An Adjoint Technique for Estimation of Interstation Phase and Group Dispersion from Ambient Noise Cross Correlations

2019 ◽  
Vol 109 (5) ◽  
pp. 1716-1728
Author(s):  
Rhys Hawkins ◽  
Malcolm Sambridge
Keyword(s):  
Ambient Noise ◽  
Signal To Noise Ratio ◽  
Spectral Element ◽  
Second Step ◽  
Earth Model ◽  
Rayleigh Surface Waves ◽  
Radial Anisotropy ◽  
Cross Correlations ◽  
Noise Correlation Function ◽  
Tomographic Inversions

Abstract A method of extracting group and phase velocity dispersions jointly for Love‐ and Rayleigh‐wave observations is presented. This method uses a spectral element representation of a path average Earth model parameterized with density, shear‐wave velocity, radial anisotropy, and VP/VS ratio. An initial dispersion curve is automatically estimated using a heuristic approach to prevent misidentification of the phase. A second step then more accurately fits the observed noise correlation function (NCF) between interstation pairs in the frequency domain. For good quality cross correlations with reasonable signal‐to‐noise ratio, we are able to very accurately fit the spectrum of NCFs and hence obtain reliable estimates of both phase and group velocity jointly for Love and Rayleigh surface waves. In addition, we also show how uncertainties can be estimated with linearized approximations from the Jacobians and subsequently used in tomographic inversions.

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

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.

Evaluating Uncertainties of Phase Velocity Measurements from Cross-Correlations of Ambient Seismic Noise

2020 ◽  
Vol 91 (3) ◽  
pp. 1717-1729
Author(s):  
Yinhe Luo ◽  
Yingjie Yang ◽  
Jinyun Xie ◽  
Xiaozhou Yang ◽  
Fengru Ren ◽  
...  
Keyword(s):  
Phase Velocity ◽  
Ambient Noise ◽  
Signal To Noise Ratio ◽  
The United States ◽  
Velocity Measurements ◽  
Phase Velocities ◽  
Phase Velocity Dispersion ◽  
Noise Data ◽  
Cross Correlations ◽  
Fitting In

Abstract Ambient-noise tomography (ANT) has become a well-established method to image the crust and uppermost mantle structures in the past 15 yr. Having a good estimate of uncertainties of phase velocity dispersion measurements in ANT is critical as they can guide the level of data fitting in tomography. However, to date, there are still no systemic studies to evaluate these uncertainties. In this study, we obtain cross correlations with different stacking durations from 17 yr of ambient-noise data recorded at 120 stations in the United States. We analyze the variations of signal-to-noise ratio (SNR) and phase velocities of cross correlations. We find that the uncertainties of phase velocities are affected by SNRs, interstation distances, and stacking durations. However, none of those three variables can be solely used as a proxy to estimate the uncertainties of phase velocity measurements. Based on our analysis, we graphically present empirical relations of uncertainties of phase velocity measurements as a function of SNR, interstation distance, and stacking duration. These relations can be employed as a guide to estimate phase velocity uncertainties in applications of ANT, assisting in evaluating the reliability of resulting models from ANT.

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

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.

Imaging azimuthal anisotropy in the alpine crust from ambient noise beamforming.

2021 ◽  
Author(s):  
Dorian Soergel ◽  
Helle Pedersen ◽  
Thomas Bodin ◽  
Anne Paul ◽  
Laurent Stehly
Keyword(s):  
Ambient Noise ◽  
Azimuthal Anisotropy ◽  
Noise Sources ◽  
Sks Splitting ◽  
Radial Anisotropy ◽  
Cross Correlations ◽  
The Alps ◽  
S Period ◽  
Lateral Heterogeneities

