Modal Attenuation Coefficients Research Articles

Perturbations of Modal Attenuation Coefficients and Group Velocities due to Depth Variations along a Shallow-Water Acoustic Track

Perturbations of Modal Attenuation Coefficients and Group Velocities due to Depth Variations along a Shallow-Water Acoustic Track

Impact of Three Solar Eclipses of 2019–2020 on the D‐Region Ionosphere Observed From a Subtropical Low‐Latitude VLF Radio Station

AbstractIonospheric impact of three solar eclipses (January 2019, December 2019, and June 2020) observed by Very Low Frequency (VLF) radio signals from a single receiver at a subtropical low‐latitude station in India is presented here. Perturbations in signal amplitudes of VLF transmitters such as the VTX (18.2 kHz), NWC (19.8 kHz), JJI (22.2 kHz), and DHO (23.4 kHz) are analyzed. Both positive, negative, and also mixed‐type of amplitude deviations are observed which are explained based on the solar eclipse obscuration profiles over the entire propagation paths. The difference in observed amplitude deviations for a VLF signal during the different solar eclipses are reproduced using the Long Wave Propagation Capability code and solar obscuration profile. Particularly, the effects of two solar eclipses on the VLF signal propagation characteristics have been analyzed. The modal attenuation coefficients of the VTX signal in the earth‐ionosphere waveguide are decreased with the increase of solar obscuration. A negative linear relationship of VLF signal attenuation with solar obscuration has been found for the first time during the solar eclipse. The relations are almost similar for the two solar eclipses of December 2019 and June 2020. Further, the percentage reduction of the D‐region electron density profiles as a function of altitude and solar obscuration during the two solar eclipses is presented.

Weighted subspace detection method based on modal attenuation law in shallow water

In this paper, the modal space detector (MSD) is investigated in shallow water environment when utilizing a vertical linear array. The processing gain of the MSD is derived, and the result demonstrates that the processing gain of the MSD degrades when the number of the propagated normal modes excited by the underwater acoustic source increases, and therefore the detection performance of the MSD decreases. By exploiting the orthogonality among the modal depth functions, the MSD can be decomposed into a group of modal subspace detectors (MSSDs). The processing gains of these MSSDs are derived as well and it is found out that the processing gain of a MSSD is in direct proportion to its corresponding modal attenuation coefficients. By designing a group of weighting coefficients based on the mode attenuation law, a weighted modal subspace detector (WMSSD) is proposed to alleviate the degradation of the processing gain processing of the MSD. We analyze the influences of acoustic source locations and sound velocity profiles (SVPs) on the detection performance of the WMSSD theoretically, and verify the theoretical analyses by comparing its processing gain with the MSD in simulation experiments. The results show that the WMSSD presents various processing gains versus different acoustic source locations. In the waveguide having a negatively-gradient SVP, there exists a ‘weak detection area’ for the WMSSD, that is, the processing gain of the WMSSD is smaller than that of the MSD when the acoustic source locations are close to sea surface. The reason is because there are inversion points on the lower-order modal depth functions and the depths of the inversion points are close to sea surface. In other most areas, the processing gain of the WMSSD is larger (even remarkably larger) than that of the MSD. In the waveguide having a positively-gradient SVP, due to the phenomenon that the modal inversion points of the lower-order modal depth functions are near sea floor, there is a contrary consequence, that is, the ‘weak detection area’ is close to sea floor. And meanwhile the WMSSD outperforms the MSD in other most areas as well. There are no modal inversion points in the waveguide having a constant SVP, and therefore the WMSSD always outperforms the MSD.

