Noise Cross-correlation Functions Research Articles

Effect of Biological Activity on Broadband Passive Fathometry

A passive fathometer can be formed by two vertically separated hydrophones. The depth can be estimated from the Green’s function between the hydrophones, which is calculated from the cross-correlation between ocean ambient noise fields received at those two hydrophones. The performance of the fathometer depends on the signal to noise ratio (SNR) and the resolution of the noise cross-correlation function. In a given environment, improved SNR and resolution of the cross-correlation function can be achieved through longer observations, more observation points, or increasing bandwidth. Long time averaging has been demonstrated, but requires that the channel be stationary over the averaging time. Hydrophone arrays are commonly used, but result in increased cost and complexity. Recent work shows that the SNR and resolution of the correlation function can also be improved by the use of the large bandwidth noise fields. This paper shows that the non-surface biological noise generated by marine animals, such as shrimp, is one of the major issues in the performance of such a broadband passive fathometer operating in shallow water. This noise tends to occur at higher frequencies. Frequencies at which significant non-surface biological noise is present cannot be used to improve fathometer performance. Consequently, the upper limit of frequencies that can be used in a passive fathometer is limited by the lower limit of the bandwidth occupied by the biological noise.

A numerical study of temporal variation of low-frequency sound observed in the obs measurement off the east coast of Taiwan

The ambient noise recorded by the OBS system deployed off the east coast of Taiwan in the TAIGER (TAiwan Integrated GEodynamics Research) project was employed to obtain the Noise Cross-correlation Functions (NCF). The data were recorded between the stations located at Yaeyama Ridge (water depth about 4000 m), starting from May of 2008 for a period of more one year. The results of NCF have shown that there exists strong microseism energy in the frequency band between 0.16 Hz and 0.35 Hz all year around, and has also demonstrated a large temporal variations as much as 5 seconds. A series of numerical simulations using OASES was conducted to investigate the effect of various waveguide propagation conditions on the temporal variation of NCF. The analysis may potentially pave the way of applying passive acoustic tomography for the monitoring of ocean climate.

Cross-correlation in band-limited ocean ambient noise fields

Observations of ambient noise in the ocean are generally band limited, because of the natural spectral shape of the noise or the restricted bandwidth of the detection system. Either way, the noise may be regarded as white noise to which a band-limiting filter has been applied. An analysis of the two-point cross-correlation function of such filtered noise is presented for two cases, isotropic and surface-generated noise. The most pronounced effects occur with high-pass and bandpass filters when the low-frequency cut-off falls well above the first few zeros in the coherence function. In this situation, the sensor separation is very many times the longest acoustic wavelength (associated with the lowest frequency) in the passband. The filtering then produces sharp pulses at correlation delays equal to the numerical value of the acoustic travel time between the sensors. Although these pulses are narrow, they have a finite width, within which a fine structure appears in the form of multiple rapid oscillations, due to the differentiating action of the filter. The number of such oscillations increases as the low-frequency roll-off of the filter becomes steeper. This fine structure is evident in several recently published experimental determinations of the cross-correlation function of band-limited ocean ambient noise.

Noise monitoring technology for objects in transition to the emergency state

Technology for determining values of noise variance, cross-correlation functions and coefficients of correlation between the useful signal and the noise is proposed for monitoring of the latent period of an object failure. The determined values form sets of informative attributes, which are equal to zero in the normal state of the object. In the course of object operation, values of elements that are different from zero are used to determine the moment and location of the fault. The technology has been applied in the monitoring system of the compressor unit at the Heydar Aliyev Baku Oil Refinery.

