Tube-wave propagation in a fluid-filled borehole generated by a single point force applied to the surrounding formation

• DOI: 10.1121/1.1508781
• Publication Date: 2002-12-12T16:44:32Z
• Authors: Pavel M. Bokov; Andrei M. Ionov
• Keywords: 01 natural sciences; 0105 earth and related environmental sciences

Propagation of tube waves in an infinite fluid-filled borehole, generated by a single-force point source placed in the elastic surrounding formation, is analyzed in the long-wave approximation. Integral representations of the precise solution are obtained both for fast and slow formations. An asymptotic analysis of tube-wave propagation in the fluid-filled borehole is performed on the basis of these two integral representations. The complete asymptotic wave field in the borehole fluid for a fast formation consists of P and SV phases and the lowest eigenmode of the Stoneley wave (tube wave). For a slow formation the conical Stoneley wave (Mach wave) is generated. It appears only behind the critical angle defined by the ratio of the S wave velocity in the formation to the low-frequency Stoneley wave velocity and decays weakly with an offset. Asymptotic wave forms are in good agreement with wave forms obtained by straightforward calculations.