Acoustic modes of propagation in the borehole and their relationship to rock properties

Abstract

Acoustic waveform measurements in boreholes have important applications in fracture hydrology and radioactive waste disposal, but ambiguities in existing interpretation techniques remain a problem. We have addressed the problem by using residue theory to predict the relative excitation of various modes contained in experimental waveforms. A plane‐geometry model involving a layer of fluid between two elastic half‐spaces is shown to provide velocity dispersion curves for propagating modes that are very similar to those for the fluid‐filled borehole. We use the plane‐geometry model to illustrate the effects of the confined borehole fluid on surface and body waves traveling along the borehole in the elastic solid. We also computed excitation functions for some of the lowest‐order symmetric modes, calculated the time‐domain response of the trapped modes following the shear head waves, and compared them to waveforms recorded in boreholes through several homogeneous formations. The insight into the mode composition of the experimental waveforms obtained in these formations is used to construct amplitude logs that should be especially sensitive to variations in the presence of fluid‐filled fractures in the borehole wall. Initial tests show the technique is most successful when the waveform is dominated by the fundamental tube wave, and yet frequencies remain relatively high. The model analysis indicates these conditions can only be obtained when the borehole diameter is not much larger than that of the logging tool.

Vibrational modes of hydraulic fractures: Inference of fracture geometry from resonant frequencies and attenuation

“…The use of quasi-static elasticity limits us to the regime where the fluid sound speed c 0 is less than the wall elastic wave speed. More exact theories, such as those developed by Krauklis [1962], Paillet and White [1982], Ferrazzini and Aki [1987], Korneev [2008], and Korneev [2010], account for inertia of the solid and make no assumptions about wavelengths being larger than the crack width, at the expense of a more complex dispersion relation. While those analyses capture the short-wavelength behavior more precisely, our approximate treatment is in complete agreement at the longer wavelengths that are the focus of this work.…”

“…The crux of such an analysis is the choice of the proper wave speed. Fluid-filled fractures act as dispersive waveguides, where waves experience dispersion due to the elasticity of the hydraulic fracture walls [Krauklis, 1962;Paillet and White, 1982;Chouet, 1986;Ferrazzini and Aki, 1987]. The frequency dependence of the wave speed must therefore be taken into account in order to correctly interpret observed resonant frequencies.…”

3-D wave propagation in fluid-filled irregular boreholes in elastic formations

“…The inverse problem of estimating the mechanical properties of the formation has also been the object of research [12,13], and this work was later extended to consider the state of fracturing and the presence of damaged zones around the borehole [14±16]. The effects of the formation anisotropy on the¯uid-®lled borehole wave propagation have been analyzed by different authors.…”

Analysis of Noise on Digital Sonic Log Data at Leg 120 Sites, Derived Synthetic Seismogram and Correlation with MCS Data at Site 747

“…Biot (1952) has developed a theory of propagation of elastic waves in boreholes. Cheng and Toksöz (1981) and Paulet and White (1982) have described the different modes of propaga- Transmitters are S1 and S2; receivers are Rl, R2, RL1, and RL5. The four shorter transit times (ttl-tt4) have different delay times than the four longer transit times (tt5-tt8).…”

“…Normal modes are sensitive to the borehole radius as well as the rigidity of the rock formation. Stoneley waves are most sensitive to the borehole radius and to the borehole wall rugosity, which may be related to the fracturing of the rock formation in hard rock such as basalt (Paulet and White, 1982).…”