Compressional Wave Speed Research Articles

Propagation of solitary waves in 2D granular media: A numerical study

The impact-induced wave propagation in a model granular material composed of closely packed linearly elastic spherical particles interacting through Hertzian contact is investigated numerically using a specially adapted molecular dynamics framework. Of particular interest is the effect of the stiffness and density mismatch between main and interstitial beads on the anisotropic nature and speed of propagation of the primary compressive wave generated by a localized impact event in an extended square-packed granular medium. Two propagation regimes are observed in the numerical simulations: the first one described by a solitary wave pattern emanating from the point of impact, and the other characterized by a directional propagation of the impact energy in the principal directions of the pack. A simple model is proposed to describe the bounds between these two propagation regimes in the parametric space defined by the mass and stiffness ratios between main and interstitial particles. Maps of the normalized maximum compressive force and wave speed are presented to quantify the anisotropy of the wave propagation response.

Mid-frequency geoacoustic inversion using bottom loss data from the Shallow Water 2006 Experiment

Geoacoustic inversion work has typically been carried out at frequencies below 1 kHz, assuming flat, horizontally stratified bottom models. Despite the relevance to Navy sonar systems many of which operate at mid-frequencies (1-10 kHz), limited inversion work has been carried out in this frequency band. This paper is an effort to demonstrate the viability of geoacoustic inversion using bottom loss data between 2 and 5 kHz. The acoustic measurements were taken during the Shallow Water 2006 Experiment off the coast of New Jersey. A half-space bottom model, with three parameters density, compressional wave speed, and attenuation, was used for inversion by fitting the model to data in the least-square sense. Inverted sediment sound speed and attenuation were compared with direct measurements and with inversion results using different techniques carried out in SW06. Inverted results of the present work are consistent with other measurements, considering the known spatial variability in this area. The observations and modeling results demonstrate that forward scattering from topographical changes is important at mid-frequencies and should be taken into account in sound propagation predictions and geoacoustic inversion. To cope with fine-scale topographic variability, measurement technique such as averaging over tracks may be necessary.

Improved quantitative calibration of rock physics models

ABSTRACT In reservoir characterization, rock-physics models provide the link between seismic observables (density, compressional and shear wave speeds) and reservoir parameters, such as porosity, lithology and fluid saturation. However, the accuracy of these predictions is rarely explored. In fact, the validation of a model representing a dataset is often limited to the analysis of a cross-plot of two arbitrary magnitudes. The objective of this paper is to improve the calibration procedure through a quantitative assessment of the reservoir property predictions using various rock-physics models. The analysis is based on an inverse rock-physics modelling that organizes the rock-physics transforms into constraint data so that the seismic variables are direct functions of the reservoir parameters. It is revealed that the predictions of reservoir quality can assist in the diagnosis of the rock microstructure itself, such as the location of clay particles in clay-rich sediments. In addition, we found that a quantitative analysis is the only way to evaluate accurately the performance of various models when studying heterogeneous datasets.

Velocity and Attenuation Characterization of the LIGO Site near Livingston, Louisiana

In April of 2009 a seismic survey utilizing explosive charges took place in Livingston parish, Louisiana. The area of the survey encompassed the location of the Laser Interferometer Gravitational-Wave Observatory (LIGO) Livingston interferometer. In this paper, we present an analysis of seismic data recorded with three of the LIGO seismometers and a geophone array that was deployed during the time of the survey. In particular, the geophone-array data are used to study the propagation of surface waves, whereas first-arrival measurements with the LIGO seismometers provide estimates of the speed of compressional seismic waves as a function of depth. We find that fundamental Rayleigh waves have a speed close to 205 m/s consistent with results from previous borehole tests and that speed of compressional waves is 1650 m/s at 25 m depth, increasing to 2300 m/s at 1 km depth. Blast spectra are further investigated to determine the Q value of the ground medium experienced by Rayleigh waves (f > 1 Hz) and body waves deeper underground. The estimated Q value is approximately 50 for the surface waves and exceeds a value of 190 for body waves propagating at depths below 100 m.

