Abstract
A homogeneous isotropic porous Biot half-space z ≥ 0 with free boundary z = 0 is considered. This half-space is excited by point sources situated on the boundary z = 0 and applied to the elastic phase. The following four sources are considered: (1) a normal force, (2) a center of tangent forces, (3) a center of rotation, and (4) a tangent force. For all these sources, the wave fields are established. Relationships between the wave fields in a porous medium and the respective wave fields in an elastic medium are investigated. The reflection coefficients on the free boundary of the porous Biot half-space are determined and studied. Bibliography: 11 titles.
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REFERENCES
M. A. Biot, “Theory of propagation of elastic waves in fluid-saturated porous solids. I. Low-frequency range,” J. Acoust. Soc. Am., 28, 168–178 (1956).
M. A. Biot, “Mechanics of deformation and acoustic propagation in porous media,” J. Appl. Phys., 33, 1482–1498 (1962).
L. A. Molotkov, “Propagation of normal waves in an isolated porous Biot layer saturated by fluid,” Zap. Nauchn. Semin. POMI, 257, 165–183 (1999).
R. Burridge and C. A. Vargas, “The fundamental solution in dynamic poroelasticity,” Geophys. J. Roy. Astr. Soc., 58, 61–90 (1979).
A. N. Norris, “Radiation from a point source and scattering theory in a fluid-saturated porous solid,” J. Acoust. Soc. Am., 77, 2012–2023 (1985).
G. Bonnet, “Basic singular solutions for a poroelastic medium in the dynamic range,” J. Acoust. Soc. Am., 82, 1758–1762 (1987).
L. A. Molotkov and A. V. Bakulin, “Sources of the type of centers of compression and dilatation in Biot models,” Zap. Nauchn. Semin. POMI, 230, 196–213 (1995).
L. A. Molotkov and A. V. Bakulin, “Jumps of displacements and stresses as seismic sources in a Biot medium,” Zap. Nauchn. Semin. POMI, 239, 164–196 (1997).
L. A. Molotkov and A. V. Bakulin, “Internal point sources in a poroelastic Biot medium,” in: P. Hubral (ed.), Amplitude-Preserving Seismic Reflection Imaging, Geophysical Press Limited (1998), pp. 73–88.
K. I. Ogurtsov and G. I. Petrashen, “Dynamic problems for an elastic half-space in the case of axial symmetry,” Uchen. Zap. Leningr. Univ., 149, 3–117 (1951).
G. I. Petrashen and I. N. Uspenski, “On wave propagation in layered-isotropic elastic media. I,” Uchen. Zap. Leningr. Univ., 208, 58–141 (1956).
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Molotkov, L.A. Sources Acting on the Free Boundary of a Porous Biot Medium and Reflection on This Boundary. Journal of Mathematical Sciences 111, 3750–3762 (2002). https://doi.org/10.1023/A:1016398212462
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DOI: https://doi.org/10.1023/A:1016398212462