Compressional Wave Speed Research Articles

The effect of moisture on compressional and shear wave speeds in unconsolidated granular materials

The effect of water vapor on the shear and compressional wave speeds in two different kinds of glass beads and in Ottawa sand has been measured. The nominal diameter of the glass beads was 125 μm and of the sand, 500 μm. The measurements were made as the water vapor was introduced slowly into the evacuated material. The vapor pressure isotherm for the beads made of titanium-barium glass was fit reasonably well by the simple BET theory. For the Ottawa sand the BET theory fit the vapor pressure isotherm if the surface area of the grains was assumed to be three times the area calculated, assuming all of the grains were spheres with a diameter of 500 μm. In these two materials the vapor had little effect on the wave speeds. For beads made of lime glass, however, the wave speeds approximately double with the introduction of water vapor, and the vapor pressure isotherm had the BET shape only if the saturated vapor pressure was assumed to be lowered by 20%. These results have been explained by assuming that a chemical reaction occurred between the lime glass and the water to form a gel. [Work supported by the USDA.]

Geoacoustic properties of sediments determined from measurements of head waves

As part of the SAX 99 experiments, head wave signals have been analyzed to determine geoacoustic properties for the sandy sediment at the shallow water site near Destin, FL. A small-aperture (2.33 m), vertical array of four hydrophones was deployed at mid-water depth over the sea floor, where the water column is 20 m deep. Transient signals were generated by an airgun, at a fixed location, resting on the ocean bottom. At a range of approximately 1 km from the source, the array was allowed to drift to vary its position; the location was measured with DGPS equipment. Two estimates of the compressional wave speed in the sandy sediment were obtained from the incoming signals: a spatially averaged value over the track between the source and receiver, determined at a single sensor from the difference in arrival times between the head wave and the water-borne wave; and a localized value, computed from the critical angle derived from the vertical directionality of the received head wave signals. A comparison of the independent local and spatially averaged estimates provides a useful consistancy check, and establishes the spatial variation of the sediment more completely than by either purely averaged or local measurements alone.

The core–mantle boundary under the Gulf of Alaska: No ULVZ for shear waves

The Earth’s core–mantle boundary (CMB) marks the boundary between the hot, molten iron core and the silicate mantle and is a thermal, chemical, and flow boundary. Previous observations of very slow compressional wavespeeds suggest that thin ultra-low-velocity zones (ULVZs), possibly composed of a mixture of molten iron and silicates, exist at the base of the mantle. A molten or partially molten layer would cause a large shear wavespeed decrease; however this velocity drop has not been observed. Here, we use core reflected ScP phases to investigate the shear properties of ULVZs. These phases reveal at least two distinct regions: one region under Central America which is distinctly average (PREM and iasp91-like) and a second region under the entire Gulf of Alaska that produces large ScP reflections with amplitudes of up to 30 times larger than calculated with average Earth models. The large amplitudes suggest a combination of focusing by CMB topography, high shear wavespeeds at the bottom of the mantle, and low attenuation (high Q) along the ScP path; high shear wavespeeds and low attenuation are opposite from what would be expected from a shear wave ULVZ. A ULVZ in compressional wavespeeds (ultra-low V p) has previously been observed in this region; however, in addition to the large amplitudes, the short-period ScP waveforms show no complexity that can be related to a ULVZ. Thus, either there is not a ULVZ under the Gulf of Alaska or, if it does exist, it is restricted to compressional wavespeed changes, precluding interpretation as partial melt but rather suggesting a chemical origin.

Laboratory Measurements of Compressional and Shear Wave Speeds through Methane Hydrate

Abstract: Simultaneous measurements of compressional and shear wave speeds through polycrystalline methane hydrate have been made. Methane hydrate, grown directly in a wave speed measurement chamber, was uniaxially compacted to a final porosity below 2%. At 277 K, the compacted material had a compressional wave speed of 3,650 ± 50 m/s. The shear wave speed, measured simultaneously, was 1,890 ± 30 m/s. From these wave speed measurements, we derive Vp/Vs, Poisson's ratio, bulk, shear, and Young's moduli.

