  This paper shows that there are three types of shape of acoustic body waves
propagating inside competent and homogeneous formations penetrated by a
borehole : simple, double, and resonant. This fact is connected to the
modifications undergone by the area located around a well after drilling in
relation to in situ state of stress. There are overstressed and understressed
vertical cylindrical zones with "bubble-shaped" cross-sections, in which
acoustic body waves are supposed to reflect. The horizontal size and the shape
of the stress modified areas depend on the values of (K1+K2)/2 - with K1=SH/Sv
(the overburden pressure) and K2=Sh/Sv -, that is to say on the in situ
horizontal stress and the anisotropy of this stress. The calculation of the
velocities of the P and S double waves allows us to evaluate the radial
thicknesses of these stress modified areas. As their values are different
according to whether they result from P or S waves, we propose an explanation
based on their wavelengths. The comparisons with other works on the in situ
stress of the studied boreholes allow us to propose a method for evaluating the
horizontal stress and its anisotropy, thanks to the estimation of the value
(K1+K2)/2.
