Seismic Wave Propagation in Porous Granular Media

Abstract

Theoretical and experimental studies have been made of the manner in which sound waves are propagated in porous granular aggregates. A cylindrical piezo-electric source is used and this simulates the explosion of a charge in a seismic shot-hole.It is found that in general two waves of volume expansion are propagated and that these involve coupled displacements of both constituents of the media. The waves are termed frame-waves, air-waves or liquid-waves depending upon the nature of the pore-filler and the relative displacements of the constituents.Theframe=waveve&city is dependent upon the strength of the frame, the densities of solid and pore-filling materials and the texture of the medium. Air-and liquid-wave velocities are related to the texture of the medium and to the density and viscosity of the pore-filler. Frame-strength is important to a lesser degree. Waves are dispersive only in the case of media of very low permeability.Attenuation is related to viscosity, texture and frequency. Scattering is probably important only at the highest frequencies and largest particle diameters used in the experiments.It is shown that porosity and permeability of a beach sand can be inferred from velocity measurements. These properties provide information regarding grain-size, sorting and the nature of the pore-filler.

The effects of sediment porosity on acoustic reflection and transmission at the seafloor

“…The Type U wave is a diffusive wave at low frequencies and becomes propagatory at nigh frequencies with a phase velocity about onetenth of that for the Type I wave. The velocity of the Type II wave in the kiloHertz region for this set of parameters happens to be close to that measured by Paterson (1956) (approximately 115 m/s) on a fully saturated beach sand at low confining pressures. The shear wave velocity predicted by Biot theory is only slightly dispersive.…”

Appendix II. Sediment Physical Properties

“…The pulse technique has either been used or described in slightly different equipment setups by Paterson (1956), Laughton (1957), Sutton et al (1957), Abernethy (1965), and others.…”

Reflection of Nonlinear Acoustic Waves from the Mechanically Free Surface of an Unconsolidated Granular Medium

“…Multiple experiments [14][15][16][17][18]24] demonstrate that in unconsolidated granular media the velocity of both longitudinal and shear acoustic waves is the power function of pressure (of normal stress) and, consequently, in accordance with equation (3), of depth coordinate theory [39,40] predicts α=1/6 both for longitudinal and shear acoustic waves [32,18]. The experimental observations of higher powers up to α=1/4 (both for longitudinal and shear waves) could be theoretically attributed to different factors [33,34,18], such as increasing with pressure number of contacts between a bead and its neighbors, i.e.…”

“…Both experiments [14][15][16][17][18] and theory [4-9, 12, 32-34] reveal power-law dependencies of elastic moduli on pressure and, consequently on depth. The peculiar feature of this gravity-induced stratification of a granular material is vanishing of the linear elastic moduli exactly at the free surface of a cohesionless granular material, where in the effective medium approximation the pressure equals zero, and the ratio of the linear modulus to the nonlinear modulus diverges.…”

“…In the currently existing terminology the most important "classical" acoustical experiments in granular medium, consisting in the measurements of the sound velocity dependences on pressure [11,[14][15][16][17][18], can be called acousto-elasticity experiments and are considered as nonlinear acoustical experiments [19,20].…”