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Francisco J. Sánchez-sesma - One of the best experts on this subject based on the ideXlab platform.
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Modeling and inversion of the microtremor H / V spectral ratio: physical basis behind the Diffuse Field approach
Earth Planets and Space, 2017Co-Authors: Francisco J. Sánchez-sesmaAbstract:Microtremor H/V spectral ratio (MHVSR) has gained popularity to assess the dominant frequency of soil sites. It requires measurement of ground motion due to seismic ambient noise at a site and a relatively simple processing. Theory asserts that the ensemble average of the autocorrelation of motion components belonging to a Diffuse Field at a given receiver gives the directional energy densities (DEDs) which are proportional to the imaginary parts of the Green’s function components when both source and receiver are the same point and the directions of force and response coincide. Therefore, the MHVSR can be modeled as the square root of 2 × ImG 11/ImG 33, where ImG 11 and ImG 33 are the imaginary parts of Green’s functions at the load point for the horizontal (sub-index 1) and vertical (sub-index 3) components, respectively. This connection has physical implications that emerge from the duality DED force and allows understanding the behavior of the MHVSR. For a given model, the imaginary parts of the Green’s functions are integrals along a radial wavenumber. To deal with these integrals, we have used either the popular discrete wavenumber method or the Cauchy’s residue theorem at the poles that account for surface waves normal modes giving the contributions due to Rayleigh and Love waves. For the retrieval of the velocity structure, one can minimize the weighted differences between observations and calculated values using the strategy of an inversion scheme. In this research, we used simulated annealing but other optimization techniques can be used as well. This last approach allows computing separately the contributions of different wave types. An example is presented for the mouth of Andarax River at Almeria, Spain.
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A computer code for forward calculation and inversion of the H/V spectral ratio under the Diffuse Field assumption
Computers & Geosciences, 2016Co-Authors: Antonio García-jerez, José Piña-flores, Francisco J. Sánchez-sesma, Francisco Luzón, Mathieu PertonAbstract:During a quarter of a century, the main characteristics of the horizontal-to-vertical spectral ratio of ambient noise HVSRN have been extensively used for site effect assessment. In spite of the uncertainties about the optimum theoretical model to describe these observations, over the last decade several schemes for inversion of the full HVSRN curve for near surface surveying have been developed.In this work, a computer code for forward calculation of H/V spectra based on the Diffuse Field assumption (DFA) is presented and tested. It takes advantage of the recently stated connection between the HVSRN and the elastodynamic Green's function which arises from the ambient noise interferometry theory.The algorithm allows for (1) a natural calculation of the Green's functions imaginary parts by using suitable contour integrals in the complex wavenumber plane, and (2) separate calculation of the contributions of Rayleigh, Love, P-SV and SH waves as well. The stability of the algorithm at high frequencies is preserved by means of an adaptation of the Wang's orthonormalization method to the calculation of dispersion curves, surface-waves medium responses and contributions of body waves.This code has been combined with a variety of inversion methods to make up a powerful tool for passive seismic surveying. H/V spectral ratios of ambient seismic noise are modeled by using full waveField.The theoretical framework is consistent with ambient noise interferometry.The method provides separate calculations of different wave modes.The software is also suitable for coda waves and any other Diffuse-like waveFields.It supports joint inversion of seismic velocity models from H/V and dispersion curves.
