source and point horizontal source. It is shown that a radial source is the effective tool for the tube wave excitation in the both high and low velocity media. 
@article{ZNSL_2006_332_a6,
     author = {P. V. Krauklis and L. A. Molotkov and A. P. Krauklis},
     title = {Tube wave from a point source, placed outside the borehole},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {99--122},
     publisher = {mathdoc},
     volume = {332},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a6/}
}
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P. V. Krauklis; L. A. Molotkov; A. P. Krauklis. Tube wave from a point source, placed outside the borehole. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 99-122. http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a6/