Elasticity of subducted basaltic crust at the lower mantle pressures: Insights on the nature of deep mantle heterogeneity

The origin of the large low velocity structures observed in the lowermost mantle is still unclear. To make new insights into deep mantle heterogeneity, we performed ab initio modeling of the elasticity of representative petrology with the pyrolitic and basaltic compositions based on the elasticities of the following mineral phases: magnesium silicate perovskite (post-perovskite), ferropericlase, calcium silicate perovskite, stishovite (CaCl 2), and calcium ferrite (titanate)-type MgAl 2O 4. Calculations elucidated that the basalt composite is ∼2% denser than the pyrolitic one through all of the pressures in the lower mantle. In addition, the shear ( V S) and bulk sound ( V Φ) velocities were found to be ∼2% slower and faster in the basalt composition in particular at ∼30 GPa and >120 GPa respectively, while both the pyrolitic and basaltic composites have almost the same compressional wave speed ( V P). Thermochemically distinct piles which are thought to be related to accumulated hot and dense subducted crusts would therefore be expected to produce as much as a −5% to −6% low velocity anomaly in the S wave but only ∼−1% in the P wave. These suggest that the basaltic pile seems less compatible to the seismological signatures of the large low velocity structures, if accompanied by thermal anomalies reaching +1000 to +1500 K.

Shear and compressional wave speeds in Hertzian granular media

It is shown that the shear wave speed in a granular medium is less than that in an elastic solid of the same shear modulus-to-density ratio. Shear and compressional wave speeds are derived for granular media using a conservation of energy approach. The grains are assumed to be spherical with elastic Hertzian contacts of constant stiffness. The affine approximation is used to determine the relative displacements of grain centers, and it is also assumed that the grains are small compared to a wavelength, consistent with the effective medium approximation. Potential and kinetic energies associated with linear motion are the same as those in an elastic solid, but it is found that shear wave propagation in a granular medium involves additional energies associated with grain rotation. The partition of energies results in a reduction in the shear wave speed, relative to an elastic solid of the same shear modulus-to-density ratio. It is shown that the reduction is an inherent property of granular media, independent of any departure from the affine approximation or fluctuations in coordination number or contact stiffness. The predicted wave speed ratios are consistent with published measurements.

Mach 5 bow shock control by a nanosecond pulse surface dielectric barrier discharge

Bow shock perturbations in a Mach 5 air flow, produced by low-temperature, nanosecond pulse, and surface dielectric barrier discharge (DBD), are detected by phase-locked schlieren imaging. A diffuse nanosecond pulse discharge is generated in a DBD plasma actuator on a surface of a cylinder model placed in air flow in a small scale blow-down supersonic wind tunnel. Discharge energy coupled to the actuator is 7.3–7.8 mJ/pulse. Plasma temperature inferred from nitrogen emission spectra is a few tens of degrees higher than flow stagnation temperature, T = 340 ± 30 K. Phase-locked Schlieren images are used to detect compression waves generated by individual nanosecond discharge pulses near the actuator surface. The compression wave propagates upstream toward the baseline bow shock standing in front of the cylinder model. Interaction of the compression wave and the bow shock causes its displacement in the upstream direction, increasing shock stand-off distance by up to 25%. The compression wave speed behind the bow shock and the perturbed bow shock velocity are inferred from the Schlieren images. The effect of compression waves generated by nanosecond discharge pulses on shock stand-off distance is demonstrated in a single-pulse regime (at pulse repetition rates of a few hundred Hz) and in a quasi-continuous mode (using a two-pulse sequence at a pulse repetition rate of 100 kHz). The results demonstrate feasibility of hypersonic flow control by low-temperature, repetitive nanosecond pulse discharges.

Observations and parabolic wave modeling of underwater pile driving impact noise.

