Finite-element simulations of Stoneley guided-wave reflection and scattering at the tips of fluid-filled fractures

Geophysics

Volumn 75, Issue 2, 2010, Pages

  Frehner, Marcel ^a,b   Schmalholz, Stefan M ^a,c  

^a GEOLOGICAL INSTITUTE   (Switzerland)

^b UNIVERSITY OF VIENNA   (Austria)

^c UNIVERSITY OF LAUSANNE   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

CRACK PROPAGATION; ELASTICITY; FINITE ELEMENT METHOD; GUIDED ELECTROMAGNETIC WAVE PROPAGATION;

AMPLITUDE RATIOS; BULK DEFORMATION; CRACK GEOMETRIES; DEFORMATION BEHAVIOR; EXPONENTIAL DECAYS; FINITE ELEMENT MESHES; FINITE ELEMENT SIMULATIONS; WAVE REFLECTIONS;

CRACK TIPS;

BODY WAVE; COMPUTER SIMULATION; CRACK; DEFORMATION; ELASTIC WAVE; ELASTICITY; FINITE ELEMENT METHOD; FRACTURE; ROCK; SEISMIC REFLECTION; SEISMIC WAVE; WAVE REFLECTION; WAVE SCATTERING; AMPLITUDE; NUMERICAL MODEL; STONELEY WAVE;

EID: 84864159644     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.3340361     Document Type: Article

References (48)