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A computer code for forward calculation and inversion of the H/V spectral ratio under the Diffuse Field assumption
Computers & Geosciences, 2016Co-Authors: Antonio García-jerez, José Piña-flores, Francisco J. Sánchez-sesma, Francisco Luzón, Mathieu PertonAbstract:During a quarter of a century, the main characteristics of the horizontal-to-vertical spectral ratio of ambient noise HVSRN have been extensively used for site effect assessment. In spite of the uncertainties about the optimum theoretical model to describe these observations, several schemes for inversion of the full HVSRN curve for near surface surveying have been developed over the last decade. In this work, a computer code for forward calculation of H/V spectra based on the Diffuse Field assumption (DFA) is presented and tested.It takes advantage of the recently stated connection between the HVSRN and the elastodynamic Green's function which arises from the ambient noise interferometry theory. The algorithm allows for (1) a natural calculation of the Green's functions imaginary parts by using suitable contour integrals in the complex wavenumber plane, and (2) separate calculation of the contributions of Rayleigh, Love, P-SV and SH waves as well. The stability of the algorithm at high frequencies is preserved by means of an adaptation of the Wang's orthonormalization method to the calculation of dispersion curves, surface-waves medium responses and contributions of body waves. This code has been combined with a variety of inversion methods to make up a powerful tool for passive seismic surveying.Comment: Published in Computers & Geosciences 97, 67-7
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Applicability of Theoretical Horizontal-to-Vertical Ratio of Microtremors Based on the Diffuse Field Concept to Previously Observed Data
Bulletin of the Seismological Society of America, 2015Co-Authors: Hiroshi Kawase, Shinichi Matsushima, Toshimi Satoh, Francisco J. Sánchez-sesmaAbstract:Abstract Horizontal-to-vertical spectral ratios of microtremors (MHVRs) have been interpreted as representing either the Rayleigh-wave ellipticity or the amplitude ratio of the sum of Rayleigh and Love waves in a horizontally layered structure. However, based on the recently established Diffuse Field concept, the theoretical form of MHVR has been proposed to be the square root of the ratio between the imaginary part of the horizontal Green’s function on the surface and that of the vertical one. The theory assumes that the energy of a waveField inside the earth will be equipartitioned among the various states in 3D space. In the case of microtremors, this may occur for randomly applied point-force loadings on the surface after sufficient lapse time to allow multiple scattering. Recent works on Diffuse Fields suggest that equipartition may arise in several ways, but understanding the emergence of equipartition in realistic settings requires further scrutiny. In the meantime, the resulting formula is quite simple, and its meaning has theoretical support from deterministic exact solutions. As references, we use observed microtremor data from several sites that were reported previously and validate the Diffuse Field method (DFM) as an alternative method to explain observed MHVR. We use only sites with reliable velocity structures to compare different methods quantitatively. As a result, we found that the DFM solutions with the corresponding 1D layered structures well explain the observed MHVRs for most of the sites. Thus, we believe that MHVR can be used to invert a 1D velocity structure by using DFM as a theoretical tool.
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Short Note Using Diffuse Field Theory to Interpret the H/V Spectral Ratio from Earthquake Records in Cibeles Seismic Station, Mexico City
2014Co-Authors: V Salinas, Antonio García-jerez, Francisco J. Sánchez-sesma, Francisco Luzón, Hiroshi Kawase, Shinichi Matsushima, Martha Suarez, A Cuellar, Michel CampilloAbstract:It has been recently demonstrated that averaging the autocorrelations of Fields produced by various almost-vertical incoming elastic body plane waves upon a layered system approximately leads to the imaginary part of the corresponding 1D Green's functions for deep sources located underneath the receiver (Kawase et al., 2011). Thus, the ensemble of these waves from deep earthquakes recorded in a station located in the epicentral zone is interpreted as a Diffuse Field. In this short note, we extend the study to consider earthquakes recorded in a station located at epicentral distances of up to hundreds of kilometers. We consider the horizontal-to-vertical spec- tral ratio (HVSR) of the averaged P, S, and coda waves and full earthquake records at the Cibeles station (Mexico City Accelerometric Network) and compare thesewith the results obtained with the corresponding HVSR for the 1D (Kawase et al., 2011) and the 3D (Sanchez-Sesma, Rodriguez, et al., 2011) Diffuse Fields models. Using the signals of 90 earthquakes recorded at Cibeles, we find that the experimental results have distinctive features compatible with the 3D signature of a Diffuse Field. We in- terpret this result as a consequence of the multiple paths that seismic waves undergo from the subducting slab to the Mexico City valley and to the multiple scattering in a complex tectonic environment. Our study strongly suggests that we can use strong- motion records from earthquakes and apply similar techniques to the ones used to analyze the ambient seismic Field.
Hiroshi Kawase - One of the best experts on this subject based on the ideXlab platform.
