Radiation efficiency of a multipole acoustic source in a fluid-filled borehole

With growing needs in oil and gas exploration and development,sing-well acoustic imaging has recently emerged as an important geophysical well-logging technology to detect geologic structures several tens of meters away from boreholes.This technology uses a logging tool to radiate and receive acoustic waves to and from the geologic structure for imaging,significantly broadening the measurement scope of well-logging technology.The acoustic waveform data from the borehole imaging survey is strongly influenced by radiation characteristics of the borehole acoustic source and the efficiency of the source to radiate acoustic energy out into the formation.A particular property of borehole radiation is that,besides radiating energy into the formation,the source excites guided waves propagating along the borehole,greatly reducing the efficiency of the borehole radiator.Thus a systematic study is needed to analyze the radiation efficiency of the borehole source for single-well imaging application.In this study, we investigate the radiation property of various borehole sources,including monopole,dipole,and quadrupole sources.We first calculate the source-generated energy flow along the borehole and the energy flow away from the borehole into the formation.The ratio ofthe latter flow relative to the former defines the radiation efficiency of the borehole source.The higher the efficiency,the more easily the source can radiate acoustic energy into the formation.Our analysis results show that the energy flow characteristics and radiation efficiency are strongly frequency-dependent and are distinctly different for various types of sources.In the lowfrequency range below a few kilohertz,the monopole source is dominated by the Stoneley waves along borehole and the radiation efficiency is very low.With increasing frequency,pseudoRayleigh waves are generated while Stoneley waves are greatly reduced,and the radiation efficiency attains a peak value around 10 kHz,which is also the nominal frequency of modern monopole logging tools.For a dipole source,the energy flow along the borehole is carried by borehole flexural waves.The radiation energy flow is carried by P,SV and SH waves,but is dominated by the contribution from SH waves.In the low-frequency range,the radiation efficiency of the dipole source is much greater than the monopole source and reaches a peak value around4 kHz.The quadrupole source characteristics are similar to those of the dipole source,except that the quadrupole radiation efficiency reaches its peak in a higher frequency range around 7kHz.In this paper,we investigate the radiation characteristics and efficiency of various borehole acoustic sources.Our theoretical results can provide a useful reference for the design and development of a single-well imaging acoustic tool.