Interface Wave Dispersion Research Articles

Physics-based characterization of soft marine sediments using vector sensors.

In a 2007 experiment conducted in the northern North Sea, observations of a low-frequency seismo-acoustic wave field with a linear horizontal array of vector sensors located on the seafloor revealed a strong, narrow peak around 38 Hz in the power spectra and a presence of multi-mode horizontally and vertically polarized interface waves with phase speeds between 45 and 350 m/s. Dispersion curves of the interface waves exhibit piece-wise linear dependences between the logarithm of phase speed and logarithm of frequency with distinct slopes at large and small phase speeds, which suggests a seabed with a power-law shear speed dependence in two distinct sediment layers. The power spectrum peak is interpreted as a manifestation of a seismo-acoustic resonance. A simple geoacoustic model with a few free parameters is derived that quantitatively reproduces the key features of the observations. This article's approach to the inverse problem is guided by a theoretical analysis of interface wave dispersion and resonance reflection of compressional waves in soft marine sediments containing two or more layers of different composition. Combining data from various channels of the vector sensors is critical for separating waves of different polarizations and helps to identify various arrivals, check consistency of inversions, and evaluate sediment density.

Bayesian inference and model selection to investigate seabed shear-wave velocity profiles via interface-wave dispersion inversion

This paper applies a general geoacoustic profile parameterization based on Bernstein polynomial basis functions to consider the form of seabed shear-wave velocity profiles via Bayesian inversion of interface (Scholte) wave dispersion. Theory and observations indicate that the shear-wave velocity profile of seabed sediments of uniform composition and density often corresponds (approximately) to a power law function of depth. Hence, past inversions have often been based on a power-law parameterization without considering independently if this form is actually required by the data. The Bernstein parameterization, based on a linear combination of Bernstein-polynomial basis functions with the polynomial order determined by the Bayesian information criterion, is general and allows the form of the profile to be determined by the data, rather than by a subjective prior choice. In this paper, measured-data inversions are compared for power-law, Bernstein-polynomial, and layered trans-dimensional parameterizations to investigate the shear-wave velocity profile form.

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.

Estimation of shear wave properties using Scholte wave inversions

Shear speeds in semi-consolidated and consolidated shallow water sediments can significantly impact compressional wave attenuation and arrival times of acoustic normal modes. 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 of the Scholte waves is closely related to the shear wave speed over a depth of 1–2 wavelengths into the seabed. A geophone system for the measurement of these interface waves, along with an inversion scheme that inverts the Scholte wave dispersion data for sediment shear speed profiles and shear attenuation has been developed. A forward model based on the dynamic stiffness method has been developed and implemented in the inversion. A new Interface Wave Sediment Profiler (iWaSP) is being currently developed for the measurement of bottom properties such as shear speed and attenuation in the top 1–2 m of a variety of sediment types (including mud) with a wideban...

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.]

J0420405 密着圧力による界面波速度分散の変化の計測([J042-04]超音波計測・解析法の新展開(4),機械材料・材料加工部門)

A contact pressure dependence on group velocity dispersion of interface waves was measured for experimentally discussing contact condition of two aluminum alloy plates with a low stiffness layer (0.3 mm-thick silicone rubber sheet) as an intermediate layer under compressive loads. The interface waves were produced by converting Rayleigh wave generated by an angled transducer and were detected after transmitting thorough the interface. At a contact pressure of 1.6 kPa, the group velocity of the interface wave was constant in the frequency range of 0.5 MHz to 1.5 MHz and was almost the same as that of Rayleigh wave propagating on the aluminum alloy substrate. Meanwhile, the group velocity of the interface wave at 3 MPa decreased with increasing frequency and showed similar behavior to a theoretical dispersion of the anti-symmetric mode in an interface waves. It is confirmed that the propagation behavior of the interface wave strongly reflected the contact pressure at the interface.