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Difference of horizontal-to-vertical spectral ratios of observed earthquakes and microtremors and its application to S-wave velocity inversion based on the Diffuse Field concept
Earth Planets and Space, 2018Co-Authors: Hiroshi Kawase, Yuta Mori, Fumiaki NagashimaAbstract:We have been discussing the validity of using the horizontal-to-vertical spectral ratios (HVRs) as a substitute for S-wave amplifications after Nakamura first proposed the idea in 1989. So far a formula for HVRs had not been derived that fully utilized their physical characteristics until a recent proposal based on the Diffuse Field concept. There is another source of confusion that comes from the mixed use of HVRs from earthquake and microtremors, although their wave Fields are hardly the same. In this study, we compared HVRs from observed microtremors (MHVR) and those from observed earthquake motions (EHVR) at one hundred K-NET and KiK-net stations. We found that MHVR and EHVR share similarities, especially until their first peak frequency, but have significant differences in the higher frequency range. This is because microtremors mainly consist of surface waves so that peaks associated with higher modes would not be prominent, while seismic motions mainly consist of upwardly propagating plain body waves so that higher mode resonances can be seen in high frequency. We defined here the spectral amplitude ratio between them as EMR and calculated their average. We categorize all the sites into five bins by their fundamental peak frequencies in MHVR. Once we obtained EMRs for five categories, we back-calculated EHVRs from MHVRs, which we call pseudo-EHVRs (pEHVR). We found that pEHVR is much closer to EHVR than MHVR. Then we use our inversion code to invert the one-dimensional S-wave velocity structures from EHVRs based on the Diffuse Field concept. We also applied the same code to pEHVRs and MHVRs for comparison. We found that pEHVRs yield velocity structures much closer to those by EHVRs than those by MHVRs. This is natural since what we have done up to here is circular except for the average operation in EMRs. Finally, we showed independent examples of data not used in the EMR calculation, where better ground structures were successfully identified from pEHVRs again. Thus we proposed here a simple empirical method to estimate S-wave velocity structures using single-station microtremor records, which is the most cost-effective method to characterize the site effects.
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Difference of horizontal-to-vertical spectral ratios of observed earthquakes and microtremors and its application to S-wave velocity inversion based on the Diffuse Field concept
Earth Planets and Space, 2018Co-Authors: Hiroshi Kawase, Yuta Mori, Fumiaki NagashimaAbstract:We have been discussing the validity of using the horizontal-to-vertical spectral ratios (HVRs) as a substitute for S-wave amplifications after Nakamura first proposed the idea in 1989. So far a formula for HVRs had not been derived that fully utilized their physical characteristics until a recent proposal based on the Diffuse Field concept. There is another source of confusion that comes from the mixed use of HVRs from earthquake and microtremors, although their wave Fields are hardly the same. In this study, we compared HVRs from observed microtremors (MHVR) and those from observed earthquake motions (EHVR) at one hundred K-NET and KiK-net stations. We found that MHVR and EHVR share similarities, especially until their first peak frequency, but have significant differences in the higher frequency range. This is because microtremors mainly consist of surface waves so that peaks associated with higher modes would not be prominent, while seismic motions mainly consist of upwardly propagating plain body waves so that higher mode resonances can be seen in high frequency. We defined here the spectral amplitude ratio between them as EMR and calculated their average. We categorize all the sites into five bins by their fundamental peak frequencies in MHVR. Once we obtained EMRs for five categories, we back-calculated EHVRs from MHVRs, which we call pseudo-EHVRs (pEHVR). We found that pEHVR is much closer to EHVR than MHVR. Then we use our inversion code to invert the one-dimensional S-wave velocity structures from EHVRs based on the Diffuse Field concept. We also applied the same code to pEHVRs and MHVRs for comparison. We found that pEHVRs yield velocity structures much closer to those by EHVRs than those by MHVRs. This is natural since what we have done up to here is circular except for the average operation in EMRs. Finally, we showed independent examples of data not used in the EMR calculation, where better ground structures were successfully identified from pEHVRs again. Thus we proposed here a simple empirical method to estimate S-wave velocity structures using single-station microtremor records, which is the most cost-effective method to characterize the site effects. Open image in new window
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Applicability of Theoretical Horizontal-to-Vertical Ratio of Microtremors Based on the Diffuse Field Concept to Previously Observed Data
