Source-receiver Arrays Research Articles

Modal formulation and paraxial approximation for acoustic wave propagation in waveguides with surface perturbations.

We propose a modal approach developed in the framework of the paraxial approximation to investigate the effects of deterministic surface perturbations in a planar waveguide. In the first part, the sensitivity of the modal amplitudes is theoretically formulated for a three-dimensional perturbation at the air-water interface. When applied to a broadband ultrasonic signal in a laboratory tank experiment, this approach results in travel-time and amplitude fluctuations that are successfully compared to experimental data recorded between two vertical source-receiver arrays that span the ultrasonic waveguide. The nonlinear shape of the modal amplitude fluctuations is of particular interest and is due to the three-dimensional nature of the surface perturbation. In the second part, a time-harmonic inversion method is built in the paraxial single-scattering approximation to image the dynamic surface perturbation from the modal transmission matrix between two source-receiver arrays. Again, the inversion results for capillary-gravity surface perturbations are successfully compared to similar inversions performed from experimental data processed with a complete set of eigenbeams extracted between the two arrays.

VELOCITY LAYERING IN THE MIDDLE BENUE TROUGH NIGERIA USING SEISMIC REFRACTION DATA

Seismic refraction data was acquired in the Middle Benue Trough which is located in the north central Nigeria with latitude 07.5-08.5oN and longitude 08.00-09.30oE. The aim was to find out how velocity vary in the near-surface layers in the area using seismic refraction data. The seismic survey was investigated at 14 acquisition stations. Two overlapping reversed profiles were shot into 14 stations. Each acquisition station was primed with 0.20kg dynamite loaded at 1.5m below the surface. The recording equipment was McSeis-160MXTM, and monitor record was processed with Microsoft Excel software to determine the velocities from both the forward and reversed shot-points. The results show two distinct layers cases. The thickness of the topmost layer varies between 2.75m and 5.45m with a mean of 4.1m. The velocity of this topmost layer varies between 399.0 ms-1 and 767.0ms-1 with a mean of 604.8ms-1. The velocity of the underlying layer (V1) varies between 1212.5ms-1 and 3257.0ms-1 with a mean of 1757.9ms-1. The velocity increases with depth into the subsurface. The results are useful in locating groundwater aquifer, and in the design of source-receiver arrays for reflection seismic.

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.

Dynamic imaging of a gravity wave caused by laser-induced breakdown in a fluid waveguide using multi-reverberated ultrasonic waves

The dynamic imaging of a gravity wave propagating at the air-water interface is a complex task that requires the sampling of every point at this interface during the gravity wave propagation. Using two source-receiver vertical arrays facing each other in a shallow water environment, we manage to isolate and identify each multi-reverberated eigenbeam that interacts with the air-water interface. The travel-time and amplitude variations of each eigenbeam are then measured during the crossing of the gravity wave. In this work, we present an ultrasonic experiment in a 1 m-long, 5 cm-deep waveguide at the laboratory scale. The waveguide transfer matrix is recorded 100 times per second at a sample rate of 1.1 MHz between two source-receiver arrays while a low-amplitude gravity wave is generated by a laser-induced breakdown at the middle of the waveguide above the water surface. The controlled and therefore repeatable breakdown causes a blast wave that interacts with the air-water interface and penetrates into the water, creating ripples at the surface that propagate in both directions. The surface deformation induced by these two wave packets is also measured by two cameras which allows for independent validation of the ultrasonic inversion. The ultrasonic inversion performed from a few thousand eigenbeams lead to accurate quantitative imaging of the dynamic of the air-water interface, using either the travel-time or the amplitude variation of the ultrasonic arrivals.

Dynamic imaging of a gravity wave caused by laser-induced breakdown in a fluid waveguide using acoustic waves

The dynamic imaging of a gravity wave propagating at the air-water interface is a complex task that requires the sampling of every point at this interface. Using two source-receiver vertical arrays facing each other in a shallow water environment, we manage to isolate and identify each multi-reverberated eigenray that interacts with the air-water interface. The travel-time and amplitude variations of each eigenray are then measured during the crossing of the gravity wave. In this work, we present an ultrasonic experiment in a 1 m-long, 5 cm-deep waveguide. At frequencies in the MHz range, the waveguide transfer matrix is recorded 100 times per second between two source-receiver arrays while a low-amplitude gravity wave is generated by a laser-induced breakdown above the water surface. The breakdown causes a blast wave that interacts with the air-water interface and penetrates into the water, creating ripples at the surface. This event is easily controlled and therefore repeatable. The inversion performed from a few thousand eigenrays leads to accurate imaging of the dynamic of the air-water interface, using either the travel-time or the amplitude variation.

