Isospeed Research Articles

Speculations on the cause of finite density and sound speed gradients near the interface of muddy sediments

Holland et al. [JASA (2013)] at the previous ASA meeting reported positive density gradients and negative sound speed gradients at the water-mud sediment interface and asked “what processes drive them.” A derivation using the Mallock-Wood relations yields a simple high-porosity approximate relation giving a negative proportionality between sound speed gradient and density gradient independent of depth and porosity. It is also argued that the solid portion of the mud consists of tiny mineral platelets, each of which carries a net negative charge. The presence of dissolved salts causes each platelet to behave as an electrical quadrupole, so that there is, on the average, a small electrical repulsive force between the platelets. With gravity taken into account, the equilibrium separation distance between two parallel vertically aligned platelets is one to two orders of magnitude greater than a typical length scale of the face of a platelet. However, when platelets touch, edge to face, there is an attractive force between platelets, and the net effect is that the platelets tend to be separated at a much shorter distance than the stand-off distance deep within the sediment. Paper reports ongoing efforts to estimate the depth over which the transition occurs.

Influence of atmospheric structure and topography on infrasonic wave propagation

The effects of topography and atmospheric structures on infrasonic wave propagation from a volcanic source were investigated using observations and numerical modeling. This paper presents the first long‐term observational data set showing spatiotemporal variations in patterns of infrasound propagation at distances of up to 60 km from a persistently active infrasound source (Sakurajima Volcano, Japan). The data show that the amplitudes of infrasonic waves received at distant stations relative to those received at a reference station close to the source can vary up to an order of magnitude over short time intervals and short distances and that they do not follow the theoretical geometric decay expected for homogeneous media. Moreover, waveforms also change significantly in both time and space. Numerical simulations were performed using a two‐dimensional finite difference time domain (2‐D FDTD) method. Effects of atmospheric structure and topography are included in a vertical section parallel to the wave propagation direction. The simulation successfully reproduced the variations of amplitudes and waveforms. Results are interpreted in terms of wave refraction due to sound and wind speed gradients and wave diffraction at topographic barriers. Our numerical results indicate that both atmospheric and topographic propagation effects are nonnegligible. To evaluate the propagation effects and determine source processes in spatially and temporally varying infrasound data, atmospheric data with a time resolution higher than is currently available are required. If the data are available, the present results suggest that the propagation effects could be evaluated using 2‐D FDTD modeling at realistic calculation times.

Statistical inference of seabed sound-speed structure in the Gulf of Oman Basin

Addressed is the statistical inference of the sound-speed depth profile of a thick soft seabed from broadband sound propagation data recorded in the Gulf of Oman Basin in 1977. The acoustic data are in the form of time series signals recorded on a sparse vertical line array and generated by explosive sources deployed along a 280 km track. The acoustic data offer a unique opportunity to study a deep-water bottom-limited thickly sedimented environment because of the large number of time series measurements, very low seabed attenuation, and auxiliary measurements. A maximum entropy method is employed to obtain a conditional posterior probability distribution (PPD) for the sound-speed ratio and the near-surface sound-speed gradient. The multiple data samples allow for a determination of the average error constraint value required to uniquely specify the PPD for each data sample. Two complicating features of the statistical inference study are addressed: (1) the need to develop a cost function that can both utilize the measured arrival structure and mitigate the effects of data errors and (2) the effect of small bathymetric slopes on the structure of the bottom interacting arrivals. [Work supported by ONR.]

Amplitude modulation of sound from wind turbines under various meteorological conditions

Wind turbine (WT) sound annoys some people even though the sound levels are relatively low. This could be because of the amplitude modulated "swishing" characteristic of the turbine sound, which is not taken into account by standard procedures for measuring average sound levels. Studies of sound immission from WTs were conducted continually between 19 August 2011 and 19 August 2012 at two sites in Sweden. A method for quantifying the degree and strength of amplitude modulation (AM) is introduced here. The method reveals that AM at the immission points occur under specific meteorological conditions. For WT sound immission, the wind direction and sound speed gradient are crucial for the occurrence of AM. Interference between two or more WTs could probably enhance AM. The mechanisms by which WT sound is amplitude modulated are not fully understood.

