scholarly journals Modeling P waves in seismic noise correlations: Application to fault monitoring using train traffic sources

2021 ◽  
Author(s):  
Korbinian Sager ◽  
Victor Tsai ◽  
Yixiao Sheng ◽  
Florent Brenguier ◽  
Pierre Boué ◽  
...  
Keyword(s):  
Green’S Function ◽  
Surface Waves ◽  
Green's Function ◽  
Seismic Waves ◽  
Low Frequency ◽  
Body Waves ◽  
Noise Sources ◽  
P Waves ◽  
Promising Alternative ◽  
Fault Monitoring

The theory of Green's function retrieval essentially requires homogeneously distributed noise sources. Even though these conditions are not fulfilled in nature, low-frequency (<1 Hz) surface waves generated by ocean-crust interactions have been used successfully to image the crust with unprecedented spatial resolution. In contrast to low-frequency surface waves, high-frequency (>1 Hz) body waves have a sharper, more localized sensitivity to velocity contrasts and temporal changes at depth. In general, their retrieval using seismic interferometry is challenging, and recent studies focus on powerful, localized noise sources. They have proven to be a promising alternative but break the assumptions of Green's function retrieval. In this study, we present an approach to model correlations between P waves for these scenarios and analyze their sensitivity to 3D Earth structure. We perform a series of numerical experiments to advance our understanding of these signals and prepare for an application to fault monitoring. In the considered cases, the character of the signals strongly diverges from Green's function retrieval, and the sensitivity to structure has significant contributions in the source direction. An accurate description of the underlying physics allows us to reproduce observations made in the context of monitoring the San Jacinto Fault in California using train-generated seismic waves. This approach provides new perspectives for detecting and localizing temporal velocity changes previously unnoticed by commonly exploited surface-wave reconstructions.

Simultaneous body and surface wave retrieval from the seismic ambient field and discrimination from unavoidably arising spurious artifacts

2020 ◽  
Author(s):  
Ali Riahi ◽  
Zaher-Hossein Shomali ◽  
Anne Obermann ◽  
Ahmad Kamayestani
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Ambient Noise ◽  
Low Frequency ◽  
The Body ◽  
Body Waves ◽  
Apparent Velocity ◽  
Noise Sources ◽  
P Waves ◽  
Seismic Ambient Noise

&lt;p&gt;We simultaneously extract both, direct P-waves and Rayleigh waves, from the seismic ambient noise field recorded by a dense seismic network in Iran. With synthetics, we show that the simultaneous retrieval of body and surface waves from seismic ambient noise leads to the unavoidable appearance of spurious arrivals that could lead to misinterpretations.&lt;/p&gt;&lt;p&gt;We work with 2 months of seismic ambient noise records from a dense deployment of 119 sensors with interstation distances of 2 km in Iran. To retrieve body and surface waves, we calculate the cross-coherency in low-frequency ranges, i.e. frequencies up to 1.2 Hz, to provide the empirical Green&amp;#8217;s functions between each pair of stations. To separate the P and Rayleigh waves, we use the polarization method that also enhances the small amplitude body waves.&lt;/p&gt;&lt;p&gt;We observe both P and Rayleigh waves with an apparent velocity of 4.9&amp;#177;0.3 and 1.8&amp;#177;0.1 km/s in the studied area, respectively, as well as S or higher mode of Rayleigh waves, with an apparent velocity of 4.1&amp;#177;0.1 km/s. Besides these physical arrivals, we also observe two spurious arrivals with similar amplitudes before/after the P and/or Rayleigh waves that render the discrimination challenging.&lt;/p&gt;&lt;p&gt;To better understanding these arrivals, we perform synthetic tests. We show that simultaneously retrieving the body and surface waves from seismic ambient noise sources will unavoidably lead to the appearance of superior arrivals in the calculation of empirical Green&amp;#8217;s functions.&lt;/p&gt;

An orthonormality relation for elastic body waves

1968 ◽  
Vol 58 (6) ◽  
pp. 1949-1954
Author(s):  
L. E. Alsop
Keyword(s):  
Green’S Function ◽  
Surface Waves ◽  
Elastic Body ◽  
Half Space ◽  
Green's Function ◽  
Body Waves ◽  
P Wave ◽  
Wave Incident ◽  
Elastic Surface

ABSTRACT Herrera's orthonormality relation for elastic surface waves is generalized for elastic body waves. As an example, the normalization of a P-wave incident on the surface of a half space is considered. The Green's function for body waves and surface waves is obtained.

