Applications Of Perturbation Theory To Acoustic Logging
For guided wave propagation in boreholes, perturbation theory is used to calculate (1) the partial derivative of the wavenumber or frequency with respect to an elastic modulus or density, (2) group velocity, and (3) the effect of a borehole with a slightly irregular cross section upon the phase v...
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| Other Authors: | |
| Format: | Technical Report |
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Massachusetts Institute of Technology. Earth Resources Laboratory
2012
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| Online Access: | http://hdl.handle.net/1721.1/75111 |
| _version_ | 1826193263439118336 |
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| author | Ellefsen, K. J. Cheng, C. H. |
| author2 | Massachusetts Institute of Technology. Earth Resources Laboratory |
| author_facet | Massachusetts Institute of Technology. Earth Resources Laboratory Ellefsen, K. J. Cheng, C. H. |
| author_sort | Ellefsen, K. J. |
| collection | MIT |
| description | For guided wave propagation in boreholes, perturbation theory is used to calculate
(1) the partial derivative of the wavenumber or frequency with respect to an elastic
modulus or density, (2) group velocity, and (3) the effect of a borehole with a slightly
irregular cross section upon the phase velocity. The method, which is developed for
a fluid-filled, cylindrical borehole through a transversely isotropic formation, relates
perturbations in formation properties (i.e., elastic moduli, densities, and interface locations) and wave properties (i.e., wavenumber and frequency) for guided waves with any
azimuthal order number. Velocity perturbations, which are calculated for three common
cross sections of irregular boreholes, show several general characteristics. The
tube and pseudo-Rayleigh waves, which have no azimuthal dependence, completely
smooth the effects of the irregularity making the velocity perturbation independent
of the wave's orientation. The perturbations for the tube wave are small because it
is a Stoneley wave, but those for the pseudo-Rayleigh wave are much larger because
the borehole shape affects the multiply-reflected part of this wave. The velocity perturbations for the flexural and screw waves are similar in character to those for the
pseudo-Rayleigh wave, but because these waves are directional, they can interact with
the irregularity to amplify or diminish the velocity perturbation. |
| first_indexed | 2024-09-23T09:36:14Z |
| format | Technical Report |
| id | mit-1721.1/75111 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:36:14Z |
| publishDate | 2012 |
| publisher | Massachusetts Institute of Technology. Earth Resources Laboratory |
| record_format | dspace |
| spelling | mit-1721.1/751112019-04-12T20:30:50Z Applications Of Perturbation Theory To Acoustic Logging Ellefsen, K. J. Cheng, C. H. Massachusetts Institute of Technology. Earth Resources Laboratory Ellefsen, K. J. Cheng, C. H. For guided wave propagation in boreholes, perturbation theory is used to calculate (1) the partial derivative of the wavenumber or frequency with respect to an elastic modulus or density, (2) group velocity, and (3) the effect of a borehole with a slightly irregular cross section upon the phase velocity. The method, which is developed for a fluid-filled, cylindrical borehole through a transversely isotropic formation, relates perturbations in formation properties (i.e., elastic moduli, densities, and interface locations) and wave properties (i.e., wavenumber and frequency) for guided waves with any azimuthal order number. Velocity perturbations, which are calculated for three common cross sections of irregular boreholes, show several general characteristics. The tube and pseudo-Rayleigh waves, which have no azimuthal dependence, completely smooth the effects of the irregularity making the velocity perturbation independent of the wave's orientation. The perturbations for the tube wave are small because it is a Stoneley wave, but those for the pseudo-Rayleigh wave are much larger because the borehole shape affects the multiply-reflected part of this wave. The velocity perturbations for the flexural and screw waves are similar in character to those for the pseudo-Rayleigh wave, but because these waves are directional, they can interact with the irregularity to amplify or diminish the velocity perturbation. Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortium Phillips Petroleum Fellowship 2012-11-29T20:26:38Z 2012-11-29T20:26:38Z 1989 Technical Report http://hdl.handle.net/1721.1/75111 Earth Resources Laboratory Industry Consortia Annual Report;1989-02 application/pdf Massachusetts Institute of Technology. Earth Resources Laboratory |
| spellingShingle | Ellefsen, K. J. Cheng, C. H. Applications Of Perturbation Theory To Acoustic Logging |
| title | Applications Of Perturbation Theory To Acoustic Logging |
| title_full | Applications Of Perturbation Theory To Acoustic Logging |
| title_fullStr | Applications Of Perturbation Theory To Acoustic Logging |
| title_full_unstemmed | Applications Of Perturbation Theory To Acoustic Logging |
| title_short | Applications Of Perturbation Theory To Acoustic Logging |
| title_sort | applications of perturbation theory to acoustic logging |
| url | http://hdl.handle.net/1721.1/75111 |
| work_keys_str_mv | AT ellefsenkj applicationsofperturbationtheorytoacousticlogging AT chengch applicationsofperturbationtheorytoacousticlogging |