Earthquake Science/Earthquake science, Feb 1, 2024
• The singularity of critical modes in a horizontally layered medium is investigated when the pha... more • The singularity of critical modes in a horizontally layered medium is investigated when the phase velocity at certain frequency of a mode is equal to the velocity of the P or S wave in a layer. • A method for calculating the eigendisplacements of these critical modes in the classical transfer matrix method is proposed. • It is found that the eigendisplacement of the critical mode whose phase velocity equal to S velocity in the bottom half-space remains constant in the bottom half-space, instead of decaying to zero with depth as normal modes. • An SH critical mode (Love mode) exists in a uniform half-space model with a phase velocity equal to the S velocity, which is similar to the classical Rayleigh mode of P-SV type in the uniform half-space, but the eigenfunction remains constant with depth.
Dense array observation and seismic interferometry have revolutionized the imaging schemes of the... more Dense array observation and seismic interferometry have revolutionized the imaging schemes of the earth structure. It is becoming possible to directly obtain the lateral variation of the ear th's str ucture b y appl ying array-based methods such as the cross-correlation beamforming (CBF) of the ambient noise to the subsets of the dense array, without tomography. CBF has been prov en to e xtract the azimuth-av eraged multimode surface wav e dispersion curv es. Howev er, the resolution of the dispersion image generated by conventional CBF is low at high frequencies in the frequenc y-v elocity (f-v) domain. Moreov er, the irre gular array geometry and unev en source distribution would bias the result of CBF, especially for the estimation of azimuthdependent velocity. In this paper , tw o beamforming (BF) es are suggested to improve the resolution of multimode dispersion images in the f-v domain. First, the geometrical spreading of the wavefield is corrected to enhance the amplitude at high frequency (or large distance) and thereby improve the resolution of the dispersion image at high frequency. We call this scheme weighted correlation beamforming (WCBF). The azimuth-averaged velocity can be estimated with sufficient resolution using WCBF by stacking the BF output at each azimuth. We show that WCBF is the 2-D Fourier transform of the spatial wavefield from the viewpoint of the wavefield transform. Secondly, a modified beamforming scheme (MCBF) is suggested to reduce the effect of uneven source and/or irregular array geometry. The delay and summation in MCBF are performed only for plane waves incident from the stationary phase region. The azimuth-dependent velocity can therefore be estimated by MCBF with less dependence on the array geometry, as well as on the uneven source distribution. In terms of the estimation of azimuth-averaged phase velocity, we show the F-J method, another array-based method for extracting multimode surface waves from ambient noise using the Fourier-Bessel transform, is the azimuth-averaged version of WCBF. The reliability of WCBF and MCBF is verified based on the synthetic and field data using the array with different geometry. The dispersion image of multimode Rayleigh wave phase velocity at local and regional scales can be generated by WCBF or MCBF with high resolution. In particular, multimode dispersion curves at the local scale can be measured by MCBF with sufficient accuracy using quite short recordings from hours to days. This offers the possibility of a rapid assessment of the media properties.
In this paper,finite frequency 3D sensitivity kernel is studied using the mode coupling method un... more In this paper,finite frequency 3D sensitivity kernel is studied using the mode coupling method under the assumption of far field and Born approximation.For the horizontal layered reference media,which is always encountered in the application of Rayleigh waves in geotechnical engineering,3D sensitivity kernel of the perturbed surface wave amplitude and phase caused by the perturbation of the shear wave velocity is computed.The effects of the mode coupling on the kernel are investigated.Studies show that under the JWKB approximation the 3D sensitivity kernel of the perturbed density and wave velocity is reduced to the 2D sensitivity kernel of the perturbed surface wave phase velocity.That means in the first step for the pure path averaged inversion the finite frequency surface wave tomography is similar to the traditional one based on ray theory,just replacing the 1D sensitivity with 2D sensitivity kernel.If the cross-mode coupling is significant,however,the traditional two-step method breaks down and the shear wave velocity should be directly inverted by introducing the 3D sensitivity kernel in finite frequency surface wave tomography.
