Nonhyperbolic reflection moveout
Published:January 01, 2012
Chapter 3 was devoted to the influence of anisotropy on normal-moveout velocity, which controls reflection traveltimes on spreadlengths typically limited by the distance between the CMP and the reflector. If the medium is anisotropic or heterogeneous, hyperbolic moveout equation parameterized by NMO velocity loses accuracy with increasing offset. Angle-dependent velocity makes reflection moveout nonhyperbolic even in a single homogeneous layer, unless the anisotropy is elliptical.
Anisotropy-induced deviations from the short-spread hyperbola for a typical VTI model (Taylor Sandstone, Figure 4.1) are illustrated by Figures 4.2–4.4. If the layer were isotropic (∈ = δ = 0), the moveout would be purely hyperbolic for any source-receiver offset. The residual moveout in Figure 4.2 is calculated as the difference between the exact traveltimes and the best-fit hyperbola found by the least-squares method. Because the spreadlength xmax is limited by the reflector depth z, the residuals for both P- and SV-waves at all offsets are small (less than 2 ms). The error of the best-fit hyperbola, however, rapidly increases with spreadlength and for the SV-wave reaches 60 ms when xmax = 2 z (Figure 4.3).
It is important to notice that even if the time residuals are small, the finite-spread (effective) moveout velocity of the best-fit hyperbola may differ from the NMO velocity (Figure 4.4). Whereas Vnmo is determined analytically in the zero-spread limit, the finite-spread moveout velocity is obtained by fitting generally nonhyperbolic data with a hyperbolic function. For instance, the
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Seismic Signatures and Analysis of Reflection Data in Anisotropic Media, Third Edition
This is a new edition of Ilya Tsvankin’s reference volume on seismic anisotropy and application of anisotropic models in reflection seismology. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media, Geophysical References Series No. 19, provides essential background information about anisotropic wave propagation, introduces efficient notation for transversely isotropic (TI) and orthorhombic media, and identifies the key anisotropy parameters for imaging and amplitude analysis. To gain insight into the influence of anisotropy on a wide range of seismic signatures, exact solutions are simplified in the weak-anisotropy approximation.