We estimate parameters of vertical transverse isotropy from the first-arrival times recorded in a 3D VSP survey over a deepwater prospect in the Gulf of Mexico. We use both conventional slowness inversion and a newly developed traveltime-extrapolation scheme to find the depth-dependent Thomsen anisotropic coefficients ? and ? and the vertical Pwave velocity VP0 over a 2,000 ft interval of an instrumented well. We also quantify their uncertainties and correlate our estimates with seismic, checkshot, and well-log data.

We find a satisfactory correlation of the obtained VP0 with that independently derived from the checkshot. Perhaps most unexpectedly, our inversion yields negative interval values of the anellipticity coefficient ?. Those negative ?, however, are consistent with the behavior of nonhyperbolic moveout observed in the seismic reflection data.


3D vertical seismic profiling (VSP) is an established technique for measuring in-situ anisotropy. The anisotropic parameters estimated from VSP data have proven to be useful in a number of applications including seismic imaging, building rockproperty models, and characterizing fractures and stresses. In practice, anisotropy is typically inverted from the P-wave slowness surfaces p which are reconstructed from the first arrival times t (White et al., 1983; Gaiser, 1990; Miller and Spencer, 1994). By definition, the slowness components (mathematical equation) (Available in full paper) are the derivatives of the traveltimes t(x) with respect to the coordinates xi of the sources and receivers. In a typical VSP geometry, the horizontal slowness components p1 and p2 are evaluated at the earth's surface, whereas the vertical component p3 is obtained at the geophone levels. To reconstruct the slowness surfaces in the borehole, one usually assumes lateral homogeneity of the overburden. Then, according to Snell's law, the horizontal slownesses p1 and p2 are preserved along the ray trajectories, and their values measured at the surface remain valid at the downhole receivers. This is no longer the case in the presence of even mild lateral velocity variations because they alter p1 and p2 leading to noticeable distortions of the reconstructed slowness surfaces and, consequently, to substantial errors in the estimated anisotropy (e.g., Gaiser, 1990; Sayers, 1997). Bakulin et al. (2000) recognized the issue and proposed an approximate correction of the horizontal slownesses for smooth lateral velocity heterogeneity. While their correction is generally perceived as useful, we confirm the observation of JÃlek et al. (2003) that it requires knowing the seismic velocity model with accuracy hardly attainable in practice.

Recent developments in anisotropy estimation from VSP data include combining the P- and S-waves and making use of their particle displacements (or the polarization vectors) in addition to the traveltimes. Such a dual slowness-polarization inversion was applied by Horne and Leaney (2000) and Williamson and Maocec (2001) to estimate the parameters of transversely isotropic media with a vertical symmetry axis (VTI) and extended by Dewangan and Grechka (2003) to arbitrary (triclinic) anisotropy.

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