Double Beamforming Algorithm Research Articles

Surface perturbation inverted from angle variations of eigenbeams in an ultrasonic waveguide.

Ocean acoustic tomography is traditionally performed using the travel-time variations of an acoustic path between a source and a receiver. In the context of shallow-water tomography and multipath propagation, the different acoustic paths can be correctly identified if the source and the receiver are arrays of transducers. Here, a double-beamforming algorithm can be applied to extract a collection of eigenbeams from the raw acoustic dataset. In this study, four observables can be measured for each eigenbeam: the travel-time, the amplitude, and the emitting and receiving angles. In this study, the sensitivity kernel (SK) formulation is used to establish a quantitative relation between a perturbation of the surface of an ultrasonic waveguide and the emitting and receiving angles of each eigenbeam. This theoretical relation is experimentally demonstrated using a forward model experiment designed to measure the SK. The SK formulation is then used in a second experiment to quantitatively and dynamically image the propagation of a surface wave traveling across the surface of the waveguide. The inversion results show that the quality of the joint inversion of the emitting and receiving angles is higher than previous results based on amplitude or travel-time observables.

Dynamic imaging of a capillary-gravity wave in shallow water using amplitude variations of eigenbeams.

Dynamic acoustic imaging of a surface wave propagating at an air-water interface is a complex task that is investigated here at the laboratory scale through an ultrasonic experiment in a shallow water waveguide. Using a double beamforming algorithm between two source-receiver arrays, the authors isolate and identify each multi-reverberated eigenbeam that interacts with the air-water and bottom interfaces. The waveguide transfer matrix is recorded 100 times per second while a low-amplitude gravity wave is generated by laser-induced breakdown at the middle of the waveguide, just above the water surface. The controlled, and therefore repeatable, breakdown results in a blast wave that interacts with the air-water interface, which creates ripples at the surface that propagate in both directions. The amplitude perturbations of each ultrasonic eigenbeam are measured during the propagation of the gravity-capillary wave. Inversion of the surface deformation is performed from the amplitude variations of the eigenbeams using a diffraction-based sensitivity kernel approach. The accurate ultrasonic imaging of the displacement of the air-water interface is compared to simultaneous measurements with an optical camera, which provides independent validation.

Time-angle sensitivity kernels for sound-speed perturbations in a shallow ocean

Acoustic waves traveling in a shallow-water waveguide produce a set of multiple paths that can be characterized as a geometric approximation by their travel time (TT), direction of arrival (DOA), and direction of departure (DOD). This study introduces the use of the DOA and DOD as additional observables that can be combined to the classical TT to track sound-speed perturbations in an oceanic waveguide. To model the TT, DOA, and DOD variations induced by sound-speed perturbations, the three following steps are used: (1) In the first-order Born approximation, the Fréchet kernel provides a linear link between the signal fluctuations and the sound-speed perturbations; (2) a double-beamforming algorithm is used to transform the signal fluctuations received on two source-receiver arrays in the time, receiver-depth, and source-depth domain into the eigenray equivalent measured in the time, reception-angle and launch angle domain; and finally (3) the TT, DOA, and DOD variations are extracted from the double-beamformed signal variations through a first-order Taylor development. As a result, time-angle sensitivity kernels are defined and used to build a linear relationship between the observable variations and the sound-speed perturbations. This approach is validated with parabolic-equation simulations in a shallow-water ocean context.

Double multiple signal characterization active large band (D-MUSICAL) for extraction of observable in acoustic tomography

In the ocean, the acoustic propagation is characterized by different arrivals. Each arrival is characterized by its observables: amplitude, arrival time, emission, and reception angles. To achieve ocean acoustic tomography, a method to separate arrivals and extract observables has been developed. Two vertical arrays are used: a source and a receive array. Until now, the double-beamforming algorithm has been used to extract observables. It allows to go from the initial (time–source depth–receiver depth) domain to the beamformed domain (time–source angle–receive angle). This algorithm is efficient thanks to the 3-D domain of estimation but shows resolution limitation in the angle domain. To improve wave separation, we develop and apply a high-resolution algorithm based on MUSIC principle, in the same 3-D domain. The proposed method, called Double-MUSICAL, is the extension on the emission angle of the 2-D MUSIC Acitve Large band method (MUSICAL). Its principle is to separate the recording space onto the two orthogonal signal and noise spaces. We present results on real data recorded in an ultrasonic tank and show that the developed method better detects and separates the first arrivals than double beamforming.