1. Achenbach, J.D., 1973, Wave propagation in elastic solids: North-Holland Publishing Company.
2. Aki, K. Fehler, M. Das, S., 1977, Source mechanism of volcanic tremor: Fluid-driven crack models and their application to the 1963 Kilauea eruption: Journal of Volcanology and Geothermal Research, 2, 259-287.jvg, JVGRDQ, 0377-0273, 10.1016/0377-0273(77)90003-8
3. Aki, K. Richards, P.G., 2002, Quantitative seismology: University Science Books.
4. Ashour, A.S., 2000, Wave motion in a viscous fluid-filled fracture: International Journal of Engineering Science, 38, 505-515., 10.1016/S0020-7225(99)00045-2
5. Barenblatt, G.I., 1996, Scaling, self-similarity, and intermediate asymptotics: Cambridge University Press.
6. Bathe, K.-J., 1996, Finite element procedures: Prentice Hall.
7. Biot, M.A., 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
8. Bourbie, T. Coussy, O. Zinszner, B., 1987, Acoustics of porous media: Editions Technip.
9. Carcione, J.M., 2001, Wave fields in real media: Wave propagation in anisotropic, anelastic and porous media: Elsevier.
10. Carcione, J.M. Helle, H.B., 2004, The physics and simulation of wave propagation at the ocean bottom: Geophysics, 69, 825-839.gpy, GPYSA7, 0016-8033, 10.1190/1.1759469
11. Chen, Z.Y. Steeb, H. Diebels, S., 2008, A new hybrid velocity integration method applied to elastic wave propagation: International Journal for Numerical Methods in Engineering, 74, 56-79.ijv, IJNMBH, 0029-5981, 10.1002/nme.2167
12. Chouet, B., 1986, Dynamics of a fluid-driven crack in three dimensions by the finite-difference method: Journal of Geophysical Research, 91, 13967-13992.jgr, JGREA2, 0148-0227, 10.1029/JB091iB14p13967
13. 1988, Resonance of a fluid-driven crack: Radiation properties and implications for the source of long-period events and harmonic tremor: Journal of Geophysical Research, 93, 4375-4400.jgr, JGREA2, 0148-0227, 10.1029/JB093iB05p04375
14. 1996, Long-period volcano seismicity: Its source and use in eruption forecasting: Nature, 380, 309-316.bnh, NATUAS, 0028-0836, 10.1038/380309a0
15. Cohen, G.C., 2002, Higher-order numerical methods for transient wave equations: Springer Verlag.
16. Dvorkin, J. Mavko, G. Nur, A., 1995, Squirt flow in fully saturated rocks: Geophysics, 60, 97-107.gpy, GPYSA7, 0016-8033, 10.1190/1.1443767
17. Faoro, I. Niemeijer, A. Marone, C. Elsworth, D., 2009, Influence of shear and deviatoric stress on the evolution of permeability in fractured rock: Journal of Geophysical Research, 114, B01201.jgr, JGREA2, 0148-0227, 10.1029/2007JB005372
18. Ferrazzini, V. Aki, K., 1987, Slow waves trapped in a fluid-filled infinite crack: Implication for volcanic tremor: Journal of Geophysical Research, 92, 9215-9223.jgr, JGREA2, 0148-0227, 10.1029/JB092iB09p09215
19. Frehner, M. Schmalholz, S.M. Podladchikov, Y., 2009, Spectral modification of seismic waves propagating through solids exhibiting a resonance frequency: A 1-D coupled wave propagation-oscillation model: Geophysical Journal International, 176, 589-600.gji, GJINEA, 0956-540X, 10.1111/j.1365-246X.2008.04001.x
20. Frehner, M. Schmalholz, S.M. Saenger, E.H. Steeb, H., 2008, Comparison of finite difference and finite element methods for simulating two-dimensional scattering of elastic waves: Physics of the earth and planetary interiors, 171, 112-121., 10.1016/j.pepi.2008.07.003
21. Groenenboom, J. Falk, J., 2000, Scattering by hydraulic fractures: Finite-difference modeling and laboratory data: Geophysics, 65, 612-622.gpy, GPYSA7, 0016-8033, 10.1190/1.1444757
22. Higham, N.J., 1996, Accuracy and stability of numerical algorithms: Society for Industrial & Applied Mathematics.
23. Hudson, J.A., 1980, Overall properties of a cracked solid: Mathematical Proceedings of the Cambridge Philosophical Society, 88, 371-384.
24. 1981, Wave speeds and attenuation of elastic-waves in material containing cracks: Geophysical Journal of the Royal Astronomical Society, 64, 133-150.gjr, GEOJAN, 0016-8009
25. Hughes, T., 1987, The finite element method: Linear static and dynamic finite element analysis: Dover Publications.
26. Ionov, A.M., 2007, Stoneley wave generation by an incident P-wave propagating in the surrounding formation across a horizontal fluid-filled fracture: Geophysical Prospecting, 55, 71-82.8uc, GPPRAR, 0016-8025, 10.1111/j.1365-2478.2006.00577.x
27. Käser, M. Dumbser, M., 2008, A highly accurate discontinuous Galerkin method for complex interfaces between solids and moving fluids: Geophysics, 73, no. 3, T23-T35.gpy, GPYSA7, 0016-8033, 10.1190/1.2870081
28. Korneev, V., 2008, Slow waves in fractures filled with viscous fluid: Geophysics, 73, no. 1, N1-N7.gpy, GPYSA7, 0016-8033, 10.1190/1.2802174
29. 2009, Resonant seismic emission of subsurface objects: Geophysics, 74, no. 2, T47-T53.gpy, GPYSA7, 0016-8033, 10.1190/1.3068448
30. Korneev, V.A. Ponomarenko, A.A. Kashtan, M., 2009, Stoneley guided waves: What is missing in Biot's theory?, in H. I. Ling, A. Smyth, and R. Betti, eds., Poromechanics IV: Proceedings of the fourth Biot conference on poromechanics: DEStech Publications Inc., 706-711.
31. Kostek, S. Johnson, D.L. Randall, C.J., 1998, The interaction of tube waves with borehole fractures, Part I: Numerical models: Geophysics, 63, 800-808.gpy, GPYSA7, 0016-8033, 10.1190/1.1444391
32. Krüger, O.S. Saenger, E.H. Shapiro, S.A., 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
33. Lindsay, R.B., 1960, Mechanical radiation: McGraw-Hill, ISBN 0-0703-7844-0.
34. Love, A.E.H., 1927, A treatise on the mathematical theory of elasticity: Dover Publications.
35. Mavko, G. Jizba, D., 1991, Estimating grain-scale fluid effects on velocity dispersion in rocks: Geophysics, 56, 1940-1949.gpy, GPYSA7, 0016-8033, 10.1190/1.1443005
36. Mavko, G. Mukerji, T. Dvorkin, J., 2003, The rock physics handbook: Tools for seismic analysis in porous media: Cambridge University Press.
37. Newmark, N.M., 1959, A method of computation for structural dynamics: Journal of the Engineering Mechanics Division, 85, 67-94.
38. Pujol, J.A., 2003, Elastic wave propagation and generation in seismology: Cambridge University Press.
39. Saenger, E.H. Gold, N. Shapiro, S.A., 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
40. Saenger, E.H. Krüger, O.S. Shapiro, S.A., 2004, 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
41. Saenger, E.H. Shapiro, S.A., 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
42. Saenger, E.H. Shapiro, S.A. Keehm, Y., 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
43. Shames, I.H. Cozzarelli, F.A., 1997, Elastic and inelastic stress analysis: Taylor & Francis.
44. Shewchuk, J.R., 1996, Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator, in C. L. Ming, and M. Dinesh, eds., Applied computational geometry: Towards geometric engineering: Springer Verlag, 203-222.
45. 2002, Delaunay refinement algorithms for triangular mesh generation: Computational Geometry, 22, 21-74., 10.1016/S0925-7721(01)00047-5
46. Virieux, J., 1986, P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method: Geophysics, 51, 889-901.gpy, GPYSA7, 0016-8033, 10.1190/1.1442147
47. Yamamoto, M. Kawakatsu, H., 2008, An efficient method to compute the dynamic response of a fluid-filled crack: Geophysical Journal International, 174, 1174-1186.gji, GJINEA, 0956-540X, 10.1111/j.1365-246X.2008.03871.x
48. Zienkiewicz, O.C. Taylor, R.L., 2000, The finite element method: Volume 1 (fifth edition): The basis: Butterworth-Heinemann.