Far-Field Radiation Patterns and Energies from Different Seismic Sources in a Fluid-Filled Borehole

Abstract

The far-field radiation patterns and energies from different axissyrnrnetrical seismic sources in a fluid-filled borehole are studied in detail under a low-frequency approximation. The range of low-frequency is discussed. The radiation patterns of the compressional and shear waves from different sources are numerically studied. The analytical expressions for the energies of the tube wave, the radiation compressional wave, and the radiation shear wave are derived. From the calculations we find that a point volume source emits almost all (>99%) its energy as tube wave which travels along the borehole and not out into the formation, and the radiation shear energy is greater than the radiation compressional energy. The radiation energy of the compressional and shear waves is greater in soft formation than in hard formation. The tangential stress source radiates all its energy into the formation as compressional and shear waves, while it does not excite the tube wave in a fluid-filled borehole, in addition, the radiation shear energy is about ten times greater than the radiation compressional energy. The radiation energies from a point volume source and a radial stress source are directly proportional to ω 4 , and the radiation energy from a tangential stress source is proportional to ω 2 . The array source constituted by identical individual source can much enhance the radiation energy.