Effect of non-parallel mean flow on the Green’s function for predicting the low-frequency sound from turbulent air jets

2012 ◽  
Vol 695 ◽  
pp. 199-234 ◽  
Author(s):  
M. E. Goldstein ◽  
Adrian Sescu ◽  
M. Z. Afsar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Low Frequency ◽  
Source Location ◽  
Parallel Flow ◽  
Numerical Calculations ◽  
Mean Flow ◽  
Frequency Sound ◽  
The Mean ◽  
Radiated Sound

AbstractIt is now well-known that there is an exact formula relating the far-field jet noise spectrum to the convolution product of a propagator (that accounts for the mean flow interactions) and a generalized Reynolds stress autocovariance tensor (that accounts for the turbulence fluctuations). The propagator depends only on the mean flow and an adjoint vector Green’s function for a particular form of the linearized Euler equations. Recent numerical calculations of Karabasov, Bogey & Hynes (AIAA Paper 2011-2929) for a Mach 0.9 jet show use of the true non-parallel flow Green’s function rather than the more conventional locally parallel flow result leads to a significant increase in the predicted low-frequency sound radiation at observation angles close to the downstream jet axis. But the non-parallel flow appears to have little effect on the sound radiated at $9{0}^{\ensuremath{\circ} } $ to the downstream axis. The present paper is concerned with the effects of non-parallel mean flows on the adjoint vector Green’s function. We obtain a low-frequency asymptotic solution for that function by solving a very simple second-order hyperbolic equation for a composite dependent variable (which is directly proportional to a pressure-like component of this Green’s function and roughly corresponds to the strength of a monopole source within the jet). Our numerical calculations show that this quantity remains fairly close to the corresponding parallel flow result at low Mach numbers and that, as expected, it converges to that result when an appropriately scaled frequency parameter is increased. But the convergence occurs at progressively higher frequencies as the Mach number increases and the supersonic solution never actually converges to the parallel flow result in the vicinity of a critical- layer singularity that occurs in that solution. The dominant contribution to the propagator comes from the radial derivative of a certain component of the adjoint vector Green’s function. The non-parallel flow has a large effect on this quantity, causing it (and, therefore, the radiated sound) to increase at subsonic speeds and decrease at supersonic speeds. The effects of acoustic source location can be visualized by plotting the magnitude of this quantity, as function of position. These ‘altitude plots’ (which represent the intensity of the radiated sound as a function of source location) show that while the parallel flow solutions exhibit a single peak at subsonic speeds (when the source point is centred on the initial shear layer), the non-parallel solutions exhibit a double peak structure, with the second peak occurring about two potential core lengths downstream of the nozzle. These results are qualitatively consistent with the numerical calculations reported in Karabasov et al. (2011).

A periodic seismic isolation foundation with an extremely broad low-frequency attenuation zone: Theoretical analysis and experimental verification

2021 ◽  
pp. 136943322110646
Author(s):  
Peng Zhou ◽  
Shui Wan ◽  
Xiao Wang ◽  
Yingbo Zhu ◽  
Muyun Huang
Keyword(s):  
Seismic Isolation ◽  
Seismic Waves ◽  
Periodic Structures ◽  
Finite Size ◽  
Low Frequency ◽  
Bridge Structure ◽  
Engineering Structures ◽  
P Waves ◽  
New Type ◽  
Dominant Frequencies