Pile driving in water produces extremely high sound levels in both surrounding air and underwater environments. In a companion work [Reinhall and Dahl] it is shown using finite element simulation that for underwater case the primary sound signal originates from a compression wave traveling down the pile at a speed in excess of Mach 3. In this work, we present measurements pile driving impact noise made from a marine construction site in Puget Sound using a vertical line array (VLA) positioned at ranges 8–15 m from full-scale impact pile driving. The measurements are modeled using the parabolic wave equation approach for which synthetic time series are generated (bandwidth 50–2050 Hz). The simulation is achieved by way of a phased array of point sources, representing one source traveling down the pile at supersonic speed. Pile end reflections are included and the process is repeated with both an up- and down-traveling time-delayed sources. With the field computed in this manner, excellent agreement is achieved between model and observations of peak pressure level, and the compression wave speed is also confirmed by way of arrival angle estimation using the VLA. Implications on transmission loss are also discussed. [Work supported by the Washington State Department of Transportation.]

A measurement system for shear speed using interface wave dispersion.

Our recent work has highlighted the effect of shear on the dispersion of acoustic normal modes. Recently, Pierce et al. showed the effect of shear on compressional wave attenuation and its frequency dependence. Potty and Miller [(2010)] showed that sediment shear speed can significantly impact compressional modal arrival times near the Airy phase. We have observed that neglecting shear in compressional wave speed inversions results in a bias in our long range sediment tomography inversions. All of these factors emphasize the importance of estimating shear wave speeds in semiconsolidated shallow water sediments. One of the most promising approaches to estimate shear speed is to invert the shear speed profile using the dispersion of seismoacoustic interface waves (Scholte waves) that travel along the sediment-water boundary. The propagation speed and attenuation of the Scholte wave are closely related to shear-wave speed and attenuation over a depth of one to two wavelengths into the seabed. A shear measurement system being developed at the University of Rhode Island based on this concept will be presented. Test data collected on land will be shown and preliminary analysis techniques will be discussed. [Work supported by the Office of Naval Research.]

GyPSuM: A joint tomographic model of mantle density and seismic wave speeds

GyPSuM is a 3‐D model of mantle shear wave (S) speeds, compressional wave (P) speeds, and density. The model is developed through simultaneous inversion of seismic body wave travel times (P and S) and geodynamic observations while using realistic mineral physics parameters linking wave speeds and density. Geodynamic observations include the global free air gravity field, divergence of the tectonic plates, dynamic topography of the free surface, and the flow‐induced excess ellipticity of the core‐mantle boundary. GyPSuM is built with the philosophy that heterogeneity that most closely resembles thermal variations is the simplest possible solution. Models of the density field from Earth's free oscillations have provided great insight into the density configuration of the mantle but are limited to very long wavelength solutions. Alternatively, scaling higher‐resolution seismic images to obtain density anomalies generates density fields that do not satisfy geodynamic observations. The current study provides a 3‐D density model for the mantle that directly satisfies geodynamic and seismic observations through a joint seismic‐geodynamic inversion process. Notable density field observations include high‐density piles at the base of superplume structures, supporting the general results of past normal mode studies. However, we find that these features are more localized and have lower amplitude than past studies would suggest. When we consider both fast and slow seismic anomalies in GyPSuM, we find that P and S wave speeds are strongly correlated throughout the mantle. However, we find a low correlation of fast S wave zones in the deep mantle (>1500 km depth) with the corresponding P wave anomalies, suggesting a systematic divergence from simplified thermal effects in ancient subducted slab anomalies. The cratonic lithosphere and D″ regions are shown to have strong compositional signatures. However, we argue that temperature variations are the primary cause of P wave speed, S wave speed, and density anomalies throughout most of the mantle.

