CALCULATION OF TRANSIENT TUBE-WAVE SIGNALS IN CROSS-BOREHOLE ACOUSTICS

Closed-form expressions are obtained for the transient acoustic pressu re in a borehole, due to the action of a volume injection (acoustic mo nopole) source in another borehole in a typical cross-well seismic set ting with a homogeneous isotropic solid formation. At the relatively l ow frequencies involved the acoustic wave motion inside a fluid-filled borehole, which may be surrounded by a structure of perfectly bonded circularly cylindrical solid shells, is dominated by tube waves. The e xcitation and propagation properties of the tube wave are modeled by r egarding the borehole as an acoustic waveguide with a compliant inner wall. The corresponding elastic wave-field quantities at the outer bor ehole wall are evaluated through a plane-strain elastostatic transfer of the stress and the elastic displacement across the shell structure. For the radiation of the wave-field quantities into the formation, th e elastodynamic Kirchhoff-Huygens integral representation is used. The acoustic pressure on the axis of the receiving borehole is evaluated with the aid of the fluid/solid acoustic reciprocity theorem. Various physical phenomena are described by the resulting expressions, includi ng pre- and postcritical phenomena (conical waves) for slow formations , and tunnelinglike phenomena for proximate boreholes in fast formatio ns.