Geodesic
On wave propagation in the elastic medium intersected by systems of parallel fractures
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 165-193

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The elastic anisotropic medium intersected by systems of parallel fractures is investigated. Every fracture is considered as a plane boundary with jumps of displacements and stresses and these jumps are linear functions of displacements and stresses averaged on the boundary. For this medium the effective model is constructed by means of the method of matrix averaging. The equations of this model describe wave propagation in the given medium and are more complicate than the equations of the elasticity theory. In particular cases the obtained equations are converted to the equations of elastic media. On the basis of the equations of the effective model, the expressions for densities of the kinetic and potential energies are derived, and the conditions of absoption in the medium are established. 
@article{ZNSL_2002_285_a12,
     author = {L. A. Molotkov},
     title = {On wave propagation in the elastic medium intersected by systems of parallel fractures},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {165--193},
     publisher = {mathdoc},
     volume = {285},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a12/}
}
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L. A. Molotkov. On wave propagation in the elastic medium intersected by systems of parallel fractures. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 165-193. http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a12/