ACOUSTIC-WAVES IN PRESSURIZED BOREHOLES - A FINITE-DIFFERENCE FORMULATION

A velocity-stress, finite difference formulation of acoustic waves in a fluid-filled, pressurized borehole yields synthetic waveforms for mo nopole or dipole sources before and after borehole pressurization. Pro cessing of these waveforms using a variation of Prony's procedure isol ates dominant arrivals in the full wave field. Differences between the slownesses of individual arrivals before and after pressurization pro vide stress-induced changes in propagation characteristics that are of importance in estimating mechanical properties of the formation. The borehole pressurization in an isotropic formation produces insignifica nt changes in the compressional head wave slownesses; and small change s in the shear head wave slownesses. The most significant changes occu r in the Stoneley and flexural slownesses at relatively higher frequen cies in the range of 5-10 kHz for a borehole of diameter 20.32 cm (8 i nches). These differences in the Stoneley and flexural slowness disper sions for a known increase in the borehole pressure can be used to cal culate the acoustoelastic coefficients of the formation. These coeffic ients are measures of nonlinear elastic parameters of the formation th at are generally larger for poorly consolidated slow formations than t hose of tightly consolidated fast formations.