The effect of the invaded zone on full wavetrain acoustic logging

Most theoretical studies of acoustic borehole logging have employed the simple model of a fluid borehole in an infinite solid. This work attempts to account for the invaded zone using a more sophisticated model that additionally includes finite concentric shells surrounding the borehole. By appropriately choosing the physical parameters of these cylindrical shells, one can study the effect of the invaded zone, mudcake, or a cased hole on acoustic wavetrain components. The model accounts for geometric attenuation, but it assumes the formation is perfectly elastic. A key consideration is the distance that the acoustic log “sees” into the formation. The body of this report is devoted to studying the effect of the invaded zone, mudcake, or steel casing on the components of the full wavetrain (P-wave, S-wave, reflected modes, and Stoneley mode). I conclude that a sonic logging tool has a very shallow depth of investigation. This depth, for P- and S-waves, depends upon the spacing between the source and receiver. An approximate rule of thumb is that if the source‐to‐receiver separation is n feet, the logging tool sees n inches into the formation. Thus, a conventional logging tool sees less than 6 inches into the surrounding formation. Since attenuation of the P- and S-wave arrivals places a practical constraint on realistic source‐to‐receiver separations, the depth of investigation is limited to a maximum of about 2 ft. Therefore, an acoustic logging tool is usually capable of measuring properties of the invaded zone only. For the reader interested in the mathematical details of this work, the method of computation is described in Appendix A.