Bulletin of the Seismological Society of America, 2015Co-Authors: Hiroshi Kawase, Shinichi Matsushima, Toshimi Satoh, Francisco J. Sánchez-sesmaAbstract:Abstract Horizontal-to-vertical spectral ratios of microtremors (MHVRs) have been interpreted as representing either the Rayleigh-wave ellipticity or the amplitude ratio of the sum of Rayleigh and Love waves in a horizontally layered structure. However, based on the recently established Diffuse Field concept, the theoretical form of MHVR has been proposed to be the square root of the ratio between the imaginary part of the horizontal Green’s function on the surface and that of the vertical one. The theory assumes that the energy of a waveField inside the earth will be equipartitioned among the various states in 3D space. In the case of microtremors, this may occur for randomly applied point-force loadings on the surface after sufficient lapse time to allow multiple scattering. Recent works on Diffuse Fields suggest that equipartition may arise in several ways, but understanding the emergence of equipartition in realistic settings requires further scrutiny. In the meantime, the resulting formula is quite simple, and its meaning has theoretical support from deterministic exact solutions. As references, we use observed microtremor data from several sites that were reported previously and validate the Diffuse Field method (DFM) as an alternative method to explain observed MHVR. We use only sites with reliable velocity structures to compare different methods quantitatively. As a result, we found that the DFM solutions with the corresponding 1D layered structures well explain the observed MHVRs for most of the sites. Thus, we believe that MHVR can be used to invert a 1D velocity structure by using DFM as a theoretical tool.
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using Diffuse Field theory to interpret the h v spectral ratio from earthquake records in cibeles seismic station mexico city
Bulletin of the Seismological Society of America, 2014Co-Authors: V Salinas, Francisco Luzón, Hiroshi Kawase, Shinichi Matsushima, Antonio Garciajerez, Francisco J Sanchezsesma, Martha Suarez, A Cuellar, Michel CampilloAbstract:Abstract It has been recently demonstrated that averaging the autocorrelations of Fields produced by various almost‐vertical incoming elastic body plane waves upon a layered system approximately leads to the imaginary part of the corresponding 1D Green’s functions for deep sources located underneath the receiver (Kawase et al. , 2011). Thus, the ensemble of these waves from deep earthquakes recorded in a station located in the epicentral zone is interpreted as a Diffuse Field. In this short note, we extend the study to consider earthquakes recorded in a station located at epicentral distances of up to hundreds of kilometers. We consider the horizontal‐to‐vertical spectral ratio (HVSR) of the averaged P , S , and coda waves and full earthquake records at the Cibeles station (Mexico City Accelerometric Network) and compare these with the results obtained with the corresponding HVSR for the 1D (Kawase et al. , 2011) and the 3D (Sanchez‐Sesma, Rodriguez, et al. , 2011) Diffuse Fields models. Using the signals of 90 earthquakes recorded at Cibeles, we find that the experimental results have distinctive features compatible with the 3D signature of a Diffuse Field. We interpret this result as a consequence of the multiple paths that seismic waves undergo from the subducting slab to the Mexico City valley and to the multiple scattering in a complex tectonic environment. Our study strongly suggests that we can use strong‐motion records from earthquakes and apply similar techniques to the ones used to analyze the ambient seismic Field. Online Material: Earthquake catalog.
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Short Note Using Diffuse Field Theory to Interpret the H/V Spectral Ratio from Earthquake Records in Cibeles Seismic Station, Mexico City
2014Co-Authors: V Salinas, Antonio García-jerez, Francisco J. Sánchez-sesma, Francisco Luzón, Hiroshi Kawase, Shinichi Matsushima, Martha Suarez, A Cuellar, Michel CampilloAbstract:It has been recently demonstrated that averaging the autocorrelations of Fields produced by various almost-vertical incoming elastic body plane waves upon a layered system approximately leads to the imaginary part of the corresponding 1D Green's functions for deep sources located underneath the receiver (Kawase et al., 2011). Thus, the ensemble of these waves from deep earthquakes recorded in a station located in the epicentral zone is interpreted as a Diffuse Field. In this short note, we extend the study to consider earthquakes recorded in a station located at epicentral distances of up to hundreds of kilometers. We consider the horizontal-to-vertical spec- tral ratio (HVSR) of the averaged P, S, and coda waves and full earthquake records at the Cibeles station (Mexico City Accelerometric Network) and compare thesewith the results obtained with the corresponding HVSR for the 1D (Kawase et al., 2011) and the 3D (Sanchez-Sesma, Rodriguez, et al., 2011) Diffuse Fields models. Using the signals of 90 earthquakes recorded at Cibeles, we find that the experimental results have distinctive features compatible with the 3D signature of a Diffuse Field. We in- terpret this result as a consequence of the multiple paths that seismic waves undergo from the subducting slab to the Mexico City valley and to the multiple scattering in a complex tectonic environment. Our study strongly suggests that we can use strong- motion records from earthquakes and apply similar techniques to the ones used to analyze the ambient seismic Field.
