Geodesic
Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 512-522 Cet article a éte moissonné depuis la source Math-Net.Ru

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Wave propagation in fractured rock in the course of seismic exploration is studied. The grid-characteristic method on hexahedral meshes is extended to the case of an elastic medium with empty and fluid-saturated cracks. The crack effect on wave propagation in the medium is taken into account by introducing cracks at the stage of grid generation with boundary conditions and conditions on the crack edges specified in explicit form. This method is used to obtain wave patterns near an extended inclined crack. The problem of numerically computing the seismic effect produced by a cluster of vertical and subvertical cracks is given in a complete three-dimensional formulation. The structure of the resulting pattern and the influence exerted by the crack-filling substance on the signal recorded on the surface are examined. 
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V. I. Golubev; I. B. Petrov; N. I. Khokhlov; K. I. Shul'ts. Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 512-522. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a13/

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