<p>Noise cross-correlations provide a good azimuthal coverage, limited only by the distribution of noise sources and the layout of the stations used. It is therefore a promising method to constrain azimuthal anisotropy. As noise cross-correlations consist mainly of surface waves, they are especially sensitive to the crust and provide good depth constraints, as opposed to SKS-splitting data that are more sensitive to the upper mantle. We use the AlpArray network as well as stations from permanent networks all across Europe to perform time-domain beamforming on noise cross-correlations. The extent and density of the AlpArray network allows us to obtain reliable measurements all across the Alps. We divide the area in smaller zones using all stations outside the zone as sources and all stations inside as a sub-array for beamforming. This allows us to estimate the quality of our measurements in a region where strong lateral heterogeneities make measurements challenging, by estimating the magnitude of bias due to heterogeneities using the cos(theta) amplitude and evaluating uncertainties with bootstrap. This way, we measure Rayleigh wave azimuthal anisotropy in several period bands between 15 s and 60 s period. Inversion of dispersion curves in specific areas allows us to constrain the depth of the observed anisotropy. The results are broadly similar to results from SKS-splitting as they are generally parallel to the mountain belt. However, we observe lower anisotropy at short periods (40 seconds and less) in the Alps themselves than in surrounding regions. We also observe several structures in the crust that are not observed with SKS-splitting data. The most striking is a strong and spatially coherent NE-oriented anisotropy to the NW of the Alps that is possibly related to Variscan inheritance (at 40 seconds and less, in the upper and lower crust).  In the Northern Apennines, we observe anisotropy perpendicular to the belt at 30 s period (middle crust) that correlates well with an area of strong radial anisotropy recently observed by Alder et al (in review) at 30 km depth. </p>

scholarly journals Radial anisotropy and S-wave velocity depict the internal to external zones transition within the Variscan orogen (NW Iberia) 

2021 ◽  
Author(s):  
Jorge Acevedo ◽  
Gabriela Fernández-Viejo ◽  
Sergio Llana-Fúnez ◽  
Carlos López-Fernández ◽  
Javier Olona ◽  
...  
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Ambient Noise ◽  
Variscan Orogeny ◽  
Low Grade ◽  
The West ◽  
Cantabrian Zone ◽  
Variscan Orogen ◽  
Nw Iberia ◽  
Radial Anisotropy

Abstract. The cross-correlation of ambient noise records registered by seismic networks has proven to be a valuable tool to obtain new insights into the crustal structure at different scales. Based on 2- to 14-s-period Rayleigh and Love dispersion data extracted from the seismic ambient noise recorded by 20 three-component broadband stations belonging to two different temporary experiments, we present the first i) upper crustal (1–14 km) high-resolution shear wave velocity and ii) radial anisotropy variation models of the continental crust in NW Iberia. The area of study represents one of the best exposed cross-sections along the Variscan orogen of western Europe, showing the transition between the external eastern zones towards the internal areas in the west. Both the 2-D maps and an E-W transect reveal a close correspondence with the main geological domains of the Variscan orogen. The foreland-fold and thrust-belt of the orogen, the Cantabrian Zone, is revealed by a zone of relatively low shear wave velocities (2.3–3.0 km/s), while the internal zones generally display higher homogeneous velocities (> 3.1 km/s). The boundary between both zones is clearly delineated in the models, depicting the arcuate shape of the orogen grain. The velocity patterns also reveal variations of the bulk properties of the rocks that can be linked to major Variscan structures, such as the basal detachment of the Cantabrian Zone or the stack of nappes involving pre-Variscan basement; or sedimentary features such as the presence of thick syn-orogenic siliciclastic wedges. Overall, the radial anisotropy magnitude varies between −5 and 15 % and increases with depth. The depth pattern suggests that the alignment of cracks is the main source of anisotropy at < 8 km depths, although the intrinsic anisotropy seems to be significant in the West-Asturian Leonese Zone, the low-grade slate belt adjacent to the Cantabrian Zone. At depths > 8 km, widespread high and positive radial anisotropies are observed, caused by the presence of subhorizontal alignments of grains and minerals in relation to the internal deformation of rocks either during the Variscan orogeny or prior to it.

scholarly journals A Comprehensive Approach to Image Watermarking, Encryption and Steganography

2015 ◽  
Vol 8 (4) ◽  
pp. 32
Author(s):  
Sabarish Sridhar
Keyword(s):  
Data Hiding ◽  
Data Transmission ◽  
Mean Squared Error ◽  
Signal To Noise Ratio ◽  
Image Watermarking ◽  
Cover Image ◽  
Second Step ◽  
Squared Error ◽  
Feature Similarity ◽  
Secure Data Transmission

Steganography, water marking and encryption are widely used in image processing and communication. A general practice is to use them independently or in combination of two - for e.g. data hiding with encryption or steganography alone. This paper aims to combine the features of watermarking, image encryption as well as image steganography to provide reliable and secure data transmission .The basics of data hiding and encryption are explained. The first step involves inserting the required watermark on the image at the optimum bit plane. The second step is to use an RSA hash to actually encrypt the image. The final step involves obtaining a cover image and hiding the encrypted image within this cover image. A set of metrics will be used for evaluation of the effectiveness of the digital water marking. The list includes Mean Squared Error, Peak Signal to Noise Ratio and Feature Similarity.