Shinichi Matsushima - One of the best experts on this subject based on the ideXlab platform.
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Applicability of Theoretical Horizontal-to-Vertical Ratio of Microtremors Based on the Diffuse Field Concept to Previously Observed Data
Bulletin of the Seismological Society of America, 2015Co-Authors: Hiroshi Kawase, Shinichi Matsushima, Toshimi Satoh, Francisco J. Sánchez-sesmaAbstract:Abstract Horizontal-to-vertical spectral ratios of microtremors (MHVRs) have been interpreted as representing either the Rayleigh-wave ellipticity or the amplitude ratio of the sum of Rayleigh and Love waves in a horizontally layered structure. However, based on the recently established Diffuse Field concept, the theoretical form of MHVR has been proposed to be the square root of the ratio between the imaginary part of the horizontal Green’s function on the surface and that of the vertical one. The theory assumes that the energy of a waveField inside the earth will be equipartitioned among the various states in 3D space. In the case of microtremors, this may occur for randomly applied point-force loadings on the surface after sufficient lapse time to allow multiple scattering. Recent works on Diffuse Fields suggest that equipartition may arise in several ways, but understanding the emergence of equipartition in realistic settings requires further scrutiny. In the meantime, the resulting formula is quite simple, and its meaning has theoretical support from deterministic exact solutions. As references, we use observed microtremor data from several sites that were reported previously and validate the Diffuse Field method (DFM) as an alternative method to explain observed MHVR. We use only sites with reliable velocity structures to compare different methods quantitatively. As a result, we found that the DFM solutions with the corresponding 1D layered structures well explain the observed MHVRs for most of the sites. Thus, we believe that MHVR can be used to invert a 1D velocity structure by using DFM as a theoretical tool.
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using Diffuse Field theory to interpret the h v spectral ratio from earthquake records in cibeles seismic station mexico city
Bulletin of the Seismological Society of America, 2014Co-Authors: V Salinas, Francisco Luzón, Hiroshi Kawase, Shinichi Matsushima, Antonio Garciajerez, Francisco J Sanchezsesma, Martha Suarez, A Cuellar, Michel CampilloAbstract:Abstract It has been recently demonstrated that averaging the autocorrelations of Fields produced by various almost‐vertical incoming elastic body plane waves upon a layered system approximately leads to the imaginary part of the corresponding 1D Green’s functions for deep sources located underneath the receiver (Kawase et al. , 2011). Thus, the ensemble of these waves from deep earthquakes recorded in a station located in the epicentral zone is interpreted as a Diffuse Field. In this short note, we extend the study to consider earthquakes recorded in a station located at epicentral distances of up to hundreds of kilometers. We consider the horizontal‐to‐vertical spectral ratio (HVSR) of the averaged P , S , and coda waves and full earthquake records at the Cibeles station (Mexico City Accelerometric Network) and compare these with the results obtained with the corresponding HVSR for the 1D (Kawase et al. , 2011) and the 3D (Sanchez‐Sesma, Rodriguez, et al. , 2011) Diffuse Fields models. Using the signals of 90 earthquakes recorded at Cibeles, we find that the experimental results have distinctive features compatible with the 3D signature of a Diffuse Field. We interpret this result as a consequence of the multiple paths that seismic waves undergo from the subducting slab to the Mexico City valley and to the multiple scattering in a complex tectonic environment. Our study strongly suggests that we can use strong‐motion records from earthquakes and apply similar techniques to the ones used to analyze the ambient seismic Field. Online Material: Earthquake catalog.