Noise Cross‐Correlation Function (NCF) is obtained by processing one‐year ambient noise observed ... more Noise Cross‐Correlation Function (NCF) is obtained by processing one‐year ambient noise observed at over 180 broad‐band stations of the North China Array. All available three‐components time series are used to extract Rayleigh and Love waves. The Signal‐to‐Noise Ratio (SNR) at different periods and the azimuth distribution of the inter‐station pairs with high SNR are discussed. The azimuth distributions of the ambient noise sources are investigated by analyzing the beamforming output. Although seasonal variations are observed from the beamforming output, the noise sources at 10~32 s are almost uniformly distributed in all directions, which allows us to perform detailed tomography successfully.
• The singularity of critical modes in a horizontally layered medium is investigated when the pha... more • The singularity of critical modes in a horizontally layered medium is investigated when the phase velocity at certain frequency of a mode is equal to the velocity of the P or S wave in a layer. • A method for calculating the eigendisplacements of these critical modes in the classical transfer matrix method is proposed. • It is found that the eigendisplacement of the critical mode whose phase velocity equal to S velocity in the bottom half-space remains constant in the bottom half-space, instead of decaying to zero with depth as normal modes. • An SH critical mode (Love mode) exists in a uniform half-space model with a phase velocity equal to the S velocity, which is similar to the classical Rayleigh mode of P-SV type in the uniform half-space, but the eigenfunction remains constant with depth.
Dense array observation and seismic interferometry have revolutionized the imaging schemes of the... more Dense array observation and seismic interferometry have revolutionized the imaging schemes of the earth structure. It is becoming possible to directly obtain the lateral variation of the ear th's str ucture b y appl ying array-based methods such as the cross-correlation beamforming (CBF) of the ambient noise to the subsets of the dense array, without tomography. CBF has been prov en to e xtract the azimuth-av eraged multimode surface wav e dispersion curv es. Howev er, the resolution of the dispersion image generated by conventional CBF is low at high frequencies in the frequenc y-v elocity (f-v) domain. Moreov er, the irre gular array geometry and unev en source distribution would bias the result of CBF, especially for the estimation of azimuthdependent velocity. In this paper , tw o beamforming (BF) es are suggested to improve the resolution of multimode dispersion images in the f-v domain. First, the geometrical spreading of the wavefield is corrected to enhance the amplitude at high frequency (or large distance) and thereby improve the resolution of the dispersion image at high frequency. We call this scheme weighted correlation beamforming (WCBF). The azimuth-averaged velocity can be estimated with sufficient resolution using WCBF by stacking the BF output at each azimuth. We show that WCBF is the 2-D Fourier transform of the spatial wavefield from the viewpoint of the wavefield transform. Secondly, a modified beamforming scheme (MCBF) is suggested to reduce the effect of uneven source and/or irregular array geometry. The delay and summation in MCBF are performed only for plane waves incident from the stationary phase region. The azimuth-dependent velocity can therefore be estimated by MCBF with less dependence on the array geometry, as well as on the uneven source distribution. In terms of the estimation of azimuth-averaged phase velocity, we show the F-J method, another array-based method for extracting multimode surface waves from ambient noise using the Fourier-Bessel transform, is the azimuth-averaged version of WCBF. The reliability of WCBF and MCBF is verified based on the synthetic and field data using the array with different geometry. The dispersion image of multimode Rayleigh wave phase velocity at local and regional scales can be generated by WCBF or MCBF with high resolution. In particular, multimode dispersion curves at the local scale can be measured by MCBF with sufficient accuracy using quite short recordings from hours to days. This offers the possibility of a rapid assessment of the media properties.
The SPAC (spatial auto-correlation) of the microtremor is widely used to infer a shallow structur... more The SPAC (spatial auto-correlation) of the microtremor is widely used to infer a shallow structure at local scale. On the regional scale, based on the dispersion curves extracted from the interstation NCFs (noise cross correlation functions), the 2D lateral variation of the surface wave velocity is usually established via pure-path inversion. The retrospective study on seismic interferometry shows that the SPAC of the microtremor in the frequency domain is equivalent to the NCFs in the time domain. Therefore, benefitting from the deployment of large and dense networks, the array-based SPAC technique can be used to process the NCFs of the subsets of the network. The lateral variation of the velocity can thereby be obtained directly without pure-path inversion. In this study, an imaging scheme of SPAC with moving subarray is applied successfully to directly obtain the phase velocity maps of Northeastern Tibetan Plateau at regional scale using the interstation NCFs from ChinArray (Phase II). The array is divided into [ 300 subarrays, and the dispersion curves of each subarray are then extracted by SPAC technique. The 2D phase velocity maps between 7 and 35 s are obtained by combining the results of all subarrays. The results are in good agreement with those obtained by classical surface wave tomography. Compared with beamforming method, the velocity at long periods measured by SPAC suffers less bias caused by the array configure at long periods. It is proved that the array-based SPAC technique with moving subarray can be used to image the earth crust structure at regional scale with quite stable measurements.
