Sound-speed Perturbations Research Articles

Broadband acoustic characterization of backscattering from a rough stratification interface.

Broadband acoustic analysis of scattering from sharp density gradients in the water column generally treat the interfaces as smooth surfaces. However, these interfaces may exhibit roughness owing to external water column forcing and local convective processes. In this work we extend broadband backscatter analysis methods to consider interface roughness by drawing upon methods developed for sea surface and seabed acoustic backscattering. The one-dimensional acoustic model from Weidner and Weber [J. Acoust. Soc. Am. 150(6), 4353-4361 (2021)], which predicts a decay in the reflected wave amplitude from stratification interfaces with increasing frequency, was expanded for surface applications. The expanded model was used to analyze the scattered pressure field from interfaces over a range of surface roughness magnitudes. Analysis of model results indicate that stratification interface roughness, quantified by the root-mean-squared interface slope angle and root-mean-squared height of the interface, modifies the model-predicted frequency-dependent backscattering. A broadband acoustic inversion procedure to remotely measure the magnitude of the vertical extent of stratification gradients and the corresponding sound speed perturbation was defined. The broadband inversion method was tested on data collected in the Baltic Sea with well-documented, strong salinity-driven stratification.

Sensitivity of phase difference between short-range acoustic multipaths to changes in sound speed and source depth

Ocean acoustic tomography often relies on precise clocks and knowledge of the range between acoustic instruments to estimate ocean-driven sound speed changes. In this study, we explore an alternative method utilizing the difference in the carrier phase between two broadband pulse arrivals to estimate small-scale changes in source depth and sound speed. By leveraging acoustic multipathing, this phase difference approach obviates the need to know the acoustic propagation's precise range and absolute travel time. Observations from a mid-frequency (1–10 kHz) acoustic experiment at short ranges (2–3 km) demonstrate the sensitivity of the difference in the 4 kHz carrier phase between two arrivals to changes in both source depth and sound speed. The difference in the arrival phase is modeled using measurements of the time-varying source depth and sound speed. The comparison between the modeled and observed arrival phase differences reveals a significant agreement, supporting the potential of using phase difference as a reliable estimator for perturbations in either source depth or sound speed for short-range acoustic propagation.

Time series prediction of shallow water sound speed profile in the presence of internal solitary wave trains

The internal waves, especially the internal solitary wave (ISW) trains, cause violent perturbations of sound speed. Sound speed profile (SSPs) facilitates the pre-understanding of the sound field distribution in the experimental sea, therefore, the real-time prediction of SSPs in the presence of ISW trains are of great significance. In this paper, an orthogonal representation of SSPs that considers the background field (background SSP) variation is proposed. Based on the statistical characteristics of time-series SSPs, high-precision SSP prediction is realized by the long short-term memory recurrent neural network (LSTM). The prediction accuracy is demonstrated with the SSP data from an experiment in the South China Sea, and the mean RMSE of SSP prediction is reduced to about 1 m/s.

Observations of the space/time scales of Beaufort sea acoustic duct variability and their impact on transmission loss via the mode interaction parameter.

The Beaufort duct (BD) is a subsurface sound channel in the western Arctic Ocean formed by cold Pacific Winter Water (PWW) sandwiched between warmer Pacific Summer Water (PSW) and Atlantic Water (AW). Sound waves can be trapped in this duct and travel long distances without experiencing lossy surface/ice interactions. This study analyzes BD vertical and temporal variability using moored oceanographic measurements from two yearlong acoustic transmission experiments (2016-2017 and 2019-2020). The focus is on BD normal mode propagation through observed ocean features, such as eddies and spicy intrusions, where direct numerical simulations and the mode interaction parameter (MIP) are used to quantify ducted mode coupling strength. The observations show strong PSW sound speed variability, weak variability in the PWW, and moderate variability in the AW, with typical time scales from days to weeks. For several hundreds Hertz propagation, the BD modes are relatively stable, except for rare episodes of strong sound speed perturbations. The MIP identifies a resonance condition such that the likelihood of coupling is greatest when there is significant sound speed variability in the horizontal wave number band 1/11<kh<1/5 km-1. MITgcm ocean model results are used to estimate sound speed fluctuations in this resonance regime.

