A sound source in a liquid‐filled borehole generates, among other excitations, compressional and shear waves in the rock which are detected in the fluid as refractions. It is practical to be able to separate the latter components. I show that this can always be achieved in principle by appropriately choosing the properties of the source. Solutions of the acoustic wave equation in the “far field” of the source are analyzed in detail. Suppose the source radiation depends upon the azimuthal angle η through some function F(η). The refracted waves are analyzed conveniently in terms of Fourier components [Formula: see text], where n and η are Fourier conjugates. For a source symmetrical about the axis of the borehole, as conventional sources are, [Formula: see text] vanishes except for n = 0. Our principal results concern the z dependence of the pressure radiation field in the drilling mud p (r, η, z) (using cylindrical polar coordinates). For a fixed n, as z → ∞, the refracted P‐wave is proportional to [Formula: see text] for n = 0, 1, … . The refracted S‐wave signal is proportional to [Formula: see text]. Thus, for an axially symmetric source, the P‐wave refraction generally dominates the S‐wave refraction as z → ∞. For an axially asymmetric source the S‐wave dominates the P‐wave. An example of an n = 1 source is a horizontally pointing dipole on the borehole axis. Higher order multipole sources also effectively produce nearly pure S‐wave signals in a borehole.
This paper is focused on the special features of the wavetrains recorded by conventional and dipole sonic logging tools in soft formations defined to be those whose shar velocity is less than the sound velocity of drilling mud. Such formations are commonn in the Gulf Coast, the Canadian Arctic, the Bass Strait of Australia, and many other region. A conventional logging tool operating at normal frequencies [Formula: see text] records P waves, water waves, and Stoneley waves in soft formations. A dipole tool records modal waves and water waves at frequencies of order 15 kHz, but produces almost pure S-wave first arrivals at low frequencies [Formula: see text] since at 1 kHz, a mode which we refer to as a “dipole Stoneley wave” is efficiently excited. For very soft materials such as clays, where the formation P-wave velocity can be less than the fluid velocity, the formation P velocity can be logged by operating a conventional sonic tool at low frequencies [Formula: see text] so as to excite a leaky mode traveling at very close to the formation P-wave velocity. Water waves are not important for high‐velocity formations where they arrive at the trailing edge of the modal part of the wavetrain. However, in soft formalions they form a prominent part of the wavetrain at normal logging frequencies [Formula: see text] and disappear at low frequencies [Formula: see text]. Water waves are carried by leaky modes.
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