Travel-time tomography in shallow water: Experimental demonstration at an ultrasonic scale

Acoustic tomography in a shallow ultrasonic waveguide is demonstrated at the laboratory scale between two source-receiver arrays. At a 1/1,000 scale, the waveguide represents a 1.1-km-long, 52-m-deep ocean acoustic channel in the kilohertz frequency range. Two coplanar arrays record the transfer matrix in the time domain of the waveguide between each pair of source-receiver transducers. A time-domain, double-beamforming algorithm is simultaneously performed on the source and receiver arrays that projects the multi-reflected acoustic echoes into an equivalent set of eigenrays, which are characterized by their travel times and their launch and arrival angles. Travel-time differences are measured for each eigenray every 0.1 s when a thermal plume is generated at a given location in the waveguide. Travel-time tomography inversion is then performed using two forward models based either on ray theory or on the diffraction-based sensitivity kernel. The spatially resolved range and depth inversion data confirm the feasibility of acoustic tomography in shallow water. Comparisons are made between inversion results at 1 and 3 MHz with the inversion procedure using ray theory or the finite-frequency approach. The influence of surface fluctuations at the air-water interface is shown and discussed in the framework of shallow-water ocean tomography.

Target detection and localization in shallow water: An experimental demonstration of the acoustic barrier problem at the laboratory scale

This study demonstrates experimentally at the laboratory scale the detection and localization of a wavelength-sized target in a shallow ultrasonic waveguide between two source-receiver arrays at 3 MHz. In the framework of the acoustic barrier problem, at the 1/1000 scale, the waveguide represents a 1.1-km-long, 52-m-deep ocean acoustic channel in the kilohertz frequency range. The two coplanar arrays record in the time-domain the transfer matrix of the waveguide between each pair of source-receiver transducers. Invoking the reciprocity principle, a time-domain double-beamforming algorithm is simultaneously performed on the source and receiver arrays. This array processing projects the multireverberated acoustic echoes into an equivalent set of eigenrays, which are defined by their launch and arrival angles. Comparison is made between the intensity of each eigenray without and with a target for detection in the waveguide. Localization is performed through tomography inversion of the acoustic impedance of the target, using all of the eigenrays extracted from double beamforming. The use of the diffraction-based sensitivity kernel for each eigenray provides both the localization and the signature of the target. Experimental results are shown in the presence of surface waves, and methodological issues are discussed for detection and localization.

Geoacoustic inversion with two source-receiver arrays in shallow water

A geoacoustic inversion scheme based on a double beamforming algorithm in shallow water is proposed and tested. Double beamforming allows identification of multi-reverberated eigenrays propagating between two vertical transducer arrays according to their emission and reception angles and arrival times. Analysis of eigenray intensities yields the bottom reflection coefficient as a function of angle of incidence. By fitting the experimental reflection coefficient with a theoretical prediction, values of the acoustic parameters of the waveguide bottom can be extracted. The procedure was initially tested in a small-scale tank experiment for a waveguide with a Plexiglas bottom. Inversion results for the speed of shear waves in Plexiglas are in good agreement with the table values. A similar analysis was applied to data collected during an at-sea experiment in shallow coastal waters of the Mediterranean. Bottom reflection coefficient was fitted with the theory in which bottom sediments are modeled as a multi-layered system. Retrieved bottom parameters are in quantitative agreement with those determined from a prior inversion scheme performed in the same area. The present study confirms the interest in processing source-receiver array data through the double beamforming algorithm, and indicates the potential for application of eigenray intensity analysis to geoacoustic inversion problems.

Geoacoustic inversion performed from two source‐receive arrays in shallow‐water waveguide.

Raylike propagation of acoustic waves in a shallow‐water waveguide between two vertical line arrays is investigated by applying a double beamforming algorithm, which performs time‐delay beamforming on both emitting and receiving arrays and allows identification of eigenrays by their emission and reception angles and arrival times. From the intensity of each eigenray, it is possible to determine reflection coefficient from the bottom of the waveguide as a function of an angle of incidence. The procedure was initially tested in a small‐scale tank experiment for an acoustic waveguide with either steel or Plexiglas bottom. By fitting an experimentally found reflection coefficient with a corresponding theoretical expression, an estimate for the speed of shear waves in the bottom material was obtained. Similar analysis was subsequently applied to the data obtained during an at‐sea experiment, which was performed between two vertical transducer arrays in shallow‐coastal waters of the Mediterranean. An angle‐dependent bottom reflection coefficient was extracted and geoacoustic inversion was performed by fitting the data with theoretical calculations, in which bottom sediments were modeled as a multilayered system. Good agreement between experiment and theory was observed. Our results indicate possible application of eigenray intensity analysis based on double beamforming algorithm for geoacoustic inversion problems.