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Short Note Using Diffuse Field Theory to Interpret the H/V Spectral Ratio from Earthquake Records in Cibeles Seismic Station, Mexico City
2014Co-Authors: V Salinas, Antonio García-jerez, Francisco J. Sánchez-sesma, Francisco Luzón, Hiroshi Kawase, Shinichi Matsushima, Martha Suarez, A Cuellar, Michel CampilloAbstract:It has been recently demonstrated that averaging the autocorrelations of Fields produced by various almost-vertical incoming elastic body plane waves upon a layered system approximately leads to the imaginary part of the corresponding 1D Green's functions for deep sources located underneath the receiver (Kawase et al., 2011). Thus, the ensemble of these waves from deep earthquakes recorded in a station located in the epicentral zone is interpreted as a Diffuse Field. In this short note, we extend the study to consider earthquakes recorded in a station located at epicentral distances of up to hundreds of kilometers. We consider the horizontal-to-vertical spec- tral ratio (HVSR) of the averaged P, S, and coda waves and full earthquake records at the Cibeles station (Mexico City Accelerometric Network) and compare thesewith the results obtained with the corresponding HVSR for the 1D (Kawase et al., 2011) and the 3D (Sanchez-Sesma, Rodriguez, et al., 2011) Diffuse Fields models. Using the signals of 90 earthquakes recorded at Cibeles, we find that the experimental results have distinctive features compatible with the 3D signature of a Diffuse Field. We in- terpret this result as a consequence of the multiple paths that seismic waves undergo from the subducting slab to the Mexico City valley and to the multiple scattering in a complex tectonic environment. Our study strongly suggests that we can use strong- motion records from earthquakes and apply similar techniques to the ones used to analyze the ambient seismic Field.
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The Optimal Use of Horizontal-to-Vertical Spectral Ratios of Earthquake Motions for Velocity Inversions Based on Diffuse-Field Theory for Plane Waves
Bulletin of the Seismological Society of America, 2011Co-Authors: Hiroshi Kawase, Francisco J. Sánchez-sesma, Shinichi MatsushimaAbstract:The coda of earthquake motions and microtremors are sometimes referred to as Diffuse-wave Fields. They are generated by the multiple scattering due to the complexity of the Earth. It is accepted that the average cross correlation between the Diffuse-Field motions at pairs of receivers, in the frequency domain, is proportional to the imaginary part of the Green’s function between these locations. The average autocorrelation of a single receiver is also proportional to the imaginary part of the Green’s function when both the source and receiver are the same. In this study we explored the application of Diffuse-Field concepts to analyze earthquake records at a site when its site effect can be described using a 1D model. We derived a corollary of Claerbout’s result for a 1D layered medium. We found that the imaginary part of the Green’s function at the free surface is proportional to the square of the absolute value of the corresponding transfer function for a plane, vertically incident wave. We considered a set of incoming plane waves (of P , SV , and SH types) with varying azimuths and incidence angles. After summing up a few hundred synthetics with inclined incidences we obtained horizontal-to-vertical (H/V) spectral ratios that match the ratios estimated from the simple theory of Diffuse Field. By using observed records in Japan, we found that the earthquake H/V ratios are quite stable and converge rapidly regardless of what part of the waveform is used, except the P -wave part. We also found that their spectral characteristics can be reproduced well by the velocity structures estimated in previous studies. However, theory and observation were not in perfect agreement, which in turn means that the inversion of a 1D structure could be accomplished by adopting the proposed theory for earthquake H/V spectral ratios.