Using cross-correlations of ambient vibrations for passive structural health monitoring of a high-speed naval ship

Previous studies have used the cross-correlation of ambient vibrations (CAVs) technique to estimate the impulse response (or Green's function) between passive sensors for passive imaging purposes in various engineering applications. The technique (CAV) relies on extracting deterministic coherent time signatures from the noise cross-correlation function computed between passive sensors, without the use of controlled active sources. Provided that the ambient structure-borne noise field remains stable, these resulting coherent waveforms obtained from CAV can then be used for structural monitoring even if they differ from the actual impulse response between the passive sensors. This article presents experimental CAV results using low-frequency random vibration data (>50 Hz) collected on an all-aluminum naval vessel (the HSV-2 Swift) operating at high speed (up to 40 kn) during high sea states. The primary excitation sources were strong wave impact loadings and rotating machinery vibrations. The consistency of the CAV results is established by extracting similar coherent arrivals from ambient vibrations between the pairs of strain gages, symmetrically located across the ship's centerline. The influence of the ship's operating conditions on the stability of the peak coherent arrival time, during the 7 days trial, is also discussed. [Sponsored by ONR, N00014-09-1-0440.]

Measuring the speed of electromagnetic waves using the cross correlation function of broadband noise at the ends of a transmission line

When one end of a transmission line is connected to a broadband noise generator, sharp peaks are visible in the cross-correlation function of the signals at both ends of the line. The speed of the electromagnetic waves can be deduced from the time when the peaks appear. The method is suitable for introducing the concepts of cross-correlation functions and noise analysis in an undergraduate physics laboratory.

Effect of earthquakes on ambient noise cross-correlation function

Surface wave tomography method based on analysis of ambient noise is widely used during the last decade. It is assumed that correlated component of noise is composed of surface waves generated by sources distributed over the Earth’s surface more or less uniformly. In such a case the cross-correlation function (CCF) at two stations may be considered as the Green’s function of surface wave. This function should be symmetric relatively to zero time. However analysis of CCF at the stations located at the East-European Platform shows that as a rule CCF is characterized with a strong asymmetry. Since “purered noise cannot be extracted from seismic records due to superposition of earthquake signals, the method for calculation of CCF includes amplitude normalization for suppression of earthquakes that reduces signals from earthquakes to a noise level. The parts of records containing waves from earthquakes are neglected because of their short duration. Present study shows that this contribution turns out to be dominant at periods larger than 20–40 s. In other words, what is assumed as a “noisered in reality is a superposition of signals from earthquakes. This fact results in distortion of the Green’s function and of surface wave dispersion curve used in surface wave tomography if in the time interval used for calculation of CCF many earthquakes occur within a small area apart of an extension of the interstation path (clustering). Numerical modeling shows how clusters of sources affect CCF and dispersion curve correspondingly. Means for reducing this effect are outlined.

Passive structural health monitoring of a high-speed naval ship from ambient vibrations

Previous studies have used the cross-correlation of ambient vibrations (CAV) technique to estimate the impulse response (or Green's function) between passive sensors for passive imaging purposes in various engineering applications. The technique (CAV) relies on extracting deterministic coherent time signatures from the noise cross-correlation function computed between passive sensors, without the use of controlled active sources. Provided that the ambient structure-borne noise field remains stable, these resulting coherent waveforms obtained from CAV can then be used for structural monitoring even if they differ from the actual impulse response between the passive sensors. This article presents experimental CAV results using low-frequency random vibration data (<50 Hz) collected on an all-aluminum naval vessel (the HSV-2 Swift) operating at high speed (up to 40 knots) during high sea states. The primary excitation sources were strong wave impact loadings and rotating machinery vibrations. The consistency of the CAV results is established by extracting similar coherent arrivals from ambient vibrations between the pairs of strain gages, symmetrically located across the ship's centerline. The influence of the ship's operating conditions on the stability of the peak coherent arrival time, during the 7 days trial, is also discussed.

Detecting remotely triggered temporal changes around the Parkfield section of the San Andreas fault