Shallow-Water Acoustic Tomography Performed From a Double-Beamforming Algorithm: Simulation Results

Recent shallow-water experiments in sea channels have been performed using two vertical coplanar densely sampled source and receive arrays. Applying a double-beamforming algorithm on the two arrays both on synthetic numerical simulations and on experimental data sets, we extract efficiently source and receive angles as well as travel times for a large number of acoustic rays that propagate and bounce in the shallow-water waveguide. We then investigate how well sound-speed variations in the waveguide are reconstructed using a ray time-delay tomography based on a Bayesian inversion formulation. We introduce both data and model covariance matrices and we discuss on the synthetic numerical example how to choose the a priori information on the sound-speed covariance matrix. We attribute the partial sound-speed reconstruction to the ray-based tomography and we suggest that finite-frequency effects should be considered as the vertical and horizontal size of the Fresnel zone significantly spreads in the waveguide. Finally, the contribution of a different set of ray angles for tomography goal is also presented.

Detection and localization of a target in shallow water between two source-receive ultrasonic arrays: A small-scale experiment demonstration.

We experimentally demonstrate the detection and localization of a wavelength‐size target in a shallow ultrasonic waveguide between two source‐receive arrays. The waveguide represents a 1.5‐km‐long, 50‐m‐deep ocean acoustic channel at the 1/1000 scale, in which two coplanar arrays would record the broadband transfer matrix around 3 kHz. Invoking reciprocity principle, we perform a time‐domain double beamforming algorithm simultaneously on the source and receive array. This array processing projects the multi‐reverberated acoustic signals recorded between each source and each receiver into an equivalent set of eigenrays defined by their launch and receive angles. Comparison is made between the intensity of each eigenray with and without the target in the ultrasonic waveguide. When detection is achieved, localization is performed through the back projection of each eigenray into the acoustic waveguide weighted by the intensity fluctuation induced by the target. The use of the diffraction‐based sensitivity kernel for each eigenray improves the localization of the target. Detection and localization experimental results will be shown in the presence of surface waves for ultrasonic arrays at 1 and 3 MHz.

The structure of raylike arrivals in a shallow-water waveguide

Acoustic remote sensing of the oceans requires a detailed understanding of the acoustic forward problem. The results of a shallow-water transmission experiment between a vertical array of sources and a vertical array of receivers are reported. The source array is used to provide additional degrees of freedom to isolate and track raylike arrivals by beamforming over both source and receiver arrays. The coordinated source-receiver array processing procedure is presented and its effectiveness in an example of tracking raylike arrivals in a fluctuating ocean environment is shown. Many of these arrivals can be tracked over an hour or more and show slowly varying amplitude and phase. The use of a double-beamforming algorithm lays the foundation for shallow-water acoustic remote sensing using travel time and source and receive angles of selected eigenrays.

Ocean acoustic tomography using a double-beamforming algorithm

Since Munk and Wunsch proposed the basis for ocean acoustic tomography, many experiments have been performed to estimate sound speed fluctuations in the ocean, using ray identification and measurement of their travel times. However, technical limitations appeared such as the precision of the arrival time measurements or the number of ray arrivals that can be extracted from the signal. Recently, technical improvements allowed more complete experiments using two vertical arrays of sensors (source array and hydrophone array). In this configuration, the signals between each source and receiver are recorded which greatly improve the available information to identify the acoustic rays. One way to increase the number of rays in the tomography algorithm is to perform double-beamforming on the source and receive arrays. With double-beamforming, ray arrivals are separated by emission angle, reception angle and arrival time. Thus, we solve more ray arrivals than with a single beamforming or with a point-to-point approach. In order to avoid previous limitations and to explore acoustical limitations, we study two simple cases through the double-beamforming algorithm: with simulated data and with ultrasonic small-scale experimental data.