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Energy Partitions among Elastic Waves for Dynamic Surface Loads in a Semi-Infinite Solid
Bulletin of the Seismological Society of America, 2011Co-Authors: Francisco J. Sánchez-sesma, Francisco Luzón, Richard L. Weaver, Hiroshi Kawase, Shinichi Matsushima, Michel CampilloAbstract:We examine the energy partitions among elastic waves due to dynamic normal and tangential surface loads in a semi-infinite elastic solid. While the results for a dynamic normal load on the surface of a half-space with Poisson ratio of 1/4 is a well-known result by Miller and Pursey (1955), the corresponding results for a dynamic tangential load are almost unknown. The partitions for the normal and tangential loads were computed independently by Weaver (1985) versus Poisson ratio (0≤ν≤1/2), using Diffuse-Field concepts within the context of ultrasonic measurements. The connection with the surface load point was not explicit, which partially explains why these results did not reach the seismological and engineering literature. The characteristics of the elastic radiation of these two cases are quite different. For a normal load, about 2/3 of the energy leaves the loaded point as Rayleigh surface waves. On the other hand, the tangential load induces a similar amount in the form of body shear waves. It is established that the energies injected into the elastic half-space by concentrated normal and tangential harmonic surface loads are proportional to the imaginary part of the corresponding components of the Green's tensor when both source and receiver coincide. The relationship between the Green's function and average correlations of motions within a Diffuse Field is clearly established.
Alain Le Bot - One of the best experts on this subject based on the ideXlab platform.
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STATISTICAL ENERGY ANALYSIS AND Diffuse Field
2019Co-Authors: Alain Le Bot, Nicolas Totaro, Laurent MaxitAbstract:Statistical energy analysis (SEA) is a statistical theory of sound and vibration based on an analogy with thermodynamics. The main relationship of statistical energy analysis, the so-called coupling power proportionality, is intimately linked with the establishment of a Diffuse vibration Field in subsystems. In this study, we explore the conditions under which a Diffuse Field is enforced. We show that when the subsystem is excited by a point force, a low damping, a high frequency but also a ergodic billiard geometry are required conditions. Then, the energy exchange between two weakly coupled subsystems is proportional to the difference of vibrational energies. But when the Field is not Diffuse, the exchange of energy does not generally follow this proportionality. Numerical simulations are provided to support the discussion.
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Review of statistical energy analysis hypotheses in vibroacoustics
Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 2014Co-Authors: Thibault Lafont, Nicolas Totaro, Alain Le BotAbstract:This paper is a discussion of the equivalence between rain-on-the-roof excitation, Diffuse Field and modal energy equipartition hypotheses when using statistical energy analysis (SEA). A first example of a simply supported plate is taken to quantify whether a Field is Diffuse or the energy is equally distributed among modes. It is shown that the Field can be Diffuse in a certain region of the frequency-damping domain with a single point force but without energy equipartition. For a rain-on-the-roof excitation, the energy becomes equally distributed, and the Diffuse Field is enforced in all regions. A second example of two plates coupled by a light spring is discussed. It is shown that in addition to previous conclusions, the power exchanged between plates agrees with the statistical prediction of SEA if and only if the Field is Diffuse. The special case of energy equipartition confirms this observation.
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STATISTICAL ENERGY ANALYSIS: CORRELATION BETWEEN Diffuse Field AND ENERGY EQUIPARTITION
2013Co-Authors: Thibault Lafont, Alain Le Bot, Nicolas TotaroAbstract:This paper studies two concepts used in Statistical Energy Analysis (SEA): the Diffuse Field and the energy equipartition. To study the equivalence between these concepts the example of a simply supported plate is taken. First, the degree of Diffuseness of the Field is quantified by a simple criterion. Then, extracting information from an analytical model, the standard deviation of modal energies is evaluated. Two maps are drawn on the frequency-damping plane in both cases. These maps allow correlating concepts of Diffuse Field and energy equipartition and validity diagrams defined by Le Bot.
Oleg I. Lobkis - One of the best experts on this subject based on the ideXlab platform.
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the mean and variance of Diffuse Field correlations in finite bodies
Journal of the Acoustical Society of America, 2005Co-Authors: Richard L. Weaver, Oleg I. LobkisAbstract:A model consisting of uniformly distributed concentrated transient sources in closed reverberant systems is used to construct predictions for the Diffuse Field correlation function and its variance. Such correlations are useful for passive imaging. It is found that the variance is small compared with the square of the mean if estimates are based on a sufficient number of sources, and if a sufficiently long data record is taken from each source. Requirements are predicted to be most onerous at high frequency. Laboratory measurements support this theory. They furthermore indicate that the fidelity of the passively obtained correlation function to an actively obtained waveform depends, not only on having sufficient passive data, but also on an informed compensation for source spectrum and receiver characteristics. It is anticipated that these arguments will be relevant to convergence rates and fidelity for passive imaging in open systems such as are found in seismology and ocean acoustics.
