Shear Wave Speed Profiles Research Articles

In situ measurements of compressional and shear wave properties during gravity coring operations

Sediment cores provide valuable insight about the physical properties of the seabed, and laboratory measurements of sediment wave speed from cores are often considered “ground truth.” However, sound-speed estimates obtained from cores can be inaccurate due to changes in pressure, temperature, and mechanical properties of the sediment caused by the removal of the core from the seabed and its subsequent transport to the laboratory. To address these issues, the Acoustic Coring System (ACS) was developed. The system uses sets of transducers mounted below the penetrating tip of a sediment corer to make in situ measurements of geoacoustic properties as the corer penetrates the seabed. Compressional wave measurements are obtained with rod-mounted piezoelectric cylinders, and shear wave measurements are obtained with bender elements mounted in flat blades. The ACS was deployed during the environmental survey for ONR Seabed Characterization Experiment (SBCEX) in 2016 and in support of the ONR Canada Basin Acoustic Propagation Experiment (CANAPE) in 2017. In both cases, the system provided measurements of the sediment sound-speed profile as a function of depth within the seabed. On-going work focused on the measurement of shear wave speed profiles and compressional and shear wave attenuation will also be presented. [Work supported by ONR.]Sediment cores provide valuable insight about the physical properties of the seabed, and laboratory measurements of sediment wave speed from cores are often considered “ground truth.” However, sound-speed estimates obtained from cores can be inaccurate due to changes in pressure, temperature, and mechanical properties of the sediment caused by the removal of the core from the seabed and its subsequent transport to the laboratory. To address these issues, the Acoustic Coring System (ACS) was developed. The system uses sets of transducers mounted below the penetrating tip of a sediment corer to make in situ measurements of geoacoustic properties as the corer penetrates the seabed. Compressional wave measurements are obtained with rod-mounted piezoelectric cylinders, and shear wave measurements are obtained with bender elements mounted in flat blades. The ACS was deployed during the environmental survey for ONR Seabed Characterization Experiment (SBCEX) in 2016 and in support of the ONR Canada Basin Acoustic...

Seismological constraints on the density, thickness and temperature of the lithospheric mantle in southwestern Tibet

We constrain the lithospheric mantle in southwest Tibet to be cold, thick, and dense by considering seismological observations, isostasy, and gravity anomalies. First, virtual deep seismic sounding (VDSS) indicates that the thickness of the crust increases from 50 ± 4 km beneath the Himalaya to 70 ± 4 km in the Lhasa terrane. This implies a ‘residual topography’ (difference between isostatic elevation of crust and true elevation) of −2.4 ± 1.5 km. Taking into account deviations from isostasy, the lithospheric mantle must be dense enough to depress the surface by 0.9 to 4.5 km. Our joint inversion of fundamental-mode Rayleigh wave dispersion and receiver functions suggests that the vertically-polarised shear-wave speed (Vsv) is 4.6 ± 0.1 kms−1 at depths of 120 to 300 km. From the shear-wave speed profile, we estimate the geotherm, which is on average 200°C below the 1350°C adiabat, and suggest that the base of the lithosphere is at a depth of 290 ± 30 km. To match the negative buoyancy, the lithospheric must be denser, on average, than ‘normal’ fertile adiabatic mantle, which rules out a depleted (harzburgite) composition. The density excess can be explained solely by thermal contraction, but we cannot rule out additional density increases due to composition. Our observations are not consistent with a depleted Indian slab underthrusting Tibet in this region, which would result in a lower average density and lower temperatures.

Surface wave tomography for the Pacific Ocean incorporating seafloor seismic observations and plate thermal evolution

Using broadband seismic waveforms recorded on the seafloor by more than 200 broadband ocean bottom seismometers, as well as those on land, we measured the phase speed dispersions of Love and Rayleigh waves up to the 4th higher mode to determine the three-dimensional radially anisotropic shear-wave speed structure in the upper mantle beneath the Pacific Ocean. The fastest anomalies at depths shallower than 100 km were located beneath southeast of the Shatsky Rise and strong radial anisotropy was located in the central Pacific at depths of 100–200 km. The isotropic shear-wave speed structures showed age dependence. From the age-bin-averaged shear-wave speed profiles and a half-space cooling model, we estimated the thermo-speed relationship for the Pacific Plate to construct a reference age-dependent shear-wave speed model, which was further used as an initial model for tomography iteration. Deviation maps in the Pacific Ocean from the reference model indicated that large negative residuals, which may be due to partial melting, anelasticity, and/or added heat from mantle plumes, were located along the ridges and beneath hotspots, and that large positive residuals were found beneath the northwestern Pacific Ocean. The use of an age-dependent reference model, as well as the incorporation of OBS data, greatly improves the accuracy of local phase speed estimates in tomography, as evident from a direct comparison with in situ array measurements.

