Borehole seismic‐source radiation pattern in transversely isotropic media

Abstract

We extend previous discussions on crosswell tomography in anisotropic formations by deriving the radiation patterns of three typical downhole seismic sources (impulsive air gun or dynamite, wall‐clamped vertical vibrators, and cylindrical bender) inside a fluid‐filled borehole embedded in a transversely isotropic (TI) formation. The method of steepest descents, in conjuncture with the low‐frequency and far‐field assumptions, is applied to the exact displacement integrals of these sources to obtain their radiation patterns asymptotically. In spite of complications caused by quasi‐P‐ and quasi‐SV‐wave coupling and wavefront triplication in homogeneous TI media, the final results can still be expressed in slowness components determined by a ray direction, which is desired when source radiation effects are to be accounted for by ray‐based tomography techniques. Tests with the radiation patterns show that while the effect of anisotropy on P‐waves is moderate, its effect on the S‐wave pattern is significant even for slightly anisotropic formations. One can predict the S‐wave pattern from the sign of the Thomsen’s measure δ*.