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Fluctuations in Diffuse Field-Field correlations and the emergence of the Green's function in open systems
The Journal of the Acoustical Society of America, 2005Co-Authors: Richard L. Weaver, Oleg I. LobkisAbstract:Recent intense interest in Diffuse Field correlation functions, with applications to passive imaging in underwater acoustics and seismology, has raised questions about the degree with which a retrieved waveform can be expected to conform to the Green's function, and in particular the degree with which a ray arrival may be discerned. On considering a simple scalar wave model consisting of Fields with distributed random sources, the difffuse Field-Field correlation function R is defined as a sum of correlation integrals, one for each of the many distinct distributed sources. It is then shown that this ensemble of Fields has a correlation function with expectation (R) equal to the Green's function. This model also lends itself to calculations of the variance of R, and thus to estimates of the degree to which an R calculated using finite amounts of data will conform to the Green's function. The model predicts that such conformation is strongest at low frequencies. Ray arrivals are detectable if sufficient data have been collected, but the amount of data needed scales in three dimensions with the square of the source-receiver separation, and the square of the frequency. Applications to seismology are discussed.
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On the emergence of the Green's function in the correlations of a Diffuse Field: pulse-echo using thermal phonons.
Ultrasonics, 2002Co-Authors: Richard Weaver, Oleg I. LobkisAbstract:It is shown that a Diffuse Field is not devoid of phase information, but has a correlation function equal to the Green's function. More specifically, the cross-correlation between Diffuse signals in two transducers is very nearly equal to the direct response of one transducer to an impulse applied to the other. This is true whether the Diffuse Field is one that was created by a distant source, or (if the detectors are sufficiently sensitive) created by thermal fluctuations in the specimen. Here we outline and review proofs, and laboratory demonstrations, from three recent archival publications.
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On the emergence of the Green's function in the correlations of a Diffuse Field
The Journal of the Acoustical Society of America, 2001Co-Authors: Oleg I. Lobkis, Richard L. WeaverAbstract:A Diffuse acoustic Field is shown to have correlations equal to the Green’s function of the body. Simple plausibility arguments for this assertion are followed by a more detailed proof. A careful version of the statement is found to include caveats in regard to how Diffuse the Field truly is, the spectrum of the Diffuse Field, and the phase of the receivers. Ultrasonic laboratory tests confirm the assertion. The main features of the direct signal between two transducers are indeed recovered by cross correlating their responses to a Diffuse Field generated by a third transducer. The quality of the recovery improves with increased averaging and the use of multiple sources. Applications are discussed.
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temperature dependence of Diffuse Field phase
Ultrasonics, 2000Co-Authors: Richard L. Weaver, Oleg I. LobkisAbstract:Abstract Diffuse Fields, which have scattered from microstructure or reflected from walls so much as to prohibit conventional analyses, are usually examined by means of the time evolution of their ultrasonic spectral energy density. The phase information is usually discarded as resisting analysis. The phase, while unpredictable is, however, robust; according to theory it remains constant if source and receiver are not disturbed. Nevertheless, in practice we do observe slow drifts of phase over time scales of minutes. Here we examine the hypothesis that the phase drifts are due to temperature fluctuations. Temperature changes on cooling from 40°C to room temperature were monitored and compared with changes in Diffuse Field phase. It was found that the reverberant ultrasonic Field in a 7 cm aluminum block evolves with temperature in a manner that is in accord with published data on the temperature dependence of the ultrasonic velocities. Our 1 MHz transient source gives rise to a complex waveform that is observed to undergo an almost pure dilation. The precision with which this shift can be measured approaches 20 ns. This is remarkable when compared with the 100 ms travel time of the signal. Thus the temperature dependence of elastic wave speed is measured with a precision limited by the precision of one's thermometer. The signal is also found to suffer some distortion which, it is suggested, is related to the different rates of change of longitudinal and shear speeds. The corresponding prediction for the degree of distortion is found to be in accord with measurements.