Possible detection of failure wave velocity using hypervelocity penetration experiments

Data for projectile penetration of silicon carbide (SiC) from two types of experiments are combined. For impact velocities, v, in the range 1.5 – 4.6 km/s the data are from reverse ballistic two-stage light-gas gun experiments with long tungsten rods. For impact velocities of about 5 – 7 km/s copper shaped charge jets are the projectile. The data exhibit an apparent inflection in the penetration velocity, u, versus impact velocity curve at u ≈ 3 km/s, corresponding to v ≈ 4.5 km/s. The apparent decrease in the slope of u versus v for u = 3 km/s, and the consequent rapid increase in the Alekseevskii and Tate target resistance term Rt with v is tentatively interpreted in terms of a failure wave in SiC. With this interpretation the propagation speed of the failure wave in SiC is about 3 km/s or 1 3 of the compressional wave speed.

Large‐scale variations in inner core anisotropy

I analyze nearly 2000 handpicked differential times of core‐penetrating compressional waves to image lateral variations in the anisotropic structure of the solid inner core. The inner core is strongly anisotropic (2–4% on average) throughout most of the western hemisphere from near the surface to its center and into the lowermost several hundred kilometers of the eastern hemisphere. In contrast, the outer half of the eastern hemisphere from 40° to 160°E (the quasi‐eastern hemisphere) exhibits very weak anisotropy with an average amplitude of only 0.5%. The symmetry direction is the fast direction and lies on or near the spin axis. Voigt's isotropic average of compressional wave speeds is the same in the eastern and western hemispheres, suggesting that there are no large‐scale lateral variations in the chemistry or temperature in the inner core. Instead, I suggest that the variations seen in anisotropy represent lateral variations in the degree of crystal alignment. The inner core appears to be organized in a very simple way with 60–90% of its volume containing well‐aligned crystals and the remaining part (uppermost 400–700 km of the quasi‐eastern hemisphere) containing less well aligned crystals. A mechanism consistent with axisymmetry and large‐scale variability of anisotropy is discussed. It incorporates the inference that the inner core is rotating faster than the mantle and that gravitational coupling to the mantle forces large‐scale inner core deformation, inducing flow with strain rates as high as 10−14 s−1. A positive feedback mechanism, related to anisotropic viscosity, may reinforce lateral variations in the strength of anisotropy.

Acoustic inversion for Biot parameters in water-saturated sand

Using an inversion of Biot’s theory, based on the formulation by Stoll, operative values of grain bulk modulus and the frame bulk and shear moduli of water-saturated sand may be extracted from measurements of compressional and shear wave speeds and reflection loss. The inversion process is nonlinear, but in practice it is well behaved and converges quite rapidly to unique values. The term grain bulk modulus, as defined in the formulation by Stoll, is not necessarily identical to the bulk modulus of the grain material, as is often assumed. Examples of the inversion will be given, and the significance of the operative values of the grain bulk modulus will be discussed. [Work supported by Office of Naval Research: Ocean Acoustics.]

The influence of gas bubbles on sediment acoustic properties: in situ, laboratory, and theoretical results from Eckernförde Bay, Baltic sea