Wide-area sound speed profile estimation based on a pre-classification scheme for sound speed perturbation modes

IntroductionThe trend of sound speed profile (SSP) inversion is towards wide-area sound speed estimation. However, the traditional inversion method of dividing the latitude and longitude grids has limitations in terms of significantly lower accuracy when samples are lacking. k-means clustering algorithm (K-means) can divide the training class to achieve high accuracy estimation.MethodThis paper proposes a grid-free pre-classification inversion scheme based on empirical orthogonal function (EOF) vectors. The scheme is based on the K-means to classify the samples according to the perturbation mode of the SSP. After classification, the SSP inversion is carried out using the self-organizing map algorithm (SOM). The experimental sea area is selected from the South China Sea, and the inversion results are evaluated using root mean square error (RMSE) as the criterion.ResultThe inversion results show that the inversion error is 2.1 m/s for the pre-classification solution and 2.7 m/s for the solution without pre-classification, a steady improvement of more than 20% in the inversion error. Accuracy is also improved by 2.14 m/s in the depth range where the sound speed perturbance is greatest.DiscussionThis pre-classification scheme has smaller inversion errors and the classification results are reasonable in terms of distribution in time and space. It provides a feasible solution for SSP inversion in sea areas where samples are lacking.

Angular Spectrum of Acoustic Pulses at Long Ranges

Long-range propagation of sound pulses in the deep ocean is considered. A new method for the estimation of the pulse angular spectrum is presented. The method is based on the Husimi transform of a wave field and can be realized with a short vertical array of nondirectional hydrophones. As a result, one obtains a diagram of the arrival pattern in the time–angle plane. The method is applied to a model of the underwater sound channel in the Sea of Japan. Special attention is paid to sound scattering on a cold synoptic eddy along the waveguide. It is shown that the synoptic eddy leads to a splitting of the individual ray’s arrivals into clusters with close angles and times. The random sound-speed perturbation induced by internal waves blurs these clusters into a fuzzy background and simultaneously broaden the angular spectrum of pulses. Nevertheless, it is found that the latter effect is relatively weak for short vertical arrays. In particular, it is shown that increasing the array length from 10 to 30 m results in the separation of the arrivals with opposite angles.

An Embedded Tactical Decision Aid Framework for Environmentally Adaptive Autonomous Underwater Vehicle Communication and Navigation

Motivated by a changing acoustic environment in the Arctic Beaufort Sea, in this article, we present a tactical decision aid framework for a human decision-maker collaborating with an autonomous underwater vehicle (AUV) to integrate the vertical sound-speed profile for underwater navigation and communication. In a predeployment phase, using modeled and real oceanographic data, we load basis function representations of the sound-speed perturbations onto one or more AUVs on deck, where a handful of weights can estimate a sound-speed profile. During deployment, these weights are updated on an AUV through a digital acoustic message to improve navigation and reciprocal communication throughout the duration of an under-ice mission. Field work applying this framework in the Beaufort Sea is presented, highlighting key decisions regarding predeployment oceanographic data assimilation, CTD cast collection, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> weight choice. Selected examples evaluate the framework’s ability to adapt to a depth-limited CTD cast and the appearance of an anomalous microlens feature in the profile. We show that the framework effectively balances the need to adapt in a changing acoustic environment in real time while maintaining operator trust in an AUV’s embedded intelligence.

Ray tracing and finite element modeling of sound propagation in a compartment fire

A compartment fire (a fire in a room or building) creates temperature gradients and inhomogeneous time-varying temperature, density, and flow fields. This work compared experimental measurements of the room acoustic impulse/frequency response in a room with a fire to numerically modeled responses. The fire is modeled using a Fire Dynamics Simulator (FDS). Acoustic modeling was performed using the temperature field computed by FDS. Room acoustics were modeled using two-dimensional ray and finite element modeling. A three-dimensional model was used to simulate an open flame. COMSOLTM Multiphysics was used for finite element acoustic modeling and BELLHOPTM for ray trace acoustics modeling. The results show that the fire causes wave-fronts to arrive earlier (due to the higher sound speed) and with more variation in the delay times (due to the sound speed perturbations). The resonance frequencies of low-frequency modes were shifted upwards. Model results are compared with data and show good agreement in observed trends.

