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Biot’s theory of wave propagation in a fluid‐filled porous elastic solid takes account of energy dissipation due to relative motion between viscous pore fluid and solid matrix. This theory has been applied to a numerical study of sound pulses propagating along a cylindrical borehole and along a plane interface. It is found that properties such as permeability affect the attenuation of the signal only at high frequencies. For the plane interface, the effect on the P-arrival is small; on the S-arrival it is moderate; and on the Stoneley‐wave it is large, but only if source and detector are close to the interface and the flow of fluid across the interface is relatively unrestricted. With a wide‐band signal, the low‐frequency pseudo‐Rayleigh wave can partially mask the S-arrival. Similar conclusions hold for the logging tool centered in the borehole, and arrivals other than the first P may be difficult to pick, especially for narrow‐band signals. The amplitude of the wave train arriving with approximately the tube‐wave velocity is particularly sensitive to the fluid‐transfer conditions at the borehole wall. The results suggest that acoustic permeability logging tools require high‐frequency signals: their performance could depend critically on the acoustic characteristics of mud cake in situ. Narrow‐band signals are not suitable for the identification of phases other than the first P-arrival; attenuation measurements probably must be based on the energies observed in gated sections of the pressure response. For signals in the seismic range, inelastic effects predicted by Biot’s theory are too small for the detection of formation properties, especially when thin impermeable beds are also present.

Elastic wave propagation in a medium consisting of two finite layers is considered. Two types of solutions are treated. The first is a Rayleigh train of waves. It is seen that for this case, when the wavelength becomes short, the waves approach two Rayleigh waves plus a possible Stoneley wave. When the wavelength becomes large, there are two waves; i.e., a flexural wave and an axial wave. Calculations are presented for this case. The propagation of SH waves is treated, but no calculations are presented.

The displacement caused by a source on an interface between two solid semi-infinite elastic media presents an excellent study in interference between direct, head and interface waves. The solution herein derived provides fresh insight into the nature of pseudo-Stoneley interface waves. As well, the evolution of the head and direct waves is discerned as they move away from the interface. The technique used to solve the problem demonstrates the simplicity of using Sherwood's (1958) method with generalized ray theory. The displacement is simply expressed in a closed form which can be rapidly evaluated and is straightforward to interpret physically.

In considering how the energy of a seismic disturbance is dissipated one is led to enquire into the possibility of the existence of waves, analogous to Rayleigh waves and Love waves, that are propagated in the interior of the earth along the junction of strata, or chiefly within a certain stratum, so that the energy is dissipated by internal viscosity without the occurrence of any appreciable surface displacement. Two surfaces of discontinuity of density and elastic properties are commonly believed to exist below that part of the earth’s crust which is accessible to geologists, namely, the junction of the granitic layer with the basic rocks, and the surface of separation of the Wiechert metallic core from the rocky shell. It becomes of interest to examine whether a wave of the Rayleigh type can be propagated along such an interface; an enquiry may also be made into the circumstances in which a wave of the Love type may exist if a stratum of uniform thickness is bounded on both sides by very deep layers of different materials.

The problem of steady‐state sound scattering by an infinite elastic circular cylinder is treated by performing a Sommerfeld‐Watson transformation on the normal‐mode series. The complex velocities of the ensuing circumferential waves are found by obtaining zeroes of a 3 × 3 determinant in the complex plane, identical to that used by Goodman and Grace in the theory of free vibrations of an elastic cylinder. We find numerically two kinds of zeroes: (α) Franz‐type zeroes, similar to (and for aluminum cylinders, almost identical with) those appearing in scattering from rigid cylinders; (β) Rayleigh‐type zeroes, as found by Goodman and Grace, which for large cylinders tend to the Rayleigh and Stoneley wave velocities, and which enter the cylinder surface at a certain critical angle. These two types correspond to the “diffracted” and the ordinary surface waves conjectured by Keller and Karal. We also consider the causality relations of sound pulses and show mathematically that they lead to arrival times in accord with the (complex) ray paths of Keller's theory. Finally, the trajectories of the zeroes in the complex plane for variations of ka and the group velocities of circumferential sound pulses have been obtained.

The Stoneley wave equation arises in the study of waves on interfaces between either two solid media or solid and liquid media. The roots of the equation are related, through the appropriate analysis, to the nature and velocity of the interface waves. In this paper, the eight roots of the Stoneley wave equation for solid-liquid interfaces are investigated analytically for all values of the equation parameters and the general pattern of the roots is elucidated.

Using three components seismometers, field measurements of under ground motions within bore-holes were carried out.In this experiment, boundary waves which could be considered as STONELEY waves were obtained. The boundary surface is between layers of clay and sand and is of about 9m depth from the ground surface.The characteristics of this wave are as follows:Tne wave velocity is 430m/sec.The period of motion is about 0.06 sec.The particle trajectories are elliptical and retrograde.The amplitude of the wave is large at the boundary surface and is decreased rapidly on leaving this surface.These results are in good agreement with those predicted by the classical theory on the STONELEY waves.

