Abstract
The two-phase effective model of a cracked medium with cracks filled with liquid is extended to the case where cracks have finite length. On the basis of the equations obtained for the generalized effective model, the expressions of kinetic and potential energies and energy streams along axes are derived. This also shows that attenuation is absent. bibliography: 6 titles.
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Literature Cited
L. A. Molotkov, “The equivalence of periodically stratified and transversal isotropic media,”Zap. Nauchn. Sem. Leningrad. Otdel. Mat Inst. Steklov (LOMI),89, 219–233 (1979).
L. A. Molotkov,The Matrix Method in the Theory of Wave Propagation in Elastic and Fluid Stratified Media [in Russian], Leningrad (1984).
T. J. Plona, K. W. Winkler, and M. Schoenberg, “Acoustic waves in alternating fluid-solid layers,”J. Acoust. Soc. Am.,81, No. 5, 1227–1234 (1987).
K. D. Mahrer and F. J. Mauk, “Seismic wave motion for a new model of hydraulic fracture with an inducced low velocity zone,”J. Geophys. Res.,92, No. 9, 9293–9309 (1987).
L. A. Molotkov and V. P. Krauklis, “On the dispersion properties of normal waves in the stratifield models of cracked media,” in:Problems in Dynamic Theory of Propagation of Seismic Waves, No. 28, 22–28 (1989).
L. A. Molotkov, “Effective model of an elastic anisotropic medium with cracks filled with liquid”, in:Problems in Dynamic Theory of Propagation of Seismic Waves, No. 29, 14–29 (1989).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 142–153, 1990.
Translated by L. A. Molotkov.
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Molotkov, L.A. The equations of the effective two-phase cracked model with finite length cracks. J Math Sci 73, 389–396 (1995). https://doi.org/10.1007/BF02362826
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DOI: https://doi.org/10.1007/BF02362826