The Beaufort Sea acoustic duct's variability and its impact on acoustic propagation using the mode interaction parameter

The Beaufort duct is a subsurface sound channel formed by cold Pacific Winter Water sandwiched between warmer Pacific Summer Water and Atlantic Water in the Western Arctic Ocean. This duct traps sound waves and allows them to travel long distances without losing energy to lossy interactions with sea ice and surface waves. This study quantifies Beaufort duct variability based on Canada Basin Acoustic Propagation Experiment (CANAPE) and Coordinated Arctic Acoustic Thermometry Experiment (CAATEX) oceanographic observations. Deterministic ocean features induce coupling between acoustic modes confined to the Beaufort duct and non-ducted modes by weakening the duct or causing it to take on an asymmetric form. A non-dimensional mode interaction parameter (MIP) can be defined using the acoustic frequency and the vertical and horizontal scales of sound speed perturbation to characterize coupling strength. It identifies three important wave propagation regimes: sudden approximation, adiabatic approximation, and maximum interaction regime (Colosi and Zinicola-Lapin, 2021). When the MIP between ducted and lossy modes is more and less than 1, strong and weak acoustic variability is predicted, respectively. Variability is high when the MIP between two ducted modes surpasses 1, but modei–mode interference patterns grow more complicated. Acoustic numerical simulations are used to demonstrate various effects.

NUMERICAL COMPARISON OF ITERATIVE AND FUNCTIONAL-ANALYTICAL ALGORITHMS FOR INVERSE ACOUSTIC SCATTERING

Abstract In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G. Novikov for the case of the Schr ̈odinger equation. In the present work, for the case of two-dimensional scalar Helmholtz equation, the efficiency of the iterative algorithm in reconstruction of middle strength scat- terers and advantages of the functional-analytical approach in recovering strong scatterers are demonstrated. A filtering procedure is considered in the space of wave vectors, which additionally increases the convergence of the iterative algorithm. Reconstruction results of sound speed perturbations demonstrate the comparable noise immunity and resolution of the considered algorithms when reconstructing middle strength scatterers. A comparative nu- merical investigation of the iterative and functional-analytical algorithms in inverse acoustic scattering problems is implemented in this work for the first time.

An acoustic scattering model for stratification interfaces.

Stable fluid bodies, such as the ocean and atmosphere, are composed of a series of increasingly dense layers, defined by density stratification interfaces in which the medium properties (e.g., temperature, salinity) change. The intensity of the stratification between the layers influences the internal mixing dynamics and entrainment, facilitating the transport of dissolved constituents within the fluid medium. Acoustic systems offer the means for high resolution observations of these interfaces, which allow for continuous data collection over broad spatial scales. Here, a one-dimensional acoustic scattering model is presented for predicting acoustic backscatter from stratification interfaces, which is widely applicable to the acoustic water column data collected with ship-mounted sonars. Model predictions based on hydrographic profiles suggest that in many oceanic cases, the density gradient perturbations can be disregarded, and sound speed perturbations alone drive the majority of the acoustic scattering. A frequency-dependent scattering intensity based on the sharpness of the stratification interface is predicted by the model, suggesting a path to remote estimations of the physical medium properties through broadband acoustic inversion.

One-sided arc averaging geometries in time–distance local helioseismology

Context. The study of solar oscillations (helioseismology) has been a very successful method of researching the Sun. Helioseismology teaches us about the structure and mean properties of the Sun. Together with mid-resolution data, the local properties were uncovered in quiet-Sun regions. However, magnetic fields affect the oscillations and prevent us from studying the properties of magnetically active regions with helioseismology. Aims. We aim to create a new methodology to suppress the negative effects of magnetic fields on solar oscillations and measure plasma properties close to active regions. Methods. The methodology consists of new averaging geometries, a non-linear approach to travel-time measurements, and a consistent inversion method that combines plasma flows and sound-speed perturbations. Results. We constructed the one-sided arc averaging geometries and applied them to the non-linear approach of travel-time measurements. Using the one-sided arc travel times, we reconstructed the annulus travel times in a quiet-Sun region. We tested the methodology against the validated helioseismic inversion pipeline. We applied the new methodology for an inversion for surface horizontal flows in a region with a circular H-type sunspot. The inverted surface horizontal flows are comparable with the output of the coherent structure tracking, which is not strongly affected by the presence of the magnetic field. We show that the new methodology suppresses the negative effects of magnetic fields up to outer penumbra. We measure divergent flows with properties comparable to the moat flow. Conclusions. The new methodology can teach us about the depth structure of active regions and physical conditions that contribute to the evolution of the active regions.

