On seismic ambient noise cross-correlation and surface-wave attenuation

Boschi, Lapo; Magrini, Fabrizio; Cammarano, Fabio; Meijde, M. van der

doi:10.1093/gji/ggz379

Cited by 10 publications

(52 citation statements)

References 27 publications

(60 reference statements)

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“…As shown by Boschi et al. (2019), the RHS of Equation 6 can be manipulated algebraically, to find an expression for the cross correlation of ambient noise where the source parameters h 2 ( ω ) and ρ conveniently cancel out. In the following, we rederive the result of Boschi et al.…”

Section: Theorymentioning

confidence: 99%

“…Equation 11 should be compared with Equation 30 of Boschi et al. (2019), i.e.,

\frac{s (x_{A}, ω) s * (x_{B}, ω)}{< {| s (boldx, ω) |^{2} >}_{x}} \approx \frac{c}{ω π I (α, ω, c)} J_{0} ((), \frac{ω | x_{A} - x_{B} |}{c}) \frac{e^{- α | x_{A} - x_{B} |}}{α},

where the mentioned algebraic error (a factor

1 / \sqrt{2 π}

) has been corrected and

I (α, ω, c) = \int_{0}^{\infty} normald r r {(||, H_{0}^{(2)} ((), \frac{ω r}{c}))}^{2} e^{- 2 α r} .

…”

Section: Theorymentioning

confidence: 99%

“…Equation 11 allows to formulate an inverse problem to determine α from cross correlations of recorded ambient signal. Because Equation 11 holds for all station pairs, it is desirable that the cost function be related to the weighted sum of the squared differences between LHS and RHS of Equation 11, calculated for each station pair; since the RHS is an oscillatory function of ω (through the Bessel function J 0 ), and α only affects its envelope but not its oscillations (e.g., Boschi et al., 2019; Prieto et al., 2009), we introduce the envelope function env to define the cost function

\begin{matrix} right C (α, ω) & left = \sum_{i, j} {|{boldx}_{i} - {boldx}_{j}|}^{2} |env [\frac{s ({boldx}_{i}, ω) s * ({boldx}_{j}, ω)}{< {{| s (x, ω) |}^{2} >}_{boldx}}]) \\ right & left {(- env [J_{0} (\frac{ω | {boldx}_{i} - {boldx}_{j} |}{c_{i j} (ω)}) {normale}^{- α | {boldx}_{i} - {boldx}_{j} |}]|}^{2}, \end{matrix}

where x i and x j denote the positions of the two receivers, and the sum spans all possible station pairs. The weight

{| x_{i} - x_{j} |}^{2}

is chosen based on the fact that larger interstation distances are associated with smaller amplitudes of the cross correlations, due to geometrical spreading, which would result in smaller absolute values of misfit if not weighted accordingly.…”

Section: Inverse Problemmentioning

confidence: 99%

“…As opposed to their speed of propagation, the amplitude of seismograms is directly related to anelastic dissipation; knowing how the Earth attenuates seismic waves, and how such attenuation changes with location within our planet, would tell us much more about its properties than we currently know. However, measures of amplitude carry important uncertainty, and the theory relating seismogram amplitude to Earth parameters is cumbersome and occasionally (e.g., Boschi et al., 2019; Menon et al., 2014) controversial.…”

Section: Introductionmentioning

confidence: 99%

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Surface‐Wave Attenuation From Seismic Ambient Noise: Numerical Validation and Application

Magrini

Boschi

2021

JGR Solid Earth

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Over the last century, seismologists have learned to constrain the velocity of seismic waves increasingly well, but its interpretation in terms of temperature, density, viscosity, and composition of the Earth's interior is nonunique and remains problematic. As opposed to their speed of propagation, the amplitude of seismograms is directly related to anelastic dissipation; knowing how the Earth attenuates seismic waves, and how such attenuation changes with location within our planet, would tell us much more about its properties than we currently know. However, measures of amplitude carry important uncertainty, and the theory relating seismogram amplitude to Earth parameters is cumbersome and occasionally (e.g., Boschi et al., 2019; Menon et al., 2014) controversial. Several studies have shown that cross correlations of seismic ambient noise approximately coincide with the surface-wave Green's function associated with the two points of observation. By analyzing the phase of the empirical Green's function, it is possible to successfully image and monitor the velocity structure of the Earth's interior (see the reviews by, e.g., Boschi & Weemstra, 2015; Campillo & Roux, 2014). The information on the anelastic properties carried by its amplitude, on the other hand, is less accurately reconstructed by cross correlation (e.g., Lehujeur & Chevrot, 2020). Initial attempts to constrain surface-wave attenuation from ambient noise (e.g., Lawrence & Prieto, 2011; Prieto et al., 2009) were based on the assumption that attenuation could be accounted for by simply taking the product of the Green's function and an exponential damping term. Tsai (2011) showed that these works omitted a multiplicative factor dependent on source parameters, which, if not accounted for, is likely to introduce a bias in the attenuation estimates; Weemstra et al. (2013) chose to treat that factor as a free parameter in their formulation of the inverse problem. However, Weemstra et al. (2014) showed an additional difficulty associated with the normalization of cross correlations, used in ambient-noise literature to reduce the effects of, e.g., strong earthquakes; spectral whitening or other normalization terms affect the amplitude of the empirical Green's function, biasing the measurements of attenuation. Boschi et al. (2019) derived a mathematical expression for the multiplicative factor relating normalized cross correlations to the Rayleigh-wave Green's function; numerical evaluation Abstract We evaluate, by numerical tests, whether surface-wave attenuation can be determined from ambient-noise data. We generate synthetic recordings of numerically simulated ambient seismic noise in several experimental setups, characterized by different source distributions and different values of attenuation coefficient. We use them to verify that the source spectrum can be reconstructed from ambient recordings (provided that the density of sources and the attenuation coefficient are known) and that true attenuation can be retrieved from normalized cross correlations ...

