Wave field simulation for heterogeneous porous media with singular memory drag force

Journal of Computational Physics

Volumn 208, Issue 2, 2005, Pages 651-674

  Lu, Jian Fei ^a,b   Hanyga, Andrzej ^b  

^a JIANGSU UNIVERSITY   (China)

^b UNIVERSITY OF BERGEN   (Norway)

Author keywords

Drag force; Dynamic permeability; Fourier pseudospectral method; Fractional derivative; Porous medium; Singular memory

Indexed keywords

CONVOLUTION; DIFFERENTIAL EQUATIONS; DRAG; FREQUENCY DOMAIN ANALYSIS; MECHANICAL PERMEABILITY; NUMERICAL METHODS; TIME DOMAIN ANALYSIS;

DRAG FORCES; DYNAMIC PERMEABILITY; FIRST ORDER DIFFERENTIAL EQUATION; FOURIER PSEUDOSPECTRAL METHODS; FRACTIONAL DERIVATIVES; HETEROGENEOUS POROUS MEDIA; PERMEABILITY MODELING; POROUS MEDIUM; SINGULAR MEMORY; WAVE-FIELD SIMULATION;

POROUS MATERIALS;

EID: 19744367302     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.03.008     Document Type: Article

References (49)

1. MA. Biot Theory of propagation of elastic waves in a fluid-saturated porous solid, I, low frequency range J. Acoust. Soc. Am. 28 1956 168-178
2. M.A. Biot Theory of propagation of elastic waves in a fluid-saturated porous solid, II: Higher frequency range J. Acoust. Soc. Am. 28 1956 179-191
3. M.A. Biot Mechanics of deformation and acoustic propagation in porous medium J. Appl. Phys. 33 1962 1482-1498
4. J. Plona Observation of a second bulk compressional wave in a porous medium at ultrasonic frequency Appl. Phys. Lett. 36 1980 259-261
5. J.P. Jones Raleigh waves in porous elastic fluid saturated solid J. Acoust. Soc. Am. 33 1961 959-962
6. H. Deresiewicz The effect of boundaries on wave propagation in a liquid filled porous solid: IV. Surface waves in a half-spaces Bull. Seism. Soc. Am. 52 1962 627-638
7. H. Deresiewicz R. Skalak On the uniqueness in dynamic poroelasticity Bull. Seism. Soc. Am. 53 1963 783-788
8. T. Senjuntichai R.K.N.D. Rajapakse Dynamic Green's functions of homogeneous poroelastic half-plane J. Eng. Mech. ASCE 120 1994 2381-2464
9. A.N. Norris Radiation from a point source and scattering theory in a fluid-saturated porous solid J. Acoust. Soc. Am. 77 1985 2012-2023
10. C. Zimmerman M. Stern Boundary-element solution of 3-D wave scatter problems in a poroelastic medium Eng. Anal. Bound. Elem. 12 1993 223-240
11. A. Hanyga M.G. Seredynska Asymptotic ray theory in poro- and viscoelastic media Wave Motion 30 1999 175-195
12. A. Hanyga Asymptotic Green's functions in poroelasticity J. Comp. Acoust. 11 2003 491-501
13. T. Ozdenvar G.A. McMechan Algorithms for staggered-grid computations for poroelastic, elastic, acoustic, and scalar wave equations Geophys. Prospecting 45 1997 403-420
14. J.M. Carcione Wave propagation in anisotropic, saturated porous media: plane-wave theory and numerical simulation J. Acoust. Soc. Am. 99 1996 2655-2666
15. J.C. Simo T.J.R. Hughes Computational inelasticity 1998 Springer New York
16. D.L. Johnson J. Koplik R. Dashen Theory of dynamic permeability and tortuosity in fluid-saturated porous-media J. Fluid Mech. 176 1987 379-402
17. S.R. Pride F.D. Morgan A.F. Gangi Drag forces of porous-medium acoustics Phys. Rev. B 47 1993 4964-4978
18. D.K. Wilson Simple, relaxational models for the acoustical properties of porous media Appl. Acoust. 50 1997 171-188
19. D.K. Wilson Relaxation-matched modeling of propagation through porous-media, including fractal pore structure J. Acoust. Soc. Am. 94 1993 1136-1145
20. Y. Champoux M.R. Stinson On acoustical models for sound-propagation in rigid frame porous materials and the influence of shape factors J. Acoust. Soc. Am. 92 1992 1120-1131
