Using Compressional and Shear Acoustic Amplitudes for The Location of Fractures
Authors: Morris R.L. , Grine D.R. , Arkfeld T.E. 
Published: December 2007

Abstract
Field results have shown that fractured zones may be located by their attendant reduction of acoustic amplitude. Laboratory and theoretical investigations confirm this technique, but interpretation of amplitude logs is complicated by the many variable factors encountered in actual logging operations. The acoustic amplitude investigations covered by this paper were made by continuous measurements of the peak amplitudes of single, and well defined compressional and shear-wave arrivals. A simultaneously recorded measurement of interval transit time or total travel time, in each case, indicated whether or not there had been continuous amplitude measurement of the same wave arrival. Investigations have shown that the angle at which a fracture plane crosses a borehole affects the attenuation of acoustic signals. Theoretically, horizontal fractures (those perpendicular to the axis of the borehole) should cause little or no attenuation of the compressional wave; this is confirmed by field examples. Shear-velocity waves, on the other hand, are significantly attenuated by horizontal fractures. While oblique fractures cause a reduction of compressional-wave amplitude, shear-wave amplitude measurements in such cases may not be as definitive. Since the early compressional arrivals are not subject to interference complications, as are shear arrivals, both measurements should be made and used to complement each other.
Introduction
An important problem in formation evaluation is the location of fractured zones. Because of the relatively low ratio of fracture void to bulk volume, down-hole measurements of formation resistivity, acoustic velocity, or density have been unsuccessful in satisfactorily detecting fractures in most cases. A Possible solution to the problem was noted on early Sonic Logs run in hard formations. Cycle-skipping. indicating weak compressional arrivals, occurred opposite suspected fractured intervals. Subsequent developments have permitted recording acoustic amplitude as well as studying scope pictures of the wave train. Several papers have shown the usefulness of these methods to locate fractures. The process of fracture detection from signal amplitude variation is complex. Laboratory and field studies have shown that the effects of a number of variables must be considered in the interpretation of amplitude changes. It is the purpose of this paper to explore the use of the acoustic signal to detect fractures, taking into consideration the effect of these other variables.
Propagation of The Acoustic Signal
A simplified representation of the sonic waves formed by a source of sound in a liquid-filled borehole is given in Fig. 1. Capital letters designate the wave when it is traveling in the mud, subscribed letters when it travels in the formation. A theoretical description of these waves for the analogous problem of wave propagation in a liquid layer over a solid half space was given by Strick. The waves labeled P and St are the direct and Stoneley waves, respectively. The theory of their propagation in a borehole has been developed by Biot and they have been observed by Pickett. The other waves in the borehole labeled PpP and P, P, are the refracted compressional arrival and the shear velocity arrival. The R wave will be mentioned later.
The Refracted Compressional Wave
If compressional velocity in the formation Vp, is enough higher than mud velocity C the first arrival in the sonic waveform is a wave that has traveled from the transmitter to the formation as a compressional wave in the mud, has been refracted at the borehole wall, and has traveled along the wall at the compressional-wave velocity in the formation. In an infinite medium, each small particle affected by a compressional wave oscillates only in the direction of wave propagation as the compressions and rarefactions travel past it. When a borehole exists. particle motion is more complex.
JPT
P. 623ˆ