Finite-difference modeling of wave propagation on microscale: A snapshot of the work in progress

Geophysics

Volumn 72, Issue 5, 2007, Pages

  Saenger, Erik H ^a,b   Ciz, Radim ^c   Krüger, Oliver S ^c   Schmalholz, Stefan M ^d   Gurevich, Boris ^e   Shapiro, Serge A ^c  

^a GEOLOGICAL INSTITUTE   (Switzerland)

^b Spectraseis AG   (Switzerland)

^c FREIE UNIVERSITÄT BERLIN   (Germany)

^d CURTIN UNIVERSITY   (Australia)

^e CSIRO   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; ELASTIC WAVES; FINITE DIFFERENCE METHOD; GAS HYDRATES; MATHEMATICAL MODELS; PHYSICAL PROPERTIES; WAVE PROPAGATION;

BIOT'S SLOW WAVE; DIGITAL ROCK METHODOLOGY; ROTATED STAGGERED GRID;

ROCKS;

ALGORITHM; BIOT THEORY; DYNAMIC PROPERTY; ELASTIC PROPERTY; ELASTIC WAVE; FINITE DIFFERENCE METHOD; P-WAVE; POROUS MEDIUM; WAVE PROPAGATION; WAVE VELOCITY;

EID: 34548534167     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.2753552     Document Type: Article

References (51)

