Tube wave signatures in cylindrically layered poroelastic media computed with spectral method
This paper describes a new algorithm based on the spectral method for the computation of Stoneley wave dispersion and attenuation propagating in cylindrical structures composed of fluid, elastic and poroelastic layers. The spectral method is a numerical method which requires discretization of the st...
| Main Authors: | , , , , |
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| Format: | Journal Article |
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Blackwell Publishing Ltd
2010
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| Online Access: | http://hdl.handle.net/20.500.11937/26521 |
| _version_ | 1848752010451484672 |
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| author | Karpfinger, F. Gurevich, Boris Valero, H. Bakulin, Andrey Sinha, B. |
| author_facet | Karpfinger, F. Gurevich, Boris Valero, H. Bakulin, Andrey Sinha, B. |
| author_sort | Karpfinger, F. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper describes a new algorithm based on the spectral method for the computation of Stoneley wave dispersion and attenuation propagating in cylindrical structures composed of fluid, elastic and poroelastic layers. The spectral method is a numerical method which requires discretization of the structure along the radial axis using Chebyshev points. To approximate the differential operators of the underlying differential equations, we use spectral differentiation matrices. After discretizing equations of motion along the radial direction, we can solve the problem as a generalized algebraic eigenvalue problem. For a given frequency, calculated eigenvalues correspond to the wavenumbers of different modes. The advantage of this approach is that it can very efficiently analyse structures with complicated radial layering composed of different fluid, solid and poroelastic layers. This work summarizes the fundamental equations, followed by an outline of how they are implemented in the numerical spectral schema. The interface boundary conditions are then explained for fluid/porous, elastic/porous and porous interfaces. Finally, we discuss three examples from borehole acoustics. The first model is a fluid-filled borehole surrounded by a poroelastic formation. The second considers an additional elastic layer sandwiched between the borehole and the formation, and finally a model with radially increasing permeability is considered. |
| first_indexed | 2025-11-14T08:01:49Z |
| format | Journal Article |
| id | curtin-20.500.11937-26521 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:01:49Z |
| publishDate | 2010 |
| publisher | Blackwell Publishing Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-265212017-09-13T15:52:27Z Tube wave signatures in cylindrically layered poroelastic media computed with spectral method Karpfinger, F. Gurevich, Boris Valero, H. Bakulin, Andrey Sinha, B. Acoustic properties Guided waves Downhole methods Numerical solutions Wave propagation This paper describes a new algorithm based on the spectral method for the computation of Stoneley wave dispersion and attenuation propagating in cylindrical structures composed of fluid, elastic and poroelastic layers. The spectral method is a numerical method which requires discretization of the structure along the radial axis using Chebyshev points. To approximate the differential operators of the underlying differential equations, we use spectral differentiation matrices. After discretizing equations of motion along the radial direction, we can solve the problem as a generalized algebraic eigenvalue problem. For a given frequency, calculated eigenvalues correspond to the wavenumbers of different modes. The advantage of this approach is that it can very efficiently analyse structures with complicated radial layering composed of different fluid, solid and poroelastic layers. This work summarizes the fundamental equations, followed by an outline of how they are implemented in the numerical spectral schema. The interface boundary conditions are then explained for fluid/porous, elastic/porous and porous interfaces. Finally, we discuss three examples from borehole acoustics. The first model is a fluid-filled borehole surrounded by a poroelastic formation. The second considers an additional elastic layer sandwiched between the borehole and the formation, and finally a model with radially increasing permeability is considered. 2010 Journal Article http://hdl.handle.net/20.500.11937/26521 10.1111/j.1365-246X.2010.04773.x Blackwell Publishing Ltd unknown |
| spellingShingle | Acoustic properties Guided waves Downhole methods Numerical solutions Wave propagation Karpfinger, F. Gurevich, Boris Valero, H. Bakulin, Andrey Sinha, B. Tube wave signatures in cylindrically layered poroelastic media computed with spectral method |
| title | Tube wave signatures in cylindrically layered poroelastic media computed with spectral method |
| title_full | Tube wave signatures in cylindrically layered poroelastic media computed with spectral method |
| title_fullStr | Tube wave signatures in cylindrically layered poroelastic media computed with spectral method |
| title_full_unstemmed | Tube wave signatures in cylindrically layered poroelastic media computed with spectral method |
| title_short | Tube wave signatures in cylindrically layered poroelastic media computed with spectral method |
| title_sort | tube wave signatures in cylindrically layered poroelastic media computed with spectral method |
| topic | Acoustic properties Guided waves Downhole methods Numerical solutions Wave propagation |
| url | http://hdl.handle.net/20.500.11937/26521 |