Influence of the noise sources motion on the estimated Green’s functions from ambient noise cross-correlations

Accurate approximations of Green’s functions retrieved from the correlations of ambient noise require a homogeneous distribution of random and uncorrelated noise sources. In the real world, the existence of highly coherent, strong directional noise generated by ships, earthquakes, and other human activities can result in biases in the ambient-noise crosscorrelations (NCCs). We have developed an adapted eigenvalue-based filter to attenuate the interference of strong directional sources. The filter is based on the statistical model of the sample covariance matrix and can separate different components of the data covariance matrix in the eigenvalue spectrum. To improve the effectiveness and make it adaptable for different data sets, a weight is introduced to the filter. Then, the NCCs can be calculated directly from the filtered data covariance matrix. This approach is applied to a 1.02 h data set of ambient noise recorded by a permanent reservoir monitoring receiver array installed on the seabed. The power spectral density indicates that the noise recordings were contaminated by strong directional noise over nearly half of the whole observation period. Beamforming and crosscorrelation results indicate that the interference still exists even after applying traditional temporal and spectral normalization techniques, whereas the adapted eigenvalue-based filter can significantly attenuate it and help to obtain improved crosscorrelations. The approach makes it possible to retrieve reliable approximations of Green’s functions over a much shorter recording time.

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Application of temporal reweighting to ambient noise cross-correlation for improved seismic Green's function

Geophysical Journal International ◽

10.1093/gji/ggaa001 ◽

2020 ◽

Vol 221 (1) ◽

pp. 265-272

Author(s):

Jiangtao Li ◽

Richard L Weaver ◽

John Y Yoritomo ◽

Xiaodong Song

Keyword(s):

Seismic Data ◽

Ambient Noise ◽

Green's Functions ◽

Cross Correlation ◽

Green’S Functions ◽

Signal To Noise Ratio ◽

Alternative Measure ◽

Signal To Noise ◽

Cross Correlations ◽

Noise Cross Correlation

SUMMARY Due to the partly diffuse character of ambient noise, the retrieval of amplitude information and attenuation from noise cross-correlations has been difficult. Here, we apply the temporal reweighting method proposed by Weaver & Yoritomo to seismic data from the USArray in the central-midwest US. The results show considerable improvements in retrieved Green's functions in both symmetry and causality. The reweighting is able to make the effective incident noise field more isotropic (though not yet truly isotropic). It produces more robust amplitude measurements and also makes both the causal and anticausal parts usable. This suggests that it could be widely applicable for retrieval of Green's functions from ambient noise for attenuation study. The results also suggest an alternative measure of signal-to-noise ratio that complements the conventional one.

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Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2018.0382 ◽

2018 ◽

Vol 474 (2218) ◽

pp. 20180382

Author(s):

Tianshi Liu ◽

Haiming Zhang

Keyword(s):

Asymptotic Analysis ◽

Surface Waves ◽

Green's Functions ◽

Green’S Functions ◽

Dispersion Relations ◽

Body Waves ◽

Spherically Symmetric ◽

Travel Times ◽

Cross Correlations ◽

The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

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Seismic interferometry: Reconstructing the earth’s reflection response

Geophysics ◽

10.1190/1.2209947 ◽

2006 ◽

Vol 71 (4) ◽

pp. SI61-SI70 ◽

Cited By ~ 73

Author(s):

Deyan Draganov ◽

Kees Wapenaar ◽

Jan Thorbecke

Keyword(s):

Particle Velocity ◽

Green's Functions ◽

Green’S Functions ◽

Reciprocity Theorem ◽

Depth Image ◽

Acoustic Medium ◽

S Wave ◽

Noise Sources ◽

Subsurface Structures ◽

Area Of Interest

In 1968, Jon Claerbout showed that the reflection response of a 1D acoustic medium can be reconstructed by autocorrelating the transmission response. Since then, several authors have derived relationships for reconstructing Green’s functions at the surface, using crosscorrelations of (noise) recordings that were taken at the surface and that derived from subsurface sources. For acoustic media, we review relations between the reflection response and the transmission response in 3D inhomogeneous lossless media. These relations are derived from a one-way wavefield reciprocity theorem. We use modeling results to show how to reconstruct the reflection response in the presence of transient subsurface sources with distinct excitation times, as well as in the presence of simultaneously acting noise sources in the subsurface. We show that the quality of reconstructed reflections depends on the distribution of the subsurface sources. For a situation with enough subsurface sources — that is, for a distribution that illuminates the subsurface area of interest from nearly alldirections — the reconstructed reflection responses and the migrated depth image exhibit all the reflection events and the subsurface structures of interest, respectively. With only a few subsurface sources, that is, with insufficient illumination, the reconstructed reflection responses are noisy and can even become kinematically incorrect. At the same time, however, the depth image, which was obtained from their migration, still shows clearly all the illuminated subsurface structures at their correct positions. For the elastic case, we review a relationship between the reflection Green’s functions and the transmission Green’s functions derived from a two-way wavefield reciprocity theorem. Using modeling examples, we show how to reconstruct the different components of the particle velocity observed at the surface and resulting from a surface traction source. This reconstruciton is achieved using crosscorrelations of particle velocity components measured at the surface and resulting from separate P- and S-wave sources in the subsurface.