The attenuation zones (AZs) of periodic structures can be used for seismic isolation design. To cover the dominant frequencies of more seismic waves, this paper proposes a new type of periodic isolation foundation (PIF) with an extremely wide low-frequency AZ of 3.31 Hz–17.01 Hz composed of optimized unit A with a wide AZ and optimized unit B with a low-frequency AZ. The two kinds of optimized units are obtained by topology optimization on the smallest periodic unit with the coupled finite element-genetic algorithm (GA) methodology. The transmission spectra of shear waves and P-waves through the proposed PIF of finite size are calculated, and the results show that the AZ of the PIF is approximately the superposition of the AZs of the two kinds of optimized units. Additionally, shake tests on a scale PIF specimen are performed to verify the attenuation performance for elastic waves within the designed AZs. Furthermore, numerical simulations show that the acceleration responses of the bridge structure with the proposed PIF are attenuated significantly compared to those with a concrete foundation under the action of different seismic waves. Therefore, the newly proposed PIF is a promising option for the reduction of seismic effects in engineering structures.

The Search of Diffusive Properties in Ambient Seismic Noise

2021 ◽  
Author(s):  
José Piña-Flores ◽  
Martín Cárdenas-Soto ◽  
Antonio García-Jerez ◽  
Michel Campillo ◽  
Francisco J. Sánchez-Sesma
Keyword(s):  
Green’S Function ◽  
Surface Waves ◽  
Green's Function ◽  
Seismic Noise ◽  
Elastic Field ◽  
Spectral Ratio ◽  
Ambient Seismic Noise ◽  
Data Sets ◽  
Original Experiment ◽  
Imaging Theory

ABSTRACT Ambient seismic noise (ASN) is becoming of interest for geophysical exploration and engineering seismology, because it is possible to exploit its potential for imaging. Theory asserts that the Green’s function can be retrieved from correlations within a diffuse field. Surface waves are the most conspicuous part of Green’s function in layered media. Thus, the velocities of surface waves can be obtained from ASN if the wavefield is diffuse. There is widespread interest in the conditions of emergence and properties of diffuse fields. In the applications, useful approximations of the Green’s function can be obtained from cross correlations of recorded motions of ASN. An elastic field is diffuse if the background illumination is azimuthally uniform and equipartitioned. It happens with the coda waves in earthquakes and has been verified in carefully planned experiments. For one of these data sets, the 1999 Chilpancingo (Mexico) experiment, there are some records of earthquake pre-events that undoubtedly are composed of ASN, so that the processing for coda can be tested on them. We decompose the ASN energies and study their equilibration. The scheme is inspired by the original experiment and uses the ASN recorded in an L-shaped array that allows the computation of spatial derivatives. It requires care in establishing the appropriate ranges for measuring parameters. In this search for robust indicators of diffusivity, we are led to establish that under certain circumstances, the S and P energy equilibration is a process that anticipates the diffusion regime (not necessarily isotropy), which justifies the use of horizontal-to-vertical spectral ratio in the context of diffuse-field theory.

On the Green function of the Lord–Shulman thermoelasticity equations

2019 ◽  
Vol 220 (1) ◽  
pp. 393-403 ◽  
Author(s):  
Zhi-Wei Wang ◽  
Li-Yun Fu ◽  
Jia Wei ◽  
Wanting Hou ◽  
Jing Ba ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Parabolic Type ◽  
Second Order ◽  
P Wave ◽  
Thermal Mode ◽  
S Wave ◽  
Order Tensor ◽  
P Waves ◽  
Thermal Conductivities

SUMMARY Thermoelasticity extends the classical elastic theory by coupling the fields of particle displacement and temperature. The classical theory of thermoelasticity, based on a parabolic-type heat-conduction equation, is characteristic of an unphysical behaviour of thermoelastic waves with discontinuities and infinite velocities as a function of frequency. A better physical system of equations incorporates a relaxation term into the heat equation; the equations predict three propagation modes, namely, a fast P wave (E wave), a slow thermal P wave (T wave), and a shear wave (S wave). We formulate a second-order tensor Green's function based on the Fourier transform of the thermodynamic equations. It is the displacement–temperature solution to a point (elastic or heat) source. The snapshots, obtained with the derived second-order tensor Green's function, show that the elastic and thermal P modes are dispersive and lossy, which is confirmed by a plane-wave analysis. These modes have similar characteristics of the fast and slow P waves of poroelasticity. Particularly, the thermal mode is diffusive at low thermal conductivities and becomes wave-like for high thermal conductivities.

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