Inverting for a deterministic surface gravity wave using the sensitivity-kernel approach.

The dynamic imaging of a deterministic gravity wave propagating at an air-water interface requires continuous sampling of every point at this interface. This sampling can be done acoustically using waves that propagate in the water column but have specular reflection points that fully scan the air-water interface. This study aims to perform this complex task experimentally, with identical ultrasonic source and receiver arrays that face each other in a 1-m-long, 5-cm-deep fluid waveguide, and with frequencies in the MHz range. The waveguide transfer matrix is recorded 100 times per second between the source-receiver arrays, while a gravity wave is generated at the air-water interface. Through the beamforming process, a large set of acoustic multi-reverberated beams are isolated and identified that interact with the air-water interface. The travel-time and amplitude modulations of each eigenbeam are measured when the surface gravity wave travels through the source-receiver plane. Linear inversion of the travel-time and amplitude perturbations is performed from a few thousand eigenbeams using diffraction-based sensitivity kernels. Inversion results using travel-times, amplitudes, or these two observables together, lead to accurate spatial-temporal patterns of the surface deformation. The advantages and limitations of the method are discussed.

Role of Scattering in Virtual Source Array Imaging

We consider imaging in a scattering medium where the illumination goes through this medium but there is also an auxiliary, passive receiver array that is near the object to be imaged. Instead of imaging with the source-receiver array on the far side of the object, we image with the data of the passive array on the near side of the object. The imaging is done with travel time migration using the cross correlations of the passive array data. We showed in [J. Garnier and G. Papanicolaou, Inverse Problems, 28 (2012), 075002] that if (i) the source array is infinite, (ii) the scattering medium is modeled by either an isotropic random medium in the paraxial regime or a randomly layered medium, and (iii) the medium between the auxiliary array and the object to be imaged is homogeneous, then imaging with cross correlations completely eliminates the effects of the random medium. It is as if we imaged with an active array, instead of a passive one, near the object. The purpose of this paper is to analyze the resolution of the image when both the source array and the passive receiver array are finite. We show with a detailed analysis that for isotropic random media in the paraxial regime, not only is imaging not affected by the inhomogeneities, but the resolution can in fact be enhanced. This is because the random medium can increase the diversity of the illumination. We also show analytically that this will not happen in a randomly layered medium, and there may be some loss of resolution in this case.

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.

Time-angle ocean acoustic tomography using sensitivity kernels: The forward problem

Broadband acoustic signals around 1 kHz propagate through shallow water oceanic waveguides of ~100 m in depth and ~2 km in range as multiple ray-like wavefronts. These acoustic arrivals can be characterized by the following observables: travel-time (TT), direction-of-arrival (DOA), and direction-of-departure (DOD). By applying double-beamforming on the point-to-point signals recorded between two source-receiver arrays, the acoustic contribution of each arrival can be separated from the multi-reverberated data and the TT, DOA, and DOD observable variations are accurately measured. This study deals with the use of time-angle sensitivity kernels (TASK) to estimate the observable variations induced by sound speed perturbations in the waveguide. This approach is based on the first order Born approximation and takes into account the finite-frequency effects associated with wave propagation. The robustness the TASK approach is analyzed and compared to numerical parabolic equation simulations involving different sound speed perturbations. For example, parameters such as the perturbation location, the value and shape of the perturbation in the waveguide are modified. The combination of several perturbations and the influence of the source-receiver array apertures on the TT, DOA, and DOD estimates are also studied.

