Inversion of reflection traveltimes for transverse isotropy

摘要

In anisotropic media, the short-spread stacking velocity is generally different from the root-mean-square vertical velocity. The influence of anisotropy makes it impossible to recover the vertical velocity (or the reflector depth) using hyperbolic moveout analysis on short-spread, common-midpoint (CMP) gathers, even if both P- and S-waves are recorded. Hence, we examine the feasibility of inverting long-spread (nonhyperbolic) reflection moveouts for parameters of transversely isotropic media with a vertical symmetry axis. One possible solution is to recover the quartic term of the Taylor series expansion for t~2 — x~2 curves for P- and SV-waves, and to use it to determine the anisotropy. However, this procedure turns out to be unstable because of the ambiguity in the joint inversion of intermediate-spread (i.e., spreads of about 1.5 times the reflector depth) P and SV move- outs. The nonuniqueness cannot be overcome by using long spreads (twice as large as the reflector depth) if only P-wave data are included. A general analysis of the P-wave inverse problem proves the existence of a broad set of models with different vertical velocities, all of which provide a satisfactory fit to the exact traveltimes. This strong ambiguity is explained by a trade-off between vertical velocity and the parameters of anisotropy on gathers with a limited angle coverage. The accuracy of the inversion procedure may be significantly increased by combining both long-spread P and SV moveouts. The high sensitivity of the long-spread SV moveout to the reflector depth permits a less ambiguous inversion. In some cases, the SV moveout alone may be used to recover the vertical S-wave velocity, and hence the depth. Success of this inversion depends on the spreadlength and degree of SV-wave velocity anisotropy, as well as on the constraints on the P-wave vertical velocity.