Measurements of modal attenuation using broadband sources in the New England Mud Patch

Measurements of underwater acoustic signals were made on a bottom-mounted horizontal line array during the Seabed Characterization Experiment (SCEx) in the New England Mud Patch south of Martha’s Vineyard in about 70 meters of water. The signals were generated by SUS (Signals, Underwater Sound) charges detonated at various locations in the experimental area at a depth of 18 m, during nearly-isovelocity conditions. The broadband signals were analyzed for modal arrival time and amplitude using time-frequency techniques. Ratios of modal amplitudes at the different hydrophones were used to estimate the modal attenuation coefficients. Hence, these estimates are independent of any uncertainty in the frequency-dependent source level of the SUS charges. These coefficients are directly related to the depth-dependent sediment attenuation profile. A sensitivity study was performed to understand how the modes sample the different layers and provides estimates of resolution kernels. Posteriori error analysis provides averages and standard deviations for the estimate of sediment attenuation as function of depth. The frequency bands of interest range from 10 Hz to 200 Hz for modes 1 to 4. We will compare our estimates of sediment attenuation with historical measurements. [Work supported by Office of Naval Research.]

Estimation of gassy layer parameters in shallow water sediment using low frequency ship noise

Sound speed in gassy sediments can reach very low values (~100 m/s) which provides high reflection coefficient for not very low frequencies (above a few tens of Hz) and specific properties of frequency dependence in the sound reflection/propagation phenomena in shallow water which allows us to estimate parameters of gassy layer (thickness and gas concentration). In the present study, shipping noise is used for estimation of mentioned parameters in Lake Kinneret (Israel). The sound noise from R/V “Hermona” was recorded at a vertical line array, moored in the lake. R/V was moving toward VLA at the speed ~4 m/s along 37 m isobath. Fourier components of the noise in the band 22–76 Hz were identified and analyzed. Mode selection was implemented to determine the mode amplitude as a function of range to the source for up to 4 normal modes. Matching mode attenuation coefficients with modeled ones for several frequencies, the thickness of the gassy layer and bubble concentration were estimated. The obtained values (thickness ~40 cm and gas content ~0.25%) correlate well with the results of direct measurements using X ray CT for cores. [This work was supported by RFBR 16-32-60194.]

Anelasticity beneath the Aegean inferred from Rayleigh wave attenuation

Anelasticity of the Earth crucially affects the propagation of seismic waves especially, in the long period range. However, even though the elastic properties of the Aegean deep lithosphère and upper mantle have been thoroughly investigated, their quantitative anelastic properties that influence the long period wavefield are still largely unknown. This work is towards contributing to the better knowledge of the deep structure of the Aegean by introducing experimental anelastic parameters via the study of long period Rayleigh waves attenuation. For this scope, fundamental mode attenuation coefficients (γ%) have been obtained for different two-station great-circle paths across the Aegean. The data used were provided by a broadband array installed in the area for 6 months in 1997. More than 1100 seismograms were analyzed in the 10-100 s range to obtain 17 sets of path average γR(T) functions. The attenuation coefficients are in the range 2.5*10~3 — 0.15 x 10' km' and correlate sufficiently with both experimental measurements in active tectonic regions elsewhere and synthetics generated with the use of an attenuation reference model inferred from other sources. By applying a stochastic uncoupled causal inversion method an average joint Qß'1 and shear velocity model representative of the under study area was obtained. Furthermore, path average JR(T) functions were combined in a continuous regionalization tomographic scheme to obtain local yR(T) and tomograms were constructed in the range 10-60 s. The most prominent feature in the tomograms is a high attenuation region in the central and north Aegean. This region is located south of the North Anatolian Trough and correlates well with a low shear velocity zone inferred from surface wave phase velocities. Moreover, it is associated with observed intense extensional deformation rates, mantle olivine anisotropy, recent volcanism and high heat flow.

Variable Mode Excitation Ratio Method for Measuring Attenuation Coefficients of LP Mode Groups

We propose a variable mode excitation ratio method for measuring the attenuation coefficients of individual transmission modes in few-mode fiber (FMF). The experimental results we obtained with 2LP mode fiber agree well with those measured by the conventional mode-selective launching method and the optical time domain reflectometer (OTDR) method. We also show that the proposed method can be applied to an FMF with more than two mode groups by measuring the transmitted power property under various mode excitation ratios with a multiple mode group combination. Finally, we reveal that our method can provide an accurate modal attenuation coefficient even if we cannot use a mode multiplexer with a sufficient mode extinction ratio.

