Massachusetts Institute of Technology. Earth Resources Laboratory
Doi
Abstract
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