Coherent Arrivals Research Articles

Passive in vivo elastography from skeletal muscle noise

Measuring the in vivo elastic properties of muscles (e.g., stiffness) provides a means for diagnosing and monitoring muscular activity: muscles typically become ‘‘harder’’ during contraction occurring through physiological changes. Standard elastography imaging techniques estimate soft tissue (e.g., skeletal muscle, breast) stiffness using propagating shear waves in the human body generated by an external active source (e.g., indentation techniques, ultrasonic radiation force). We demonstrated a passive in vivo elastography technique without an active external radiation source. This technique instead uses cross-correlations of contracting skeletal muscle noise recorded with skin-mounted sensors. The coherent arrivals emerge from a correlation process that accumulates contributions over time from noise sources whose propagation paths pass through both sensors successively. Each passive sensor becomes a virtual in vivo shear wave source. The results point to a low-cost, noninvasive technique for monitoring biomechanical in vivo muscle properties. The efficacy of the passive elastography technique originates from the high density of cross paths between all sensor pairs potentially achieving the same sensitivity obtained from active elastography methods. The application of this passive elastography technique for constructing biomechanical models of in vivo muscle properties will be discussed.

Characterization of small local noise sources with array seismology

ABSTRACTSeismic noise is often regarded as a stochastic, incoherent and unwanted signal. However, at a closer look, noise also contains coherent signals which can be used to characterize its sources and/ or the subsurface. Here, we propose the use of array seismological methods for engineering purposes to locate and identify small, local noise sources. A detailed knowledge of noise sources enables appropriate measures to be taken to mitigate unwanted noise effects. As a case study, we report results from a temporary array of ten seismic broadband stations which were installed at the building site of a high‐precision physics laboratory. Standard analyses of power spectra and amplitude measurements indicate that the highest noise amplitudes are caused by heavy trucks passing by. Burst‐like coherent waves, excited by vehicles, appear to have a recurring pattern. Using array techniques, we were able to measure the slowness and backazimuth of the coherent arrivals. These could be identified as Rayleigh waves generated at small pot‐holes and bumps of a near‐by road and were found to propagate with a speed of 130–200 m/s.

Using human body shear wave noise for passive elastography

An elastography imaging technique based on passive measurement of shear wave ambient noise generated in the human body (e.g., due to the heart, muscles twitches, and blood flow system) has been developed. This technique merges two recent research developments in medical imaging and physics: (1) recent work on the efficacy of elastographic imaging demonstrating that shear waves are excellent candidates to image tissue elasticity in the human body and (2) theory and experimental verification in ultrasonics, underwater acoustics, and seismology of the concept of extracting coherent Green’s function from random noise cross correlations. These results provide a means for coherent passive imaging using only the human body noise field, without the use of external active sources. Coherent arrivals of the cross correlations of recordings of human body noise in the frequency band 2–50 Hz using skin-mounted accelerometers allows us to estimate the local shear velocity of the tissues. The coherent arrivals emerge from a correlation process that accumulates contributions over time from noise sources whose propagation paths pass through both sensors. The application of this passive elastography technique for constructing biomechanical models of in vivo muscles’ properties will be discussed.

Imaging Global Seismic Phase Arrivals by Stacking Array Processed Short-Period Data

For decades, seismic data stacking has been used to improve the signal-to-noise ratio (SNR) of coherent arrivals in seismic recordings. Seismic arrays are especially well-suited for this task and have been used to detect and identify typically weak seismic arrivals ( e.g., Birtill and Whiteway 1965; Green et al. 1965). Seismic arrays are deployments of no fewer than three seismometers with uniform instrumentation that allow the recorded time series to be stacked as an ensemble. Typical array apertures range from 2 km to 200 km (Rost and Garnero 2004) and consist of 10 to 100 stations. All seismic array elements receive a centralized time signal, minimizing possible timing errors. Stations are deployed in specialized configurations to ensure a high coherence of transient signals in the wavefield, while the statistical noise component is uncorrelated between stations (Haubrich 1968). Special techniques have been developed to process seismic array data (for a review, see Rost and Thomas 2002), enabling the use of subtle arrivals in the seismic wavefield for seismic analysis and thus holding promise for higher resolution snapshots of the structure of the Earth's interior ( e.g. , Vidale and Benz 1993; Vidale and Earle 2000; Rost et al. 2005b). With increasing numbers of temporary and permanent array installations, data are becoming readily available for further high-resolution studies of the Earth's interior. In this paper we present a method to extract array-specific information ( e.g., vertical incidence angle-slowness) from a large number of array recordings. Slowness, time, and amplitude information from array recordings of individual earthquakes are combined into a single summary trace per earthquake, then stacked with other summary traces from a multitude of earthquakes recorded at the same seismic array. As a test case we process short-period array data from the Canadian Yellowknife Array (YKA) to highlight seismic phases …