Detecting temporal changes in fault zone properties at seismogenic depth have been a long-sought goal in the seismological community for many decades. Recent studies based on waveform analysis of repeating earthquakes have found clear temporal changes in the shallow crust and around active fault zones associated with the occurrences of large nearby and teleseismic earthquakes. However, repeating earthquakes only occur in certain locations and their occurrence times cannot be controlled, which may result in inadequate sampling of the interested regions or time periods. Recent developments in passive imaging via auto- and cross-correlation of ambient seismic wavefields (e.g., seismic noise, earthquake coda waves) provide an ideal source for continuous monitoring of temporal changes around active fault zones. Here we conduct a systematic search of temporal changes along the Parkfield section of the San Andreas fault by cross-correlating relatively high-frequency (0.4–1.3 Hz) ambient noise signals recorded by 10 borehole stations in the High Resolution Seismic Network. After using stretch/compressed method to measure the delay time and the decorrelation-index between the daily noise cross-correlation functions (NCCFs), we find clear temporal changes in the median seismic velocity and decorrelation-index associated with the 2004 M6.0 Parkfield earthquake. We also apply the same procedure to the seismic data around five regional/teleseismic events that have triggered non-volcanic tremor in the same region, but failed to find any clear temporal changes in the daily NCCFs. The fact that our current technique can detect temporal changes from the nearby but not regional and teleseismic events, suggests that temporal changes associated with distance sources are very subtle or localized so that they could not be detected within the resolution of the current technique (∼0.2%).

Comparison of four techniques for estimating temporal change of seismic velocity with passive image interferometry

Passive image interferometry (PII) is becoming a powerful tool for detecting the temporal variations in the Earth’s structure, which applies coda wave interferometry to the waveforms from the cross-correlation of seismic ambient noise. There are four techniques for estimating temporal change of seismic velocity with PII: moving-window cross-correlation technique (MWCCT), moving-window cross-spectrum technique (MWCST), stretching technique (ST) and moving-window stretching technique (MWST). In this paper, we use the continuous seismic records from a typical station pair near the Wenchuan MS8.0 earthquake fault zone and generate three sets of waveforms by stacking cross-correlation function of ambient noise with different numbers of days, and then apply four techniques to processing the three sets of waveforms and compare their results. Our results indicate that the techniques based on moving-window (MWCCT, MWCST and MWST) are superior in detecting the change of seismic velocity, and the MWCST can give a better estimate of velocity change than the other moving-window techniques due to measurement error. We also investigate the clock errors and their influences on measuring velocity change. We find that when the clock errors are not very large, they have limited impact on the estimate of the velocity change with the moving-window techniques.

Retrieval of deterministic ray travel times from noise cross-correlations.

Two-point correlation functions of diffuse wave fields are known to approximate the deterministic Green’s functions that describe wave propagation between the two points. The deterministic ray travel times retrieved from cross-correlations of ambient noise recorded on vertical line arrays of hydrophones serve as the input data for passive acoustic thermometry and tomography of the water column. Accuracy of the sound-speed and water temperature inversions is largely controlled by the accuracy of the ray travel time measurement. Achieving oceanographically relevant results requires the relative error of the passive travel time measurements to be less than 0.1%. Often, the absolute error of the travel time measurement needs to be small compared to the acoustic wave period. In this paper, stationary-point analysis of an asymptotic, high-frequency integral representation of the noise cross-correlation function is used to determine ways for accurate retrieval of ray travel times. Limitations on the accuracy of the travel time retrieval due to noise anisotropy, medium non-stationarity, source and receiver motion, and finite noise averaging times are discussed. [Work supported by ONR.]

Velocity structure of the upper mantle of the East European platform according to seismic noise data

Crosscorrelation functions of noise are construct ed on 119 interstation paths from seismic noise records at stations of Eastern Europe. Dispersion curves of the group velocity of Rayleigh waves obtained from the crosscorrelation functions are used for constructing the threedimensional distribution of the velocity of transverse waves on the East European platform and in adjacent regions by methods of surfacewave tomog� raphy. The mean velocity in the crust is minimum in the region of the Caspian depression and Black Sea basin ( 3.7 km/s). The upper mantle beneath the Baltic and Ukrainian shields is characterized by increased velocity and the absence of the asthenospheric layer. Reduced velocities are noted in the upper mantle of the Black Sea basin. A lowvelocity anomaly in the shape of a ver� tical column is revealed at depths of 200 −300 km in the central part of the Dnieper-Donets aulacogen, which confirms the existence of a paleorift in this region.