1. Arns, C. H., M. A. Knackstedt, W. V. Pinczewski, and E. J. Garboczi, 2002, Computation of linear elastic properties from microtomographic images: Methodology and agreement between theory and experiment: Geophysics, 67, 1396-1405. gpy GPYSA7 0016-8033 10.1190/1.1512785
2. Bedford, A., 1986, Application of Biot's equations to a medium of alternating fluid and solid layers: Journal of Wave-Material Interaction, 1, 34-53. bb2 ZZZZZZ 0887-0586
3. Biot, M. A., 1956, Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range and II. Higher-frequency range: Journal of the Acoustical Society of America, 28, 168-191. jas JASMAN 0001-4966 10.1121/1.1908239
4. Bohlen, T., and E. H. Saenger, 2006, Accuracy of heterogeneous staggered-grid finite-difference modeling of Rayleigh waves: Geophysics, 71, no. 4, T109-T115. gpy GPYSA7 0016-8033 10.1190/1.2213051
5. Brekhovskikh, L. M., 1981, Waves in layered media: Academic Press Inc.
6. Carcione, J. M., G. C. Herman, and A. P. E. ten Kroode, 2002, Seismic modeling: Geophysics, 67, 1304-1325. gpy GPYSA7 0016-8033 10.1190/ 1.1500393
7. Ciz, R., E. H. Saenger, and B. Gurevich, 2006, Pore scale numerical modelling of elastic wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers: Journal of the Acoustical Society of America, 120, 642-648. jas JASMAN 0001-4966 10.1121/1.2216687
8. Crase, E., 1990, High-order (space and time) finite-difference modeling of the elastic wave equation: 60th Annual International Meeting, SEG, Expanded Abstracts, 987-991.
9. Dablain, M. A., 1986, The application of high-order differencing to the scalar wave equation: Geophysics, 51, 54-66. gpy GPYSA7 0016-8033 10.1190/1.1442040
10. Dai, J., H. Xu, F. Snyder, and N. Dutta, 2004, Detection and estimation of gas hydrates using rock physics and seismic inversion: Examples from the northern deep water Gulf of Mexico: The Leading Edge, 23, 60-66. lee LEEDFF 1070-485X 10.1190/1.1645456
11. Dai, N., A. Vafidis, and E. R. Kanasewich, 1995, Wave propagation in heterogeneous, porous media: A velocity-stress, finite-difference method: Geophysics, 60, 327-340. gpy GPYSA7 0016-8033 10.1190/1.1443769
12. Dutta, N. C., 1980, Theoretical analysis of observed second bulk compressional waves in a fluid-saturated porous solid at ultrasonic frequencies: Applied Physics Letters, 37, 898-900. apl APPLAB 0003-6951 10.1063/1.91851
13. Emmerich, H., and M. Korn, 1987, Incorporation of attenuation into time-domain computations of seismic wavefields Geophysics, 52, 1252-1264. gpy GPYSA7 0016-8033 10.1190/1.1442386
14. Gei, D., and J. M. Carcione, 2003, Acoustic properties of sediments saturated with gas hydrate, free gas and water: Geophysical Prospecting, 51, 141-157. 8uc GPPRAR 0016-8025 10.1046/j.1365-2478.2003.00359.x
15. Graves, R. W., 1996, Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences: Bulletin of the Seismological Society of America, 86, 1091-1106. bss BSSAAP 0037-1106
16. Grechka, V., and M. Kachanov, 2006, Effective elasticity of fractured rocks: A snapshot of the work in progress Geophysics, 71, no. 6, W45-W58. gpy GPYSA7 0016-8033 10.1190/1.2360212
17. Guerin, G., and D. Goldberg, 2002, Sonic waveform attenuation in gas hydrate-bearing sediments from the Mallik 2L-38 research well, Mackenzie Delta, Canada: Journal of Geophysical Research, 107, no. B5, EPM 1-1-EPM 1-12. jgr JGREA2 0148-0227
18. Gurevich, B., 2002, Effect of fluid viscosity on elastic wave attenuation in porous rocks: Geophysics, 67, 264-270. gpy GPYSA7 0016-8033 10.1190/1.1451798
19. Gurevich, B., R. Ciz, and A. I. M. Dennemann, 2004, Simple expressions for normal incidence reflection coefficients from an interface between fluid-saturated porous materials Geophysics, 69, 1372-1377. gpy GPYSA7 0016-8033 10.1190/1.1836811
20. Gurevich, B., O. Kelder, and D. M. J. Smeulders, 1999, Validation of the slow compressional wave in porous media: Comparison of experiments and numerical simulations: Transport in Porous Media, 36, 149-160. tpm TPMEEI 0169-3913 10.1023/A:1006676801197
21. Holberg, O., 1987, Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena: Geophysical Prospecting, 35, 629-655. 8uc GPPRAR 0016-8025 10.1111/j.1365-2478.1987.tb00841.x
22. Kachanov, M., 1992, Effective elastic properties of cracked solids: Critical review of some basic concepts: Applied Mechanics Reviews, 45, no. 8, 304-335. amk AMREAD 0003-6900
23. Kelly, K. R., R. W. Ward, S. Treitel, and R. M. Alford, 1976, Synthetic seismograms: A finite-difference approach: Geophysics, 41, 2-27. gpy GPYSA7 0016-8033 10.1190/1.1440605
24. Kindelan, M., A. Kamel, and P. Sguazzero, 1990, On the construction and efficiency of staggered numerical differentiators for the wave equation Geophysics, 55, 107-110. gpy GPYSA7 0016-8033 10.1190/1.1442763
25. Kristek, J., and P. Moczo, 2003, Seismic-wave propagation in viscoelastic media with material discontinuities: A 3D fourth-order staggered-grid finite-difference modeling: Bulletin of the Seismological Society of America, 93, 2273-2280. bss BSSAAP 0037-1106
