Cased borehole effects on downhole seismic measurements 1

Both approximate and exact formulations for the interaction of an incident elastic wave with a cased borehole are presented. In the approximate method, simple and explicit formulae are derived for the pressure in fluid at low frequencies. In the exact method, elastic potentials in each annulus are represented as a superposition of fundamental solutions to the Helmholtz equations. Continuity of displacements and stresses across layer boundaries are used to determine unknown coefficients. A global matrix algorithm is employed to compute simultaneously these coefficients in individual layers. Calculations show that, in cased boreholes, the borehole effects on downhole seismic measurements are more significant than in open boreholes. A strong resonance occurs in the fluid for SV‐wave incidence from a soft formation. This resonance is prominent even at very high frequencies because the tube‐wave velocity is raised well above the formation shear velocity by the steel pipe. At a particular angle of incidence of a plane P‐wave, the pressure in the fluid is near zero at low frequencies (the cased borehole screening phenomenon). For hard formations and frequencies above 1 kHz, the cased borehole influence on a downhole geophone measurement is significant, especially at grazing incidence. For soft formations, both the pressure in the fluid and the solid displacement on the borehole wall show strong dependence on frequency and angle of incidence, even at low frequencies.