Coherent Arrivals Research Articles

Joint Inversion of Receiver Functions and Apparent Incidence Angles to Determine the Crustal Structure of Mars

AbstractRecent estimates of the crustal thickness of Mars show a bimodal result of either ∼20 or ∼40 km beneath the InSight lander. We propose an approach based on random matrix theory applied to receiver functions (RFs) to further constrain the subsurface structure. Assuming a spiked covariance model for our data, we first use the phase transition properties of the singular value spectrum of random matrices to detect coherent arrivals in the waveforms. Examples from terrestrial data show how the method works in different scenarios. We identify three previously undetected converted arrivals in the InSight data, including the first multiple from a deeper third interface. We then use this information to jointly invert RFs with the absolute S‐wave velocity information in the polarization of body waves. Results show a crustal thickness of 43 ± 5 km beneath the lander with two mid‐crustal interfaces at depths of 8 ± 1 and 21 ± 3 km.

Alternating projections-based gridless compressive beamforming with co-prime arrays

Direction-of-arrivals (DOAs) estimation, beamforming, retrieves the angles of several sources from the outputs of receiving a sensor array. Compressive beamforming is a sparse signal recovery approach and has shown superior performance on DOA estimation. To overcome the angular searching grid issue, gridless techniques have been proposed. Most methods require a uniform linear array and use standard convex solvers that are computationally expensive. We propose a gridless compressive beamformer based on alternating projections. This method estimates DOAs by projecting a solution matrix alternatively. One projection works for measured-data-fitting, and the other works for having sparse DOAs. Our approach improves speed and accuracy and deals with arbitrary-shaped linear arrays. We validate the method using experimental data and test the DOA performance for a single snapshot, multiple snapshots with coherent arrivals, and co-prime arrays, a well-known non-uniform array.

SuperSoundcompass: a high-accuracy acoustic localization sensor using a small-aperture microphone array

Although miniaturized acoustic localization sensors have significant advantages in many fields, such as video conferencing, smart homes, intelligent scene monitoring, and robot audition, it is challenging to achieve high localization accuracy using them. In this study, a miniaturized acoustic localization sensor called SuperSoundcompass is developed. The system consists of seven identical microelectromechanical systems microphones distributed on a circular substrate with a radius of 4.5 cm. A high localization accuracy can be obtained with a limited number of acoustic sensors with compressive sensing applied. In order to verify the effectiveness of SuperSoundcompass, a series of simulations and experiments are performed under various conditions, such as low signal-to-noise ratio, coherent arrivals, and snapshot-starved data. The average root-mean-square error of SuperSoundcompass at 0 dB is 1.81∘. The results confirm its excellent performance in terms of accuracy.

Observation of a New Long‐Period (16‐s) Persistent Tremor Originating in the Gulf of Guinea

AbstractA new persistent microseismic tremor, with a narrowband period centered near 16 s, was discovered in the primary microseism spectral peak by analyzing seismic waveforms recorded by African, European, and American seismometers. This tremor may generate coherent arrivals in noise cross‐correlation functions (NCFs), which could potentially bias ambient noise tomography. Using an envelope‐stacking method, we discovered that the 16‐s tremor source is in the coastal region of the Gulf of Guinea and is probably isolated from the previously reported 26‐s tremor source. The nature of the newly identified 16‐s tremor, like the 26‐ and 27‐s tremors, is similar to a volcanic tremor radiated by the Mayotte volcanic system, thereby suggesting that the excitation of all the Gulf of Guinea tremors may be related to volcanic activities. Thus, this study implies that there may still be active volcanoes in the gulf.