Distribution of seismic wave speed changes associated with the 12 May 2008 Mw 7.9 Wenchuan earthquake

We used continuous recordings in Sichuan, China to track the temporal change of the seismic wave speed at a regional scale, for 2 years including the Wenchuan Mw 7.9 earthquake. The data are recorded by a temporary network of 156 broad‐band seismographs in a region that covers the southern 2/3 of the fault activated during the earthquake. A doublet analysis applied on the codas of seismic noise cross correlation functions is used to detect temporal velocity changes. We found clear evidence that the seismic velocity drops by up to 0.08% in the fault region just after the earthquake with fluctuations within 0.02% before the earthquake. We compared the measurements in different sub‐arrays to get a spatial distribution of the velocity changes. This distribution is consistent with the volumetric strain change during the Wenchuan earthquake and shows that the co‐seismic velocity change is not controlled by the response of sediments.

Cross-correlation function of acoustic fields generated by random high-frequency sourcesa)

Long-range correlations of noise fields in arbitrary inhomogeneous, moving or motionless fluids are studied in the ray approximation. Using the stationary phase method, two-point cross-correlation function of noise is shown to approximate the sum of the deterministic Green's functions describing sound propagation in opposite directions between the two points. Explicit relations between amplitudes of respective ray arrivals in the noise cross-correlation function and the Green's functions are obtained and verified against specific problems allowing an exact solution. Earlier results are extended by simultaneously accounting for sound absorption, arbitrary distribution of noise sources in a volume and on surfaces, and fluid inhomogeneity and motion. The information content of the noise cross-correlation function is discussed from the viewpoint of passive acoustic characterization of inhomogeneous flows.

Monitoring of phreatic eruptions using Interferometry on Retrieved Cross-Correlation Function from Ambient Seismic Noise: Results from Mt. Ruapehu, New Zealand

Since the last major eruption in 1995–96 Mt. Ruapehu has erupted twice, on 4 October 2006 and on 25 September 2007. These events occurred without any clear precursors and were mostly phreatic explosions. The technique of “Interferometry on Retrieved Cross-Correlation Function from Ambient Seismic Noise” (IRCCASN) is used to monitor subtle temporal changes of Mt. Ruapehu's elastic properties. The computation of Cross-Correlation Functions of seismic noise recorded at several stations around the volcano allowed us to observe variations during the 2006 eruption period. The comparison between a Reference Cross-Correlation Function and a Current Cross-Correlation Function allows us to infer relative seismic velocity variations. A 0.8% decrease of relative seismic velocity in the edifice, starting two days before the 2006 eruption, was observed. This drop is due to a reversible and ephemeral effect, which can be attributed to a pressurization of a magma pocket beneath the east flank of Ruapehu due to new magma entering a small reservoir. This pressure increase produced an inflation of the east flank of Ruapehu and opened fractures in this area leading to a localised drop of seismic velocity. We conducted the same analysis for the 2007 eruption but no significant seismic velocity variation was observed. This difference is possibly due to the varying time scales of pressurization for the two events and also the IRCCASN time resolution. An analysis of the seismicity before these two eruptions allows us to propose a conceptual model which explains the velocity drop for the 2006 eruption and the lack of velocity variations for the 2007 eruption. Since there was no surface deformation recorded by the GeoNet GPS network, we modelled the maximum radius and pressure change for a simple Mogi point source at 5 km depth that produced no deformation. We inferred the maximum fresh magma volume of ∼ 0.0017 km 3 entering the reservoir as a detectability threshold for GPS ground deformation measurements.

Emergence of deterministic Green’s functions from noise generated by finite random sources

Two-point correlation functions of sufficiently diffuse wave fields generated by uncorrelated random sources are known to approximate deterministic Green's functions between the two points. This property is utilized increasingly for passive imaging and remote sensing of the environment. Here we show that the relation between the Green's functions and the noise cross-correlation function holds under much less restrictive conditions than previously thought. It can even hold when ambient noise sources have correlation ranges large compared to the wavelength. Admissible correlation ranges are limited from above by the size of the Fresnel zone at wave propagation between the points where noise cross correlation is evaluated.