RSNA/QIBA efforts to standardize shear wave speed as a biomarker for liver fibrosis staging

Commercial shear elasticity systems have been available to clinicians for several years for characterizing liver stiffness. The Radiological Society of North America (RSNA) established a Quantitative Imaging Biomarker Alliance (QIBA) committee on Ultrasound Shear Wave Speed to help achieve better consistency between the shear wave speed and elastic modulus values reported by different manufacturer systems. An inter-laboratory study of shear wave speed estimation was conducted at academic, industry and clinical laboratories using commercial ultrasound and magnetic resonance elastography systems in elastic (Phase I) and viscoelastic (Phase II) homogeneous, isotropic tissue-mimicking phantoms. In the elastic phantoms, shear wave speeds from different systems were within ±5% of the grand mean of all system measurements. Different appraisers and replicate measurements at a given site were not sources of significant variability in shear wave speed measurements. In the viscoelastic phantoms, shear wave speeds from different systems were within ±15% of the grand mean of all systems, with the stiffest phantoms at the deepest focal depth (7 cm) having the greatest measurement variance. Magnetic resonance elastography measurements at 140 Hz in the viscoelastic phantoms were consistent to within ±5% of thosemade with the ultrasound shear elasticity systems, while measurements made at 60 Hz had a mean bias of -2.6% relative to ultrasound systems. A method for reporting group shear wave velocities using both displacement and velocity data, along with shear wave phase velocity analysis, has been developed as a common calibration approach for the phantoms. An open-source repository of research scanner shear wave sequences and processing code has been created to allow manufacturers to have a calibration standard to assess compliance with the QIBA US shear wave speed profile and to achieve more consistent results to facilitate more rapid clinical adoption of this technology to evaluate liver fibrosis.

Characterization of soft marine sediments using vector sensors

Horizontally and vertically polarized interface waves with phase speeds of 45–375 m/s were observed in the North Sea using a horizontal linear array of three-component seismometers [H. Dong et al., J. Acoust. Soc. Am. 134, 176–184 (2013)]. The waves were generated by a low-frequency shear wave source on the seafloor, which operated in the 2–60 Hz band. Dispersion curves of the interface waves exhibit linear dependences between the logarithm of phase speed and logarithm of frequency, with distinct slopes at large and small phase speeds. This suggests a geoacoustic model consisting of two sediment layers with power-law dependences of the shear wave speed on depth below seafloor [O. A. Godin and D. M. F. Chapman, J. Acoust. Soc. Am. 110, 1890–1907 (2001)]. In this paper, dispersion curves of interface waves are inverted for the shear wave speed profile in the sediments. Observations of lateral wave arrivals are used to corroborate the geoacoustic model suggested by the surface wave dispersion and constrain c...

Finite element modeling of Rayleigh wave propagation in a laboratory sand tank

Rayleigh waves were measured in a laboratory sand tank using an array of accelerometers. This tank allows for the measurement of interface waves for various sediment and soil arrangements in a well-controlled laboratory setting. Rayleigh waves were excited by simple impulsive sources including dropped balls and hammer impacts. In this study, a finite element modeling tool developed by Sandia National Laboratories was used to simulate the sand tank during these excitations. Different modeling scenarios were investigated. Time series of the Rayleigh wave arrivals were modeled at the sensor locations using time domain analysis. A calibrated bender element system was also developed to provide direct measurements of the shear wave speed profile at selected depths. These data were used to develop the material property input parameters for the finite element analysis. The simulated time series at the sensor locations are compared to the accelerometer data. [Work supported by Army Research Laboratory and BOEM.]

A comparison between directly measured and inferred wave speeds from an acoustic propagation experiment in Currituck Sound.

An acoustic propagation experiment was conducted in Currituck Sound to characterize low-frequency propagation in a very-shallow-water estuarine environment. The water column properties were homogeneous over the study area, and the emphasis of this work is on understanding the propagation effects induced by the estuarine bed. During the experiment, low-frequency sound propagation measurements of waterborne sound and interface waves were acquired, and direct measurements of the compressional and shear wave properties were obtained at high frequencies. The propagation data consist of signals from a Combustive Sound Source recorded on bottom mounted geophones and a vertical line array of hydrophones. A statistical inference method was applied to obtain an estimate of the sediment compressional and shear wave speed profiles as a function of depth within the estuarine bed. The direct measurements were obtained in situ by inserting probes 30 cm into the sediment. Sediment acoustics models were fit to the high-frequency in situ data to enable comparison with the inferred low-frequency wave speeds. Overall, good agreement was found between the directly measured and inferred wave speeds for both the compressional and shear wave data.