Using a Time‐Based Subarray Method to Extract and Invert Noise‐Derived Body Waves at Long Beach, California

AbstractThe reconstruction of body waves from the cross‐correlation of random wavefields has recently emerged as a promising approach to probe the fine‐scale structure of the Earth. However, because of the nature of the ambient noise field, the retrieval of body waves from seismic noise recordings is highly challenging and has only been successful in a few cases. Here, we use seismic noise data from a 5,200‐node oil‐company survey to reconstruct body waves and determine the velocity structure beneath Long Beach, California. To isolate the body wave energy from the ambient noise field, we divide the entire survey into small‐aperture subarrays and apply a modified double‐beamforming scheme to enhance coherent arrivals within the cross‐correlated waveforms. The resulting beamed traces allow us to identify clear refracted P waves traveling between different subarray pairs, which we then use to construct a high‐resolution 3D velocity model of the region. The inverted velocity model reveals velocity variations of the order of 3% and strong lateral discontinuities caused by the presence of sharp geologic structures such as the Newport‐Inglewood fault (NIF). Additionally, we show that the resolution that is achieved through the use of high‐frequency body waves allows us to illuminate small geometric variations of the NIF that were previously unresolved with traditional passive imaging methods.

Enhanced Resolution of the Subducting Plate Interface in Central Alaska From Autocorrelation of Local Earthquake Coda

AbstractSubducting plates below 10‐km depth are primarily imaged using phases from teleseismic earthquakes at frequencies dominantly below 1 Hz, resulting in low‐resolution images compared to fault zone thickness. Here we image the plate boundary zone in Alaska using scattered body wave arrivals in local earthquake coda to produce a higher‐resolution image of the slab. An autocorrelation method successfully extracts coherent arrivals from the local earthquake signals. Our autocorrelation results image interfaces associated with the subducting oceanic plate at higher resolution than our teleseismic receiver functions, with increased coherence and sharper boundaries. Our results provide one of the first coherent structural images of the seismogenic zone using scattered local body waves. Amplitudes suggest that seismic wave speed decreases with increasing depth within the low‐velocity zone, supporting lithologic rather than purely overpressure models for the zone in our region. Similar methodologies using dense stations could provide higher‐resolution images to characterize crustal and uppermost mantle boundaries globally.

Performance comparisons of array invariant and matched field processing using broadband ship noise and a tilted vertical array.

This paper compares the localization performance of array invariant (AI) and matched field processing (MFP) using a ship of opportunity radiating random noise (200-900 Hz) and a tilted vertical array. AI is a deterministic approach to source-range estimation (i.e., depth-blind), exploiting the dispersion characteristics of broadband signals with minimal/no knowledge of the environment in shallow water. It involves time-domain plane-wave beamforming to separate multiple coherent arrivals (eigenrays) in beam angle and travel time, called "beam-time migration," from which the source range is directly estimated. In contrast, MFP is a model-based approach that requires accurate knowledge of the environment and array geometry (e.g., array tilt) to generate "replicas" for all possible source locations, finding the best match in the two-dimensional ambiguity surface of range and depth. While AI and MFP are both sensitive to array tilt, AI is equipped with self-calibration capability to estimate the array tilt and source range simultaneously. With the array tilt information from AI incorporated, the performance of MFP for range estimation can be comparable to that of AI to such an extent that the environmental knowledge is accurate.

Simultaneous estimation of array tilt and source range using broadband ship noise and a vertical array

The array invariant, a robust approach to source-range estimation in shallow water, is based on the dispersion characteristics of broadband signals in ideal waveguides. It involves time-domain planewave beamforming using a vertical line array (VLA) to separate multiple coherent arrivals (eigenrays) in beam angle and travel time. Typically, a probe signal (i.e., a cooperating source) is required to estimate the Green’s function, but the array invariant has been recently extended to a ship of opportunity radiating random signals using a ray-based blind deconvolution. Still, one major drawback is its sensitivity to the array tilt, shifting the beam angles and adversely affecting the array invariant parameter that determines the source range. In this paper, a simple optimization algorithm for simultaneous estimation of the array tilt and the source range is presented. The method is applied to a ship of opportunity (200–900 Hz) circling around a 56-m long VLA at a speed of 3 knots (1.5 m/s) at ranges of 1.8-3.6 km in approximately 100-m deep shallow water. It is found that the standard deviation of the relative range error significantly reduces to about 4%, from 14% with no compensation of the array tilt.

Sparse broadband time varying acoustic response modeling and estimation from an undersampled vertical array with application to underwater communications.

