Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures
A new spectral-method algorithm can be used to study wave propagation in cylindrically layered fluid and elastic structures. The cylindrical structure is discretized with Chebyshev points in the radial direction, whereas differentiation matrices are used to approximate the differential operators. We...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
Society of Exploration Geophysics
2010
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| Online Access: | http://hdl.handle.net/20.500.11937/43302 |
| _version_ | 1848756653491486720 |
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| author | Karpfinger, F. Valero, H. Gurevich, Boris Bakulin, Andrey Sinha, B. |
| author_facet | Karpfinger, F. Valero, H. Gurevich, Boris Bakulin, Andrey Sinha, B. |
| author_sort | Karpfinger, F. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A new spectral-method algorithm can be used to study wave propagation in cylindrically layered fluid and elastic structures. The cylindrical structure is discretized with Chebyshev points in the radial direction, whereas differentiation matrices are used to approximate the differential operators. We express the problem of determining modal dispersions as a generalized eigenvalue problem that can be solved readily for all eigenvalues corresponding to various axial wavenumbers. Modal dispersions of guided modes can then be expressed in terms of axial wavenumbers as a function of frequency. The associated eigenvectors are related to the displacement potentials that can be used to calcu-late radial distributions of modal amplitudes as well as stress components at a given frequency.The workflow includes input parameters and the construction of differentiation matrices and boundary conditions that yield the generalized eigenvalue problem. Results from this algorithm for a fluid-filled borehole surrounded by an elastic formation agree very well with those from a root-finding search routine. Computational efficiency of the algorithm has been demonstrated on a four-layer completion model used in a hydrocarbon-producing well. Even though the algorithm is numerically unstable at very low frequencies, it produces reliable and accurate results for multilayered cylindrical structures at moderate frequencies that are of interest in estimating formation properties using modal dispersions. |
| first_indexed | 2025-11-14T09:15:37Z |
| format | Journal Article |
| id | curtin-20.500.11937-43302 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:15:37Z |
| publishDate | 2010 |
| publisher | Society of Exploration Geophysics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-433022019-02-19T04:28:02Z Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures Karpfinger, F. Valero, H. Gurevich, Boris Bakulin, Andrey Sinha, B. A new spectral-method algorithm can be used to study wave propagation in cylindrically layered fluid and elastic structures. The cylindrical structure is discretized with Chebyshev points in the radial direction, whereas differentiation matrices are used to approximate the differential operators. We express the problem of determining modal dispersions as a generalized eigenvalue problem that can be solved readily for all eigenvalues corresponding to various axial wavenumbers. Modal dispersions of guided modes can then be expressed in terms of axial wavenumbers as a function of frequency. The associated eigenvectors are related to the displacement potentials that can be used to calcu-late radial distributions of modal amplitudes as well as stress components at a given frequency.The workflow includes input parameters and the construction of differentiation matrices and boundary conditions that yield the generalized eigenvalue problem. Results from this algorithm for a fluid-filled borehole surrounded by an elastic formation agree very well with those from a root-finding search routine. Computational efficiency of the algorithm has been demonstrated on a four-layer completion model used in a hydrocarbon-producing well. Even though the algorithm is numerically unstable at very low frequencies, it produces reliable and accurate results for multilayered cylindrical structures at moderate frequencies that are of interest in estimating formation properties using modal dispersions. 2010 Journal Article http://hdl.handle.net/20.500.11937/43302 10.1190/1.3380590 Society of Exploration Geophysics fulltext |
| spellingShingle | Karpfinger, F. Valero, H. Gurevich, Boris Bakulin, Andrey Sinha, B. Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures |
| title | Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures |
| title_full | Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures |
| title_fullStr | Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures |
| title_full_unstemmed | Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures |
| title_short | Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures |
| title_sort | spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures |
| url | http://hdl.handle.net/20.500.11937/43302 |