Hydroacoustic observations of the 2004 megathrust earthquake and other events

Hydroacoustic signals (T-waves) generated by the 2004 Great Sumatra earthquake were recorded by a network of 5 small hydroacoustic arrays located in the Indian Ocean at distances of 2800 to 7000 km from the epicenter. The array configurations allow for accurate determination of the receiver-to-source azimuth given coherent arrivals. Analysis of a series of 10-s windows within the T-wave coda shows that the receiver-to-source azimuth varies smoothly as a function of time, suggesting a nonstationary T-wave source. Apparent motion in the T-wave source has also been observed for many small-scale earthquakes and, for those events, reflects T-wave excitation over a broad expanse of the seafloor. For small-scale earthquakes, it is shown that the variations in the source azimuth are predictable using a seafloor scattering model. The azimuthal variations for the great Sumatra event are shown to be inconsistent with a small-scale source and are thus indicative of the rupture velocity. The data indicate that the rupture proceeded in two distinct phases; initially it progressed northwest at approximately 2.4 km/s along the Sunda trench. At 600 km from the epicenter, the rupture slowed to approximately 1.5 km/s.

Extracting coherent coda arrivals from cross‐correlations of long period seismic waves during the Mount St. Helens 2004 eruption

We computed cross‐correlations of seismic waves generated by Long‐Period (LP) events in the frequency band [0.8–2.2 Hz]. The data were recorded in the vicinity of Mount St Helens (MSH) during an eruptive period from September to December 2004. The time symmetric coherent coda arrivals of the time‐derivative of the cross‐correlation function (DCF), resulting from scattering and topographic effects in MSH area, correspond to arrivals of the Green's function (GF) between the two stations. The DCF waveforms computed on an hourly basis show a remarkable consistency over time periods of several hours but show temporal variations on longer time‐scales. We investigated the emergence rate of the symmetric arrivals of the DCF and discussed their potential applications for volcano monitoring.

Crustal Scattering and Some Artifacts in Receiver Function Images

The existing 2D and 3D depth imaging approaches using multichannel teleseismic receiver functions (RFs) can result in significant artifacts caused by misinterpretation of signal-generated noise resulting from broadside scattering within the crust. A synthetic example using acquisition geometry of the 1993 Cascadia experiment shows that scattering of the primary P -wave arrivals from a sedimentary accretionary wedge could produce RF events close to those observed in real data. Quasi-linear crustal structures with significant velocity contrasts near Moho depths, such as subduction zones, should create particularly strong and coherent noise arrivals. Conventional interpretations of these arrivals based on assumptions of their origin in mode conversions could lead to images of spurious dipping structures of landward dips steeper than ∼10° that may be very difficult to distinguish from the true structures. Detailed analysis of prestack, premigration RF data is required for correct identification of the signal-generated noise and validation of the resulting depth images. Identification of scattered events in RF records could also help constrain major crustal structures, such as crustal sutures and subduction fault zones, and particularly those with strong Moho expressions. Manuscript received 10 June 2003.

Using ocean ambient noise for array element localization

Time delays, associated with the direct and surface reflected arrivals, between the elements of a bottom hydrophone array can be extracted using ambient noise cross correlations [Sabra et al., J. Acoust. Soc. Am. 114, 2462 (2003)]. This is confirmed using long-time noise recordings that were collected in May 1995 near the S. California coast at an average depth of 21 m. The noise is mainly biological in the frequency range of 350–700 Hz [D’Spain et al., J. Acoust. Soc. Am. 99, 2453 (1996)]. These coherent wavefront arrivals across the array’s aperture are used for array element localization.