21. S.R. Pride J.G. Berryman J.M. Harris Seismic attenuation due to wave-induced flow J. Geophys. Res. 109 2004 B01201
22. B. Gurevich S.L. Lopatnikov Velocity and attenuation of elastic-waves in finely layered porous rocks Geophys. J. Int. 121 1995 933-947
23. S. Gelinsky S.A. Shapiro T. Muller B. Gurevich Dynamic poroelasticity of thinly layered structures Int. J. Solids Struct. 35 1998 4739-4751
24. S.A. Shapiro T.M. Muller Seismic signatures of permeability in heterogeneous porous media Geophysics 64 1999 99-103
25. M. Batzle R. Hofmann D.-H. Han J. Castagna Fluids and frequency dependent seismic velocity of rocks The Leading Edge 20 2001 168-171
26. S.K. Chang H.L. Liu D.L. Johnson Low-frequency tube waves in permeable rocks Geophysics 53 1988 519-527
27. Y. Bernabe The frequency dependence of harmonic fluid flow through networks of cracks and pores Pure Appl. Geophys. 149 1997 489-506
28. S.R. Pride M.W. Haartsen Electroseismic wave properties J. Acoust. Soc. Am. 100 1996 1301-1315
29. S.R. Pride Governing equations for the coupled electromagnetics and acoustics of porous-media Phys. Rev. B 50 1994 15678-15696
30. E. Charlaix A.P. Kushnick J.P. Stokes Experimental-study of dynamic permeability in porous-media Phys. Rev. Lett. 61 1988 1595-1598
31. M.Y. Zhou P. Sheng 1st-principles calculations of dynamic permeability in porous-media Phys. Rev. B 39 1989 12027-12039
32. L. Yuan O.P. Agrawal A numerical scheme for dynamic systems containing fractional derivatives J. Vibr. Acoust. 124 2002 321-324
33. A. Hanyga Wave propagation in media with singular memory Math. Comp. Model. 34 2001 1399-1421
34. I. Podlubny Fractional differential equations 1998 Academic Press San Diego
35. F.A.L. Dullien Porous media: Fluid transport and pore structure 1979 Academic Press New York, London
36. MA. Biot General theory of three-dimensional consolidation J. Appl. Phys. 12 1941 155-164
37. N.H. Ricker Transient waves in visco-elastic media 1977 Elsevier Amsterdam
38. J.F. Lu J.H. Wang The scattering of elastic waves by holes of arbitrary shapes in saturated soil Acta Mech. Sin. 34 2002 904-913
39. J. Dvorkin A. Nur Dynamic poroelasticity - a unified model with the squirt and the Biot mechanisms Geophysics 58 1993 524-533
40. J. Virieux P-SV wave propagation in heterogeneous medium: velocity-stress finite difference method Geophysics 51 1986 889-901
41. R. Gorenflo F. Mainardi Fractional calculus: Integral and differential equations of fractional order in: A. Carpinteri F. Mainardi (Ed.) Fractals and fractional calculus in continuum mechanics 1997 Springer Wien and New York 223-276
42. K. Diethelm N.J. Ford A.D. Freed A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dyn. 29 2002 3-22
43. M. Seredyńska A. Hanyga Nonlinear Hamiltonian equations with fractional damping J. Math. Phys. 41 2000 2135-2156
44. J. Padovan Computational algorithm for finite element formulation involving fractional operator Comput. Mech. 2 1987 275-282
45. M. Enelund P. Olsson Damping described by fading memory - analysis and application to fractional derivative models Int. J. Solids Struct. 36 1999 939-970
46. P.J. Davis P. Rabinowitz Methods of numerical integration 1984 Academic Press Prlando, FL
47. J.M. Carcione Wave fields in real media: Wave propagation in anisotropic, anelastic, and porous media 2001 Pergamon Amsterdam
48. A.V. Oppenheim R.W. Schafer Discrete-time signal processing 1999 Prentice-Hall Englewood Cliffs, NJ
49. R. Kosloff D. Kosloff Absorbing boundaries for wave propagation problems J. Comput. Phys. 63 1986 363-376