Retrieval of amplitude and attenuation from ambient seismic noise: synthetic data and practical considerations

2020 ◽  
Vol 222 (1) ◽  
pp. 544-559
Author(s):  
Lianqing Zhou ◽  
Xiaodong Song ◽  
Richard L Weaver
Keyword(s):  
Numerical Simulation ◽  
Seismic Data ◽  
Seismic Noise ◽  
Ambient Noise ◽  
Linear Array ◽  
Noise Source ◽  
Synthetic Data ◽  
Real Data ◽  
Noise Correlation ◽  
Theoretical Derivation

SUMMARY Ambient noise correlation has been used extensively to retrieve traveltimes of surface waves. However, studies of retrieving amplitude information and attenuation from ambient noise are limited. In this study, we develop methods and strategies to extract Rayleigh wave amplitude and attenuation from ambient noise correlation, based on theoretical derivation, numerical simulation, and practical considerations of real seismic data. The synthetic data included a numerical simulation of a highly anisotropic noise source and Earth-like temporally varying strength. Results from synthetic data validate that amplitudes and attenuations can indeed be extracted from noise correlations for a linear array. A temporal flattening procedure is effective in speeding up convergence while preserving relative amplitudes. The traditional one-bit normalization and other types of temporal normalization that are applied to each individual station separately are problematic in recovering attenuation and should be avoided. In this study, we propose an ‘asynchronous’ temporal flattening procedure for real data that does not require all stations to have data at the same time. Furthermore, we present the detailed procedure for amplitude retrieval from ambient noise. Tests on real data suggest attenuations extracted from our noise-based methods are comparable with those from earthquakes. Our study shows an exciting promise of retrieving amplitude and attenuation information from ambient noise correlations and suggests practical considerations for applications to real data.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

A linear algorithm for ambient seismic noise double beamforming without explicit crosscorrelations

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. F1-F8
Author(s):  
Eileen R. Martin
Keyword(s):  
Correlation Functions ◽  
Seismic Noise ◽  
Ambient Noise ◽  
Computational Cost ◽  
Body Waves ◽  
Ambient Seismic Noise ◽  
Noise Correlation ◽  
Dense Array ◽  
Near Surface ◽  
Noise Interferometry

Geoscientists and engineers are increasingly using denser arrays for continuous seismic monitoring, and they often turn to ambient seismic noise interferometry for low-cost near-surface imaging. Although ambient noise interferometry greatly reduces acquisition costs, the computational cost of pair-wise comparisons between all sensors can be prohibitively slow or expensive for applications in engineering and environmental geophysics. Double beamforming of noise correlation functions is a powerful technique to extract body waves from ambient noise, but it is typically performed via pair-wise comparisons between all sensors in two dense array patches (scaling as the product of the number of sensors in one patch with the number of sensors in the other patch). By rearranging the operations involved in the double beamforming transform, I have developed a new algorithm that scales as the sum of the number of sensors in two array patches. Compared to traditional double beamforming of noise correlation functions, the new method is more scalable, easily parallelized, and it does not require raw data to be exchanged between dense array patches.

scholarly journals Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB203-WB210 ◽  
Author(s):  
Gilles Hennenfent ◽  
Lloyd Fenelon ◽  
Felix J. Herrmann
Keyword(s):  
Seismic Data ◽  
First Generation ◽  
Second Generation ◽  
Synthetic Data ◽  
Curvelet Transform ◽  
Real Data ◽  
Sampled Data ◽  
Regularized Inversion ◽  
Irregularly Sampled Data ◽  
Fast Discrete Curvelet Transform

We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an [Formula: see text]-regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct [Formula: see text]-regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular record-ing locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined nonequispaced curvelet reconstruction with sparsity-promoting inversion (NCRSI) for the regularization and interpolation of irregularly sampled data. We demonstrate that for a pure regularization problem the reconstruction is very accurate. The signal-to-reconstruction error ratio in our example is above [Formula: see text]. We also conduct combined interpolation and regularization experiments. The reconstructions for synthetic data are accurate, particularly when the recording locations are optimally jittered. The reconstruction in our real data example shows amplitudes along the main wavefronts smoothly varying with limited acquisition imprint.