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Rapid Global Finite-Frequency Ambient Noise Source Inversion

10.5194/egusphere-egu2020-7662 ◽

2020 ◽

Author(s):

Jonas Igel ◽

Laura Ermert ◽

Andreas Fichtner

Keyword(s):

Ambient Noise ◽

Noise Source ◽

Computational Cost ◽

User Interaction ◽

Real Data ◽

Source Distribution ◽

Source Inversion ◽

Finite Frequency ◽

Noise Sources ◽

Cross Correlations

Common assumptions in ambient noise seismology such as Green&#8217;s function retrieval and equipartitioned wavefields are often not met in the Earth. Full waveform ambient noise tomography methods are free of such assumptions, as they implement knowledge of the time- and space-dependent ambient noise source distribution, whilst also taking finite-frequency effects into account. Such methods would greatly simplify near real-time monitoring of the sub-surface. Additionally, the distribution of the secondary microseisms could act as a new observable of the ocean state since its mechanism is well understood (e.g. Ardhuin et al., 2011).To efficiently forward-model global noise cross-correlations we implement (1) pre-computed high-frequency wavefields obtained using, for example, AxiSEM (Nissen-Meyer et al., 2014), and (2) spatially variable grids, both of which greatly reduce the computational cost. Global cross-correlations for any source distribution can be computed within a few seconds in the microseismic frequency range (up to 0.2 Hz). Similarly, we can compute the finite-frequency sensitivity kernels which are then used to perform a gradient-based iterative inversion of the power-spectral density of the noise source distribution. We take a windowed logarithmic energy ratio of the causal and acausal branches of the cross-correlations as measurement, which is largely insensitive to unknown 3D Earth structures.Due to its parallelisation on a cluster, our inversion tool is able to rapidly invert for the global microseismic noise source distribution with minimal required user interaction. Synthetic and real data inversions show promising results for noise sources in the North Atlantic with the structure and spatial distribution resolved at scales of a few hundred kilometres. Finally, daily noise sources maps could be computed by combining our inversion tool with a daily data download and processing toolkit.

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Improving cross-correlations of ambient noise using an rms-ratio selection stacking method

Geophysical Journal International ◽

10.1093/gji/ggaa232 ◽

2020 ◽

Vol 222 (2) ◽

pp. 989-1002

Author(s):

Jinyun Xie ◽

Yingjie Yang ◽

Yinhe Luo

Keyword(s):

Short Duration ◽

Ambient Noise ◽

Signal To Noise Ratio ◽

Ambient Noise Tomography ◽

Noise Sources ◽

Time Duration ◽

Crust And Upper Mantle ◽

Phase Velocities ◽

Noise Data ◽

Cross Correlations

SUMMARY Stacking of ambient noise correlations is a crucial step to extract empirical Green's functions (EGFs) between station pairs. The traditional method is to linearly stack all short-duration cross-correlation functions (CCFs) over a long period of time to obtain final stacks. It requires at least several months of ambient noise data to obtain reliable phase velocities at periods of several to tens of seconds from CCFs. In this study, we develop a new stacking method named root-mean-square ratio selection stacking (RMSR_SS) to reduce the time duration required for the recovery of EGFs from ambient noise. In our RMSR_SS method, rather than stacking all short-duration CCFs, we first judge if each of the short-duration CCF constructively contributes to the recovery of EGFs or not. Then, we only stack those CCFs which constructively contribute to the convergence of EGFs. By applying our method to synthetic noise data, we demonstrate how our method works in enhancing the signal-to-noise ratio of CCFs by rejecting noise sources which do not positively contribute to the recovery of EGFs. Then, we apply our method to real noise data recorded in western USA. We show that reliable and accurate phase velocities can be measured from 15-d long ambient noise data using our RMSR_SS method. By applying our method to ambient noise tomography (ANT), we can reduce the deployment duration of seismic stations from several months or years to a few tens of days, significantly improving the efficiency of ANT in imaging crust and upper-mantle structures.

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