Comparison and evaluation of physics-based outdoor sound propagation assessment schemes

Evaluating the effectiveness of outdoor sound propagation assessment schemes using experimentally collected data is a complex task. Specifically, when the acoustic data collected assume non-Gaussian distributions with differing sample sizes per assigned class, traditional parametric statistical techniques may not be used. As an alternative, this research introduces an original cost function to evaluate and compare various methods aimed at defining acoustic propagation classes based on meteorological measurements. Class assignments in each scheme are based on the atmospheric stability, the strength of the vertical effective sound speed gradient, and the vertical effective sound speed profile. The acoustic data included in this analysis were generated by a high-energy impulsive source and gathered at source-to-receiver distances of 1, 2, 4, and 8 km. The results indicate that the assessment scheme based on the strength of the effective sound speed gradient most effectively classifies the peak level sound propagation sampled in temperate and desert climate conditions at these distances.

Nocturnal boundary layer profiles and measured frequency dependent influence on sound propagation

During four evenings including one night the sound propagation up to a distance of 200m south and north of a railway line was measured and the sound exposure level difference between the distances 25 and 200m from a railway line was calculated. At the same time the meteorological situation was measured with a tethered balloon up to a height of 100m. These measurements were compared with calculated wind and temperature profiles and a reasonable fit of the measured with the theoretical profiles were found.The A-weighted sound exposure level differences were correlated with the effective sound speed gradient with respect to atmospheric stability. In the case of upwind sound propagation a difference of the A-weighted sound level in the range of 10dB between stable and not stable (adiabatic and instable) meteorological situation was found (7dB in the frequency range between 315 and 3150Hz) and in the case of downwind sound propagation in the range of 3dB(A).The stability of the nocturnal layer is expressed with the Obukhov length L which includes (in the bulk definition) a relation of the wind speed gradient to the temperature gradient. The effective sound speed gradient includes the sum of the wind speed gradient and temperature gradient. The main result is that the description of sound propagation should be improved by use of the Obukhov length to include the stability effects of the atmosphere which is especially necessary in the case of upwind sound propagation during the nocturnal boundary layer.

On the time‐mean state of ocean models and the properties of long range acoustic propagation

Receptions on three vertical hydrophone arrays from basin‐scale acoustic transmissions in the North Pacific during 1996 and 1998 are used to test the time‐mean sound‐speed properties of the World Ocean Atlas 2005 (WOA05), of an eddying unconstrained simulation of the Parallel Ocean Program (POP), and of three data‐constrained solutions provided by the estimating the circulation and climate of the ocean (ECCO) project: a solution based on an approximate Kalman filter from the Jet Propulsion Laboratory (ECCO‐JPL), a solution based on the adjoint method from the Massachusetts Institute of Technology (ECCO‐MIT), and an eddying solution based on a Green's function approach from ECCO, Phase II (ECCO2). Predictions for arrival patterns using annual average WOA05 fields match observations to within small travel time offsets (0.3–1.0 s). Predictions for arrival patterns from the models differ substantially from the measured arrival patterns, from the WOA05 climatology, and from each other, both in terms of travel time and in the structure of the arrival patterns. The acoustic arrival patterns are sensitive to the vertical gradients of sound speed that govern acoustic propagation. Basin‐scale acoustic transmissions, therefore, provide stringent tests of the vertical temperature structure of ocean state estimates. This structure ultimately influences the mixing between the surface waters and the ocean interior. The relatively good agreement of the acoustic data with the more recent ECCO solutions indicates that numerical ocean models have reached a level of accuracy where the acoustic data can provide useful additional constraints for ocean state estimation.