26. Krüger, O. S., E. H. Saenger, S. J. Oates, and S. A. Shapiro, 2007, A numerical study on reflection coefficients of fractured media: Geophysics, 72, no. 3, D61-D67. gpy GPYSA7 0016-8033 10.1190/ 1.2732690
27. Krüger, O. S., E. H. Saenger, and S. A. Shapiro, 2005, Scattering and diffraction by a single crack: An accuracy analysis of the rotated staggered grid: Geophysical Journal International, 162, 25-31. gji GJINEA 0956-540X 10.1111/j.1365-246X.2005.02647.x
28. Marfurt, K. J., 1984, Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations: Geophysics, 49, 533-549. gpy GPYSA7 0016-8033 10.1190/1.1441689
29. Mavko G.T. Mukerji, and J. Dvorkin, 1998, The rock physics handbook: Cambridge University Press.
30. Moczo, P., and J. Kristek, 2005, On the rheological models used for time-domain methods of seismic wave propagation Geophysical Research Letters, 32, L01306. gpr GPRLAJ 0094-8276 10.1029/2004GL021598
31. Moczo, P., J. Kristek, V. Vavrycuk, R. J. Archuleta, and L. Halada, 2002, 3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities: Bulletin of the Seismological Society of America, 92, 3042-3066. bss BSSAAP 0037-1106 10.1785/0120010167
32. Moczo, P., J. O. A. Robertsson, and L. Eisner, 2007, The finite-difference time-domain method for modelling of seismic wave propagation, in R. S. Wu, and V. Maupin, eds., Advances in Geophysics, 48, 421-516. gpy GPYSA7 0016-8033
33. Norris, A. N., 1985, A differential scheme for the effective moduli of composites: Mechanics of Materials, 4, 1-16. mhm MSMSD3 0167-6636 10.1016/0167-6636(85)90002-X
34. Orlowsky, B., E. H. Saenger, Y. Guéguen, and S. A. Shapiro, 2003, Effects of parallel crack distributions on effective elastic properties - A numerical study: International Journal of Fracture, 124, no. (3-4), L171-L178. ijf IJFRAP 0376-9429 10.1023/B:FRAC.0000022563.29991.80
35. Plona, T., 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
36. Quiroga-Goode, G., and J. M. Carcione, 1997, Heterogeneous modelling behaviour at an interface in porous media: Computational Geosciences, 1, 109-125. cgo CGEODT 0098-3004
37. Rasolofosaon, P. N. J., 1988, Importance of the interface hydraulic condition on the generation of second bulk compressional wave in porous media: Applied Physics Letters, 37, 898-900. apl APPLAB 0003-6951 10.1063/1.91851
38. Roberts, A. P., and E. J. Garboczi, 2002, Computation of the linear elastic properties of random porous materials with a wide variety of microstructure: Proceedings of the Royal Society of London A, 458, 1033-1054. pln PRLAAZ 0962-8444 10.1098/rspa.2001.0900
39. Rytov, S. M., 1956, Acoustical properties of a thinly laminated medium: Soviet Physical Acoustics, 2, 68-80.
40. Saenger, E. H., and T. Bohlen, 2004, Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid: Geophysics, 69, 583-591. gpy GPYSA7 0016-8033 10.1190/ 1.1707078
41. Saenger, E. H., N. Gold, and S. A. Shapiro, 2000, Modeling the propagation of elastic waves using a modified finite-difference grid: Wave Motion, 31, 77-92. wvm WAMOD9 0165-2125 10.1016/ S0165-2125(99)00023-2
42. Saenger, E. H., O. S. Krüger, and S. A. Shapiro, 2004a, Effective elastic properties of randomly fractured soils: 3D numerical experiments: Geophysical Prospecting, 52, 183-195. 8uc GPPRAR 0016-8025 10.1111/j.1365-2478.2004.00407.x
43. 2004b Numerical considerations of fluid effects on wave propagation: Influence of the tortuosity: Geophysical Research Letters, 31, L21613. gpr GPRLAJ 0094-8276 10.1029/2004GL020970
44. Saenger, E. H., and S. A. Shapiro, 2002, Effective velocities in fractured media: A numerical study using the rotated staggered finite-difference grid: Geophysical Prospecting, 50, 183-194. 8uc GPPRAR 0016-8025 10.1046/j.1365-2478.2002.00309.x
45. 2006, Effective elastic properties of fractured rocks: Dynamic versus static considerations: International Journal of Fracture, 139, 569-576. ijf IJFRAP 0376-9429 10.1007/s10704-006-0105-4
46. Saenger, E. H., S. A. Shapiro, and Y. Keehm, 2005, Seismic effects of viscous Biot-coupling: Finite difference simulations on micro-scale: Geophysical Research Letters, 32, L14310. gpr GPRLAJ 0094-8276 10.1029/ 2005GL023222
47. Vavakin, A. S., and R. L. Salganik, 1978, Effective elastic characteristics of bodies with isolated cracks, cavities and rigid nonhomogeneities: Mekhanika Tverdogo Tela, 13, no. 2, 95-107.
48. Virieux, J., 1986, Velocity-stress finite-difference method Geophysics, 51, 889-901. gpy GPYSA7 0016-8033 10.1190/1.1442147
49. von Neumann, J., 1943, Mathematische grundlagen der quantenmechanik: Dover Publ. Inc.
50. Zahradník, J., and E. Priolo, 1999, Heterogeneous formulations of elastodynamic equations and finite-difference schemes: Geophysical Journal International, 120, 663-676. gji GJINEA 0956-540X 10.1111/ j.1365-246X.1995.tb01844.x
51. Zimmermann, R. W., 1991, Compressibility of sandstones: Elsevier Science Publ Co., Inc.