P-wave seismic attenuation by slow-wave diffusion: Numerical experiments in partially saturated rocks

Geophysics

Volumn 72, Issue 4, 2007, Pages

  Picotti, Stefano ^a   Carcione, José M ^a   Rubino, J Germán ^b   Santos, Juan E ^b,c  

^a ISTITUTO NAZIONALE DI OCEANOGRAFIA E DI GEOFISICA SPERIMENTALE OGS   (Italy)

^b UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

^c PURDUE UNIVERSITY   (United States)

Author keywords

Finite element analysis; Rocks; Seismic waves

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; EQUATIONS OF MOTION; FINITE ELEMENT METHOD; LITHOLOGY; MATHEMATICAL MODELS; POROUS MATERIALS; PRESSURE GRADIENT; SEISMIC PROSPECTING; SEISMIC WAVES;

P-WAVE SEISMIC ATTENUATION; PARTIALLY SATURATED ROCKS; SEISMIC FREQUENCIES; SLOW-WAVE DIFFUSION;

ROCKS;

ALGORITHM; FINITE ELEMENT METHOD; FLUID FLOW; FLUID PRESSURE; P-WAVE; POROUS MEDIUM; PRESSURE GRADIENT; SEISMIC ATTENUATION;

EID: 34447331931     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.2740666     Document Type: Article

References (55)

