Energy Partitioning and Attenuation of Guided Waves in a Radially Layered Borehole

Abstract

Recently published results (Tubman et al., 1984; Baker,. 1984) indicate that synthetic full waveform acoustic logs generated in cased or damaged boreholes differ significantly from those generated in an open hole with the same formation parameters. In particular, the guided waves appear to be the most affected by such radial layering. In order to gain some understanding of these effects, the amplitude response and energy distribution of the pseudo-Rayleigh and Stoneley waves are studied for the cased and invaded borehole models. The expressions derived by Cheng et al. (1 982) are used to calculate partition coefficients (partial derivatives of phase velocity with respect to body wave velocities) for the guided wave modes. The attenuation of the guided wave can then be represented by the sum of the layer attenuation values weighted by their respective partition coefficients. The results indicate that the attenuation of the Stoneley wave is dominated by the fluid attenuation at all frequencies in fast formations, both in the open hole geometry and in the presence of casing or invaded zones. In a slow formation, the Stoneley wave attenuation becomes more sensitive to the shear wave attenuation of the formation at higher frequencies in both the open and cased hole situations. For the pseudo-Rayleigh wave, the introduction of casing reduces the effect of the fluid attenuation, while the presence of an invaded zone reduces the effect of the formation shear attenuation. Plots of the partition coefficients indicate that the casing and invasion layers are most important over a limited frequency range which is related to the thickness of the layer. Radial displacement curves illustrate the depth of penetration of the various frequency components of the pseudo-Rayleigh wave.