Double beamforming processing in a seismic prospecting context

The use of larger numbers of sensors is becoming more common at the large, continental scale for deep-structure imaging in seismology, and at a smaller scale with exploration geophysics objectives. Seismic arrays require array processing from which new types of observables contribute to a better understanding of the wave propagation complexity. From among these array processing techniques, this study focuses on a way to select and identify different phases between two source-receiver arrays based on the double beamforming (DBF) method. At the exploration geophysics scale, the goal is to identify and separate low-amplitude body waves from high-amplitude dispersive surface waves. A synthetic data set from a finite-difference time-domain simulation is first used to validate the array processing method. From directional information obtained with DBF, and due to the double-plane wave projection, it is demonstrated that surface and body waves can be extracted with a higher efficacy compared to classical beamforming even at short offset. A seismic prospecting data set in a laterally heterogeneous medium is then investigated. This data set is a high-resolution survey which provides a perfect control on source and receiver arrays geometry. The separation between the direct surface and body waves is observed after DBF and ray bending is discussed from the additional azimuthal information.

Acoustical tomography in the shallow water ocean: Dream or reality?

Acoustical tomography in shallow waters relies on the identification and tracking of stable ray arrivals. The variation of the arrival time of these rays is used to solve the inverse problem and to estimate the physical properties as sound speed variations associated to internal waves or currents. In practice, however, technical difficulties appear (1) when the number of resolved eigenrays in this multipath environment is too small using a set of point-to-point recordings or (2) when the travel-time fluctuations are dominated by the fast-evolving surface that blur the slower internal-wave driven perturbations around the thermoclyne. Recent experimental studies based on laboratory-scaled demonstrators showed the efficiency of array processing algorithms in combination with source-receiver arrays to tackle issue (1) above. Depending on the waveguide geometry, the acquisition procedure can also be adjusted to provide a separation between the slow and fast travel-time fluctuations. Inversion results based on laboratory experiments are presented that focus on the dynamics of (1) a gravity wave at the air-water interface and (2) a thermal plume in the water column. Finally, these results are discussed in the framework of ocean acoustic research.

Analyzing sound speed fluctuations in shallow water from group-velocity versus phase-velocity data representation

Data collected over more than eight consecutive hours between two source-receiver arrays in a shallow water environment are analyzed through the physics of the waveguide invariant. In particular, the use of vertical arrays on both the source and receiver sides provides source and receiver angles in addition to travel-times associated with a set of eigenray paths in the waveguide. From the travel-times and the source-receiver angles, the eigenrays are projected into a group-velocity versus phase-velocity (Vg-Vp) plot for each acquisition. The time evolution of the Vg-Vp representation over the 8.5-h long experiment is discussed. Group speed fluctuations observed for a set of eigenrays with turning points at different depths in the water column are compared to the Brunt-Väisälä frequency.

Automated Data Fusion and Visualization for Impact-Echo Testing of Concrete Structures

An automated data fusion and visualization process is developed for nondestructive evaluation and direct visualization of internal defects of concrete structures based on impact-echo testing using source-receiver arrays. In the process, the ratio between the amplitudes of major echo peaks in the frequency spectrum (after noise reduction) and the bottom echo signal is proposed as a feature parameter for data fusion. The fused results then go through image segmentation, which combines thresholding and region growing to extract defect regions for visualization. The effectiveness of the automated data fusion and visualization process is validated using both numerical simulation and experimental testing.

Multisensor data fusion for impact-echo testing of concrete structures

Based on the investigation of spatial variations of impact-echo signals for different source and receiver locations, a simple multisensor data fusion strategy is proposed to increase the accuracy of nondestructive evaluation of concrete structures using the impact-echo test. The data fusion strategy fuses the ratios between spectral amplitudes of the delamination and concrete bottom echo signals (D/B ratios) from multiple source–receiver arrays. The fused D/B ratios demonstrate different characteristics for test locations above the delamination, above the sound concrete, and across the delamination boundary. These characteristics can be used to accurately locate the delamination and its boundaries without increasing testing time. The applicability of the multisensor data fusion for impact-echo testing is validated using both numerical simulation and experimental testings.