Estimating the parameter sensitivity of acoustic mode quantities for an idealized shelf-slope front.

The acoustic modes of an idealized three-dimensional model for a curved shelf-slope ocean front [Lin and Lynch, J. Acoust. Soc. Am. 131, EL1-EL7 (2012)] is examined analytically and numerically. The goal is to quantify the influence of environmental and acoustic parameters on acoustic field metrics. This goal is achieved by using conserved quantities of the model, including the dispersion relation and a conservation of mode number. Analytic expressions for the horizontal wave numbers can be extracted by asymptotic approximations and perturbations, leading to accurate and convenient approximations for their parameter dependence. These equations provide the dependence on model parameter changes of both the real horizontal wavenumbers, leading to modal phase speeds and other metrics, and the imaginary parts, leading to modal attenuation coefficients. Further approximations for small parameter changes of these equations characterize the parameter sensitivities and produce assessments of environmental and acoustic influences.

Estimation of Rayleigh wave modal attenuation from near-field seismic data using sparse signal reconstructions

This study is related to the application of sparse signal reconstruction in estimation of Rayleigh-wave modal attenuation coefficients from near-field multichannel seismic data. A two-step approach was proposed. At the first step, the Rayleigh-wave modes are resolved and their phase velocities are estimated by a reconstruction of signal that is represented to be sparse in terms of wave velocity. At the second step, this time the signal is represented to be sparse in terms of attenuation parameter and then recovered optimally from the measurement equation that includes the modal phase velocities estimated above. The attenuation values corresponding to the dominant peak components of the estimated sparse signal vector are chosen as modal attenuation coefficients. Results from synthetic and real-field data show the high performance of proposed approach overcoming noise and the adverse near-field effects.

Sound speed and attenuation in muddy sediments from low-frequency acoustic measurements

While there have been numerous theoretical and experimental studies on the properties of marine granular sands, there are significantly fewer studies on sediments classified as muds. The validity of geoacoustic models for muddy sediments has not been successfully tested due to the lack of inverted low-frequency sound speed and attenuation from acoustic measurements. The ONR-sponsored Seabed Characterization Experiment (SBCE), conducted in a mud patch on the New England continental shelf in the spring of 2017, provides an opportunity to make substantial improvements in understanding the physical mechanisms controlling sound propagation in muddy sediments. Acoustic signals (e.g., 31g explosive and combustive source signals) detonated at various ranges, depths and azimuths were measured in SBCE. This paper utilizes these measured signals to extract the acoustic normal mode characteristics including modal dispersive curve with Airy phase structure, modal amplitude, modal attenuation coefficient, and mode depth function. These normal mode characteristics are used in geo-acoustic inversion algorithms to estimate low-frequency sound speed and attenuation in muddy sediments as a function of frequency. The performance of different inversion methods using different normal mode characteristics is discussed. [Work supported by ONR Ocean Acoustics.]

Sound focusing in shallow water using a vertical phased array

Vertical phased array is an efficient and complex equipment in underwater acoustics. Single-mode excitation and time-reversal sound focusing are two typical techniques based on vertical phased array, but both of them have some shortcomings. In order to realize sound focusing at variable distance and depth using vertical phased array, two techniques are proposed in this paper. One of them is the Green's function construction of target sound field based on normal mode eigen-function and attenuation coefficient extraction, and the other is controllable sound focusing based on optimal target sound field determination. Simulation and experiment results are presented. This technique indicates a method for objective depth detecting in shallow water.