Inversion of shear wave speed in coastal sediments using interface waves

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). Interface wave data from a small scale experiment conducted in very shallow water in coastal Rhode Island will be presented. The University of Rhode Island’s shear measurement system consisting of vertical axis and 3-axis geophones were used to collect data in 3 m of water. Interface waves were excited by dropping a weight from a research vessel. Modeling of interface waves will be carried out using Finite Element Method (FEM) and a dynamic stiffness matrix model. Sediment properties will be inferred based on the modeling and data-model comparison. The estimated sediment properties will be compared with historic core data from the field test location. [Work supported by Office of Naval Research.]

Estimation of seabed shear-wave velocity profiles using shear-wave source data

This paper estimates seabed shear-wave velocity profiles and their uncertainties using interface-wave dispersion curves extracted from data generated by a shear-wave source. The shear-wave source generated a seismic signature over a frequency range between 2 and 60 Hz and was polarized in both in-line and cross-line orientations. Low-frequency Scholte- and Love-waves were recorded. Dispersion curves of the Scholte- and Love-waves for the fundamental mode and higher-order modes are extracted by three time-frequency analysis methods. Both the vertically and horizontally polarized shear-wave velocity profiles in the sediment are estimated by the Scholte- and Love-wave dispersion curves, respectively. A Bayesian approach is utilized for the inversion. Differential evolution, a global search algorithm is applied to estimate the most-probable shear-velocity models. Marginal posterior probability profiles are computed by Metropolis-Hastings sampling. The estimated vertically and horizontally polarized shear-wave velocity profiles fit well with the core and in situ measurements.

Measurement and modeling of Scholte waves in shallow water

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 will be presented. Modeling of interface waves will be carried out using Finite Element Method (FEM) and a wave number integration model (OASES). Sediment properties will be inferred based on the modeling and data-model comparison. [Work supported by Office of Naval Research.]

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]

Estimation of shear-velocity profiles using shear source data in marine environment

This paper estimates seabed shear-velocity profiles and their uncertainties using interface-wave dispersion curves extracted from data generated by a shear source. The data were collected by 4C ocean bottom cable in a testing experiment of a shear source in the North Sea. The shear source generated a seismic signature over a frequency range between 2 and 60 Hz and was polarized in both in-line and cross-line orientation. Low-frequency Scholte- and Love-wave were recorded. Dispersion curves of the Scholte- and Love-wave for the fundamental mode and higher-order modes are extracted by different time-frequency analysis method. Both vertical (SV) and horizontal (SH) polarized shear-velocity profiles are estimated by Scholte- and Love-wave dispersion curves, respectively. Bayesian approach is used for the inversion. Differential evolution (DE) global search algorithm is applied to estimate the most-probable shear-velocity models. Marginal posterior probability profiles are computed by Metropolis-Hastings sampling. The estimated SV- and SH-velocity profiles are compared and the results provide possibility of studying seabed anisotropy. We thank Statoil ASA for permission to publish the data. The work is partly supported by NFR under Grant No. 186923/I30.

Estimation of shear speed using interface wave dispersion

Our recent work has highlighted the effect of shear on the dispersion of acoustic normal modes. Specifically, sediment shear speed can significantly impact compressional modal arrival times near the airy phase. In addition to underwater acoustic propagation effects, 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 semi-consolidated 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. Results from the tests conducted at Narragansett Bay in water depths ranging from 10 to 25 m using the shear measurement system, developed at the University of Rhode Island based on this concept, will be presented. Combustive sound source (CSS) will be used to generate interface waves. Data collected during these tests will be shown and preliminary estimates of the shear speed will be presented and 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.]

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.]

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.

Bayesian evidence computation for model selection in non-linear geoacoustic inference problems

This paper applies a general Bayesian inference approach, based on Bayesian evidence computation, to geoacoustic inversion of interface-wave dispersion data. Quantitative model selection is carried out by computing the evidence (normalizing constants) for several model parameterizations using annealed importance sampling. The resulting posterior probability density estimate is compared to estimates obtained from Metropolis-Hastings sampling to ensure consistent results. The approach is applied to invert interface-wave dispersion data collected on the Scotian Shelf, off the east coast of Canada for the sediment shear-wave velocity profile. Results are consistent with previous work on these data but extend the analysis to a rigorous approach including model selection and uncertainty analysis. The results are also consistent with core samples and seismic reflection measurements carried out in the area.