Inversion of ocean environmental variations via time-reversal acoustics

Time-reversal (TR) processing is derived from the invariance of the wave equation for a lossless medium to change of the sign of the time variable. By retransmitting the TR version of the time-dispersed received signal propagated from a probe source (PS) to a source–receiver array (SRA), one can reacquire the probing pulse at the PS location (time compression and spatial focusing) when the waveguide environment is time invariant. However, if some environmental variations occur between the two transmissions, the retrofocusing signal will be defocused. This paper presents an inversion method of ocean environmental variations, which exploits the focusing/defocusing effect measured at the PS location in the presence of environmental perturbations between the PS transmission and the SRA retransmission. Specifically, inversion of the sound speed profile represented in terms of the empirical orthogonal functions is developed. Examples of the method applied to synthetic data are provided to demonstrate the method’s feasibility.

Group speed versus phase speed analysis of sound speed fluctuations in a shallow water ocean

Data collected during eight consecutive hours between two source-receiver arrays in a shallow water environment (Roux et al, J. Acoust. Soc. Am. 124, 3430-3439, 2008) are analyzed using the physics associated with the waveguide invariant. In particular, the use of vertical arrays on both the source and receiver sides provide launch and receive angles in addition to the travel times associated with each eigenray path in the waveguide. From travel times and source-receiver angles, each eigenray amplitude is projected into group velocity-phase velocity (vg-vp) space for each acquisition. The time evolution of the vg-vp representation during the 8-hour long experiment is discussed. Group speed fluctuations observed for a set of eigenrays with upper turning points at or near the thermocline are compared to independent sound speed measurements obtained by a CTD chain at two locations in the area.

Spatial room acoustics descriptors from a concentric source-receiver array: potential applications for auditoria

Electroacoustic transducer arrays, both microphones and loudspeakers, are emerging as promising tools for measuring and evaluating room acoustics – accounting for source directivity and the angular distribution of the received room reflections over time. This study examines the potential of a concentric source-receiver array for characterizing the spatial response of rooms. Using this concept, the acoustic response at a point in a room is represented by a matrix of impulse responses comprising the combined spherical harmonic series for source and receiver. The spatial analysis of this matrix yields the spatial room response for a source of arbitrary directivity and orientation (limited by the spherical harmonic order implemented). The reduction of such data to parameters can be approached in many ways, and this paper considers the mean and standard deviation of diffusivity index for an nth order cardioid source. Measurements from a prototype transducer are presented. In auditoria, this approach could be well suited to the evaluation of acoustic conditions on stage, and should be especially relevant to describing the effect of acoustics on solo performance.

Dynamic tomography of a gravity wave at the interface of an ultrasonic fluid waveguide

Based on single-scattering effects, the diffraction-based sensitivity kernels which make the link between the acoustic perturbations and the medium fluctuations have been extensively studied. This research has been recently extended to perturbations at the air–water interface in an ultrasonic waveguide that scales down with a 1-km-long, 50-m-deep ocean acoustic channel in the kilohertz regime. Using array processing between two source-receiver arrays, the sensitivity kernel for both time and amplitude has been experimentally measured and theoretically calculated for each acoustic echo reverberated in the waveguide in response to a small and local surface elevation. In the present work, an ultrasonic experiment is performed during which the waveguide transfer matrix between the source-receiver arrays is recorded 50 times per second while a low-amplitude gravity wave is generated at the water–air interface. The acoustic inversion performed from the surface sensitivity kernels permits to follow the gravity wave dynamics at any point of the surface between the source and the receiver arrays.

Perspective of tomography inversion using direction-of-arrival and direction-of-departure

In the ocean, local sound speed variations induce acoustic path changes. Travel-time (TT) variations of acoustic paths are classically used to perform ocean tomography inversion. Initially introduced to cope with multi-arrival interferences and to separate eigenray paths, source–receiver arrays combined with array processing techniques now give access to new observables that could be used for tomography such as direction-of-arrivals (DOAs) and direction of departure (DOD). The cumulative use of TT, DOA, and DOD in the inversion process first requires to study the forward problem which links sound speed variations to these observables measured through array processing from two source–receiver arrays. The so-called sensitivity kernels are established using (1) the first order Born approximation that relates the sound speed variation to the amplitude and phase change of the perturbed received signal and (2) a first order Taylor development which links the received signal perturbations to the relevant observables. In the present work, theoretical TT, DOA, and DOD sensitivity kernels are compared with parabolic equation simulations and tank experiment estimations.

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.