Model selection for profile structure in Bayesian geoacoustic inversion

This paper considers model selection in Bayesian geoacoustic inversion, specifically, the role of seabed parameterization in resolving geoacoustic profile structure. Bayesian inversion is formulated in terms of the posterior probability density (PPD) over the model parameters which are sampled numerically: Metropolis-Hastings sampling in principal-component space enhanced by parallel tempering is employed here. A key aspect of quantitative geoacoustic inversion is that of parameterizing the seabed model. Trans-dimensional (trans-D) inversion methods model the seabed as a sequence of discontinuous uniform layers and sample probabilistically over the number of layers. However, in some cases it may be expected for seabed properties to vary as smooth, continuous gradients which are not well represented by uniform layers. Most gradient-based inversions assume a representative functional form, such as a power law. A recent alternative is based on a linear combination of Bernstein-polynomial basis functions. This approach is more general and allows the form of the profile to be determined by the data, rather than by a subjective model choice. This paper compares trans-D, power-law, and Bernstein-polynomial inversions for the problem of estimating seabed shear-wave speed profiles from the dispersion of interface waves. Simulations and data from Oslofjorden and/or the North Sea will be considered.

Field measurements of interface waves and geoacoustic characterization of near surface sediment and soil

There is a need for rapid and nondestructive sensing of near-surface shear properties of the ground and seafloor. Our approach is to measure interface wave dispersion and invert these measurements to extract a shear wave speed profile. Field measurements of interface waves using geophones and accelerometers will be presented. A laser Doppler vibrometer (LDV) will also be incorporated in the suite of sensors for the measurement of wave properties. Data from these sensors will be compared to understand the coupling of the sensors into the soil or sediment and its effect on the measurements. Geoacoustic and geotechnical properties will be estimated using the interface wave data. The uncertainty and resolution of the estimates in different sediment/soil types will be explored. The Interface Wave Testing Facility at the University of Rhode Island will also be used to understand the surface wave propagation characteristics in different type of sediments/soils. [Work supported by Army Research Office and the Office of Naval Research.]

Modeling explosion generated Scholte waves in sandy sediments with power law dependent shear wave speed.

Experimental measurements of Scholte waves from underwater explosions collected off the coast of Virginia Beach, VA in shallow water are presented. It is shown here that the dispersion of these explosion-generated Scholte waves traveling in the sandy seabed can be modeled using a power-law dependent shear wave speed profile and an empirical source model that determines the pressure time-series at 1 m from the source as a function of TNT-equivalent charge weight.

Laboratory and field measurements of Rayleigh waves

There is a need for rapid and nondestructive sensing of near-surface shear properties of the ground and seafloor. Our approach on land is to measure Rayleigh wave dispersion and invert these measurements to extract a shear wave speed profile. A portable surface wave inversion system has been developed that employs an array of six accelerometers to measure Rayleigh waves excited by simple impulsive sources in the laboratory and in the field. To verify the shear wave speed estimated by the Rayleigh waves, a calibrated bender element system was also developed to provide independent measurements of the shear wave speed profile at selected depths. The bender element system was placed in a test tank initially filled with mason sand and the Rayleigh wave inversion system was deployed on the surface of the sand in the tank. The estimated shear wave speeds were then compared to the results of the bender element system as well measurements by a dynamic cone penetrometer and laser vibrometer. The approach allows for the measurement of shear speeds in for various sediment and soil arrangements in the well-controlled laboratory setting as well in the field. [Work supported by Army Research Office and ONR.]

The Zagros core: Deformation of the continental lithospheric mantle

The Zagros of Iran form one of the youngest collisional orogenic belts on Earth. At shallow depths, shortening across the Zagros is accommodated by folding in the sediments, high‐angle thrust faulting in the basement and thickening of the lower crust, but how shortening is accommodated by the lithospheric mantle has been uncertain largely because the upper mantle seismic structure has been poorly known. We map the lateral variations in upper mantle shear wave speed beneath this region using a large, multimode surface wave data set. The upper mantle is slow for most of the Middle East, but a high shear wave speed lid extending to ∼225 km depth exists beneath the Zagros. We use aT(Vs, z) relation to convert the shear wave speed profiles to temperature profiles and fit these with geotherms to identify the base of the lithosphere. The upper mantle temperatures from the seismic model are consistent with temperatures derived from geochemical modeling. The lithosphere is less than ∼120 km thick over the region except for a thick lithospheric root beneath the Zagros, implying that shortening in the mantle is accommodated by lithospheric thickening. The composition of the volcanic rocks from above the area of the thickened lithosphere has depleted magma source regions with densities ∼60 kg m−3 less than the MORB source. Elsewhere in the Middle East the volcanic source regions have compositions and densities similar to that of MORB. The shortening across the Zagros is accommodated by lithospheric thickening but the cool thickened lithosphere has been stabilized from delamination by depletion.