Empirical investigation of wireless sensor network performance in noisy environments

2014 ◽  
Vol 12 (1) ◽  
pp. 29-38
Author(s):  
Silvanus Teneng Kiyang ◽  
Robert Van Zyl
Keyword(s):  
Ambient Noise ◽  
Network Performance ◽  
Signal To Noise Ratio ◽  
Real Life ◽  
Wireless Sensor ◽  
Mathematical Tool ◽  
Content Type ◽  
The Real ◽  
Test Platform ◽  
Set Up

Purpose – The purpose of this work is to assess the influence of ambient noise on the performance of wireless sensor networks (WSNs) empirically and, based on these findings, develop a mathematical tool to assist technicians to determine the maximum inter-node separation before deploying a new WSN. Design/methodology/approach – A WSN test platform is set up in an electromagnetically shielded environment (RF chamber) to accurately control and quantify the ambient noise level. The test platform is subsequently placed in an operational laboratory to record network performance in typical unshielded spaces. Results from the RF chamber and the real-life environments are analysed. Findings – A minimum signal-to-noise ratio (SNR) at which the network still functions was found to be of the order 30 dB. In the real-life scenarios (machines, telecommunications and computer laboratories), the measured SNR exceeded this minimum value by more than 20 dB. This is due to the low ambient industrial noise levels observed in the 2.4 GHz ISM band for typical environments found at academic institutions. It, therefore, suggests that WSNs are less prone to industrial interferences than anticipated. Originality/value – A predictive mathematical tool is developed that can be used by technicians to determine the maximum inter-node separation before the WSN is deployed. The tool yields reliable results and promises to save installation time.

scholarly journals New measurements of long-period radial modes using large earthquakes

2020 ◽  
Vol 224 (2) ◽  
pp. 1211-1224
Author(s):  
S Talavera-Soza ◽  
A Deuss
Keyword(s):  
Inner Core ◽  
Cross Coupling ◽  
Earth Model ◽  
Cylindrical Anisotropy ◽  
Long Period ◽  
Centre Frequency ◽  
The Earth ◽  
Radial Anisotropy ◽  
Crucial Information ◽  
Quality Factor Q

SUMMARY Radial modes, nS0, are long-period oscillations that describe the radial expansion and contraction of the whole Earth. They are characterized only by their centre frequency and quality factor Q, and provide crucial information about the 1-D structure of the Earth. Radial modes were last measured more than a decade ago using only one or two earthquakes. Here, we measure radial modes using 16 of the strongest and deepest earthquakes of the last two decades. By introducing more earthquake data into our measurements, we improve our knowledge of 1-D attenuation, as we remove potential earthquake bias from our results. For mode 0S0, which is dominated by compressional energy, we measure a Q value of 5982, much higher than previously measured, and requiring less bulk attenuation in the Earth than previously thought. We also show that radial modes cross-couple (resonate) strongly to their nearest spheroidal mode due to ellipticity and inner core cylindrical anisotropy. Cross-coupling improves the fit between data and synthetics, and gives better estimates of the centre frequency and attenuation value of the radial modes. Including cross-coupling in our measurements results in a systematic shift of the centre frequencies of radial modes towards the Preliminary Reference Earth Model. This shift in centre frequencies, has implications for the strength of the radial anisotropy present in the uppermost inner core, with our cross-coupling results agreeing with lower values of anisotropy than the ones inferred from just measuring the modes in self-coupling (isolation). Furthermore, cross-coupling between radial modes and angular-order two modes provides constraints on cylindrical inner core anisotropy, that will help us improve our knowledge of the 3-D structure of the inner core.

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