The Influence of 3-D Structure on the Propagation of Seismic Waves Away from Earthquakes

The seismic records from significant earthquakes are profoundly affected by 3-D variations in crustal structure both in the source zone itself and in propagation to some distance. Even in structurally complex zones such as Japan and Mexico relatively coherent arrivals are found associated with different classes of propagation paths. The presence of strong lateral variations can disrupt the arrivals, and impose significant variations in propagation characteristics for different directions from the source as illustrated by observations for the 1995 Kobe and 2000 Tottori-ken Seibu earthquakes in western Japan. Such effects can be modelled in 3 dimensions using a hybrid scheme with a pseudospectral representation for horizontal coordinates and finite differences in depth. This arrangement improves parallel implementation by minimising communication costs. For a realistic 3-D model for the structure in western Japan the 3-D simulations to frequencies close to 1 Hz provide a good representation of the observations from subduction zones events such as the 1946 Nankai earthquake and the 2000 Tottori-ken Seibu earthquake. The model can therefore be used to investigate the pattern of ground motion expected for future events e.g., in current seismic gaps.

Separation of signal and coherent noise by migration filtering

A key issue in wavefield separation is to find a domain where the signal and coherent noise are well separated from one another. A new wavefield separation algorithm, called migration filtering, separates data arrivals according to their path of propagation and their actual moveout characteristics. This is accomplished by using forward modeling operators to compute the signal and the coherent noise arrivals. A linearized least‐squares inversion scheme yields model estimates for both components; the predicted signal component is constructed by forward modeling the signal model estimate. Synthetic and field data examples demonstrate that migration filtering improves separation of P-wave reflections and surface waves, P-wave reflections and tube waves, P-wave diffractions, and S-wave diffractions. The main benefits of the migration filtering method compared to conventional filtering methods are better wavefield separation capability, the capability of mixing any two conventional transforms for wavefield separation under a general inversion framework, and the capability of mitigating the signal and coherent noise crosstalk by using regularization. The limitations of the method may include more than an order of magnitude increase in computation costs compared to conventional transforms and the difficulty of selecting the proper modeling operators for some wave modes.

Vibroseis recording techniques and data reduction from the Jemez Tomography Experiment

Abstract The Jemez Tomography Experiment (JTEX) is a multidisciplinary study focused on the Valles Caldera and the Jemez Mountains, New Mexico. The objectives of the project are to create a high resolution crustal model of the subsurface structure of this silicic volcanic system and to develop an interpretation of its volcanic evolution. Use of Vibroseis sources in the acquisition of refraction/wide-angle reflection seismic data provided challenges beyond conventional explosive-source data. Processing of the JTEX Vibroseis data is an involved procedure consisting of sorting, cross-correlating, filtering, and stacking numerous individual seismograms in the production of final record sections. However, excellent results (high signal-to-noise seismograms at relatively small spacings) are obtainable with coherent arrivals at source-receiver distances of more than 60 km. The primary drawback in this approach lies in the massive volume of data that is necessary to produce record sections. One benefit of the Vibroseis source used during JTEX was a method to decrease effective seismogram spacing. This technique, dubbed a “source-offset” technique, provides smaller overall seismograph station spacing by moving the Vibroseis sources during acquisition and leaving deployed seismographs stationary. After station corrections, this method effectively decreases station spacings and increases detail in resulting record sections. Various shallow crustal heterogeneities create travel-time advances and delays that affect the source-offset data differently than single-source data. Synthetic modeling demonstrates small travel-time discrepancies associated with the source-offset technique. However, the addition of traces with smaller station intervals clarifies secondary arrivals within record sections and aids in interpretation of these arrivals with a minimum amount of field effort required.

On the interpretation of subevents in teleseismic waveforms: The 1994 Bolivia deep earthquake revisited