Bayesian Inversion of Multimode Interface-Wave Dispersion From Ambient Noise

This paper applies nonlinear Bayesian inversion to estimate seabed shear-wave speed profiles and their uncertainties using interface-wave dispersion curves extracted from ocean ambient noise, and compares the resolution of seabed structure for fundamental mode and multimode data. Ambient noise recordings were collected for 2.15 h at hydrophones of an entrenched ocean bottom cable in the North Sea. Scholte-wave dispersion curves for the fundamental mode and several higher order modes within the frequency range 0.25–3.9 Hz are extracted from cross correlations of noise recordings at sensor pairs via the slowness-frequency transform. The Bayesian information criterion is used to determine the preferred model parameterizations in terms of the number of sediment layers supported by the data for inversions based on the fundamental mode alone and on the first three modes. Adaptive hybrid optimization and Metropolis–Hastings sampling are applied to estimate the optimum a posteriori shear-wave speed models and to compute marginal posterior probability distributions and profiles. The results show quantitatively that multimode inversion provides higher resolution of shallow shear-wave speed structure with smaller uncertainties at all depths than inversion of the fundamental mode alone.

Shear wave speed inversions using scholte wave dispersion

Shear speeds in semi-consolidated and consolidated shallow water sediments can significantly impact compressional wave attenuation and arrival times of acoustic normal modes. In addition, shear properties of sediments are directly related to the strength of the sediments in geotechnical applications. All of these factors emphasize the importance of estimating shear speeds in shallow water sediments. One of the most promising approaches to estimate shear speed is to invert the shear speed profile using the dispersion of interface waves (Scholte waves). The propagation speed and attenuation of the Scholte wave are closely related to shear-wave speed and attenuation over a depth of 1-2 wavelengths into the seabed. Data from the tests conducted in Narragansett Bay and off Block Island in water depths ranging from 10 m to 25 m using the shear measurement system, developed at the University of Rhode Island, will be presented. Combustive Sound Source (CSS) was be used to generate interface waves during these tests. An inversion algorithm to estimate the shear wave speed profile in the sediment will be presented. Estimates of the shear speed will be compared with ground truth data. [Work supported by Office of Naval Research]

Bayesian inversion of seabed interface-wave dispersion from ambient noise

This paper applies Bayesian inversion to estimate seabed shear-wave speed profiles and their uncertainties using interface-wave dispersion curves extracted from ocean ambient noise, and compares the resolution of seabed structure for fundamental-mode and multi-mode data. Ambient-noise recordings were collected for 2.15 h at hydrophones of an entrenched ocean-bottom cable in the North Sea. Scholte-wave dispersion curves for the fundamental mode and several higher-order modes within the frequency range 0.26–3.8 Hz are extracted from cross-correlations of noise recordings at sensor pairs via slowness-frequency transform. The Bayesian information criterion is used to determine the preferred model parameterizations in terms of the number of sediment layers supported by the data for inversions based on the fundamental mode alone and on the first three modes. Adaptive-hybrid optimization and Metropolis-Hastings sampling are applied to estimate the most-probable shear-wave speed models and to compute marginal posterior probability profiles. The results show quantitatively that multi-mode inversion provides higher-resolution of shear-wave speed structure at shallow depths and smaller uncertainties at all depths than inversion of the fundamental mode alone. [We thank StatOil for providing data.]

Bayesian Inversion of Interface-Wave Dispersion for Seabed Shear-Wave Speed Profiles

This paper applies Bayesian inversion to estimate seabed shear-wave speed profiles and their uncertainties from interface-wave dispersion data. A nonlinear formulation is developed to estimate the most probable profile together with marginal probability distributions and credibility intervals from the posterior probability density (PPD) using adaptive hybrid optimization and Metropolis-Hastings sampling (MHS). To address correlated data errors, a full error covariance matrix is estimated from residual analysis, and rigorous a posteriori statistical tests are applied to validate the covariance estimate and the assumption of a multivariate Gaussian error distribution. The most appropriate parameterization for the shear-wave speed profile is determined using the Bayesian information criterion (BIC), which provides the simplest model consistent with the resolving power of the data. Parameterizations considered vary in the number and type of layers, and include layers with uniform speed, and with linear and power-law shear-speed gradients. For the data considered here, a power-law parameterization is indicated, which is consistent with theoretical expectations for uniform, unconsolidated sediments under overburden pressure. The maximum depth to which the dispersion data constrain the shear-speed profile is investigated using an approximate analytic formula for power-law profiles and repeated inversions in which the maximum depth to an underlying half-space is systematically increased.