Acoustic turbidity caused by the presence of gas bubbles in seafloor sediments is a common occurrence worldwide,but is as yet poorly understood. The Coastal Benthic Boundary Layer experiment in the Baltic off northern Germany was planned to better characterize the acoustic response of a bubbly sediment horizon. In this context, in situ measurements of compressional wave speed and attenuation were made over the frequency range of 5–400 kHz in gassy sediments of Eckernförde Bay. Dispersion of compressional speed data was used to determine the upper limit of the frequency of methane bubble resonance at between 20 and 25 kHz. These data, combined with bubble size distributions determined from CT scans of sediments in cores retained at ambient pressure, yield estimates of effective bubble sizes of 0.3–5.0 mm equivalent radius. The highly variable spatial distribution of bubble volume and bubble size distribution is used to reconcile the otherwise contradictory frequency-dependent speed and attenuation data with theory. At acoustic frequencies above resonance (>25 kHz) compressional speed is unaffected by bubbles and scattering from bubbles dominates attenuation. At frequencies below resonance (<1 kHz) ‘compressibility effects’ dominate, speed is much lower (250 m s -1) than bubble-free sediments, and attenuation is dominated by scattering from impedance contrasts. Between 1.5 and 25 kHz bubble resonance greatly affects speed and attenuation. Compressional speed in gassy sediments (1100–1200 m s -1) determined at 5–15 kHz is variable and higher than predicted by theory (<250 m s -1). These higher measured speeds result from two factors: speeds are an average of lower speeds in gassy sediments and higher speeds in bubble-free sediments; and the volume of smaller-sized bubbles which contribute to the lower observed speeds is much lower than total gas volume. The frequency-dependent acoustic propagation is further complicated as the mixture of bubble sizes selectively strips energy near bubble resonance frequencies (very high attenuation) allowing lower and higher frequency energy to propagate. It was also demonstrated that acoustic characterization of gassy sediments can be used to define bubble size distribution and fractional volume.

Broadband bottom-interacting acoustics in shallow waters

Understanding broadband acoustic propagation in shallow-water ocean environments presents a host of challenges for the acoustics community. Insufficient environmental and experimental data make quantitative assessments of predictive models very difficult. On the other hand, due to substantial cost incurred in obtaining the ground truth and high-resolution geoacoustic data, the information is usually limited to a single or at most very few geological cores in a region. For acoustic applications, geological data need to be converted to a set of geoacoustic parameters such as compressional and shear wave speeds, their attenuation profiles, and the bulk density of sediment. In recent years several experiments of broadband acoustic propagation in shallow-water environments have been performed using airgun sources in different water depths. These experiments have been conducted in regions with some geological information. A procedure to convert the measured geological parameters into geoacoustic data in conjunction with the empirical orthogonal functions (EOF) has allowed the creation of statistical and frequency-dependent sediment profiles suitable for propagation modeling. Parabolic equation (PE) and normal mode models have been used to assess the physics of sound propagation in these regions. The results of these investigations are summarized here with regards to the geoacoustic inversion in shallow-water regions.

Shallow-water geoacoustic inversions of seafloor properties in Spencer Gulf

Preliminary results of an experiment to characterize the geoacoustic properties of the upper few meters of the seafloor in Spencer Gulf, Southwestern Australia, will be presented. The aim of the experiment was to estimate the compressional and shear wave speeds, compressional wave absorption, and sediment density using different inversion techniques and compare the results for consistency. To this end, four measurement methodologies were used, which were: (1) transmission loss measurements, using the support vessel as a moving source, (2) ambient noise coherence measurements, (3) bottom reflectivity measurements, using frequency modulated pings and the sound of imploding light bulbs as sources, and (4) grab bottom samples. The transmission loss measurements show a distinct modal interference structure as a function of source frequency and source–receiver separation, and can be inverted for the average sediment acoustical properties along the source–receiver track. The ambient noise coherence measurements can be inverted for the noise field vertical directional density function, which in turn yields the critical angle of the seafloor averaged over a 5- to 10-km disk. [Work supported by DSTO, Australia, and ONR, USA.]

Inversion for the compressional wave speed profile of the bottom from synthetic aperture experiments conducted in the Hudson Canyon area

In September 1988, a series of acoustic propagation experiments were conducted in the Hudson Canyon area. These included synthetic aperture experiments in which a source transmitting a set of four pure tones was towed toward/away from a vertical array of 24 receivers. Data obtained at 50 Hz during one of the synthetic aperture experiments are used to obtain a model for the compressional wave speed profile in the bottom using a modal inverse method. This model is further refined using 175 Hz data. The ability of the inferred model to predict the field at 50 Hz and higher frequencies is examined.