Seismic signal band estimation by interpretation of f-x spectra

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 251-260 ◽  
Author(s):  
Gary F. Margrave
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Signal ◽  
Radial Component ◽  
Resolving Power ◽  
Random Fluctuation ◽  
Corner Frequency ◽  
Potential Signal ◽  
Signal Band

The signal band of reflection seismic data is that portion of the temporal Fourier spectrum which is dominated by reflected source energy. The signal bandwidth directly determines the spatial and temporal resolving power and is a useful measure of the value of such data. The realized signal band, which is the signal band of seismic data as optimized in processing, may be estimated by the interpretation of appropriately constructed f-x spectra. A temporal window, whose length has a specified random fluctuation from trace to trace, is applied to an ensemble of seismic traces, and the temporal Fourier transform is computed. The resultant f-x spectra are then separated into amplitude and phase sections, viewed as conventional seismic displays, and interpreted. The signal is manifested through the lateral continuity of spectral events; noise causes lateral incoherence. The fundamental assumption is that signal is correlated from trace to trace while noise is not. A variety of synthetic data examples illustrate that reasonable results are obtained even when the signal decays with time (i.e., is nonstationary) or geologic structure is extreme. Analysis of real data from a 3-C survey shows an easily discernible signal band for both P-P and P-S reflections, with the former being roughly twice the latter. The potential signal band, which may be regarded as the maximum possible signal band, is independent of processing techniques. An estimator for this limiting case is the corner frequency (the frequency at which a decaying signal drops below background noise levels) as measured on ensemble‐averaged amplitude spectra from raw seismic data. A comparison of potential signal band with realized signal band for the 3-C data shows good agreement for P-P data, which suggests the processing is nearly optimal. For P-S data, the realized signal band is about half of the estimated potential. This may indicate a relative immaturity of P-S processing algorithms or it may be due to P-P energy on the raw radial component records.

scholarly journals High-Resolution Seismic Data Deconvolution by A0 Algorithm

Geosciences ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 497
Author(s):  
Fedor Krasnov ◽  
Alexander Butorin
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Resolving Power ◽  
New Information ◽  
Geological Information ◽  
The Matrix ◽  
Complex Models ◽  
Practical Development

Sparse spikes deconvolution is one of the oldest inverse problems, which is a stylized version of recovery in seismic imaging. The goal of sparse spike deconvolution is to recover an approximation of a given noisy measurement T = W ∗ r + W 0 . Since the convolution destroys many low and high frequencies, this requires some prior information to regularize the inverse problem. In this paper, the authors continue to study the problem of searching for positions and amplitudes of the reflection coefficients of the medium (SP&ARCM). In previous research, the authors proposed a practical algorithm for solving the inverse problem of obtaining geological information from the seismic trace, which was named A 0 . In the current paper, the authors improved the method of the A 0 algorithm and applied it to the real (non-synthetic) data. Firstly, the authors considered the matrix approach and Differential Evolution approach to the SP&ARCM problem and showed that their efficiency is limited in the case. Secondly, the authors showed that the course to improve the A 0 lays in the direction of optimization with sequential regularization. The authors presented calculations for the accuracy of the A 0 for that case and experimental results of the convergence. The authors also considered different initialization parameters of the optimization process from the point of the acceleration of the convergence. Finally, the authors carried out successful approbation of the algorithm A 0 on synthetic and real data. Further practical development of the algorithm A 0 will be aimed at increasing the robustness of its operation, as well as in application in more complex models of real seismic data. The practical value of the research is to increase the resolving power of the wave field by reducing the contribution of interference, which gives new information for seismic-geological modeling.

Rapid Global Finite-Frequency Ambient Noise Source Inversion

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

<p>Common assumptions in ambient noise seismology such as Green’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).</p><p>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.</p><p>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.</p>

Near-surface imaging using ambient-noise body waves

2016 ◽  
Vol 4 (3) ◽  
pp. SJ55-SJ65 ◽  
Author(s):  
Pascal Edme ◽  
David F. Halliday
Keyword(s):  
Ambient Noise ◽  
Body Wave ◽  
Synthetic Data ◽  
Real Data ◽  
Body Waves ◽  
Seismic Survey ◽  
Subsurface Imaging ◽  
Near Surface ◽  
Deconvolution Technique ◽  
Zero Offset

We have introduced a workflow that allows subsurface imaging using upcoming body-wave arrivals extracted from ambient-noise land seismic data. Rather than using the conventional seismic interferometry approach based on correlation, we have developed a deconvolution technique to extract the earth response from the observed periodicity in the seismic traces. The technique consists of iteratively applying a gapped spiking deconvolution, providing multiple-free images with higher resolution than conventional correlation. We have validated the workflow for zero-offset traces with simple synthetic data and real data recorded during a small point-receiver land seismic survey.