Predictions of acoustic backscattering from oceanic stratification interfaces

The ocean is primarily composed of a series of increasingly dense fluid layers, defined by density stratification interfaces where medium properties, such as temperature and salinity, drive changes in medium density and compressibility. The transport of dissolved constituents (e.g., oxygen, heat, salt) between these oceanic fluid layers is strongly influenced by the intensity of the stratification interface. Active acoustics allow for high resolution observations of these interfaces, offering continuous data collection over broad spatial scales. In this work, we present a one-dimensional acoustic scattering model for predicting acoustic backscatter from stratification interfaces. The model is widely applicable to acoustic water column data collected with ship-mounted sonars and preliminary results, based on hydrographic profiles, suggest that, in many oceanic cases, sound speed perturbations drive the majority of acoustic scattering. Additionally, modeling results predict a frequency modulated backscattering intensity based on the sharpness of the stratification interface, suggesting the potential for remote estimation of medium properties through broadband acoustic inversion.

Analysis of Time–Distance Helioseismology for Detection of Emerging Active Regions

Abstract A time–distance helioseismic technique, similar to the one used by Ilonidis et al., is applied to two independent numerical models of subsurface sound-speed perturbations to determine the spatial resolution and accuracy of phase travel time shift measurements. The technique is also used to examine pre-emergence signatures of several active regions observed by the Michelson Doppler Imager and the Helioseismic Magnetic Imager. In the context of similar measurements of quiet-Sun regions, three of the five studied active regions show strong phase travel time shifts several hours prior to emergence. These results form the basis of a discussion of noise in the derived phase travel time maps and possible criteria to distinguish between true and false-positive detection of emerging flux.

A mode based broadband scattering model for deep water sound propagation

Internal-wave induced sound-speed perturbations cause phase and intensity fluctuations of time-fronts. This paper focuses on predictions for broadband Transmission Losses (TL), time wander, and Scintillation Index (SI), along various sections of a typical deep water time-front. These statistics are usually predicted using Monte-Carlo Parabolic Equation (PE) simulations, or the high frequency based path-integral method. A physics based model that fully connects the wave-field statistics, and the internal wave spectrum, to the broadband statistics is not yet available. This paper uses the mode-based transport theory approach to predict the pressure field scattering at different frequencies, and from that the broadband statistics. This requires calculations for cross-modal correlations over mode number and frequency, which becomes computationally intensive for large bandwidths. This paper considers the adiabatic phase coherence to simplify the computations, and tests the final predictions against PE simulations and observations from the Philippine Sea 2010 experiment.

Plasma flows and sound-speed perturbations in the average supergranule

Context. Supergranules create a peak in the spatial spectrum of photospheric velocity features. Even though they have some properties of convection cells, their origin is still being debated in the literature. The time–distance helioseismology constitutes a method that is suitable for investigating the deep structure of supergranules. Aims. Our aim is to construct the model of the flows in the average supergranular cell using fully consistent time–distance inverse methodology. Methods. We used the Multi-Channel Subtractive Optimally Localised Averaging inversion method with regularisation of the cross-talk. We combined the difference and the mean travel-time averaging geometries. We applied this methodology to travel-time maps averaged over more than 104 individual supergranular cells. These cells were detected automatically in travel-time maps computed for 64 quiet days around the disc centre. The ensemble averaging method allows us to significantly improve the signal-to-noise ratio and to obtain a clear picture of the flows in the average supergranule. Results. We found near-surface divergent horizontal flows which quickly and monotonously weakened with depth; they became particularly weak at the depth of about 7 Mm, where they even apparently switched sign. The amplitude of the ‘reversed’ flow was comparable to the background flows. The inverted vertical flows and sound-speed perturbations were spoiled by unknown systematic errors. To learn about the vertical component, we integrated the continuity equation from the surface. The derived estimates of the vertical flow depicted a sub-surface increase from about 5 m s−1 at the surface to about 35 m s−1 at the depth of about 3 Mm followed by a monotonous decrease to greater depths. The vertical flow remained positive (an upflow) and became indistinguishable from the background at the depth of about 15 Mm. We further detected a systematic flow in the longitudinal direction. The course of this systematic flow with depth agrees well with the model of the solar rotation in the sub-surface layers.

