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1 | 1 | \published{Geophysical Prospecting, v. 52, 247-259 (2004)} |
2 | | -\title{On anelliptic approximations for $qP$ velocities in |
3 | | -transversally isotropic media} |
| 2 | +\title{On anelliptic approximations for $qP$ velocities in VTI media} |
4 | 3 |
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5 | 4 | |
6 | 5 | \author{Sergey Fomel} |
7 | 6 |
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8 | 7 | \maketitle |
9 | 8 |
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10 | 9 | \begin{abstract} |
11 | | -I develop a unified approach for approximating phase and group |
12 | | - velocities of $qP$ seismic waves in a transversally isotropic medium |
13 | | - with the vertical axis of symmetry (VTI). While the exact phase |
14 | | - velocity expressions involve four independent parameters to |
15 | | - characterize the elastic medium, the proposed approximate |
16 | | - expressions use only three parameters. This makes them more |
17 | | - convenient for use in surface seismic experiments, where estimation |
18 | | - of all the four parameters is problematic. The three-parameter |
19 | | - phase-velocity approximation coincides with the previously published |
20 | | - ``acoustic'' approximation of Alkhalifah. The group velocity |
21 | | - approximation is `new and noticeably more accurate than some of the |
22 | | - previously published approximations. I demonstrate an application of |
23 | | - the group velocity approximation for finite-difference computation |
24 | | - of traveltimes. |
| 10 | +A unified approach to approximating phase and group velocities of qP seismic waves |
| 11 | +in a transversely isotropic medium with vertical axis of symmetry (VTI) is developed. |
| 12 | +While the exact phase-velocity expressions involve four independent parameters to |
| 13 | +characterize the elastic medium, the proposed approximate expressions use only three |
| 14 | +parameters. This makes them more convenient for use in surface seismic experiments, |
| 15 | +where the estimation of all four parameters is problematic. The three-parameter phase-velocity approximation coincides with the previously published ‘acoustic’ approximation of Alkhalifah. The group-velocity approximation is new and noticeably more |
| 16 | +accurate than some of the previously published approximations. An application of |
| 17 | +the group-velocity approximation for finite-difference computation of traveltimes is |
| 18 | +shown. |
25 | 19 | \end{abstract} |
26 | 20 |
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27 | 21 | \section{Introduction} |
@@ -675,9 +669,7 @@ \section{Application: Finite-difference traveltime computation} |
675 | 669 | vertical velocity is taken equal to the NMO velocity $V_n$.} |
676 | 670 |
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677 | 671 | \section{Conclusions} |
678 | | - |
679 | | -I have developed a general approach for approximating both phase and group |
680 | | -velocities in a VTI medium. Suggested approximations use three elastic |
| 672 | +A general approach to approximating both phase and group velocities in a VTI medium has been developed. The suggested approximations use three elastic |
681 | 673 | parameters as opposed to the four parameters in the exact phase velocity |
682 | 674 | expression. The phase velocity approximation coincides with the acoustic |
683 | 675 | approximation of \cite{GEO63-02-06230631,GEO65-04-12391250} but is derived |
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