Abstract Understanding fault‐zone permeability is crucial in model‐based assessment of fluid migration, earthquake nucleation, and hydrothermal or hydrocarbon systems. Vertical seismic profiling (VSP) often captures Stoneley (tube) waves generated by fluid‐formation coupling in and around a borehole. Tube waves offer valuable constrains to local hydraulic properties. Full simulation of the generation of tube waves using Biot's poroelastic equations is very important, but computationally demanding due to the multiscale nature of the problem, involving fine‐scale borehole geometry and long‐wavelength seismic wave propagation in the layered media. We develop a semi‐analytical approach that can predict borehole pressure response of a normally incident plane P wave in layered poroelastic media, including irregularities in the borehole radius. The model accounts for three key mechanisms for tube‐wave generation: (a) due to elastic impedance contrasts, (b) due to fluid infiltration from poroelastic layers, and (c) due to borehole‐radius changes. Using a propagator‐matrix formulation under low‐frequency assumptions, we derive closed‐form expressions for the tube‐wave amplitudes and validate them using finite‐difference poroelastic simulations. The results show that elastic boundaries produce tube waves with opposite polarities, while a thin porous layer and a thin elastic layer generate asymmetric responses with notably different frequency spectra. Our approach improves upon previous effective‐source models by accounting for the tube‐wave velocity contrasts and ensuring the consistency with the poroelastic theory. This efficient modeling framework enables clearer interpretation of VSP data in fault zones, providing insights that aid in quantitative estimation of the local hydraulic properties.
Minato et al. (Sun,) studied this question.