Shear Waves From Explosive Sources

Abstract

This experimental study of the generation of shear waves hy explosive sources stemmed from Heelan' s theoretical result that pressure acting on the wall of a cylindrical hole in a solid should radiate shear waves quite as effectiveI> as compressional waves. The measurements confirm this expectation. but good overall agreement was not achieved until expressions were derived which take into account radiation from strong water-pulse waves in the shothole.Our results show that the ratio of shear-to-compressional amplitudes generated 1)~ an explosive source increases as the charge size decreases. .it an angle of 4.5 degrees, the ratio is approximately unity for a charge consisting of 10 It of Primacord. \Ve found that the shot-generated water pulse (tube wave) is a strong shear source, continuouslv generating shear energy in the formation as it travels in the borehole. This drastically affects the directivity of Siwaves and in Pierre shale gives a pattern whose maximum is near-vertical. This suggests the possibility of prospectivg with shear waves, using a distributed charge detonated at shear velocity to generate substantial downwardthrection shear energy in the earth. However, the substantially larger attenuation of shear waves compared to compressional waves has discouraged us from I' ursuing this further. Stonelcy has concluded that the .TfI and SV velocities will he different in this type of material and that IThen a shear wave is traveling vertically its velocity will he the .S1-velocity. Several authors have discussed velocities in laminated media, where the media arc made of two materials, each homogeneous and isotropic, with the laminae of irregular thickness. They show that when the laminae are horizontal, the compressional velocity is greater horizontally than vertically and, for horizontally traveling shear waves, the SH lrelocity is greater than the SI' velocity. Background ior this work \vas a theory for the radiation of elastic waves, from a cylindrical source of finite length in an infinite medium, developed by Heelan (1953). His development sho\ved that \vhen a uniform, lateral pressure acts upon the lvalls of a cylindrical cavity, both compressional and shear \\-aves ate generated. The shear waves are polarized in the plane that includes the direction of propagation and the axis

Tube waves, seismic waves and effective sources

“…The far-field low-frequency displacements thus obtained are a generalization of the results obtained by Lee and Balch (1982) who derived them by a stationary phase approximation to the exact solution for a point source in a fluid-filled borehole. White and Sengbush (1963) addressed also the case where the shear wave speed of the formation was slower than the tube wave speed.…”

“…Other Previous Work White and Sengbush (1963) computed the low-frequency far-field radiation from a point source in a fluid-filled borehole by integrating the contribution from the pressure wave propagating along the borehole at the tube wave speed. In doing this they used a result obtained by Heelan (1953) who computed the far-field low-frequency displacements due to a transient pressure applied to a short length of an empty cylindrical borehole.…”

The use of monopole and dipole sources in crosswell surveying

“…The finite difference method (Stephen et al, 1985;Randall, 1991;Leslie and Randall, 1992;Yoon and McMechan, 1992;Cheng et al, 1995;Peng and Toksö z, 1995), the boundary integral approach (Bouchon and Schmitt, 1989), the boundary element method (Bouchon, 1993;Dong et al, 1995) and hybrid methods (White and Sengbush, 1963;Ben-Menahem and Kostek, 1990;De Hoop et al, 1994) are among the techniques most often used. Peng et al (1996) made use of both the borehole coupling theory and the global matrix formulation for computing synthetic seismograms in a layered medium.…”

Wave motion between two fluid-filled boreholes in an elastic medium

“…White and Sengbush [25] applied a hybrid modeling technique by recognizing that, at low frequencies, the tube wave dominates the acoustic wave motion in the boreholē uid. They subsequently introduced the motion of moving sources to model the acoustic tube-wave radiation into the formation, using Heelan's [26] far ®eld expressions for the acoustic radiation caused by a transient pressure applied on a circular cylinder of ®nite extent.…”