Remote Infrasound Monitoring of Mount Etna: Observed and Predicted Network Detection Capability

Volcanic eruptions are valuable calibrating sources of infrasonic waves worldwide detected by the International Monitoring System (IMS) of the Comprehensive Nuclear Test-Ban-Treaty Organization (CTBTO) and other experimental stations. In this study, we assess the detection capability of the European infrasound network to remotely detect the eruptive activity of Mount Etna. This well-instrumented volcano offers a unique opportunity to validate attenuation models using multi-year near-and far-field recordings. The seasonal trend in the number of detections of Etna at the IS48 IMS station (Tunisia) is correlated to fine temporal fluctuations of the stratospheric waveguide structure. This observed trend correlates well with the variation of the effective sound speed ratio which is a proxy for the combined effects of refraction due to sound speed gradients and advection due to along-path wind on infrasound propagation. Modeling results are consistent with the observed detection capability of the existing regional network. In summer, during the downwind season, a minimum detectable amplitude of ~10 Pa at a reference distance of 1 km from the source is predicted. In winter, when upwind propagation prevails, detection thresholds increase up to ~100 Pa. However, when adding four experimental arrays to the IMS network, the corresponding thresholds decrease down to ~20 Pa in winter. The simulation results provide here a realistic description of long- to mid-range infrasound propagation and allow predicting fine temporal fluctuations in the European infrasound network performance with potential application for civil aviation safety.

Reflectionless acoustic gravity waves in the Earth’s atmosphere

The vertical wave propagation in an inhomogeneous compressible atmosphere is studied in the framework of a linear theory. Under specific conditions imposed on atmospheric parameters, solutions can be found in the form of travelling waves with variable amplitudes and wave numbers that do not reflect in the atmosphere in spite of its strong inhomogeneity. Model representations for the sound speed have been found, for which waves can propagate in the atmosphere without reflection. A wave energy flux retains these reflectionless profiles, which confirms that energy can be transferred to high altitudes. The number of these model representations is fairly large, which makes it possible to approximate real vertical distributions of the sound speed in the Earth’s atmosphere using piecewise reflectionless profiles. The Earth’s standard atmosphere is shown to be well approximated by four reflectionless profiles with weak jumps in the sound speed gradient. It has been established that the Earth’s standard atmosphere is almost completely transparent for the considered vertical acoustic waves in a wide range of frequencies, which is confirmed by observational data and conclusions derived using numerical solutions of original equations.

Demonstration of Comparison Methods for Ocean Model Validation

In recent years an increasing amount of oceanographic data has become available. This includes observations as well as data from hydrodynamic ocean models. Validation is required for establishing the necessary confidence in new sources of data. Generally ocean models and other data sources such as satellite imagery are validated by comparing the output to conventional observations or the output of established ocean models. Methods of comparison used in literature range from refined statistical methods to comparisons of snapshots. This work collects descriptions of some of the most widely used comparison methods. The capabilities and limitations of each method are demonstrated using examples from modelled and observed oceanographic data. The work has a particular focus on how to determine discrepancies on vertical gradients in the oceanographic parameters since acoustic propagation is sensitive to errors in the sound speed gradient.

Acoustic scattering from density and sound speed gradients: Modeling of oceanic pycnoclines

A weak-scattering model that allows prediction of acoustic scattering from oceanic pycnoclines (and the accompanying sound speed gradients) based on hydrographic profiles is described. Model predictions, based on profiles from four locations, indicate that scattering from oceanic pycnoclines is measurable using standard scientific sonars operating at frequencies up to 200 kHz but generally only for pycnocline thicknesses less than 10 m. Accurate scattering models are key to assessing whether acoustic remote sensing can be used to map oceanic pycnoclines and for determining whether scattering from pycnoclines needs to be taken into account when estimating, for instance, zooplankton abundance from acoustic data.

The influence of environmental conditions on estimation of source distance and height using a single vertical array

The performance of microphone arrays outdoors is influenced by the environmental conditions. Numerical simulations indicate that, while horizontal arrays are hardly affected, direction-of-arrival (DOA) estimation with vertical arrays becomes biased in presence of ground reflections and sound speed gradients. Turbulence leads to a huge variability in the estimates by reducing the ground effect. Ground effect can be exploited by combining classical source localization with an appropriate propagation model (ground effect inversion). Not only does this allow the source elevation and range to be determined with a single vertical array but also it allows separation of sources which can no longer be distinguished by far field localization methods. Furthermore, simulations provide detail of the achievable spatial resolution depending on frequency range, array size and localization algorithm and show a clear advantage of broadband processing. Outdoor measurements with one or two sources confirm the results of the numerical simulations.