Acoustic wave propagation through solar granulation: Validity of effective-medium theories, coda waves

Context. The frequencies, lifetimes, and eigenfunctions of solar acoustic waves are affected by turbulent convection, which is random in space and in time. Since the correlation time of solar granulation and the periods of acoustic waves (∼5 min) are similar, the medium in which the waves propagate cannot a priori be assumed to be time independent. Aims. We compare various effective-medium solutions with numerical solutions in order to identify the approximations that can be used in helioseismology. For the sake of simplicity, the medium is one dimensional. Methods. We consider the Keller approximation, the second-order Born approximation, and spatial homogenization to obtain theoretical values for the effective wave speed and attenuation (averaged over the realizations of the medium). Numerically, we computed the first and second statistical moments of the wave field over many thousands of realizations of the medium (finite-amplitude sound-speed perturbations are limited to a 30 Mm band and have a zero mean). Results. The effective wave speed is reduced for both the theories and the simulations. The attenuation of the coherent wave field and the wave speed are best described by the Keller theory. The numerical simulations reveal the presence of coda waves, trailing the ballistic wave packet. These late arrival waves are due to multiple scattering and are easily seen in the second moment of the wave field. Conclusions. We find that the effective wave speed can be calculated, numerically and theoretically, using a single snapshot of the random medium (frozen medium); however, the attenuation is underestimated in the frozen medium compared to the time-dependent medium. Multiple scattering cannot be ignored when modeling acoustic wave propagation through solar granulation.

Change in acoustic impulse response of a room due to a fire.

A room fire creates temperature gradients and inhomogeneous time varying temperature, density, and flow fields. Experimental measurements of the room acoustic impulse/frequency response are presented and compared with a ray traced model. The results show that the fire causes wave-fronts to arrive earlier (due to the higher sound speed) and with more variation in the delay times (due to the sound speed perturbations). The frequency response shows that the modes are shifted up in frequency and high frequency (>2500 Hz) modes are significantly attenuated. Model results are compared with data and show good agreement in observed trends.

A General Formulation for Computing Spherical Helioseismic Sensitivity Kernels while Incorporating Systematical Effects

Abstract As helioseismology matures and turns into a precision science, modeling finite-frequency, geometric, and systematical effects is becoming increasingly important. Here we introduce a general formulation for treating perturbations of arbitrary tensor rank in spherical geometry using fundamental ideas of quantum mechanics and their extensions in geophysics. We include line-of-sight projections and center-to-limb differences in line formation heights in our analysis. We demonstrate the technique by computing a travel-time sensitivity kernel for sound-speed perturbations. The analysis produces the spherical harmonic coefficients of the sensitivity kernels, which leads to better-posed and computationally efficient inverse problems.

Cross-Spectral Density Sensitivity Kernels in Surface Noise Field

The main factors affecting the spatial characteristics of surface noise fields are changes in sound speed and sea surface boundary perturbations due to mesoscale ocean phenomena and wind-induced noise, respectively. This study derived the surface noise cross-spectral density sensitivity kernel for sound speed changes and local boundary perturbations and analyzed their effects on cross-spectral density. Numerical results show that the sound speed perturbations of any position in the entire observation plane changes the surface noise cross-spectral density function in surface noise with finite frequency. The cross-spectral density between two receivers in the vertical direction is the most sensitive to the sound speed changes of the region between two receivers. Additionally, the influence depends on the relationship between the wavelength of sound wave and the distance of two receivers. Scattering on the surface boundary perturbation would lead to fluctuations in the cross-spectral density function. When the boundary perturbation along the horizontal direction is distant from two receivers, the cross-spectral density sensitivity kernel for surface scattering oscillates, and the influence of boundary perturbation on the cross-spectral density function gradually weakens. Finally, the period of the cross-spectral density sensitivity kernel oscillations is a half wavelength of the sound wave.