AN ANALYTICAL AND NUMERICAL STUDY OF P-WAVE MOVEOUT AT SHORT OFFSETS FOR TRANSVERSE ISOTROPIC MEDIA

摘要

Li, R., Uren, N.F. and McDonald, J.A., 2002. An analytical and numerical study of P-wave moveout at short offsets for transverse isotropic media. Journal of Seismic Exploration, 11: 341-362. Normal moveout (NMO) correction is one of the important procedures in carrying out seismic data processing. However, a single representative NMO velocity may be difficult to determine in the presence of velocity anisotropy. An equation for zero-offset NMO velocity for transverse isotropy has previously been derived. This equation has been used as the short offset NMO velocity, and it was believed to be valid for any degree of anisotropy. The limitations and accuracy of this equation for short offsets need to be examined. In this paper, the P-wave moveout at short offsets has been studied using analytic derivations and numerical modeling experiments. A series of equations has been derived for phase velocity, ray velocity, curvature of the t~2 vs. x~2 curve and moveout velocity. Using the measured elastic parameters for sedimentary anisotropic rocks, numerical simulations have been conducted to examine the above expressions and the zero offset NMO equation. Computer generated results with exact equations have been used as standards against which to compare the performance of our expressions and those previously derived. We show that the use of a zero offset equation for short offsets is applicable for a range of transverse isotropy, but it can become unsuitable outside this range. Our modified equation can be used to obtain more accurate results. At short offsets, the analytical expressions derived here are expansions of up to third-order in the phase velocity angle. These expressions can be used for all degrees of anisotropy at small phase angles. When offsets increase, the expressions need to be modified by using higher-order expansions. A good knowledge of the moveout velocity should help us to obtain good depth estimations, which, in turn, will lead to accurate seismic interpretation.