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GEOPHYSICS, VOL. 62, NO. 3 (MAY-JUNE 1997); P. 713 722, 7 FIGS., 1 TABLE. P -wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry Andreas R¨uger * ABSTRACT The study of P -wave reflection coefficients in anisot- ropic media is important for amplitude variation with offset (AVO) analysis. While numerical evaluation of the reflection coefficient is straightforward, numerical solu- tions do not provide analytic insight into the influence of anisotropy on the AVO signature. To overcome this difficulty, I present an improved ap- proximation for P -wave reflection coefficients at a hor- izontal boundary in transversely isotropic media with vertical axis of symmetry (VTI media). This solution has the same AVO-gradient term describing the low-order angularvariationofthereflectioncoefficientastheequa- tions published previously, but is more accurate for large incidence angles. The refined approximation is then ex- tended to transverse isotropy with a horizontal axis of symmetry (HTI), which is caused typically by a system of vertical cracks. Comparison of the approximate reflec- tion coefficients for P -waves incident in the two vertical symmetry planes of HTI media indicates that the az- imuthal variation of the AVO gradient is a function of the shear-wave splitting parameter γ , and the anisotropy parameter describing P -wave anisotropy for nearverti- cal propagation in the vertical plane containing the sym- metry axis. INTRODUCTION Reflectionandtransmissionofplanewavesataplanebound- ary between two isotropic media is one of the most fundamen- talproblemsinwavepropagation.Zoeppritz(1919)wasamong the first to publish the solution to this problem invoking conti- nuity of stress and displacement at the reflecting horizon. One important practical application of the reflection coeffi- cient studies is the analysis of amplitude variations with offset Presented at the 65th Annual International Meeting, Society of Exploration Geophysicists. Manuscript received by the Editor July 24, 1995; revised manuscript received August 1, 1996. * Center for Wave Phenomena, Colorado School of Mines, Golden, Colorado 80401-1887. c ± 1997 Society of Exploration Geophysicists. All rights reserved. (AVO). The variation of P -wave amplitudes with incidence angle provides one of the few direct hydrocarbon indicators (Ostrander, 1984) and has drawn substantial attention within the geophysical community. Conventional AVO analysis is based on analytic expressions for P -wave reflection coefficients in isotropic media, and it needs to be modified if anisotropy is present on either side of the reflecting boundary. Reflection and transmission of plane wavesataninterfacebetweentwoanisotropicmediahavebeen discussed, for example, in Musgrave (1970), Henneke (1972), Keith and Crampin (1977) and Daley and Hron (1977). The solution for reflection coefficients at interfaces of anisotropic media is very involved algebraically, and the general solu- tion requires a numerical inversion of 6 × 6 matrices. The
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This note was uploaded on 02/10/2011 for the course GEOL 4330 taught by Professor Chesnokov during the Spring '11 term at University of Houston - Downtown.

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