scholarly journals Applications of a Realistic Model for CCD Imaging

1995 ◽  
Vol 167 ◽  
pp. 371-372
Author(s):  
Steve B. Howell ◽  
William J. Merline
Keyword(s):  
Computer Model ◽  
Noise Source ◽  
Synthetic Data ◽  
Real Data ◽  
Realistic Model ◽  
Point Sources ◽  
Ccd Imaging ◽  
Insight Into

We have constructed a computer model for simulation of point sources imaged on CCDs. An attempt has been made to ensure that the model produces “data” that mimic real data taken with two-D detectors. To be realistic, such simulations must include randomly generated noise of the appropriate type from all sources. The synthetic data are output as simple one-D integrations, as two-D radial slices, and as three-D intensity plots. Each noise source can be turned on or off so they can be studied independently as well as in combination to provide insight into the image components.

scholarly journals Prediction of Acoustic Energy Radiated by Bubble Produced by Raindrops

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Qi Li ◽  
Shu Liu ◽  
Dajing Shang
Keyword(s):  
Ambient Noise ◽  
Sound Pressure ◽  
Noise Source ◽  
Tap Water ◽  
Acoustic Energy ◽  
Underwater Noise ◽  
Theoretical Derivation ◽  
Dipole Radiation ◽  
Sinusoidal Oscillator ◽  
Series Of Experiments

Underwater noise produced by rainfall is an important part of underwater ambient noise. The bubbles produced by raindrops are the main noise source of underwater noise. Generally, the sound pressure signal of individual bubbles is easily contaminated by tank reverberation, hydrodynamic flow, and laboratory electrical noise. In order to solve this problem, this study proposes a method for calculating the acoustic energy of the bubble produced by a raindrop when the latter falls onto a plane water surface. For this purpose, a series of experiments was conducted in a 15 m × 9 m × 6 m reverberation tank filled with tap water. The bubble produced by a raindrop behaves as a simple exponentially damped sinusoidal oscillator. Based on the dipole radiation pattern, a formula was derived to predict the sound energy of these bubbles. The damping coefficient of the bubble formed by raindrops is found to differ appreciably from the empirical value of the bubble formed by other mechanisms. The resonance frequency of the bubbles is found to decrease with time. It is due to the rapid increase in the distance between the bubble and the interface. Then, the formula is optimized by using these two improved variables. The experimental results agree well with the theoretical derivation.

scholarly journals Synthetic Modeling of Ambient Seismic Noise Tomography Data

2021 ◽  
Vol 873 (1) ◽  
pp. 012096
Author(s):  
Firman Syaifuddin ◽  
Andri Dian Nugraha ◽  
Zulfakriza ◽  
Shindy Rosalia
Keyword(s):  
Seismic Noise ◽  
Ambient Noise ◽  
Noise Analysis ◽  
Reference Signal ◽  
Synthetic Data ◽  
Data Modeling ◽  
The United States ◽  
Ambient Seismic Noise ◽  
Near Surface ◽  
Tomography Method

Abstract Ambient seismic noise tomography is one of the most widely used methods in seismological studies today, especially after a comprehensive Earth noise model was published and noise analysis was performed on the IRIS Global Seismographic Network. Furthermore, the Power Spectral Density technique was introduced to identify background seismic noise in the United States. Many studies have been carried out using the ambient seismic noise tomography method which can be broadly grouped into several groups based on the objectives and research targets, such as to determine the structure of the earth’s crust and the upper mantle, to know the thickness of the sedimentary basins, to know the tectonic settings and geological structures, to know volcanic systems and geothermal systems, knowing near-surface geological features and as a monitoring effort the Ambient Noise Tomography method carried out by repeated measurements or time lapse. In this study, we investigate the characteristics of the ambient noise seismic tomography method, both its advantages and limitations of the method by utilizing synthetic data modeling using a simple geological model. Synthetic data is generated based on 1D dispersion curve forward modelling and the forward modeling of surface waves travel time for each period, which is then convoluted with the wavelets of each periods, then doing reverse correlation using a reference signal to produce synthetic recording data. We found that the estimate target depth and vertical resolution depend on the recorded data periods and the synthetic data modeling can be used as a basis in determining the acquisition design.

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