1. Arntsen, B., and J. M. Carcione, 2001, Numerical simulation of the Biot slow wave in water-saturated Nivelsteiner sandstone: Geophysics, 66, 890-896. gpy GPYSA7 0016-8033 10.1190/1.1444978
2. Ben-Menahem, A., and S. G. Singh, 1981, Seismic waves and sources: Springer-Verlag.
3. Berryman, J. G., 1980, Confirmation of Biot's theory: Applied Physics Letters, 33, 382-384. apl APPLAB 0003-6951 10.1063/1.91951
4. Biot, M. A., 1956a, Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range: Journal of the Acoustical Society of America, 28, 168-171. jas JASMAN 0001-4966 10.1121/ 1.1908239
5. 1956b, Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range: Journal of the Acoustical Society of America, 28, 179-191. jas JASMAN 0001-4966 10.1121/1.1908239
6. 1962, Mechanics of deformation and acoustic propagation in porous media: Journal of Applied Physics, 33, 1482-1498. jap JAPIAU 0021-8979 10.1063/ 1.1728759
7. Brenner, S. C., and L. R. Scott, 1994, The mathematical theory of finite element methods: Springer-Verlag.
8. Cadoret, T., D. Marion, and B. Zinszner, 1995, Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones: Journal of Geophysical Research, 100, 9789-9803. jgr JGREA2 0148-0227 10.1029/95JB00757
9. Carcione, J. M., 1998, Viscoelastic effective rheologies for modeling wave propagation in porous media: Geophysical Prospecting, 46, 249-270. 8uc GPPRAR 0016-8025 10.1046/j.1365-2478.1998.1000333.x
10. 2007, Wave fields in real media: Wave propagation in anisotropic, anelastic, porous, and electromagnetic media: Handbook of Geophysical Exploration, 38, Elsevier (2nd ed., revised and extended).
11. Carcione, J. M., H. B. Helle, and N. H. Pham, 2003, White's model for wave propagation in partially saturated rocks: Comparison with poroelastic numerical experiments: Geophysics, 68, 1389-1398. gpy GPYSA7 0016-8033 10.1190/1.1598132
12. Carcione, J. M., and S. Picotti, 2006, P-wave seismic attenuation by slow-wave diffusion: Effects of inhomogeneous rock properties: Geophysics, 71, no. 3; O1-O8. gpy GPYSA7 0016-8033 10.1190/1.2194512
13. Chin, R. C. Y., J. G. Berryman, and G. W. Hedstrom, 1985, Generalized ray expansion for pulse propagation and attenuation in fluid-saturated porous media: Wave Motion, 7, 43-66. wvm WAMOD9 0165-2125 10.1016/ 0165-2125(85)90026-5
14. Dasgupta, R., and R. A. Clark, 1998, Estimation of Q from surface seismic reflection data: Geophysics 63, 2120-2128. gpy GPYSA7 0016-8033 10.1190/1.1444505
15. Diallo, M. S., M. Prasad, and E. Appel, 2003, Comparison between experimental results and theoretical predictions for P-wave velocity and attenuation at ultrasonic frequency: Wave Motion, 37, 1-16. wvm WAMOD9 0165-2125 10.1016/S0165-2125(02)00018-5
16. Douglas, J. Jr., J. E. Santos, and D. Sheen, 2001, Nonconforming Galerkin methods for the Helmholtz equation: Numerical Methods for Partial Differential Equations, 17, 475-494. ar6 NMPDEB 0749-159X 10.1002/num.1023
17. Douglas, J. Jr., J. E. Santos, D. Sheen, and L. Bennethum, 1993, Frequency domain treatment of one-dimensional scalar waves: Mathematical Models and Methods in Applied Sciences, 3, 171-194. ali MMMSEU 0218-2025 10.1142/S0218202593000102
18. Douglas, J. Jr., J. E. Santos, D. Sheen, and X. Ye, 1999, Nonconforming Galerkin methods based on quadrilateral elements for second-order elliptic problems: RAIRO Mathematical Modeling and Numerical Analysis (M2AN), 33, 747-770. ali MMMSEU 0218-2025
19. Dutta, N. C., and H. Óde, 1979a, Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model) - Part I: Biot theory: Geophysics, 44, 1777-1788. gpy GPYSA7 0016-8033 10.1190/1.1440938
20. Dutta N.C., Óde H.1979b, Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model) - Part II: Results: Geophysics, 44, 1789-1805. gpy GPYSA7 0016-8033 10.1190/1.1440939
21. Dutta, N. C., and A. J. Seriff, 1979, On White's model of attenuation in rocks with partial saturation: Geophysics, 44, 1806-1812. gpy GPYSA7 0016-8033 10.1190/1.1440940
22. Dvorkin, J., G. Mavko, and A. Nur, 1995, Squirt flow in fully saturated rocks: Geophysics, 60, 97-107. gpy GPYSA7 0016-8033 10.1190/1.1443767
23. Friedman, A. S., 1963, Pressure-volume-temperature relationships of gases, virial coefficients: In American Institute of Physics Handbook: McGraw-Hill Book Co.
24. Geertsma, J., and D. C. Smit, 1961, Some aspects of elastic wave propagation in fluid-saturated porous solids: Geophysics, 26, 169-181. gpy GPYSA7 0016-8033 10.1190/1.1438855
25. Gelinsky, S., and S. A. Shapiro, 1997, Dynamic-equivalent medium approach for thinly layered saturated sediments: Geophysical Journal International, 128, F1-F4. gpy GPYSA7 0016-8033
26. Gurevich, B., and S. L. Lopatnikov, 1995, Velocity and attenuation of elastic waves in finely layered porous rocks: Geophysical Journal International, 121, 933-947. gji GJINEA 0956-540X 10.1111/ j.1365-246X.1995.tb06449.x
27. Gurevich, B., V. B. Zyrianov, and S. L. Lopatnikov, 1997, Seismic attenuation in finely layered porous rocks: Effects of fluid flow and scattering: Geophysics, 62, 319-324. gpy GPYSA7 0016-8033 10.1190/ 1.1444133
