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B ore h ol e A c oustic W a v e s

B ore h ol e a c oustic w a v e s m a y be a s sim p l e or a s c om p l e x a s th e f orm a tions in w h ic h th e y p rop a g a te . A n und e rsta nd ing of w a v e - p rop a g a tion ba sic s is e sse ntia l f or a p p re c ia tion of m od e rn sonic - l og g ing te c h nol og y .

J a k ob B . U . H a l d orse n D a v id L inton J oh nson T om P l ona

B ik a sh S inh a

H e nri- P ie rre V a l e ro K e nne th W ink l e r

Ridgefield, Connecticut, USA

For help in preparation of this article, thanks to Jeff Alford, Houston, Texas; and Andy Hawthorn and Don Williamson, Sugar Land, Texas.

Everyday sounds come from many sources. Keyboards click, crickets chirp, telephones ring and people laugh. Understanding the informa- tion contained in these sounds is something that most people do without thinking. For most, deciphering the sounds they hear is much more important than knowing what sound waves are and how they travel. However, for geoscientists and others who must understand the information contained in sound waves traveling in the Earth, it is essential to know what sound waves are and how they travel. This article reviews the basic types of acoustic sources and the sound waves that travel in rocks near a borehole. We also discuss the effects that variations in rock properties have on acoustic waves.

The acoustic waves recorded by a sonic- logging tool depend on the energy source, the path they take and the properties of the formation and the borehole. In wireline logging, there are two primary types of sources, monopole and dipole. A monopole transmitter emits energy equally in every direction away from its center, while a dipole transmitter emits energy in a preferred direction.

From a monopole transmitter located in the center of the borehole, a spherical wavefront travels a short distance through the borehole fluid until it meets the borehole wall. Part of the energy is reflected back into the borehole, and part of the energy causes waves to propagate in the formation (next page, top). The direction of wave propagation is always perpendicular to the

wavefront. This simple case also assumes the formation is homogeneous and isotropic, and that the sonic tool itself has no other effect on wave propagation.1

The 3D cylindrical setting of the wellbore complicates this explanation, which can be simplified by examining a vertical plane through the axis of a vertical borehole. In the resulting 2D system, spherical wavefronts become circles and propagate in one plane. In a 3D world, wave- fronts propagate everywhere outward from the source and surround the borehole symmetrically. In the 2D simplification, when the wavefront in the borehole mud meets the borehole wall, it generates three new wavefronts. A reflected wavefront returns toward the borehole center at speed Vm. Compressional, P-, and shear, S-, waves are transmitted, or refracted, through the interface and travel in the formation at speeds Vp and Vs, respectively. In this simplest case of a hard, or fast, formation, Vp > Vs > Vm. Once the refracted P-wave becomes parallel to the borehole wall, it propagates along the borehole-formation interface at speed Vp, faster than the reflected borehole-fluid wave. According to Huygens principle, every point on an interface excited by a P-wave acts as a secondary source of P-waves in the borehole as well as P- and S-waves in the formation. The combination of these secondary waves in the borehole creates a new linear wavefront called a head wave.2

This first head wave in the mud is known as the compressional head wave, and its


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