Bottom loss measurements and their use in studying the physics of sound propagation in marine sediments

Bottom reflection loss measurements have been conducted for four decades and have provided key insights into the physics of propagation in marine sediments. The advantage of bottom loss as an analysis quantity is that, in principle, it completely isolates the role of the seabed and permits separation and identification of key physical mechanisms. For example, it was early deep water bottom loss measurements that first made it clear that strong positive sediment sound speed gradients existed and the concomitant surprising realization that the dominant seabed interacting path was the refracted and not reflected path over a wide angular and frequency band. In this talk, various discoveries from bottom loss measurements are discussed including the role of sediment layering, attenuation gradients, and shear waves.

Second-Order Sensitivity of Acoustic Travel Times to Sound Speed Perturbations

The second-order sensitivity of finite-frequency acoustic travel times to sound speed perturbations in range-independent environments is studied. Using the notion of peak arrivals and the normal-mode representation of the Green's function first- and second-order perturbation expressions are derived for the travel times in terms of the underlying perturbations in the Green's function and finally in the sound speed profile. The resulting theoretical expressions are numerically validated. Assuming small and local perturbations the non-linear effects appear to be strongest for sound speed perturbations taking place close to the lower turning depths of the corresponding eigenrays. At the upper turning depths ― in the case of temperate propagation conditions ― the effects are much weaker due to the larger sound speed gradients. The magnitude of the second-order sensitivity of travel times relative to the first-order sensitivity can be used to obtain an estimate for the limits of linearity.

Sound field of a fast moving source in a horizontally stratified medium above an impedance plane.

A continuous source motion model is developed for computing the sound fields of a uniformly moving monopole source in a horizontally stratified atmosphere. The numerical model is based on the Lorentz transformation and the one-dimensional fast field formulation. The global matrix method and a bounded Green’s function solution expressed in the wavenumber domain is used in the numerical implementation. The solution is then expressed in the Lorentz frame. A transformation is performed to map the spatial Lorentz frame quantities into a reception time history in the stationary frame. Numerical results for an elevated source in a downward refracting atmosphere demonstrates the importance of a continuous source motion model especially at high Mach numbers in the presence of sound speed gradients where the pseudo-stationary source approximation becomes questionable. Coupled with the convective effects of continuous source motion and a frequency dependent ground impedance model, the resulting sound fields are significantly different from those predicted due to a pseudo-stationary source. Fluctuations on the order of 20 dB are predicted in the interference pattern in the far-field. A shift of the interference onset time to lower values is predicted when the source Mach number and/or sound speed gradient is increased.

On Experience in using the remote acoustic method of partial reflections in studies of the lower troposphere

Using the phenomenon of the partial reflection of acoustic waves from anisotropic wind-velocity and temperature inhomogeneities in the lower troposphere is justified in determining the structure of these inhomogeneities. The data (obtained with the method of bistatic acoustic sounding) on signals reflected from stratified inhomogeneities in the lower 600-m layer of the troposphere are given. A detonation-type pulsed acoustic source was used. The methods of isolating a small (in amplitude) reflected signal against the background of noise and determining the reflecting-layer height and the partial-reflection coefficient from the measured parameters (time delay and amplitude) of a reflected signal are presented. The method of estimating the vertical gradients of the effective sound speed and the squared acoustic refractive index from the partial-reflection coefficient previously calculated is described on the basis of an Epstein transition-layer model. The indicated parameters are experimentally estimated for concrete cases of recording reflected signals. A comparison of our estimates with independent analogous data simultaneously obtained for the same parameters with monitoring instruments (a sodar and a temperature profiler) has yielded satisfactory results.