Parts I and II of this report compare the experimentally observed pressure response for the impulse excited fluid/solid interface problem with that derived from a corresponding theoretical investigation. In the experiment a pressure wave is generated in the system by a spark and detected with a small barium titanate probe. The output of the probe is displayed on an oscilloscope and photographed. Two cases are investigated: one where the transverse wave velocity is lower than the longitudinal wave velocity of the fluid and the other where the transverse wave velocity is higher. Both of these observed responses are shown to agree even as to details of wave-form, with exact computations made for a delta-excited line source. This comparison is justified by making an approximate calculation for the decaying point source and showing that at these distances it does not differ appreciably from the delta-excited line source. In the case of low transverse wave velocity one finds, besides critically refractedP, direct, and reflected waves, a Stoneley type of interface wave. Although the emphasis in recent years has been towards minimizing the importance of Stoneley waves, the evidence here is that a Stoneley wave can be the largest contributor to a response curve. In the case of high transverse wave velocity the critically refractedPwave is smaller, and the Stoneley wave, though it tends to maintain a rather constant amplitude, becomes compressed in time and arrives very soon after the reflexion. Between the critically refractedPwave and the direct arrivals one finds both experimentally and theoretically a pressure build-up preceding the arrival time that might be expected for a critically refracted transverse wave. In part III this pressure build-up is investigated and found to consist of the superposition of three arrivals. The most prominent of these is a pseudo-Rayleigh wave. The others are the critically refracted transverse wave and the build-up to the later arriving Stoneley wave. Detailed investigation of the pseudo-Rayleigh wave shows it to have the velocity of a true Rayleigh wave which is independent of the existence of the fluid. Furthermore, it has the same retrograde particle motion as the true Rayleigh wave. However, it is radiating into the fluid as it progresses and therefore has many of the properties of a critically refracted arrival when measurements are made in the fluid. Mathematically it differs from the true Rayleigh wave in that its origin is not from a pole on the real axis of the plane of the variable of integration, but rather from a pole which lies on a lower Riemann sheet in the complex plane. In the high transverse wave velocity case this pole is not too far removed from the real axis and the imaginary part of the pole location might be interpreted as a decay factor. The real part, however, yields only approximately the velocity of the pseudo-Rayleigh wave, for the actual velocity as pointed out above is precisely that of the true Rayleigh wave velocity. The migration of this complex pole explains why such a pseudo-Rayleigh wave was not observed in parts I and II in the low transverse velocity case. The problem under discussion is intimately related to the classic work of Horace LambOn the propagation of tremors over the surface of an elastic solid.One need make only a minor re-interpretation of the source function in order to compare directly the wave-forms (excluding of course the Stoneley wave contribution). Finally, a method is suggested for obtaining the solid rigidity of bottom sediments in watercovered areas fromin situmeasurements of the pseudo-Rayleigh wave and/or Stoneley wave velocities and arrival times

The equation governing elastic waves propagating along a solid-solid interface is found to have sixteen (16) independent roots on its eight (8) associated Riemann sheets. The range of existence (in terms of material parameters) for the real root corresponding to the propagation of Stoneley waves has long been known. It is found that outside this range there are two types of behavior. If the material of greater density has a velocity slightly greater than that of the material of lesser density, the unattenuated Stoneley waves make a transition to attenuated Interface waves, i.e., they leak energy away from the interface as they propagate along it. If the more dense material has a velocity more than about three times that of the less dense, then the Interface-wave root disappears and energy is propagated along the interface as Rayleigh waves. This Rayleigh-wave propagation is associated with a different root of the fundamental equation. On the other hand, if the material of greater density has a velocity much lower than that of the material of lower density (a case that is difficult to find physically), then no energy will be propagated along the interface at all. This result was unexpected. Some rather interesting behavior of the 16 roots was noted as the physical parameters were varied over a wide range. In addition to the normal collisions between pairs of roots, and between individual roots and branch points (with attendant Riemann sheet jumping), it was found that some roots go through the point at infinity and return with a change in sign. At least one unexpected case of a multiple root was found. Another case was noted in which a pair of complex roots change quadrants in the complex phase-velocity plane, leading to a discontinuity in root type. Finally, it was noted that, in a cyclic variation of the material parameters, it is possible to choose a path such that the roots, when followed individually, will not return to their original values. In fact, as many as five cycles in parameter space can be accomplished before the roots return. All this strange mathematical behavior seems to have no physical significance, but has been presented to increase understanding of the general behavior of the dispersion relations associated with elastic-wave propagation.

Seismic wave propagation in a heterogeneous wave guide was studied using data obtained from several antarctic expeditions. The upper part of a polar ice sheet forms a wave guide in which a variety of body wave phases and surface waves can be propagated. The relative energy in successive compressional wave multiples can be predicted approximately from classical ray theory and measured velocity data. A compressional wave train observed on the Ross Ice Shelf appears to result from constructive interference of successive compressional wave multiples. Such wave trains are not recorded on the polar plateau, since the conditions for constructive interference do not exist. Analysis of surface wave dispersion from sites on the polar plateau and the Ross Ice Shelf suggests that the plateau wave guide is essentially isotropic but that the wave guide on the shelf is transversely isotropic and that compressional wave velocity anisotropy of up to 20% may be found. This suggests that the base of the wave guide is probably deeper than indicated by refraction data.

