Geodesic
Evaluation of fluid-filled fractures during acoustic measurements on the tube waves
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 121-128

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Problem of reflection, transmission and conversion of tube wave at the fracture intersecting a borehole is investigated. We consider a case, when the acoustic tool is placed inside a borehole and the fracture divides two different elastic half-spaces and filled by a porous material. 
@article{ZNSL_2005_324_a6,
     author = {A. P. Krauklis and P. V. Krauklis},
     title = {Evaluation of fluid-filled fractures during acoustic measurements on the tube waves},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--128},
     publisher = {mathdoc},
     volume = {324},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a6/}
}
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A. P. Krauklis; P. V. Krauklis. Evaluation of fluid-filled fractures during acoustic measurements on the tube waves. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 121-128. http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a6/