Full‐wave synthetic acoustic logs in radially semiinfinite saturated porous media

The wave field generated by a point source in an axisymmetric fluid‐filled borehole embedded in a saturated porous formation is studied in both the spectral domain and time domain. The formation is modeled following Biot theory modified in accordance with homogenization theory. When the borehole wall is permeable, guided waves can be significantly affected by the permeability of the formation. Whatever the formation, fast or slow, Stoneley‐wave phase velocity and energy decrease and attenuation (in the sense of [Formula: see text]) increases with increasing permeability. These effects are more important in the very low‐frequency range, where Darcy’s law governs the fluid motion and the wave energy at the interface is maximum, than at higher frequencies. The effects increase and persist over a larger frequency range with decreasing viscosity and increasing compressibility of the saturant fluid, with increasing pore‐fluid volume, and with decreasing borehole radius. In contrast, the effects decrease with decreasing stiffness of the formation because of more efficient coupling of the interface wave to the surrounding medium. When present, the first pseudo‐Rayleigh mode also carries useful information. Fluid flow affects only the attenuation of the pseudo‐Rayleigh mode’s Airy phase; an increase in attenuation may be used to detect permeable zones and to infer the saturant fluid properties. However, the most reliable types of information are the formation shear‐wave velocity and attenuation from the low‐frequency part of the mode. In the time domain, all the modes overlap. Any signal processing should then be performed in the frequency domain, where mode spectra are more easily separable. The frequency band of the actual logging tool has to be large enough to ensure significant amplitude for each mode. Finally, the larger the number of receivers and the offset range, the better.