Accuracy of the deterministic travel time retrieval from cross-correlations of non-diffuse ambient noise

Measurements of long-range cross-correlations of ambient noise underlie acoustic noise interferometry, a promising technique for passive remote sensing of the environment. Previously established simple, exact relations between deterministic Green's functions and the cross-correlation function of perfectly diffuse noise do not necessarily hold for noise fields in the ocean and atmosphere. Here, the method of a stationary phase is applied to study the information content of the cross-correlation function of non-diffuse noise and to quantify the accuracy of passive measurements of the acoustic travel times.

Retrieval of Green's function having coda waves from the cross-correlation function in a scattering medium illuminated by a randomly homogeneous distribution of noise sources on the basis of the first-order Born approximation

SUMMARY The retrieval of Green's function of scalar waves for a given medium is possible from the cross-correlation function (CCF) of noises in the equi-partition state. For making such a state, there are two typical ways to illuminate receivers: one is an illumination by noise sources randomly distributed on a surrounding spherical shell with large radius compared with the receiver separation; another is an illumination by the randomly homogeneous distribution of noise sources. In both cases, the wave velocity can be well evaluated from the peak lag time of the noise CCF. Furthermore, it is interesting whether Green's function having coda in a scattering medium is retrieved from the noise CCF. We proved Green's function retrieval for the former case in a previous work. Here, using the first-order Born approximation, we mathematically shows the retrieval of Green's function having coda in a scattering medium with small dissipation from the noise CCF for the latter case. A model for the scattering medium is mathematically given by a distribution of velocity anomalies represented by delta functions. Using the prolate spheroidal coordinates for the integration over the distributed noise sources, we prove that the derivative of CCF with respect to lag time is proportional to the convolution of the noise source auto-correlation function and antisymmetrized Green's function that has a coda tail caused by single scattering and an exponential decay term caused by dissipation. We note that Green's function retrieval is possible for this type of noise distribution even though the time reversal symmetry and energy conservation are broken.

Retrieval of Green's function having coda from the cross-correlation function in a scattering medium illuminated by surrounding noise sources on the basis of the first order Born approximation

SUMMARY The peak lag time of the cross-correlation function (CCF) of random noise at two receivers give the wave propagation velocity. This idea has been widely used for the velocity tomography analysis. Recently, there were reports on the temporal change in the coda portion of CCF or autocorrelation function of ambient noise as a measure of the medium property. Here, we propose a simple concrete model for the retrieval of Green’s function having a coda tail in a scattering medium without dissipation from the CCF of noise. The scattering medium is mathematically given by a distribution of velocity anomalies represented by delta functions. We suppose that waves are radiated from stationary noise sources, which are randomly distributed on a surrounding spherical shell with a large radius compared with the dimension of the scattering medium. Using the first order Born approximation, we show that the derivative of CCF with respect to lag time gives the antisymmetrized Green’s function having a coda tail in the framework of the single scattering approximation.

Implication of seismic noise for determining the structure of the upper Earth Rock Mass

An assertion that the cross-correlation function of seismic noise, considered as a result of the superposition of the surface waves, excited by the sources, randomly distributed over the Earth’s surface, determines the Green function of the surface wave is verified by numerical modeling. The maximum wave periods, for which this assertion is correct, are estimated and the errors in determination of the phase and group velocity of the surface waves are evaluated. The procedure for the determination of the correlation function and estimation from it of the group velocity are tested thoroughly based on the example of the pair of the BJT and TLY stations in Asia. This procedure is used for obtaining the group and phase velocities of the Rayleigh waves on the traces between the OBN-ARU and PUL-ARU stations. The velocity sections of the transverse waves are built based on the dispersion curves of the phase and group velocities of averages along these traces. The region of the lowered velocity in the upper mantle at depths of 150–300 km is revealed on both traces. From the analysis of correlation functions, which are subjected to narrow-band filtering, it is shown that the frequency composition of noise varies from the East and from the West from the profiles between the stations: in the East (Siberia) the noise has an appreciably lower-frequency than in the West (Western Europe).