  In vertical seismic profiling (VSP), Stoneley (tube) waves are generated due
to the coupling between the borehole fluid and the surrounding poroelastic
formation. The tube waves have been exploited in the past to infer the in-situ
hydraulic properties. In order to understand better the physical mechanisms
underlying the generation of tube waves at a fault zone, we develop a new model
that calculates the pressure responses in a borehole. The model incorporates
simultaneous effects of elastic impedance boundaries, fluid infiltration from
poroelastic formation, and irregularities in the borehole radius. The
analytical tube-wave amplitudes are derived from the new model assuming a
normally incident plane P wave, verified by complete numerical solutions for
Biot's theory of dynamic poroelasticity. We find that the upgoing and downgoing
tube waves due to an elastic impedance boundary have opposite polarities, and
those excited by a thin poroelastic layer have different wave shapes. The model
also enables the prediction of a VSP response at a major fault zone in Japan
(Nojima fault). Our quantitative evaluation suggests that tube waves are
generated by elastic impedance boundaries and borehole irregularities around
the main shear zone of the fault, as well as due to the presence of several
porous layers. We also find that the modeled amplitudes agree well with the
observation, especially when assuming a heterogeneous permeability
distribution. The developed model and the presented results will be crucial in
quantitatively interpreting the VSP data in order to estimate the fault zone's
hydraulic properties.
