Geodesic
Tube waves in a~borehole filled by a~mixture of solid and fluid particles
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 154-161

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Kinematic and dynamic parameters of the lowfrequency waves propagating in the two-phase mixture of the solid and fluid particles are investigated. It is shown, that in this model two tube waves propagate at that time as only one tube wave propagates in the fluidfilled well. The dispersion and attenuation of tube waves are studied. 
@article{ZNSL_2003_297_a9,
     author = {P. V. Krauklis and L. A. Krauklis},
     title = {Tube waves in a~borehole filled by a~mixture of solid and fluid particles},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {154--161},
     publisher = {mathdoc},
     volume = {297},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a9/}
}
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P. V. Krauklis; L. A. Krauklis. Tube waves in a~borehole filled by a~mixture of solid and fluid particles. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 154-161. http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a9/