BOREHOLE SEISMIC-SOURCE RADIATION-PATTERN IN TRANSVERSELY ISOTROPIC MEDIA

We extend previous discussions on crosswell tomography in anisotropic formations by deriving the radiation patterns of three typical downhol e seismic sources (impulsive air gun or dynamite, wall-clamped vertica l vibrators, and cylindrical bender) inside a fluid-filled borehole em bedded in a transversely isotropic (TI) formation. The method of steep est descents, in conjuncture with the low-frequency and far-field assu mptions, is applied to the exact displacement integrals of these sourc es to obtain their radiation patterns asymptotically. fn spite of comp lications caused by quasi-P- and quasi-SV-wave coupling and wavefront triplication in homogeneous TI media, the final results can still be e xpressed in slowness components determined by a ray direction, which i s desired when source radiation effects are to be accounted for by ray -based tomography techniques. Tests with the radiation patterns show t hat while the effect of anisotropy on P-waves is moderate, its effect on the S-wave pattern is significant even for slightly anisotropic for mations. One can predict the S-wave pattern from the sign of the Thoms en's measure delta.