Stoneley-wave velocities for a solid-solid interface were calculated for a wide range of elastic parameters. For density ratio ρ1/ρ2 1 VST / b 1 is almost independent of σ2. Results are given in graphical form: For ρ1/ρ2 < 1 and 0 ≦ σ1 ≦ 0.50, graphs of ρ1/ρ2 vs. V ST /b1 are given for σ2 = 0.00, 0.10, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.48, and 0.50. For ρ1/ρ2 > 0 and 0 ≦ σ2 ≦ 0.50, graphs of ρ1/ρ2 vs. V ST /b1 are given for σ1 = 0.00, 0.10, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.48, and 0.50.

International audience; A theory is developed for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid. The emphasis of the present treatment is on materials where fluid and solid are of comparable densities as for instance in the case of water‐saturated rock. The paper denoted here as Part I is restricted to the lower frequency range where the assumption of Poiseuille flow is valid. The extension to the higher frequencies will be treated in Part II. It is found that the material may be described by four nondimensional parameters and a characteristic frequency. There are two dilatational waves and one rotational wave. The physical interpretation of the result is clarified by treating first the case where the fluid is frictionless. The case of a material containing viscous fluid is then developed and discussed numerically. Phase velocity dispersion curves and attenuation coefficients for the three types of waves are plotted as a function of the frequency for various combinations of the characteristic parameters.

A theory is developed for the propagation of two-dimensional unattenuated waves in a system consisting of a liquid layer overlying an infinitely thick solid. Special attention is given to the interaction between the Stoneley type of wave and the Rayleigh wave. It is shown that the type of wave discussed corresponds to a dispersion branch for which the velocity varies continuously from a value lower than the velocity of sound in the liquid to that of the Rayleigh waves. The possible importance of this fact is pointed out in connection with the interpretation of the T phase of shallow-focus submarine earthquakes. The physical nature of these waves is illustrated by showing that they exist at the interface of a massless solid and an incompressible fluid.

The results of two different methods for determining the rigidity modulus of a soft sediment are compared. In one method the resonant characteristics of a torsionally oscillating rod which are sensitive to the shear acoustic impedance of the sediment in which the rod is imbedded determine the complex rigidity. The second method utilizes the observation of the phase velocity of an interface wave at the water-sediment boundry. Shear wave speeds computed from the experimental data from both methods are quite similar in magnitude. For the sediment used here, the average value of shear wave speed determined from the interface wave experiment was 33 m/sec while the shear wave speed determined from the measured rigidity was 29 m/sec. The difference lies within experimental uncertainty. Trends in the mass-physical properties of the sediments are investigated by comparing graphically the dependence of both the real and imaginary parts of the complex rigidity on density, porosity, sound speed, silt and clay percentages, Poisson's ratio and density times sound speed squared. http://archive.org/details/acomparisonoftwo1094514919 Lieutenant, United States Navy Approved for public release; distribution is unlimited.

The velocity and attenuation of Stoneley waves that propagate along the water/sediment interface are measured. These values are then used in the determination of the shear velocity and attenuation constants of the sediment.

The attenuation and phase velocities of the first four creeping wave modes on a solid elastic cylinder have been calculated numerically as a function of frequency. An additional mode was found which is interpreted as the Stoneley wave. In the high‐frequency (or infinite cylinder radius) limit, all the creeping wave phase velocities approach the bulk wave velocity of the external medium, whereas the Stoneley wave approaches a lower velocity. These calculations apply to an elastic cylinder in a liquid medium. The liquid‐liquid case, which is similar to the electromagnetic situation, and the air‐solid case, approaching the rigid cylinder limit, are derived as special cases. Computer programs were developed to carry out the calculations, which in most cases cover the range 5 ≤ ka ≤ 200.

In the study of acoustic scattering by a solid elastic cylinder inbedded in a liquid, one finds a class of surface waves with speeds close to the sound speed in the liquid. The surface wavenumbers are found from the roots of a 3 × 3 determinant in the complex wavenumber plane. The behavior of these modes for large cylinders has been determined analytically and their dispersion curves calculated. It is found that, as the cylinder radius approaches infinity, one of the surface waves tends toward the Stoneley wave for the solid elastic halfspace. The others, which are the Franz‐type modes, tend toward the liquid wavenumber in the limit of infinite radius. Similar analytic techniques are being used to study the Rayleigh and “Whispering Gallery”‐type surface waves.

WAVES at the interface between two Isotropic solid half-spaces subject to continuity of stress and displacement were first studied by Stoneley1 in 1924 and subsequently by other geophysicists, notably Sezawa and Kanai2. In 1947, Scholte3 discussed the range of existence of such waves and Owen4 has shown that out of 900 isotropic materials, only thirty combinations provide an interface along which a Stoneley wave can propagate.