Seismic signatures of stellar cores of solar‐like pulsators: Dependence on mass and age

AbstractUseful information from the inner layers of stellar pulsators may be derived from the study of their oscillations. In this paper we analyse three diagnostic tools suggested in the literature built from the oscillation frequencies computed for a set of main sequence models with masses between 1.0 M⊙ and 1.6 M⊙, to check what information they may hold about stellar cores. For the models with convective cores (M ≥ 1.2 M⊙) we find a relation between the frequency slopes of the diagnostic tools and the size of the jump in the sound speed at the edge of the core. We show that this relation is independent of the mass of the models. In practice, since the size of the jump in the sound speed is related to the age of the star, using these seismic tools we may, in principle, infer the star's evolutionary state. We also show that when combining two of the three diagnostic tools studied, we are able to distinguish models with convective cores from models without a convective core but with strong sound speed gradients in the inner layers (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A deterministic (non-stochastic) low frequency method for geoacoustic inversion

It is well known that multiple frequency sources are necessary for accurate geoacoustic inversion. This paper presents an inversion method which uses the low frequency (LF) spectrum only to estimate bottom properties even in the presence of expected errors in source location, phone depths, and ocean sound-speed profiles. Matched field processing (MFP) along a vertical array is used. The LF method first conducts an exhaustive search of the (five) parameter search space (sediment thickness, sound-speed at the top of the sediment layer, the sediment layer sound-speed gradient, the half-space sound-speed, and water depth) at 25 Hz and continues by retaining only the high MFP value parameter combinations. Next, frequency is slowly increased while again retaining only the high value combinations. At each stage of the process, only those parameter combinations which give high MFP values at all previous LF predictions are considered (an ever shrinking set). It is important to note that a complete search of each relevant parameter space seems to be necessary not only at multiple (sequential) frequencies but also at multiple ranges in order to eliminate sidelobes, i.e., false solutions. Even so, there are no mathematical guarantees that one final, unique "solution" will be found.

Seismic imaging of variable water layer sound speed in Rockall Trough, NE Atlantic and implications for seismic surveying in deep water

Abstract Natural variation in sound speed within ocean water can degrade sub-seabed images from 2D, 3D and 4D seismic reflection datasets. Degrading effects include vertical offset of reflections between adjacent or intersecting sail lines and difficulties in suppressing multiples from water layer reverberations. Here we investigate water layer variability in Rockall Trough, offshore Ireland, in water depths ranging from 200 m to 3.5 km. A compilation of vertical sound speed profiles, calculated from temperature and salinity profiles obtained by probes lowered from ships, shows that the mean sound speed in the water layer mostly varies between 1490 and 1500 m s −1 . Vertical offsets of up to about 15 ms two-way travel time are predicted at seismic line intersections. A significant amount of the total observed sound speed variability can occur along a single seismic sail line. These effects result mainly from spatial and temporal fluctuations in the thicknesses of, and vertical sound speed gradients within, an upper layer of North Atlantic Central Water and a mid-depth layer of Mediterranean Outflow Water. Seismic sections across Rockall Trough commonly show lateral variability in reflectivity within these same two water layers. Some reflective packages contain lens-shaped structures consisting of reflective rims and transparent cores and with diameters between 10 and 50 km. Other reflective packages have abrupt, almost vertical boundaries and no distinct transparent core. We infer that the lateral boundaries of the reflective packages are likely to be associated with significant variations in average water layer sound speed. When processing 2D, 3D and 4D seismic surveys of regions of high oceanic variability, such as Rockall Trough, it is necessary to employ techniques that can solve for and then remove the effect of significant fluctuations in water layer sound speed over time periods as short as a few hours and distances as short as a kilometre.

Modeling gradients in ocean acoustics.

Modeling acoustic propagation in the ocean requires a representation of the ocean sound speed. For a 1‐D, range independent ocean, probably the most common representation comprises constant sound speed layers and/or gradient layers. Gradients of the form 1/c2(z), admitting an exact solution for the acoustic pressure field in terms of Airy functions, are commonly employed. A disadvantage of using the Airy functions is that they are specific to that profile. For more general profiles, the best representation may be a stack of constant sound speed layers for which the pressure field is expressible in terms of simple exponentials. As an example, computing the backscattering strength from a stack of layers containing volume heterogeneities requires evaluation of an integral proportional to the 4th power of the pressure field. Integrating the simple exponential solutions for constant sound speed layers is trivial. Integrating a product of four Airy functions, either analytically or numerically, is not. If the medium is represented only by constant sound sound speed layers, what is the best way to choose the layers, and how many layers are needed? These questions are investigated by employing an algorithm originally due to Fuchs (1968). [Work partially supported by ONR.]