28. Ha, T., J. E. Santos, and D. Sheen, 2002, Nonconforming finite element methods for the simulation of waves in viscoelastic solids: Computer Methods in Applied Mechanics Engineering, 191, 5647-5670. cme CMMECC 0045-7825 10.1016/S0045-7825(02)00469-3
29. Helle, H. B., N. H. Pham, and J. M. Carcione, 2003, Velocity and attenuation in partially saturated rocks - Poroelastic numerical experiments: Geophysical Prospecting, 51, 551-566. 8uc GPPRAR 0016-8025 10.1046/j.1365-2478.2003.00393.x
30. Hill, R., 1964, Theory of mechanical properties of fiber-strengthened materials: Journal of Mechanics and Physics of Solids, 11, 357-372. jmx JMPSA8 0022-5096 10.1016/0022-5096(63)90036-X
31. Johnson, D. L., 2001, Theory of frequency dependent acoustics in patchy-saturated porous media: Journal of the Acoustical Society of America, 110, 682-694. jas JASMAN 0001-4966 10.1121/1.1381021
32. Jones, T. D., 1986, Pore-fluids and frequency dependent-wave propagation rocks: Geophysics, 51, 1939-1953. gpy GPYSA7 0016-8033 10.1190/ 1.1442050
33. Krief, M., J. Garat, J. Stellingwerff, and J. Ventre, 1990, A petrophysical interpretation using the velocities of P and S waves (full waveform sonic): The Log Analyst, 31, 355-369. 9sw ZZZZZZ 0024-581X
34. Mavko, G., T. Mukerji, and J. Dvorkin, 1998, The rock physics handbook: tools for seismic analysis in porous media: Cambridge University Press.
35. Mochizuki, S., 1982, Attenuation in partially saturated rocks: Journal of Geophysical Research, 87, 8598-8604. jgr JGREA2 0148-0227
36. Morse, P. M., and K. U. Ingard, 1986, Theoretical acoustics: Princeton University Press.
37. Müller, T. M., and B. Gurevich, 2004a, One-dimensional random patchy saturation model for velocity and attenuation in porous rocks: Geophysics, 69, 1166-1172. gpy GPYSA7 0016-8033 10.1190/1.1801934
38. 2004b, Seismic attenuation and dispersion due to wave-induced flow in 3-D inhomogeneous porous rocks: 74th Annual International Meeting, SEG, Expanded Abstracts.
39. 2005, Wave-induced fluid flow in random porous media: Attenuation and dispersion of elastic waves: Journal of the Acoustical Society of America, 117, 2732-2741. jas JASMAN 0001-4966 10.1121/1.1894792
40. Nedelec, J. C., 1980, Mixed finite elements in R 3: Journal of Numerical Mathematics, 35, 315-341. num NUMMA7 0029-599X 10.1007/BF01396415
41. Norris, A. N., 1993, Low-frequency dispersion and attenuation in partially saturated rocks: Journal of Acoustical Society of America, 94, 359-370. jas JASMAN 0001-4966 10.1121/1.407101
42. O'Connell, R., and B. Budiansky, 1974, Seismic velocities in dry and saturated cracked solids: Journal of Geophysical Research, 79, 5412-5426. jgr JGREA2 0148-0227
43. Picotti, S., and J. M. Carcione, 2006, Estimating seismic attenuation (Q) in the presence of random noise: Journal of Seismic Exploration, 15, 165-181. 9dy ZZZZZZ 0963-0651
44. Plona, T. J., 1980, Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies: Applied Physics Letters, 36, 259-261. apl APPLAB 0003-6951 10.1063/1.91445
45. Pride, S. R., J. G. Berryman, and J. M. Harris, 2004, Seismic attenuation due to wave-induced flow: Journal of Geophysical Research, 109, B01201; http://dx.doi.org/10.1029/2003JB002639. jgr JGREA2 0148-0227 10.1029/2003JB002639 10.1029/2003JB002639
46. Pride, S. R., E. Tromeur, and J. G. Berryman, 2002, Biot slow wave effects in stratified rock: Geophysics, 67, 271-281. gpy GPYSA7 0016-8033 10.1190/1.1451799
47. Quan, Y., and J. M. Harris, 1997, Seismic attenuation tomography using the frequency shift method: Geophysics, 62, 895-905. gpy GPYSA7 0016-8033 10.1190/1.1444197
48. Raviart, P. A., and J. M. Thomas, 1975, Mixed finite element method for 2nd-order elliptic problems: Mathematical Aspects of the Finite Element Methods: Lecture Notes of Mathematics, 606, Springer.
49. Santos, J. E., and D. Sheen, 2007, Finite-element methods for the simulation of waves in composite saturated poroviscoelastic media: SIAM Journal of Numerical Analysis, 45, 389-420. sja SJNAEQ 0036-1429 10.1137/ 050629069
50. Shapiro, S. A., and T. M. Müller, 1999, Seismic signatures of permeability in heterogeneous porous media: Geophysics, 64, 99-103. gpy GPYSA7 0016-8033 10.1190/1.1444536
51. Smeulders, D. M. J., 2005, Experimental evidence for slow compressional waves: Journal of Engineering Mechanics, 131, 908-917. 979 JENMDT 0733-9399 10.1061/(ASCE)0733-9399(2005)131:9(908)
52. White, J. E., 1975, Computed seismic speeds and attenuation in rocks with partial gas saturation: Geophysics, 40, 224-232. gpy GPYSA7 0016-8033 10.1190/1.1440520
53. White, J. E., N. G. Mikhaylova, and F. M. Lyakhovitskiy, 1975, Low-frequency seismic waves in fluid saturated layered rocks: Izvestija Academy of Sciences USSR, Physics of the Solid Earth, 11, 654-659. ize IPSEBQ 0001-4354
54. Wood, A. W., 1955, A textbook of sound: MacMillan Co.
55. Zyserman, F. I., P. M. Gauzellino, and J. E. Santos, 2003, Dispersion analysis of a non-conforming finite element method for the Helmholtz and elastodynamic equations: International Journal of Numerical Methods in Engineering, 58, 1381-1395. ijv IJNMBH 0029-5981 10.1002/nme.822