Sparse broadband time varying acoustic response functions associated with horizontally stratified environments can be well estimated from an undersampled vertical array. The sparsity of the arrivals here is captured by means of a two component Gaussian mixture model. The implied posterior expectation of the bifrequency function serves to attenuate low amplitude non-coherent arrivals while leaving coherent arrivals at the array unchanged. This estimate of the acoustic response specifies a time varying increment operator that unravels the time varying motion between the source and receiver array allowing for a further sparsification of the response. This additional improved sparsity allows for improved coherent multipath combining at the receiver. The model is applied to a three element vertical array during a set of broadband acoustic observations in the shallow waters of Buzzard's Bay, MA. M-ary orthogonal spread spectrum acoustic transmissions at 32.5 kHz center frequency and 25 kHz bandwidth are considered. With M = 4, throughput rates of 95 bps are tested. At 2 km and at a receive signal-to-noise ratio per element of -15.5 dB, a 3 element undersampled vertical array achieved bit error rates less than 10-5.

Array invariant-based calibration of array tilt using a source of opportunity.

The array invariant, a robust approach to source-range estimation in shallow water, is based on the dispersion characteristics of broadband signals in ideal waveguides. It involves time-domain plane-wave beamforming using a vertical line array (VLA) to separate multiple coherent arrivals in beam angle and travel time. Typically, a probe signal (i.e., a cooperating source) is required to estimate the Green's function, but the array invariant has been recently extended to a ship of opportunity radiating random signals using a ray-based blind deconvolution [Byun, Kim, Cho, Song, and Byun, J. Acoust. Soc. Am. 142, EL286-EL291 (2017)]. Still, one major drawback is its sensitivity to the array tilt, shifting the beam angles and adversely affecting the array invariant parameter that determines the source range. In this paper, a simple optimization algorithm for simultaneous estimation of the array tilt and the source range is presented. The method is applied to a ship of opportunity (200-900 Hz) circling around a 56-m long VLA at a speed of 3 knots (1.5 m/s) at ranges of 1.8-3.6 km in approximately 100-m deep shallow water. It is found that the standard deviation of the relative range error significantly reduces to about 4%, from 14% with no compensation of the array tilt. The estimated tilt angle displayed as a function of the ship's azimuth angle reveals that the VLA is tilted about 3° towards the northwest, suggesting that the array invariant can serve as a remote sensing technique for calibration of the array tilt using a source of opportunity.

Accessing the diffracted wavefield by coherent subtraction

AbstractDiffractions have unique properties which are still rarely exploited in common practice. Aside from containing subwavelength information on the scattering geometry or indicating small-scale structural complexity, they provide superior illumination compared to reflections. While diffraction occurs arguably on all scales and in most realistic media, the respective signatures typically have low amplitudes and are likely to be masked by more prominent wavefield components. It has been widely observed that automated stacking acts as a directional filter favouring the most coherent arrivals. In contrast to other works, which commonly aim at steering the summation operator towards fainter contributions, we utilize this directional selection to coherently approximate the most dominant arrivals and subtract them from the data. Supported by additional filter functions which can be derived from wave front attributes gained during the stacking procedure, this strategy allows for a fully data-driven recovery of faint diffractions and makes them accessible for further processing. A complex single-channel field data example recorded in the Aegean sea near Santorini illustrates that the diffracted background wavefield is surprisingly rich and despite the absence of a high channel count can still be detected and characterized, suggesting a variety of applications in industry and academia.

Research on Conventional Beamforming Based on Compressive Sensing

Compressive sensing, or compressive sampling (for short, CS) is a novel sensing/sampling paradigm. With the rapid development of the theory and algorithms for sparse recovery in finite dimensions, compressive sensing has already inspired some notable investigation in the context of Direction Of Arrival (DOA) estimation. In this paper, we show how CS can be applied in the DOA estimation and be solved by the well-established toolbox, CVX. In order to ensure a high spatial resolution, the conventional compressive beamforming formulation is further extended to a virtual array case. Numerical simulations illustrate the effectiveness of the DOA estimation algorithm based on CS. In addition, numerical tests also show that under some challenging scenarios such as low SNR, coherent arrivals and few snapshots, compressive beamforming based on virtually expanded array (for convenience, called V-CS) can distinguish closely spaced sources and has higher resolving probability than conventional compressive beamforming.