We evaluate the methodologies that aim at resolving the space‐time slip distribution during large earthquakes. In one common approach, the source process of an event is assumed to be composed of a series of subevents. Critical points in teleseismic body waves, such as peaks and coherent arrivals, are viewed as discrete points in the spatiotemporal history of an earthquake. We show that these features can be interpreted as the instantaneous centroid locations of the moment release history. We demonstrate this result with an analysis of the Mw=8.2 Bolivia 1994 deep event. We reconstruct the slip distribution in two contrasting ways. First, broadband P waves are interpreted as being composed of subevents. Five peaks in the moment release rate are located relative to the onset of the rupture using the azimuthal variations of onset‐to‐peak times. Second, we invert broadband P waves for the slip distribution on a subhorizontal fault. We use a nonlinear tomographic imaging technique called simulated annealing and an L1 misfit norm. Rupture velocities appear to be <2 km s−1, and largest slip values are found to the east and north of the onset in a 40 by 50 km region. The instantaneous centroids of the moment release history correspond closely to the locations found using the subevent analysis. However, especially near the middle and the end of the rupture, the instantaneous centroid locations are in regions of little moment release. We discuss how the subevent analysis and the instantaneous centroid approach lead to dissimilar interpretations of rupture processes, especially for events with length to width ratios near unity. Another result of this study is that the rupture of the 1994 Bolivia event appears to end 50 km to the northwest of the onset, implying that the slip area is larger that previously thought. Comparing the slip distribution with the aftershock distribution suggests that more than one physical mechanism is necessary to account for the rupture process of this great deep event.

Noise reduction and detection of weak, coherent signals through phase-weighted stacks

SUMMARY We present a new tool for efficient incoherent noise reduction for array data employing complex trace analysis. An amplitude-unbiased coherency measure is designed based on the instantaneous phase, which is used to weight the samples of an ordinary, linear stack. The result is called the phase-weighted stack (PWS) and is cleaned from incoherent noise. PWS thus permits detection of weak but coherent arrivals. The method presented can easily be extended to phase-weighted cross-correlations or be applied in the z-p domain. We illustrate and discuss the advantages and disadvantages of PWS in comparison with other coherency measures and present examples. We further show that our non-linear stacking technique enables us to detect a weak lowermantle P-to4 conversion from a depth of approximately 840 km on array data. Hints of an 840 km discontinuity have been reported; however, such a discontinuity is not yet established due to the lack of further evidence.

Mid-frequency measurements of array signal and noise characteristics

Experiments using seismic-type arrays with lengths in terms of wavelengths /spl lambda/, from 20/spl lambda/ at 50 Hz to 143/spl lambda/ at 340 Hz have been conducted in the Mediterranean Sea and Northwest Atlantic Basin to ranges of 750 km. Signal-gain cumulative distribution functions (CDFs) were experimentally determined as a function of acoustic aperture and integration time. We found that for an array 143/spl lambda/ long that when the combined effects of array shape and multipath vertical arrival angle structure were contained in an off-broadside beam; when the coherent integration times were O(10 s); when peak tracking was used; and when incoherent averaging was O(35 min); then array signal gain degradations were O(1 dB). However, when incoherent averaging O(3-5 min) was used without peak tracking the average signal-gain degradation was O(3 dB). Degradations in signal gain were found to be caused by the differences in vertical arrival angle of the paths, array shape deformation, and beam wander due to system motion. After compensation for array shape and motion, the major environmental cause of signal gain degradation, for off-broadside arrivals, was the vertical arrival structure of the paths, a characteristic of the sound channel. Broadside arrivals are less sensitive to these effects and, when the deformations are small, phase randomness due to volume scattering appears to be the limiting factor. Beam noise levels (BNLs) forward of broadside were found to be dominated by coherent arrivals from the bottom-reflected tow-ship noise. Consequently, aft beams were utilized to measure the CDFs for the ambient BNLs. Ambiguous BNL results at different headings yielded an average directional response consistent with the shipping distributions for moderate aperture lengths (50/spl lambda/) with BNLs decreasing with 3 dB per aperture doubling between 25/spl lambda/ and 50/spl lambda/. Different and more varied results were found for apertures between 50/spl lambda/ and 100/spl lambda/, showing that beam-noise statistics change as the system resolves individual ships.

Regional wave propagation in southern California and Nevada: Observations from a three‐component seismic array

