The quintessential goal of sensor array signal processing is the estimation of parameters by fusing temporal and spatial information, captured via sampling a wavefield with a set of judiciously placed antenna sensors. The wavefield is assumed to be generated by a finite number of emitters, and contains information about signal parameters characterizing the emitters. A review of the area of array processing is given. The focus is on parameter estimation methods, and many relevant problems are only briefly mentioned. We emphasize the relatively more recent subspace-based methods in relation to beamforming. The article consists of background material and of the basic problem formulation. Then we introduce spectral-based algorithmic solutions to the signal parameter estimation problem. We contrast these suboptimal solutions to parametric methods. Techniques derived from maximum likelihood principles as well as geometric arguments are covered. Later, a number of more specialized research topics are briefly reviewed. Then, we look at a number of real-world problems for which sensor array processing methods have been applied. We also include an example with real experimental data involving closely spaced emitters and highly correlated signals, as well as a manufacturing application example.

Two decades of array signal processing research: the parametric approach

Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.

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The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media

Cross-correlation of 1 month of ambient seismic noise recorded at USArray stations in California yields hundreds of short-period surface-wave group-speed measurements on interstation paths. We used these measurements to construct tomographic images of the principal geological units of California, with low-speed anomalies corresponding to the main sedimentary basins and high-speed anomalies corresponding to the igneous cores of the major mountain ranges. This method can improve the resolution and fidelity of crustal images obtained from surface-wave analyses.

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High-resolution surface-wave tomography from ambient seismic noise.

SUMMARY Ambient noise tomography is a rapidly emerging field of seismological research. This paper presents the current status of ambient noise data processing as it has developed over the past several years and is intended to explain and justify this development through salient examples. The ambient noise data processing procedure divides into four principal phases: (1) single station data preparation, (2) cross-correlation and temporal stacking, (3) measurement of dispersion curves (performed with frequency‐time analysis for both group and phase speeds) and (4) quality control, including error analysis and selection of the acceptable measurements. The procedures that are described herein have been designed not only to deliver reliable measurements, but to be flexible, applicable to a wide variety of observational settings, as well as being fully automated. For an automated data processing procedure, data quality control measures are particularly important to identify and reject bad measurements and compute quality assurance statistics for the accepted measurements. The principal metric on which to base a judgment of quality is stability, the robustness of the measurement to perturbations in the conditions under which it is obtained. Temporal repeatability, in particular, is a significant indicator of reliability and is elevated to a high position in our assessment, as we equate seasonal repeatability with measurement uncertainty. Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.

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Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements

Acoustic propagation is characterized by three major factors: attenuation that increases with signal frequency, time-varying multipath propagation, and low speed of sound (1500 m/s). The background noise, although often characterized as Gaussian, is not white, but has a decaying power spectral density. The channel capacity depends on the distance, and may be extremely limited. Because acoustic propagation is best supported at low frequencies, although the total available bandwidth may be low, an acoustic communication system is inherently wideband in the sense that the bandwidth is not negligible with respect to its center frequency. The channel can have a sparse impulse response, where each physical path acts as a time-varying low-pass filter, and motion introduces additional Doppler spreading and shifting. Surface waves, internal turbulence, fluctuations in the sound speed, and other small-scale phenomena contribute to random signal variations. At this time, there are no standardized models for the acoustic channel fading, and experimental measurements are often made to assess the statistical properties of the channel in particular deployment sites.

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Underwater acoustic communication channels: Propagation models and statistical characterization

Senior level/graduate level text/reference presenting state-of-the- art numerical techniques to solve the wave equation in heterogeneous fluid-solid media. Numerical models have become standard research tools in acoustic laboratories, and thus computational acoustics is becoming an increasingly important branch of ocean acoustic science. The first edition of this successful book, written by the recognized leaders of the field, was the first to present a comprehensive and modern introduction to computational ocean acoustics accessible to students. This revision, with 100 additional pages, completely updates the material in the first edition and includes new models based on current research. It includes problems and solutions in every chapter, making the book more useful in teaching (the first edition had a separate solutions manual). The book is intended for graduate and advanced undergraduate students of acoustics, geology and geophysics, applied mathematics, ocean engineering or as a reference in computational methods courses, as well as professionals in these fields, particularly those working in government (especially Navy) and industry labs engaged in the development or use of propagating models.

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Computational Ocean Acoustics

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A short historical overview of matched-field processing (MFP) is followed by background material in both ocean acoustics and array processing needed for MFP. Specific algorithms involving both quadratic and adaptive methods are then introduced. The results of mismatch studies and several algorithms designed to be relatively robust against mismatch are discussed. The use of simulated MFP for range, depth and bearing location is examined, using data from a towed array that has been tilted to produce an effective vertical aperture. Several experiments using MFP are reviewed. One successfully demonstrated MFP at megameter ranges; this has important consequences for experiments in global tomography. Some unique applications of MFP, including how it can exploit ocean inhomogeneities and make tomographic measurements of environmental parameters, are considered. >

An overview of matched field methods in ocean acoustics

An experiment conducted in the Mediterranean Sea in April 1996 demonstrated that a time-reversal mirror (or phase conjugate array) can be implemented to spatially and temporally refocus an incident acoustic field back to its origin. The experiment utilized a vertical source–receiver array (SRA) spanning 77 m of a 125-m water column with 20 sources and receivers and a single source/receiver transponder (SRT) colocated in range with another vertical receive array (VRA) of 46 elements spanning 90 m of a 145-m water column located 6.3 km from the SRA. Phase conjugation was implemented by transmitting a 50-ms pulse from the SRT to the SRA, digitizing the received signal and retransmitting the time reversed signals from all the sources of the SRA. The retransmitted signal then was received at the VRA. An assortment of runs was made to examine the structure of the focal point region and the temporal stability of the process. The phase conjugation process was extremely robust and stable, and the experimental results were consistent with theory.

Phase conjugation in the ocean: Experimental demonstration of an acoustic time-reversal mirror

[1] It has been demonstrated experimentally and theoretically that an estimate of the Green's function between two seismic stations can be obtained from the time-derivative of the long-time average cross correlation of ambient noise between these two stations. This TDGF estimate from just the noise field includes all tensor components of the Green's function and these Green's function estimates can be used to infer Earth structure. We have computed cross correlations using 1 to 30 continuous days of ambient noise recorded by over 150 broadband seismic stations located in Southern California. The data processing yielded thousands of cross-correlation pairs, for receiver separations from 4–500 km, which clearly exhibit coherent broadband propagating dispersive wavetrains across frequency band 0.1–2 Hz.

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William A. Kuperman

Papers

Computational Ocean Acoustics

Computational Ocean Acoustics

An overview of matched field methods in ocean acoustics

Phase conjugation in the ocean: Experimental demonstration of an acoustic time-reversal mirror

Extracting time-domain Green's function estimates from ambient seismic noise