Head wave data inversion for geoacoustic parameters of the ocean bottom off Vancouver Island

As a part of the Pacific Shelf-93 experiment, small explosive charges were used as underwater sound sources on the continental shelf off Vancouver Island. Broadband acoustic signals received by a vertical line array show the rich structure of precursors arriving prior to the direct water wave. Kinematic properties of the precursors are found to be consistent with those of head waves with different numbers of reflections at the ocean surface and bottom. Power spectra of the precursors reveal complicated interference structure, including deep nulls at relatively low frequencies. Positions of the nulls in the frequency domain and their depth dependence are shown to be sensitive to the variation of compressional wave speed in the bottom. A combination of beamforming, spectral analysis, and travel-time considerations is applied to separate and identify individual head wave arrivals in the sequence of precursor signals. Range- and depth-dependence of the travel times for individual head waves are inverted to determine compressional wave speeds in two distinct subbottom layers and to estimate the thickness of the sediment layers. The frequency- and range-dependence of the head waves amplitudes are analyzed to estimate the compressional wave attenuation. [Work supported by NSERC.]

A practical model for high-frequency seabed bistatic scattering strength

The authors have previously reported a model for bistatic scattering by elastic seabeds. This model is extended here to cases of larger roughness by replacing the rough-interface perturbation approximation with the small-slope approximation [Yang and Broschat, J. Acoust. Soc. Am. 96, 1796–1804 (1994)]. Consistency with older models is shown by comparisons of calculations for silt and sand examples. Correlations between volume fluctuations of different types (e.g., density and compressional wave speed) are considered, and it is shown that the effects of such correlations are more readily observed in bistatic scattering measurements as opposed to backscattering measurements. Finally, the importance of elastic effects in scattering by rocky seabeds is illustrated. [Work supported by ONR.]

Simultaneous Reconstruction of Compressional Wave Speed and Density Profiles from Modal Eigenvalues

In this paper we present a simple approach for estimating the compressional wave speed and density profiles of sediments in a shallow water environments from modal eigenvalues. Methods published earlier in the literature called for data at two frequencies and had to make the assumption that the density profile is a continuous function. Further, the processing scheme was difficult to implement. The method presented here requires data from only one frequency and allows for discontinuities in the density profile. The performance of the proposed method is studied using synthetic data.

Estimating the compressional and shear wave speeds of a shallow water seabed from the vertical coherence of ambient noise in the water column

Due to the multiple bottom reflections encountered in shallow water environments, the spatial structure of the ambient noise field depends strongly on the geoacoustic properties of the seabed, which are invariant over time scales associated with most measurements. The vertical directionality and coherence are relatively stable features of the noise that are determined primarily by the seabed, rather than temporal variations in the surface source distribution. In this paper, estimates of the compressional and shear wave speeds are determined from ambient noise measurements over shear supporting seabeds. Using a model of wind-generated noise over an elastic seabed, it is shown that the noise is sensitive to the compressional and shear wave speeds in the upper few meters of seabed. An inversion procedure is developed based on a matched field of the complex, broadband coherence from a single hydrophone pair. Using ambient noise data from two shear supporting sites, compressional and shear wave estimates are obtained that are in good agreement with independent surveys. For one site where the bedrock is exposed, a half-space model of the seabed yields reasonable estimates of the seabed parameters. For the other site, the presence of a thin sedimentary layer results in a low estimate from the half-space model. However, when the layer is included in the model, the estimates of the underlying bedrock are in good agreement with a seismic survey.

Effects of cross correlation between different types of medium perturbations on seabed scattering

Sound scattering from the seabed can be generally attributed to two major mechanisms connected with seabed roughness and volume inhomogeneities. Each of these two mechanisms in turn can contain different components. For unconsolidated (fluid) sediments, volume inhomogeneities are due to spatial fluctuations of two different parameters, the density and compressibility, or the density and compressional wave speed, with respect to their mean values. For elastic bottoms, one more fluctuating parameter, shear wave speed, is to be considered. The roughness component can be attributed to the water–sediment interface and to various internal interfaces in the seabed medium as well. In this paper, the effects of cross correlations between the roughness of different interfaces and between the volume fluctuations of different parameters, as well as possible volume–roughness correlations, are examined using a first-order perturbation model. Expressions for the bottom scattering cross section involve corresponding cross-correlation and cross-spectral matrices of seabed medium perturbations. Frequency-angular dependencies of the scattering strength in monostatic and bistatic cases are analyzed for various types of seabed stratification and correlated irregularities. Comparisons are presented for the cases of strongly correlated, anticorrelated, and partially correlated perturbations. Examples are given where the cross-correlation effects are important and should be taken into account in development of methods for inversions of seabed properties. [Work supported by ONR.]

