Green's functions and radiation patterns in poroelastic solids revisited

Geophysical Journal International

Volumn 178, Issue 1, 2009, Pages 327-337

  Karpfinger, Florian ^a   Müller, Tobias M ^b   Gurevich, Boris ^a,b  

^a CURTIN UNIVERSITY   (Australia)

^b CSIRO   (Australia)

Author keywords

Body waves; Theoretical seismology; Wave propagation

Indexed keywords

BIOT THEORY; BODY WAVE; GREEN FUNCTION; POROELASTICITY; SEISMOLOGY; WAVE PROPAGATION;

EID: 67650115087     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2009.04116.x     Document Type: Article

References (38)

1. Aki, K. & Richards, P.G., 2002. Quantitative Seismology, University Science Books Sausalito, California.
2. Allard, J.-F., Bourdier, R. & Depollier, C., 1986. Biot waves in layered media, J. appl. Phys., 60(6), 1926-1929.
3. Backus, G. & Mulcahy, M., 1976a. Moment tensors and other phenomenological descriptions of seismic sources; i. continuous displacements, Geophys. J. Int., 46(2), 341-361.
4. Backus, G. & Mulcahy, M., 1976b. Moment tensors and other phenomenological descriptions of seismic sources; ii. discontinuous displacements, Geophys. J. Int., 47(2), 301-329.
5. Biot, M., 1956a. Theory of propagation of elastic waves in a fluid saturated porous solid. i-low frequency range, J. acoust. Soc. Am., 28, 168-178.
6. Biot, M., 1956b. Theory of propagation of elastic waves in a fluid saturated porous solid. ii-high frequency range, J. acoust. Soc. Am., 28, 179-191.
7. Biot, M., 1962. Mechanics of deformation and acoustic propagation in porous solids, J. appl. Phys., 33, 1482-1498.
8. Biot, M. & Willis, D., 1957. The elastic coefficients of the theory of consolidation, J. appl. Mech., 24, 594-601.
9. Bonnet, G., 1987. Basic singular solutions for a poroelastic medium in the dynamic range, J. acoust. Soc. Am., 82(5), 1758-1762.
10. Boutin, C., 1987. Green functions and associated sources in infinite and stratified poroelastic media, Geophys. J. R. astr. Soc., 90, 521-550.
11. Boutin, C., 1991. Integral representation and sources in isotropic poroelastic media, in Transport Processes in Porous Media, pp. 521-538, Kluwer Academic Publishers.
12. Burridge, R. & Vargas, C., 1979. The fundamental solutions in dynamic poroelasticity, Geophys. J. R. astr. Soc, 58, 61-90.
13. Chandler, R.N. & Johnson, D.L., 1981. The equivalence of quasistatic flow in fluid-saturated porous media and Biot's slow wave in the limit of zero frequency, J. appl. Phys., 52(5), 3391-3395.
14. Chapman, C., 2004. Fundamentals of Seismic Wave Propagation, Cambridge University Press.
15. Chen, J., 1994a. Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. part i: Two-dimensional solution., Int. J. Solids Struct., 31(10), 1447-1490.
16. Chen, J., 1994b. Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. part ii: Three-dimensional solution., Int. J. Solids Struct., 31(2), 169-202.
17. Gassmann, F., 1951. Über die Elastizität poröser Medien, Viertel. Naturforsch. Ges. Zürich, 96(1), 1-23.
18. Johnson, D.L., Koplik, J. & Dashen, R., 1987. Theory of dynamic permeability and tortuosity in fluid-saturated porous media, J. Fluid Mech., 176, 379-402.
19. Jost, M. & Herrmann, R., 1989. A student's guide to and review of moment tensors, Seismol. Res. Lett., 60, 37-57.
20. Kupradze, V., 1979. Three-dimensional Problems of the Mathmatical Theory of Elasticity and Thermoelasticity, North-Holland, Amsterdam.
21. Kurkjian, A.L., Coates, R.T., White, J.E. & Schmidt, H., 1994. Finite-difference and frequency-wavenumber modeling of seismic monopole sources and receivers in fluid-filled boreholes, Geophysics, 59(7), 1053-1064.
22. Lu, J.-F., Jeng, D.-S. & Williams, S., 2008. A 2.5-d dynamic model for a saturated porous medium: Part i. Green's function, Int. J. Solids Struct., 45(2), 378-391.
23. Molotkov, L.A. & Bakulin, A., 1998. Internal point sources in poroelastic Biot medium, in Amplitude-Preserving Seismic Reflection Imaging, Seismic application series, Vol. 2, pp. 73-88, ed. Hubral, P., Geophysical Press.
24. Müller, T.M., 2006. Spatiotemporal pore pressure evolution due to fluid-mass point sources in dynamic poroelasticity, Geophys. J. Int., 165(3), 906-912.
25. Müller, T.M. & Gurevich, B., 2005. A first-order statistical smoothing approximation for the coherent wave field in random porous media, J. acoust. Soc. Am., 117(4), 1796-1805.
26. Norris, A.N., 1985. Radiation from a point source and scattering theory in a fluid-saturated porous solid, J. acoust. Soc. Am., 77(6), 2012-2023.
27. Norris, A.N., 1992. On the correspondence between poroelasticity and thermoelasticity, J. appl. Phys., 71(3), 1138-1141.
28. Norris, A.N., 1994. Dynamic Green's functions in anisotropic piezoelectric, thermoelastic and poroelastic solids, Proc. R. Soc. Lond., 447, 175-188.
29. Philippacopoulos, A., 1998. Spectral Green's dyadic for point sources in poroelastic media, J. Eng. Mech., 124(1), 24-30.
30. Pride, S.R., 1994. Governing equations for the coupled electromagnetics and acoustics of porous media, Phys.Rev. B, 50, 15678-15696.
31. Pride, S.R. & Haartsen, M.W., 1996. Electroseismic wave properties, J. acoust. Soc. Am., 100(3), 1301-1315.
32. Rudnicki, J.W., 1986. Fluid mass sources and point forces in linear elastic diffusive solids, Mech. Mat., 5, 383-393.
33. Rudnicki, J.W. & Freund, L., 1981. On energy radiation from seismic sources, Bull. seism. Soc. Am., 71, 583-595.
34. Sahay, P., 2001. DynamicGreen's function for homogeneous and isotropic porous media, Geophys. J. Int., (147),622-629.
35. Schanz, A. & Pryl, D., 2004. Dynamic fundamental solutions for compressible and incompressible modeled poroelastic continua, Int. J. Solids Struct., 41, 4047-4073.
36. Wang, H., 2000. Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology, Princeton University Press.
37. Wenzlau, F. & Müller, T., 2009. Finite-difference modeling of wave propagation and diffusion in poroelastic media, Geophysics, in press.
38. Wu, R.-S. & Ben-Menahem, A., 1985. The elastodynamic near field, Geophys. J. Int., 81(3), 609-621.