Estimation of geoacoustic model parameters from modal amplitude information

This paper analyzes an approach for estimating geoacoustic model parameters from information contained in normal modes of a broadband signal. Propagating modes are resolved by time-warping deconvolved signals from light bulb sound sources deployed at short ranges in shallow water. Amplitudes of the resolved modes contain information about sediment sound attenuation through the modal attenuation coefficient. However, the coefficient also depends on the sediment sound speed and density. A sequential inversion approach was developed that enables effective use of modal amplitudes to estimate sound attenuation in sediments. The inversion is based on a sequential Bayesian approach applied to features of resolved modal data that are highly sensitive to specific geoacoustic model parameters. Travel times of modal frequency components are inverted first for sediment sound speed and sediment layer thickness, and these estimates are used in subsequent stages. The effects of errors in estimates from previous stages a...

Seabed attenuation inversion from broadband reverberation measurements in the Yellow Sea

The Yellow Sea 1996 experiment was the first joint China-U.S. shallow water experiment conducted in August, 1996. The water depth is 75 m with a deviation of ±1 m at the experimental area. The seabed sound speed and attenuation in this experiment have been successfully estimated using the sound propagation measurements [Wan, Zhou, and Rogers, J. Acoust. Soc. Am. 128(2), 2010]. During this experiment, the monostatic reverberation data produced by 1-kg TNT shots provide a spatial sampling of the acoustic field and contains the information of seabed acoustic properties. Thus, the present paper uses the inverted seabed sound speed from the aforementioned propagation measurements as a constraint condition and analyzes the reverberation data for seabed attenuation inversion. The broadband normal mode filter is applied to the reverberation data received by a 32-element vertical line array. The reverberation level of the first three modes is obtained as a function of range to extract the modal attenuation coefficients. The seabed attenuation is inferred by minimizing the difference between the theoretical and measured modal attenuation coefficients. The inverted seabed attenuation over a frequency range of 400–1000 Hz shows non-linear frequency dependence.

Spectrum of sound intensity fluctuations due to mode coupling in the presence of moving nonlinear internal waves and bottom parameters estimation

Temporal fluctuations of intensity of sound pulses (300±30 Hz) are studied in the presence of nonlinear internal waves (NIW) moving at the some angle with direction of an acoustic track providing mode coupling. In the episode of Shallow Water 2006 experiment, considered in the work, angle between wave front of NIW and source-receiver direction is about 10 degrees. It was shown that there is main maximum in the spectrum measured at fixed depth ~8 cph and set of smaller peaks ( ~15 cph, ~25 cph, and ~35 cph) in accordance with the theory proposed by authors earlier. Besides, there is maximum in the spectrum of total intensity (summarized over depth or over all hydrophones of vertical line array) at the frequency ~15 cph. In authors opinion, the last one is determined by coupling of propagating modes (excited by the source) having maximal difference in modal attenuation coefficients (in given case modes 2 and 4). Role of horizontal refraction is small. Using the spectrum speed of NIW and bottom attenuation coefficient (in our case ~0.2 dB/wavelength) are determined. Mentioned parameters are in a good agreement with estimations obtained by other methods. [Work was supported by BSF.]

Joint estimation of modal attenuation and velocity from multichannel surface wave data

We evaluated a method for the simultaneous analysis of velocity and attenuation of multichannel surface wave data. It allowed us to estimate the phase velocity and attenuation curves using an array of receivers, possibly unevenly spaced, and a set of multiple shots at different locations. After reviewing the properties of surface waves in dissipative media, the estimation algorithm was evaluated. It was based on the estimation of the complex wavenumber of multiple normal modes. It can be considered as a high-resolution subspace-based method able to deal with irregularly sampled multichannel-multishot data. The interference between multiple modes was considered without the need of a prior specific multimode Rayleigh spreading function, so that multiple modal attenuation curves can be extracted. The validity of the approach was tested using synthetic data, with small and large mode interference, as well as with multimode real data. The benefits and the robustness of the proposed method were particularly relevant with data with multiple modes. The possibility of considering multiple shot points into a receiver array allowed the increase of the modal resolution without increasing the receiver aperture, thus without compromising the lateral resolution. The estimation of the modal attenuation coefficient enabled the estimation of the subsurface material damping ratio, and the definition of a dissipative propagation model.

