In this section, I show the application of the technique previously explained to a cross-well data set recorded at BP's Devine test site, located southwest of San Antonio, Texas. A sketch of the geology at this site is shown in Figure . This test site has been cited in recent publications to illustrate the application of different techniques. For example, Harris (1988) reports cross-well seismic measurements using a cylindrical piezoelectric bender transducer both as a source and as a receiver. Miller and Chapman (1991) and Onishi and Harris (1991) concentrate on the problem of estimating velocity anisotropy from cross-well data (tomographically and by head-wave analysis, respectively). Lazaratos et al. (1991) present reflection images also from the cross-well data and Raikes (1991) studies the propagation of S-waves from a multicomponent VSP.
The cross-well data I will use in this paper are P-waves with frequencies between 200 Hz and 4000 Hz. They were recorded between two cased boreholes (Wilson 2 and Wilson 4) whose separation at the surface was 330 ft. Receivers were separated 10 ft and sources 20 ft. Figure shows the corresponding sonic logs at each well. Although the variations are mainly 1-D, it is possible to identify from the logs small dips ( 1 degree) from one well to the other as well as small lateral variations within thin layers (for example, the top of the Del Rio clay).
1660 traveltimes were picked from a small data set of only 26 gathers. From these traveltimes only those corresponding to angles less than 45 degrees between source and receiver were kept for the inversion.
Figure shows positions of sources and receivers for 10% of the data set. Notice how irregular the ray coverage is specially in terms of horizontal rays, not present in large portions of the medium. The horizontal velocities estimated in those areas, unlike the rest of the medium, will be the horizontal NMO velocities, that is, horizontal velocities of the best fitting ellipses.
The starting model (not shown) consisted of 140 horizontal layers 5 ft thick. The velocity for all layers was 12000 ft/sec. Layers thinner than 1 ft were not allowed in the model. The inversion was not constrained to match the vertical velocities or depth of certain layers using information derived from the sonic logs, although the information of dips is already present in the initial model.
The inversion produced a model with horizontal layers (all dips less than 0.1 degree) and vertical axes of symmetry. Therefore, and .Figure shows the horizontal and vertical velocities as well as an average sonic log from the two wells, blocked every 7 ft. The first thing we notice from Figure is that for almost all depths. We also notice that Vz is much closer to the sonic log than Vx, which is more than 30% larger than the log velocity in the shale and clay intervals. The vertical velocity contrast between limestone and shale is greater than 70%. Still, the inversion does a good job in estimating Vz. For this model, the average absolute value of the residuals is 0.2 ms (twice the sampling interval). 12 layers were eliminated during the inversion procedure.
These results agree with the ones presented by Miller and Chapman (1991) and Onishi and Harris (1991).
Figure also shows that the elliptical velocity model explains most of the P-wave anisotropy at this site. However, note that the estimated vertical velocity (NMO velocity) is in general smaller than the log velocity, which indicates that the elliptical model is not fully adequate to describe the possible transverse isotropic nature of this medium. In a few places (top of the clay, for example) the estimated vertical velocities are larger than the log velocity. This is probably because of lateral variations in the real medium that are not correctly described by the model of heterogeneities.
In order to better characterize the nature of the anisotropy, additional wave types and measurement directions (from a VSP survey for example) are needed.