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Section: Theorymentioning

confidence: 99%

“…Equation 11 should be compared with Equation 30 of Boschi et al. (2019), i.e.,

\frac{s (x_{A}, ω) s * (x_{B}, ω)}{< {| s (boldx, ω) |^{2} >}_{x}} \approx \frac{c}{ω π I (α, ω, c)} J_{0} ((), \frac{ω | x_{A} - x_{B} |}{c}) \frac{e^{- α | x_{A} - x_{B} |}}{α},

where the mentioned algebraic error (a factor

1 / \sqrt{2 π}

) has been corrected and

I (α, ω, c) = \int_{0}^{\infty} normald r r {(||, H_{0}^{(2)} ((), \frac{ω r}{c}))}^{2} e^{- 2 α r} .

…”

Section: Theorymentioning

confidence: 99%

\begin{matrix} right C (α, ω) & left = \sum_{i, j} {|{boldx}_{i} - {boldx}_{j}|}^{2} |env [\frac{s ({boldx}_{i}, ω) s * ({boldx}_{j}, ω)}{< {{| s (x, ω) |}^{2} >}_{boldx}}]) \\ right & left {(- env [J_{0} (\frac{ω | {boldx}_{i} - {boldx}_{j} |}{c_{i j} (ω)}) {normale}^{- α | {boldx}_{i} - {boldx}_{j} |}]|}^{2}, \end{matrix}

where x i and x j denote the positions of the two receivers, and the sum spans all possible station pairs. The weight

{| x_{i} - x_{j} |}^{2}

Section: Inverse Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Surface‐Wave Attenuation From Seismic Ambient Noise: Numerical Validation and Application

Magrini

Boschi

2021

JGR Solid Earth

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“…Something similar would be particularly useful for constraining the attenuation properties of the region (e.g. Tsai, 2011;Boschi et al, 2019). Other possible applications of our dataset are connected to signalprocessing tasks.…”

Section: Possible Applicationsmentioning

confidence: 99%

Local earthquakes detection: A benchmark dataset of 3-component seismograms built on a global scale

Magrini

Jozinović

Cammarano

et al. 2020

Artificial Intelligence in Geosciences

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Machine learning is becoming increasingly important in scientific and technological progress, due to its ability to create models that describe complex data and generalize well. The wealth of publicly-available seismic data nowadays requires automated, fast, and reliable tools to carry out a multitude of tasks, such as the detection of small, local earthquakes in areas characterized by sparsity of receivers. A similar application of machine learning, however, should be built on a large amount of labeled seismograms, which is neither immediate to obtain nor to compile. In this study we present a large dataset of seismograms recorded along the vertical, north, and east components of 1487 broad-band or very broad-band receivers distributed worldwide; this includes 629,095 3component seismograms generated by 304,878 local earthquakes and labeled as EQ, and 615,847 ones labeled as noise (AN). Application of machine learning to this dataset shows that a simple Convolutional Neural Network of 67,939 parameters allows discriminating between earthquakes and noise single-station recordings, even if applied in regions not represented in the training set. Achieving an accuracy of 96.7, 95.3, and 93.2% on training, validation, and test set, respectively, we prove that the large variety of geological and tectonic settings covered by our data supports the generalization capabilities of the algorithm, and makes it applicable to real-time detection of local events. We make the database publicly available, intending to provide the seismological and broader scientific community with a benchmark for time-series to be used as a testing ground in signal processing.

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A review of near-surface QS estimation methods using active and passive sources

et al. 2022

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Seismic attenuation and the associated quality factor (Q) have long been studied in various sub-disciplines of seismology, ranging from observational and engineering seismology to near-surface geophysics and soil/rock dynamics with particular emphasis on geotechnical earthquake engineering and engineering seismology. Within the broader framework of seismic site characterization, various experimental techniques have been adopted over the years to measure the near-surface shear-wave quality factor (QS). Common methods include active- and passive-source recording techniques performed at the free surface of soil deposits and within boreholes, as well as laboratory tests. This paper intends to provide an in-depth review of what Q is and, in particular, how QS is estimated in the current practice. After motivating the importance of this parameter in seismology, we proceed by recalling various theoretical definitions of Q and its measurement through laboratory tests, considering various deformation modes, most notably QP and QS. We next provide a review of the literature on QS estimation methods that use data from surface and borehole sensor recordings. We distinguish between active- and passive-source approaches, along with their pros and cons, as well as the state-of-the-practice and state-of-the-art. Finally, we summarize the phenomena associated with the high-frequency shear-wave attenuation factor (kappa) and its relation to Q, as well as other lesser-known attenuation parameters.

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On seismic ambient noise cross-correlation and surface-wave attenuation

Cited by 10 publications

References 27 publications

Surface‐Wave Attenuation From Seismic Ambient Noise: Numerical Validation and Application

Surface‐Wave Attenuation From Seismic Ambient Noise: Numerical Validation and Application

Local earthquakes detection: A benchmark dataset of 3-component seismograms built on a global scale

A review of near-surface QS estimation methods using active and passive sources

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