DOA Estimation Based on Spatial Time-frequency Analysis

With the rapid development of the theory and algorithms for time-frequency analysis, it has already inspired some notable investigation in the context of Direction Of Arrival (DOA) estimation. In this paper, we show how time-frequency analysis can be applied in the DOA domain and achieve a higher spatial resolution. In order to combine all the relevant STFD points, the joint diagonalization technique is proposed. At the same time, our work adopts Minimum Variance Distortionless Response processor (MVDR), rather than MUSIC, to avoid the estimation of the signal subspace and noise subspace. Numerical simulations illustrate the effectiveness of the DOA estimation algorithm based on the STFDs structure and also show that under some challenging scenarios such as low SNR, coherent arrivals and few snapshots, our proposed algorithms can distinguish closely spaced sources compared with conventional methods.

Very low signal to noise ratios coherent communications with an M-ary orthogonal spread spectrum signaling scheme

Considered here is the use of an M-ary orthogonal spread spectrum signal set for coherent symbol detection at very low signal to noise ratios (SNR). We consider symbols that are convolutionally orthogonal over the entire multipath delay spread of the channel and allow for the minimum mean square error (MMSE) estimation of an observed acoustic response function with minimal computational effort at the receiver. We employ these signals with an assumed sparsity prior to implement a joint symbol and broadband channel estimation scheme for coherent detection without the use of intra-packet training symbols of any kind. The approach allows us to compensate for the shared time varying Doppler process of the various coherent arrivals. The approach is demonstrated with at-sea recordings at extremely low received SNR.

Coherent Multipath Direction-of-Arrival Resolution Using Compressed Sensing

For a sound field observed on a sensor array, performance of conventional high-resolution adaptive beamformers is affected dramatically in the presence of coherent multipath signals, but the directions-of-arrival (DOAs) and power levels of these arrivals can be resolved with compressed sensing (CS). When the number of multipath signals is sufficiently small, a CS approach can be used by formulating the problem as a sparse signal recovery problem. CS overcomes the difficulty of resolving coherent arrivals at an array by directly processing the sensor outputs without first estimating a sensor covariance matrix. CS is compared to the adaptive minimum-variance-distortionless-response (MVDR) spatial processor with spatial smoothing. Though spatial smoothing produces improved results by preprocessing the sensor array covariance matrix to decorrelate the coherent multipath components, it reduces the effective aperture of the array and hence reduces the resolution. An empirical study with a uniform linear array (ULA) demonstrates that CS outperforms MVDR beamformer with spatial smoothing in terms of spatial resolution and bias and variance of DOA and power estimates. Analysis of the shallow-water HF97 ocean acoustic experimental data shows that CS is able to recover the DOAs and power levels of the multipath signals with superior resolution compared to MVDR with spatial smoothing.

Detailed Analysis of the Far‐Regional Seismic Coda in Kazakhstan Using Array Processing

Abstract An analysis of seismic coda phases recorded by five small aperture arrays in Kazakhstan and Russia is performed. The characteristics of the coda phases are obtained using array processing providing estimates of direction of propagation, frequency content, and apparent propagation velocity of coherent arrivals propagating through the arrays. A statistical analysis, using the coda characteristics of the whole dataset (far‐regional earthquakes) recorded by the arrays, is performed leading to a time‐azimuth distribution of the detected waves. Long Lg ‐coda wavetrains clearly dominate the far‐regional seismic records. The later part of an Lg ‐coda wavefield is generally expected to consist of omnidirectional and multiple scattered waves; still, in the present study, preferential propagation directions of scattered waves are identified in seismic signals, even for a lapse time larger than 1200 s. The comparison of the Lg ‐coda characteristics for two different groups of earthquakes and for the different arrays shows that the geometrical configuration of the event array strongly influences the back‐azimuthal distribution of detected waves. More precisely, temporal variations of the Lg ‐coda characteristics are identified: (1) as a transitory regime in the early part of the coda where arrival directions deviate from the epicenter back azimuth (eastward or westward); (2) as a final regime where the later part of the Lg coda observed by the two northern arrays exhibits incoherent phases with random propagation directions; and (3) as a final regime for the three southern arrays, which reveals coherent arrivals propagating from array‐specific back azimuths not related to the epicenter back azimuth. Electronic Supplement: Figures showing frequency content of detections.