Acoustic calibration of the signal propagation path in the shallow water

The propagation of low-frequency pulsed frequency-modulated signals in the shallow water (80m deep) is analyzed. The characteristics of the first five modes in the frequency range from 25 to 155 Hz are found by the correlation analysis of signal spectra. The group velocities and mode attenuation coefficients are used to reconstruct the acoustic characteristics of the sea bottom. A model of the sea bottom is developed, which allows one to formulate the model of transfer function along the signal propagation path.

Determination of leaky Lamb wave modal attenuation coefficient on a solid plate

Leaky Lamb wave is practically important in an immersion technique of nondestructive evaluation for a solid plate. It is necessary to determine its modal attenuation coefficient in order to evaluate plate defects in industry and to diagnose osteoporosis in medical applications. In this study we present a method to determine the modal attenuation coefficient of leaky Lamb wave using two-dimensional Fourier filtering. A complex leaky Lamb wave signal from a solid plate can be decomposed into several modal signals on frequency-space domain through two-dimensional Fourier filtering. It makes possible to experimentally determine the modal attenuation coefficient along an aluminum plate in water. It is well explained by theoretical estimation with the dispersion relation of leaky Lamb wave.

Constraining the kinetics of mantle phase changes with seismic data

In a system where two phases coexist, a seismic wave can disrupt the pre-existing equilibrium and induce a re-equilibration process. Because the kinetics of the phase change is not instantaneous, the transformation induces an attenuation of the wave that can be quantified using an appropriate physical theory. Kinetics of Earth′s phase transitions are not well known: in this paper we show that they can be constrained by seismic attenuation data. We quantify the influence of a phase transition upon seismic mode attenuation and body wave reflexion coefficient. We perform a numerical application for the olivine to wadsleyite transition at 410 km depth, assuming a phase loop thickness of 10 km. We show that the relaxation time that controls the frequency band of attenuation and the velocity at which the interface evolves when submitted to a pressure disequilibrium, is likely larger than 7000 s. For this kinetics slower than typical seismic waves periods, the transformation loop does not affect S waves attenuation but potentially that of P waves and normal modes.

Averaged transmission loss expressions in shallow water waveguides with sandy‐silty sediments.

Relatively simple approximations for transmission loss in shallow water based on ray theory were presented by Marsh and Schulkin (1962), Weston (1971), Smith (1974), and Rogers (1981). Formulas for averaged transmission loss versus range in stratified shallow water waveguides over sandy‐silty sediments are derived entirely from mode theory. Results are contrasted with other mode based expressions obtained by Brekhovskikh (1960) and Grachev (1983). Convenient expressions for loss in Pekeris waveguides are developed by approximating the mode number dependence of the attenuation coefficients as quadratic, which is valid in Westons’s mode stripping region. Similar loss expressions for environments with downward refracting linear sound speed profiles are constructed using modal attenuation coefficient approximations for the “limiting mode” of Denham (1969). This quantity illustrates how changes in environmental parameters, particularly thermocline strength and depth, produce corresponding changes in averaged transmission loss. The loss formulas have several terms, each having a natural physical interpretation, and each is compared with the well known results of Rogers from ray theory. The corresponding expressions have the same parameter dependence, thereby providing a modal foundation for Rogers’s formulas. [Work partially supported by the ONR.]

Relation of sound absorption and shallow water modal attenuation to plane wave attenuation

Prediction of attenuation of acoustic fields in weakly absorbing media often uses the substitution of (omega/c)-->(omega/c)+ialpha(pw) into the idealized equations for constant frequency, with alpha(pw) representing the local plane wave attenuation coefficient. This assumption is flawed whenever the local absorption of sound is proportional to the square of the gradient of the acoustic pressure, as is the case when the absorption is caused by fluid velocity relaxation. A realistic analysis yields an improved weighting function over depth for determination of guided mode attenuation coefficients.