Non-linear waveform inversion for surface waves with a neighbourhood algorithm-application to multimode dispersion measurements

SUMMARY A new technique for multimode dispersion measurement has been developed by employing fully non-linear waveform inversion for a path-specific 1-D profile using a neighbourhood algorithm (NA). One-dimensional models derived from waveform inversion are quite sensitive to the model parametrization and the reference model used to start the inversion. With different approaches to the parametrization of the shear wave speed profile, we can find models with significant differences in velocity variation with depth, which provide similar levels of fit to the observed waveforms. Although the models differ, the calculated phase dispersion for the first few modes of the surface waves are very close indeed. We therefore regard the 1-D models derived from the multimode waveform inversion as an implicit description of the path-specific dispersion for each of the modes. The inversion procedure using NA samples a substantial number of models and we select the 1-D wave speed model that achieves minimum misfit. Phase speeds for each mode branch are then calculated from the model parameters with the minimum misfit. Because we use the 1-D models as a summary of the average multimode dispersion along the path, we do not need to make assumptions concerning the nature of anisotropy. We can employ simple isotropic models and the method can be applied to both Rayleigh and Love waves independently. The new method is applied to sets of paths in the Australian region and provides stable measurements of multimode dispersion from a single seismogram. The multimode phase speeds measured using the NA inversion can be used to retrieve phase velocity maps as a function of frequency for higher-mode branches as well as the fundamental mode, which will be crucial constraints on 3-D Earth models.

Green's function for the vector wave equation in a mildly heterogeneous continuum

In this work, a fundamental solution is derived for the case of time-harmonic elastic waves originating from a point source and propagating in a three-dimensional, unbounded heterogeneous medium with a Poisson's ratio of 0.25. The first step in the solution procedure is to transform the displacement vector in the Navier equations of dynamic equilibrium through scaling by the square root of the position-dependent shear modulus. Following imposition of certain constraints that are subsequently used to derive the depth profile of the elastic moduli and of the density, it becomes possible to employ Helmholtz's vector decomposition so as to generate two scalar wave equations for the dilational and rotational components of the wave motion, a process which again generates additional constraints. The corresponding Green's function is then synthesized in the conventional way followed for homogeneous media. Consideration of all intermediate constraints shows that the elastic moduli and the density all have quadratic variation with respect to the depth coordinate z, while the pressure and shear wavespeed profiles are constant and correspond to reference values at z = 0. The present methodology is based on earlier algebraic transformation techniques applied for the case of scalar wave propagation. The methodology is finally illustrated through a number of examples involving a commonly encountered geological medium.

Determination of compressional wave and shear wave speed profiles in sea ice by crosshole tomography—Theory and experiment

Sea ice is a heterogeneous material whose acoustic properties are functions of time and space. Results of a crosshole tomography experiment conducted in multi-year ice with the objective of determining the spatial structure of the compressional and shear wave speeds from travel time measurements made with high-frequency pulses are presented here. The results of the experiment indicate that the wave speeds can be determined from such a crosshole experiment with good resolution. The compressional and shear wave speed contour maps indicate that the spatial variations of the wave speeds are complex with regions of low speed. Low-speed regions observed are likely caused by high brine volume content. Resolution and variance studies performed on the estimates are also presented. Material properties such as Poisson’s ratio, salinity, and elastic and shear moduli of sea ice are obtained from the estimates of compressional and shear wave speeds. By measuring the amplitude of the transmitted and received signals along specific paths, estimates of the attenuation coefficients at different depth intervals are obtained. Spatial variability observed in the estimates is believed to be due to scattering by inhomogeneities in the material.

Determination of compressional and shear wave speed profiles and attenuation in sea ice

Sea ice is a very heterogeneous material with brine channels, layers of varying density and crystal size, and a porous skeletal layer at the ice-water interface. Acoustic propagation under ice in the Arctic has been studied by many investigators, and efforts to predict the measured field by theory has met with limited success. One of the likely causes is the lack of adequate information on the anelastic properties of sea ice. A cross-hole tomography experiment designed to measure the spatial and temporal structure of the anelastic properties of sea ice will be described. Results of a lake experiment and an experiment conducted in the Canadian Arctic during 1989 will be presented.