Multipath propagation of sound in a shallow tidal channel and its implications on tomographic current measurements

A pilot observational experiment with Fluvial Acoustic Tomography (FAT) system was conducted in the Grand Passage, Nova Scotia, Canada, in 2014, to assess the capabilities of FAT in continuous monitoring of transport in a tidal channel. To implement the tomographic measurements, two broadband FAT transceivers operated at 7 kHz central frequency were positioned in both sides of the channel emitting a pulse every 30 s for 4 days. Three coherent arrivals were identified in the acoustic receptions. This paper investigates the influence of physical characteristics of water and current shear on multipath propagation of sound in well-mixed conditions of the channel. At the end, we report the comparison between FAT and reference velocity data collected by a moving-boat ADCP.

Spatial coherence of the seismic wavefield continuously recorded by the USArray

AbstractWe use a method based on the array covariance matrix eigenvalues to study the level of spatial coherence and of isotropy of the seismic wavefield continuously recorded during 2010 by the USArray. First, we observe that the raw data are often dominated by local sources. To remove their influence, we apply spectral and temporal normalizations to the input signals. We notice that this widely used preprocessing in ambient‐noise seismology does not fully homogenize the seismic wavefield and that some strongly coherent arrivals persist. Among these persistent signals generated by teleseismic sources we detect (1) seismic waves emitted by strong earthquakes, (2) a nearly continuous quasi‐monochromatic signal at 26 s period, and (3) multiday coherent wave trends in the spectral band of oceanic microseisms (0.07–0.2 Hz). For the latter, beamforming analysis shows that while most of the signals are composed of surface waves, some are dominated by body waves likely generated in the deep ocean.

Spatial time-frequency DOA estimation based on joint diagonalization using Jacobi rotation

Direction-of-arrival (DOA) estimation consists of locating closely spaced sources impinging from different directions in the presence of considerable noise or interference. Recently, this problem has been solved using spatial time-frequency distribution (STFD) information that is available in the array signals. In this work, a new joint diagonalization approach based on Jacobi rotation, which can efficiently combine all of the relevant STFD points, is proposed to achieve superior DOA resolutions and suppressed sidelobes in the spatial spectrum. It is discovered that our proposed Jacobi technique leads to a non-orthogonal joint diagonalization structure and can avoid pre-whitening the signal component of the observation. In addition, we further adopt the minimum variance distortionless response (MVDR) processor instead of the MUltiple SIgnal Classification (MUSIC) algorithm to avoid the estimation of the signal subspace and noise subspace in the time-frequency DOA domain. Finally, computer simulations of several frequently encountered types of challenging scenarios (such as low SNR and coherent arrivals) show that significant improvements are achieved by our proposed approach in comparison to the existing techniques.

Downtown Los Angeles 52-Story High-Rise and Free-Field Response to an Oil Refinery Explosion

The ExxonMobil Corp. oil refinery in Torrance, California, experienced an explosion on 18 February 2015, causing ground shaking equivalent to a magnitude 2.0 earthquake. The impulse response for the source was computed from Southern California Seismic Network data for a single force system with a value of 2 × 105 kN vertically downward. The refinery explosion produced an air pressure wave that was recorded 22.8 km away in a 52-story high-rise building in downtown Los Angeles by a dense accelerometer array that is a component of the Community Seismic Network. The array recorded anomalous waveforms on each floor displaying coherent arrivals that are consistent with the building's elastic response to a pressure wave caused by the refinery explosion. Using a finite-element model of the building, the force on the building on a floor-by-floor scale was found to range up to 1.42 kN, corresponding to a pressure perturbation of 7.7 Pa.