Nonelliptic transverse isotropy may cause pronounced nonhyperbolic moveout of long-spread P-wave reflection data. Lateral heterogeneity may alter the moveout in much the same way, and one can expect that a given P-wave reflection moveout may be interpreted equally well in terms of parameters of homogeneous transversely isotropic (TI) or laterally heterogeneous (LH) isotropic models.

Here, the common-midpoint (CMP) moveout of a P-wave reflected from a horizontal interface beneath a weakly laterally heterogeneous medium that is also weakly transversely isotropic is represented analytically in the form similar to that in homogeneous TI media. Both the normal-moveout (NMO) velocity and the quartic moveout coefficient contain derivatives of the zero- offset traveltime t0 and the NMO velocity Vnmo with respect to the lateral coordinate.

Despite the presence of heterogeneity, nonhyperbolic velocity analysis can be performed in the same way as in homogeneous TI models. If all parameters of the medium are linear functions of the lateral coordinate, heterogeneity does not influence the results of inversion for the anisotropic parameterη. However, to find η in the case of general lateral heterogeneity, the second derivative of Vnmo and the fourth derivative of t0 are needed. Since these high-order derivatives are calculated from the data measured at discrete points by numerical differentiation, stability of η estimation is further reduced as compared to that in homogeneous TI media. Consequently, the trade-off between anisotropy and heterogeneity significantly complicates the inversion of P-wave reflection traveltimes, even in the simplest model of a single plane layer.

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