Synthetic seismograms by normal-mode summation: a new derivation and numerical examples

SUMMARY We present a new derivation of the explicit expression of displacement in response to a point dislocation source in terms of the summation of the Earth's normal modes. Starting from the well-known formal expression of normal-mode summation, we obtain the explicit expressions of displacements for the three conventional components in seismology (vertical, radial and transverse). Aided by the generalized spherical harmonics and coordinate transformation, our derivation is more comprehensive and concise and easier to handle. Numerical examples of normal-mode synthetics in different but realistic Earth models for a variety of source–receiver geometries are presented to illustrate the influence of self-gravitation, attenuation and radial anisotropy on waveforms. We also examine how waveforms of Love and Rayleigh waves are affected by the density and P-wave velocity structures in the upper mantle. Results show that the shear-wave structure obtained from surface wave tomography may be biased if the sensitivities of surface waves to the variation of density and compressional wave speed are not properly taken into account in the inversion.

Noise cross-correlation sensitivity kernels

SUMMARY We determine finite-frequency sensitivity kernels for seismic interferometry based upon noise cross-correlation measurements. Under the assumptions that noise is spatially uncorrelated but non-uniform, we determine ensemble-averaged cross correlations between synthetic seismograms at two geographically distinct locations. By minimizing a measure of the difference between observed and simulated ensemble cross correlations—subject to the constraint that the simulated wavefield satisfies the seismic wave equation—we obtain ensemble sensitivity kernels. These ensemble kernels reflect the sensitivity of ensemble cross-correlation measurements to variations in model parameters, for example, mass density, shear and compressional wave speeds and the spatial distribution of noise. Ensemble kernels are calculated based upon the interaction between two wavefields: an ensemble forward wavefield and an ensemble adjoint wavefield. To obtain the ensemble forward wavefield, one first calculates a generating wavefield obtained by inserting a signal determined by the characteristics of the noise at the location of the first receiver, saving the results of this calculation at locations where noise is generated, that is, typically on (a portion of) the Earth's surface. Next, one uses this generating wavefield as the source of the ensemble forward wavefield associated with the first receiver. The ensemble adjoint wavefield is obtained by using measurements between simulated and observed ensemble cross correlations as a seismic source located at the second receiver. The interaction between ensemble forward and adjoint wavefields ‘paints’ ensemble sensitivity kernels. We illustrate the construction of ensemble kernels and their nature in two and three dimensions using a spectral-element method. In addition to a ‘banana-doughnut’ feature connecting the two receivers, as in traditional finite-frequency earthquake tomography, some noise cross-correlation sensitivity kernels exhibit hyperbolic ‘jets’ protruding from each receiver in a direction away from the other receiver. Ensemble sensitivity kernels for long-period (T > ∼ 50 s) non-uniform noise in global models exhibit sensitivity along the minor and major arcs. These kernels reflect the fact that measurements typically involve long time-series that include multi-orbit surface waves. Like free oscillations, such measurements are sensitive to structure along the great circle through the two receivers. From the perspective of noise cross-correlation tomography, we discuss strategies for inversions in terrestrial and helioseismology.

Comments on “On pore fluid viscosity and the wave properties of saturated granular materials including marine sediments” [J. Acoust. Soc. Am. 122, 1486–1501 (2007)

The ability of the grain shearing (GS) and viscous grain shearing (VGS) models to relate geophysical and acoustic properties is tested by a method based on the claimed tight coupling between compressional and shear wave speeds and attenuations, which allows the test result to be quantified in a single parameter. The VGS model is claimed to provide a better fit to the measured sound speed and attenuation in sandy sediments below 10 kHz. In situ measurements of wave speeds and attenuations from the Sediment Acoustics Experiment 1999 (SAX99) and published laboratory measurements by Prasad and Meissner [Geophysics 57, 710-719 (1992)] on a number of sand samples were used to test the models. By this metric, the SAX99 data show that the VGS model is no better than the original GS model because the improved agreement of compressional wave speeds at low frequencies is achieved at the expense of gross overestimation of the shear wave attenuation. When applied to the measurements by Prasad and Meissner, it is shown that the GS models are not applicable at any significant confining pressures, and at zero pressure they may only be applicable to a small subset of the sand samples.