We present results from a study conducted to characterize regional wave propagation in southern California and Nevada. The data are from events whose paths sample the southern Coast Ranges, the southern Sierra Nevada Mountains and the southern Basin and Range. These regional earthquake data were recorded by a small‐aperture three‐component seismic array located at the Piñon Flat Observatory, southern California. The data are analyzed using a statistical array processing algorithm that provides estimates of the propagation direction, frequency, wavenumber, and particle motion polarization characteristics of the coherent arrivals observed at the array. Perhaps the most striking feature shared by these data is the extent to which the P, S and Lg wave trains are composed of coherent, forward scattered/multipathed energy. The nature of the P, S and Lg wave trains suggests that spatially anisotropic scattering plays an important role in regional wave propagation in southern California and Nevada, and that scattering sources are located not on elliptical shells whose foci are the source and the receiver but instead in a limited volume subparallel to the path of the direct arrivals. The high‐amplitude, coherent nature of numerous of the Pg and Lg coda waves suggests that strong scattering in the source zone plays an important role in shaping the Pg and Lg wave trains. While the P, S and Lg wave trains for these regional events share some general characteristics they also exhibit fairly significant differences. These differences illustrate the important role regional and source zone structure play in shaping the wave field, and the need to account for both complex scattering and three‐dimensional propagation effects in regional waveform modeling. The coda for these regional data do not begin to exhibit a character consistent with the random scattering model for coda generation until the arrival of the surface waves. The fact that much of the surface wave coda cannot be effectively modeled as plane waves suggests that it is not the product of scattering from distant heterogeneities.

Backscattered coherent noise and seismic reflection imaging of the oceanic crust: An example from the rift valley of the Mid‐Atlantic Ridge at 23°N

Seismic reflection surveys shot over oceanic crust are contaminated by source‐generated coherent noise that limits the identification and interpretation of subbasement reflections. Coherent noise arrivals are generated around the seismic line by scattering from the upper surface of the basaltic layer and by backscattering of turning waves from the underside of the same interface; both types of arrival may be enhanced by conventional common midpoint (CMP) stacking. Some turning arrivals also exhibit negative moveout in a CMP gather due to the increase of crustal velocity with depth. In unsedimented areas, coherent arrivals scattered from the top of the seafloor can be aligned by dip moveout, with or without a subsequent zero‐offset migration prestack, and suppressed, but turning arrivals will usually remain. Turning arrivals generated by linear features in the seafloor, such as fault scarps, appear on a stack section as nearly linear coherent arrivals, the apparent dip of which is related to the features' angle to the seismic line. After migration, these turning wave arrivals can extend close to the topography that produced them and continue to late times, leading to the possibility that such arrivals might be incorrectly interpreted as intrusions that crosscut, but do not offset, the Moho. Careful identification of crustal reflections on a seismic profile along the MARK area rift valley indicates that the Snake Pit hydrothermal field marks the northern limit of identifiable crustal reflections, at least some of which appear to be related to magma injection. The recent extensive volcanism of the northern MARK area may well be a result of faulting caused by the stong northward growth of the southern spreading center, permitting melt to rise more easily to shallow crustal levels.

A new spatial smoothing scheme for direction-of-arrivals of correlated sources

The performance of second-order methods in signal processing for spatial analysis is limited by the correlation between sources. The popular approach of spatial smoothing groups an equally spaced array into subarrays and then averages the covariance matrices of the subarrays to decorrelate coherent arrivals. In the new method proposed here, the decomposition is applied on the eigenvector spanning the signal subspace to reform the source subspace basis. Results of simulation show that the new scheme is more robust to noise. Comparison is made with the conventional spatial smoothing method in terms of variances on the estimated directions.

Imaging scattering structures in the lower mantle by migration of long‐period S waves

A simplified wave field migration method is applied to long‐period tangential component recordings to image lower mantle heterogeneity beneath Alaska. Observed wave field complexities are dominated by coherent arrivals between direct S (or sS) and the core‐reflected ScS (or sScS) phases. A relative waveform inversion method is used to objectively extract the time and amplitude of the three main spikes in each wavetrain, removing the effects of source time function, receiver, and instrument responses. The timing of the intermediate arrivals relative to S or ScS is used to define the volumetric position of scattering ellipsoids in the lower mantle, with intersections of ellipsoids illuminating possible regions of isotropic scattering. While a complete waveform migration is not viable due to the very limited ray path coverage and the band‐limited data, the kinematics and relative amplitudes of the scattered arrivals are still valuable for assessing the origin of the waveform complexity. In this region, which displays particularly uniform existence of an extra arrival in the data, the simplest interpretation is that a scattering surface with lateral dimensions exceeding 1500 km at a depth near 2600 km in the mantle is responsible for the extra phase. This is consistent with previous interpretations involving a one‐dimensional model with a rapid shear velocity increase or discontinuity 240–280 km above the core‐mantle boundary. The proposed methodology can potentially image both heterogeneities or layering in the D″ region as well as scattering from midmantle structure, although data limitations will continue to be a major obstacle.

