Radiation characteristics of a borehole multipole source in permeable porous formations

Borehole acoustic reflection imaging technology has been widely applied in hydrocarbon exploration. A detailed understanding of the radiation characteristics of borehole acoustic sources is crucial for imaging performance analysis and method optimization, particularly in formations with high porosity and permeability. This study, based on Biot–Rosenbaum theory, derives analytical expressions for the radiation directivity and wavefield energy flux of multipole sources in permeable porous media using the steepest descent method and the complex Poynting vector. A comprehensive parametric analysis is conducted to assess how poroelastic properties and source frequency influence the radiation behavior of different wave modes. Results reveal that a slow P-wave component emerges in permeable porous media and that increasing porosity and permeability substantially attenuate the radiation efficiency of multipole sources. Dipole radiation efficiency shifts toward lower frequencies, accompanied by broadened spectral responses. The SV-wave efficiency transitions from a dual-peak to a single low-frequency pattern. Although the SH-wave remains the dominant mode, its imaging capability degrades markedly under high-porosity and high-permeability conditions. A field reflection imaging case validates the theoretical predictions. These findings offer theoretical support for evaluating and interpreting the performance of acoustic imaging in permeable porous reservoirs.