Estimation of seismic interface wave dispersion in geoacoustic inversion.

Shear wave velocity variation as depth in underwater environment is closely related to dispersion of seismic interface waves traveling along the water/sediment boundary. An estimate of the dispersion of seismic interface waves can be obtained by time-frequency analysis. There are different methods for the time-frequency analysis to estimate dispersion of the interface waves. Phase velocity dispersion can be estimated by multi-sensor method, while group velocity dispersion can be estimated by single-sensor method. Multi-sensor method uses array data by knowing sensor-spacing, which gives the average estimate of the phase velocity within the ranges covered by the array. Single-sensor method uses one trace at a time by knowing the distance between source and the sensor, and gives the local group velocity estimate. In this paper, time-frequency analysis methods for both phase- and group-velocity estimations are presented. An experimental example for estimation of shear wave velocity variation as depth in the upper layers of the sediment is presented by inverting the estimated dispersion relations of seismic interface waves [Work supported by NFR under No. 186923/I30].

Dispersion of interface waves in sediments with power-law shear speed profiles. I. Exact and approximate analytical results

In the upper tens of meters of ocean bottom, unconsolidated marine sediments consisting of clay, silt, or fine sand with high porosity are "almost incompressible" in the sense that the shear wave velocity is much smaller than the compressional wave velocity. The shear velocity has very large gradients close to the ocean floor leading to strong coupling of compressional and shear waves in such "soft" sediments. The weak compressibility opens an avenue for developing a theory of elastic wave propagation in continuously stratified soft sediments that fully accounts for the coupling. Elastic waves in soft sediments consist of "fast" waves propagating with velocities close to the compressional velocity and "slow" waves propagating with velocities on the order of the shear velocity. For the slow waves, the theory predicts the existence of surface waves at the ocean-sediment boundary. In the important special case of the power-law depth-dependence of shear rigidity, phase and group velocities of the interface waves are shown to scale as a certain power of frequency. An explicit, exact solution was obtained for the surface waves in sediments characterized by constant density and a linear increase of shear rigidity with depth, that is, for the case of shear speed proportional to the square root of the depth below the sediment-water interface. Asymptotic and perturbation techniques were used to extend the result to more general environments. Theoretical dispersion relations agreed well with numerical simulations and available experimental data and, as demonstrated in a companion paper [D. M. F. Chapman and O. A. Godin, J. Acoust. Soc. Am 110, 1908 (2001)] led to a simple and robust inversion of interface wave travel times for shear velocity profiles in the sediment.

Dispersion of interface waves in sediments with power-law shear speed profiles. II. Experimental observations and seismo-acoustic inversions.

The propagation of seismic interface waves is investigated in soft marine sediments in which the density is constant, the shear modulus is small, and the profile of shear speed c(s) versus depth z is of the power-law form c(s) (z) = c0z(v), in which c0 and v are constants (0< v < 1). Both the phase speed V and the group speed U of interface waves scale with frequency as f(v/(v -1)) and they obey the simple relation U= (1 - v) V. These relations are derived in a simple way using ray theory and the WKB method; a companion paper [O. A. Godin and D. M. F. Chapman, J. Acoust. Soc. Am. 110, 1890 (2001)] rigorously derives the same result from the solutions to the equations of motion. The frequency scaling is shown to exist in experimental data sets of interface wave phase speed and group speed. Approximate analytical formulas for the dispersion relations (phase and group speed versus frequency) enable direct inversion of the profile parameters c0 and v from the experimental data. In cases for which there is multi-mode dispersion data, the water-sediment density ratio can be determined as well. The theory applies to vertically polarized (P-SV) modes as well as to horizontally polarized (SH) modes (that is, Love waves).