Seismic wave-field observations at a dense, small-aperture array located on a landslide in the Santa Cruz Mountains, California

Abstract A rectangular (4 by 5) array of short-period three-component seismometers with 15-m spacing was deployed to record several U.S. Geological Survey calibration explosions detonated around the Santa Cruz Mountains. The array was located at a site where an earlier station had recorded frequency-dependent polarized site resonances for aftershocks of the 1989 Loma Prieta earthquake. The site is on a hillside believed to be a landslide structure, with the near surface consisting of poorly sorted sediments and weathered rocks with dipping subsurface layers. The primary objective was to explore the site effects in this complex three-dimensional soft-rock environment, characteristic of much of the Loma Prieta source region. The direct P waves from four nearby (15 to 20 km) explosions at easterly azimuths from the array show counterclockwise arrival azimuth anomalies of 30° to 50°. These deflections are attributed to the presence of more than one dipping velocity contrast beneath the array, with dips of from 10° to 50° and dip directions generally toward the south. One such boundary may correspond to the landslide slip surface, and the presence of dipping velocity contrasts underlying the site is probably responsible for some of the observed directional site resonance. A slowness vector analysis demonstrates that arrivals early in the P coda have similar azimuthal anomalies, while later scattered arrivals come from many azimuths. Particle motions indicate that the more coherent arrivals in the coda are comprised of scattered P waves and Rayleigh waves, probably associated with scattering from the rough topography in the region. The coda displays greater spatial coherency along the hill strike than down the slope, consistent with a wedge-shaped landslide. The overall wave-field spatial coherence, CCC(f, Δx), decreases with increasing frequency, f, and spatial offset, Δx, and on average can be well represented by CCC(f, Δx) = e−cfΔx, with c = 0.6 km−1 Hz−1 for the vertical P wave in the first 1-sec window. This behavior is comparable to that found for previously studied hard-rock locations.

Earthquake site response in Santa Cruz, California

Abstract Aftershocks of the 1989 Loma Prieta, California, earthquake are used to estimate site response in a 12-km2 area centered on downtown Santa Cruz. A total of 258 S-wave records from 36 aftershocks recorded at 33 sites are used in a linear inversion for site-response spectra. The inversion scheme takes advantage of the redundancy of the large data set for which several aftershocks are recorded at each site. The scheme decomposes the observed spectra into source, path, and site terms. The path term is specified before the inversion. The undetermined degree of freedom in the decomposition into source and site spectra is removed by specifying the site-response factor to be approximately 1.0 at two sites on crystalline bedrock. The S-wave site responses correlate well with the surficial geology and observed damage pattern of the mainshock. The site-response spectra of the floodplain sites, which include the heavily damaged downtown area, exhibit significant peaks. The largest peaks are between 1 and 4 Hz. Five floodplain sites have amplification factors of 10 or greater. Most of the floodplain site-response spectra also have a smaller secondary peak between 6 and 8 Hz. Residential areas built on marine terraces above the floodplain experienced much less severe damage. Site-response spectra for these areas also have their largest peaks between 1 and 4 Hz, but the amplification is generally below 6. Several of these sites also have a secondary peak between 6 and 8 Hz. The response peaks seen at nearly all sites between 1 and 4 Hz are probably caused by the natural resonance of the sedimentary rock column. The higher amplifications at floodplain sites may be caused by surface waves generated at the basin margins. The secondary peak between 6 and 8 Hz at many sites may be a harmonic of the 1- to 4-Hz peaks. We used waveforms from a seven-station approximately linear array located on the floodplain to calculate the apparent velocity and azimuth of propagation of coherent arrivals within moving windows of the S-wave codas. The initial windows give results that are consistent with direct S-wave arrivals. The apparent velocities are high (greater than 4.0 km/sec), and azimuths are from the source. Waves arriving later than 2 sec after the direct S waves have apparent velocities of less than 1 km/sec, indicating that they are surface waves, and arrive from divergent azimuths. This analysis indicates that after the direct S-wave arrival, long-duration shaking comes from surface waves that are generated at the basin margin and reverberate in the floodplain sediments.