R. Burridge
S. Kostek
Schlumberger-Doll Res., Ridgefield, CT 06877-4108
A. L. Kurkjian
Schlumberger Cambridge Res., Cambridge CB3 0EL, England
The radiation of waves from a monopole source in a fluid-filled borehole into an elastic medium is considered. A simple asymptotic analysis, based on the smallness of the ratio of the borehole radius to the wavelength, reveals the interaction between tube waves and seismic waves. The pressure field in a tube wave acts as a secondary source of seismic waves and conversely an incoming seismic wave excites a tube wave. The asymptotic analysis leads to a characterization of these sources in terms of the solution to two-dimensional elastostatic problems. These may be solved exactly when the borehole has an elliptical cross section even in an anisotropic formation. Also the borehole need not be straight provided that its radius of curvature is large compared with a wavelength. The problem of two boreholes, one containing a source and the other a receiver (crosswell tomography geometry) is analyzed and an explicit expression for the received signal is derived.