Earthquake fault superhighways

Motivated by the observation that the rare earthquakes which propagated for significant distances at supershear speeds occurred on very long straight segments of faults, we examine every known major active strike-slip fault system on land worldwide and identify those with long (> 100 km) straight portions capable not only of sustained supershear rupture speeds but having the potential to reach compressional wave speeds over significant distances, and call them “fault superhighways”. The criteria used for identifying these are discussed. These superhighways include portions of the 1000 km long Red River fault in China and Vietnam passing through Hanoi, the 1050 km long San Andreas fault in California passing close to Los Angeles, Santa Barbara and San Francisco, the 1100 km long Chaman fault system in Pakistan north of Karachi, the 700 km long Sagaing fault connecting the first and second cities of Burma, Rangoon and Mandalay, the 1600 km Great Sumatra fault, and the 1000 km Dead Sea fault. Of the 11 faults so classified, nine are in Asia and two in North America, with seven located near areas of very dense populations. Based on the current population distribution within 50 km of each fault superhighway, we find that more than 60 million people today have increased seismic hazards due to them.

Elastic imaging and time-lapse migration based on adjoint methods

We have drawn connections between imaging in exploration seismology, adjoint methods, and emerging finite-frequency tomography. All of these techniques rely on spatial and temporal constructive interference between observed and simulated waveforms to map locations of structural anomalies. Modern numerical methods and computers have facilitated the accurate and efficient simulation of 3D acoustic, (an)elastic, and poroelastic wave propagation. Using a 2D cross section of the SEG/EAGE salt model, we have determined how such waveform simulations might be harnessed to improve onshore and offshore seismic imaging strategies and capabilities. We have found that the density sensitivity kernel in adjoint tomography is related closely to the imaging principle in exploration seismology, and that in elastic modeling the impedance kernel actually is a better diagnostic tool for reflector identification. The shear- and compressional-wave speed sensitivity kernels in adjoint tomography are related closely to finite-frequency banana-doughnut kernels, and these kernels are well suited for mapping larger-scale structure, i.e., for transmission tomography. These ideas have been substantiated by addressing problems in subsalt time-lapse migration.

Single-crystal elasticity of (Mg 0.9Fe 0.1)O to 81 GPa

Ferropericlase is the second most abundant mineral in Earth's lower mantle and knowledge of its elastic properties at relevant conditions is needed to adequately interpret seismic observations in terms of the mineralogy and thermal state of the deep Earth. Here, we report the complete elastic tensor of (Mg 0.9Fe 0.1)O ferropericlase to 81.2 GPa at room temperature measured by Brillouin spectroscopy and X-ray diffraction in the diamond-anvil cell. Our data indicate that the spin transition of iron between 45 and 63 GPa dramatically affects the longitudinal and off-diagonal elements of the elastic stiffness tensor c 11 and c 12, whereas it leaves the shear constant c 44 almost unaffected. Based on our results, the spin transition markedly changes the pressure (and temperature) dependence of the compressional and bulk sound velocities and must be taken into account in any attempt to match average radial seismic velocity profiles with mineral physics observations. The different pressure dependence of compressional (and bulk) and shear sound velocities across the high-spin to low-spin (HS–LS) transition implies that the spin transition might be best observed in the v p / v s ratio and its pressure (and temperature) derivative. We also point out the possibility that the spin transition leads to an anti-correlated temperature dependence of shear and compressional wave speeds in certain pressure–temperature regimes in Earth's lower mantle.

