Transient acoustic waves in a fluid-filled borehole with a horizontal bed boundary separating two solid formations

Abstract

In a previous paper the acoustic logging problem of a pulsed point source in a fluid-filled borehole with a horizontal bed boundary separating two fluid formations was solved with the hybrid method. In this paper the method is extended to treat the case when there are two elastic solid formations outside the borehole that are separated by the horizontal bed boundary. The equations of the hybrid method for elastic formations are derived and are more complicated than the fluid case. The steps of the implementation of the numerical procedure are also discussed. Based on the method, the sonic waveforms, including the compressional and shear head waves and the normal mode arrivals, are calculated. Transmission coefficients of the head waves across the bed boundary are also calculated.