The variation of modal wave numbers with geoacoustic parameters in layered media

Analytic expressions are derived for the variation of modal wave numbers due to variations in five basic properties of a layered environment: the compressional wave speed, shear wave speed, density, and thickness of any layer, and the depth of an interface between layers. Both fluid and solid layers are permitted. The layers may absorb energy, and the modal wave numbers and their variations are generally complex valued. The analytic expressions provide an efficient way to linearize the relation between the modal wave numbers and many geoacoustic parameters, for use in field sensitivity studies, range-dependent propagation models, partially linearized matched-field inversion schemes, and in the study of modes generally.

Membrane waves on a cylindrical shell with an axial rib

A test facility has been set up to study the effect of structural modifications on membrane waves in cylindrical shells. Previous research on submerged shells has shown the importance of membrane waves in the mid-frequency, high aspect angle regimes. These shear and compressional waves are important because they are the principle determinants of the shell’s radiation and scattering properties. Flexural waves serve mainly as modifiers of the membrane waves because they are poorly coupled to the acoustic medium. The current test structure is a thin plastic shell. The advantages of plastic include higher damping, a lower compressional wave speed, and easy machining. Single modes up to n=6 are generated using an axisymmetric source array and the resulting accelerations are measured with an axial line array. The measured accelerations are separated into flexural, compressional and shear waves. Data collected on the unmodified plastic shell show excellent agreement with theory. Membrane and flexural waves in both forward and backward propagation directions are clearly seen. The experimental dispersion curves closely match theoretical predictions. Recent modifications to the shell involve the addition of an axial rib. Data from the modified shell will be presented. [Work supported by ONR.]

An idealized model for the frame elasticity of sand

An idealized model of the poroelasticity of dry- and water-saturated sand is hypothesized. The model addresses the nature of the grain–grain contact, and it is based on frame shear and bulk moduli inverted from measured acoustic and shear wave speeds as a function of pressure. The experimental data are from E. Hamilton [J. Geophys. Res. 76, 579–605 (1971)] in which both the compressional and shear wave speeds were measured as a function of the differential pressure in dry- and brine-saturated sand sediments of grains sizes approximately 0.137 and 0.7 mm. The inversion is based on Biot’s theory. The results suggest quantifiable effects due to adhesion between grains and pore fluid, partial lubrication of the grain–grain contact by the pore fluid, and a solid grain–grain contact area that changes with applied pressure. [Work supported by ONR, Code 321 OA.]

High-frequency bistatic scattering from elastic seafloors.

A high-frequency model of bistatic sound scattering is considered assuming an elastic seabed with spatially fluctuating bulk parameters and a slightly rough surface. The first-order perturbation solution is used to obtain an approximate expression for the bistatic scattering strength, different geometric configurations are considered, and the dependence of bistatic scattering strength upon the incident and scattered grazing angles, as well as the ‘‘bistatic,’’ or azimuthal angle, is computed for various seabed types. The parameters of the model include mean values for bulk properties and parameters defining the spectra of fluctuations in bulk properties and seabed relief. The influence of shear elasticity is examined by comparison with the case of a fluid seabed having the same density and compressional wave speed. It is shown that shear effects on both roughness and volume components of scattering are small for sands which consequently can be treated as acoustic fluids for realistic shear velocities (approximately 300 m/s and less). For consolidated sediments and rock, shear effects are dominant, complicated, and very sensitive to bottom parameters. Volume scattering exhibits a strong dependence on correlations between the parameter fluctuations as well as their spectral aspect ratio. [Work supported by ONR.]