High-resolution seismic and resistivity profiling of a buried Quaternary subglacial valley: Northern Alberta, Canada

High-resolution seismic and resistivity profiles were acquired to assist in the delineation of a buried Quaternary subglacial valley, the existence of which was first discovered by drilling. One aspect of this valley is the glacial sediments that host substantial methane at shallow depths (~50 m or less). Geophysical well logs indicate that the glacial sediments in this area generally have lower compressional wave speeds V P 10 Ω·m than adjacent undisturbed Cretaceous-age rocks, which have V P >2200 m/s and r 300 m) valley. The reflection profile reveals a complex series of events consistent with heterogeneous deposition. One major reflection dips eastward across the valley. The reflection character changes abruptly on either side of this event, with dipping clinoform reflections beneath and nearly horizontal reflections above. These may be related to changes in deposition processes beneath a retreating ice sheet, as has been suggested by earlier workers. The buried valley's basal reflections are complex and possibly reflect glaciotectonic deformation or block plucking. The near-surface methane gas is within, but at the edge of, the valley. The methane gas–saturated zone displays anomalously high resistivities both in the well logs and in resistivity tomography.

Finite-frequency kernels for wave propagation in porous media based upon adjoint methods

We determine finite-frequency kernels for wave propagation in porous media based upon adjoint methods. These sensitivity kernels may be obtained based upon two numerical simulations for each source: one calculation for the current model and a second, ‘adjoint’, calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. The adjoint equations for a porous medium are identical to the usual Biot equations, with the exception of the adjoint source term, which involves time-reversed measurements of the differences between simulations and data. Isotropic poroelastic wave propagation is governed by eight primary model parameters which appear in the original Biot equations. These parameters include four moduli: the shear modulus of the frame plus three bulk moduli. We consider two alternative parameterizations: one involving density-normalized moduli corresponding to squared wave speeds, and a second involving the poroelastic shear and compressional wave speeds. The alternative parameterizations lead to density-sensitivity kernels that are small, reflecting the fact that the traveltime of a poroelastic wave is governed by wave speed, not density. We systematically investigate and illustrate the sensitivity of the fast and slow compressional waves and the shear wave to the poroelastic model parameters using a 2-D spectral-element method. The poroelastic sensitivity kernels presented herein form the basis of tomographic imaging and inversion in porous media.

The applicability of a small towed array system to the ocean bottom sediment classification problem.

An autonomous array system is uniquely suited to perform near bottom (≈1 m) measurements of horizontal wave number spectra that estimate water and interface wave numbers. Synthetic coherent processing provides the required gain to observe the interface wave peak 40–50 dB below the peaks of water modes. Comparable measurements were performed with an array of seismometers (Muir et al., 1991). These spectra contain the information necessary to perform inversions that account for compressional and shear wave speed gradients. Spatial transforming the computed pressure field produces spectra comparable with measurements. Variations of the geoacoustic profiles show that the present gradient produces additional identifiable spectral structure corresponding to shear waves trapped within the sediments. In the experiments discussed, the sound source was at the bottom and the array was towed by a vehicle. However, it is feasible to either use a source of sound on the vehicle or on a companion vehicle to do surveys. This method is a fast, efficient, and accurate ocean acoustic measurement tool useful in rapid waveguide characterization with the appropriate inversion technology. (Work partially sponsored by ONR‐OA.)

Compressional Wave Speed Dispersion and Attenuation in Carbonate Sediments, Kaneohe Bay, Oahu, HI

In situ compressional wave speed and attenuation measurements between 20 and 100 kHz were made at two carbonate sediment sites in Kaneohe Bay, on the windward side of the Hawaiian island of Oahu. Velocities increased with frequency from 1691 to 1708 m/s at a coarse sediment site (HC, porosity=0.45) and from 1579 to 1585 m/s at a fine-grained sediment site (HF, porosity=0.56). Effective attenuation increased with frequency from 15 to 75 dB/m at HC and from 22 to 62 dB/m at HF. Values of sound speed at these sites are within the range of those reported in the literature for silicate sands of the same porosity. Attenuation values of these reef-derived carbonate sands are higher than many of those reported in the literature for silicate sands and they appear to be linearly related to frequency (?=0.65f). Sound-speed and attenuation data were compared to predictions of two sediment geoacoustic models, Biot-Stoll and grain shearing (GS). In both models, two unknown parameters were varied to find best fits at each site to: 1) both attenuation and sound-speed data and 2) sound-speed data only. Both models yielded similar fits, which differ significantly from the measured data.