We have measured radial anisotropy in the crust beneath the northern part of North China by joint... more We have measured radial anisotropy in the crust beneath the northern part of North China by jointly inverting Rayleigh and Love wave phase velocities at periods less than 35 s from 14 months of ambient noise data recorded by 222 broad-band seismic stations. We also estimate the azimuthal anisotropy of phase velocity from Rayleigh wave data. The fast direction of azimuthal anisotropy varies with periods, NE-SW orientation at short and intermediate periods (10-16 s) and NW-SE orientation at periods larger than 20 s. The NE-SW oriented fast direction of azimuthal anisotropy may be related to the fossilized structural fabrics due to the compression during the Indosinian orogeny from late Palaeozoic to middle Mesozoic. The NW-SE trend of anisotropic fabric in the lower crust and uppermost mantle is probably associated with the later lithospheric extension. The observed radial anisotropy also shows a two-layer feature, negative radial anisotropy (Vsh < Vsv) in the upper crust and positive (Vsh > Vsv) in the middle-lower crust. The compressional tectonics from late Palaeozoic to middle Mesozoic may cause crustal materials align vertically throughout the crust. This vertical fabric could make Vsh slower than Vsv. However, the lithospheric extension in the late Mesozoic to Cenozoic time could overprint the older fabric in the middle and lower crust by magma intrusion and underplating. Horizontal alignment of the material or intruded melt sills due to the extension probably produce the observed strong positive radial anisotropy in the middle and lower crust.
The method of spectrum analysis of surface waves (SASW) is discussed briefly. The analysis of the... more The method of spectrum analysis of surface waves (SASW) is discussed briefly. The analysis of the dispersion curves of Rayleigh waves in the frequencywavenumber (fk) domain is suggested due to the problems encountered in SASW. Three models of the layered media are considered according to typical situations in practice. All the modes that can be effectively excited are analyzed. The excitation and propagation characteristics of the Rayleigh waves are investigated by numerical simulation. The effects of some parameters such as number of channels and distance (s) between the source and the first receiver on the dispersion curves are investigated in detail for three models. Some important results about the number of receiver channels, relative error, mode jumping, and other aspects are obtained. It is found that reliable dispersion curves can be obtained by fk analyses when the distance between the first receiver and the source is greater than one half the wavelength (0.5λ).Key words: dispersion curves, Rayleigh waves, SASW, frequencywavenumber domain, mode jumping.
The French national research project SENSO aims at providing a methodology combining several non ... more The French national research project SENSO aims at providing a methodology combining several non destructive testing methods to evaluate indicators required for assessing the durability of concrete cover. A large set of 0.5m x 0.25m x 0.12m slabs has been built for various water/cement ratios, aggregate sizes and type. Those slabs have been subsequently studied under controlled water saturation level, chloride content and carbonation depth. To perform the numerous surface wave phase velocity dispersion curve measurements required for the data base, LCPC has designed a small size portable robot that records seismograms with a laser interferometer as a receiver. In this paper we describe the robot, the experimental protocol together with the signal processing technique used. Surface wave phase velocity is sensitive to shear and Young moduli (controlled by destructive tests) and to water content that are not necessarily uniform with depth and dispersion of surface wave is observed. Preliminary results of dispersion curves inversion illustrate these variations. Résumé Le projet national SENSO a pour objectif de définir une méthodologie qui combine plusieurs méthodes non destructives pour évaluer des indicateurs nécessaires à l'étude de la durabilité des bétons. Un jeu de plus de 100 dalles de 0,5 m x 0, 25 m x 0,12 m a ainsi été réalisé avec différents rapports eau/ciment, tailles et types de granulats. Pour mener à bien les nombreux essais à différentes teneurs en eau, teneurs en Cl-et profondeurs de carbonatation le LCPC a conçu un robot portable qui enregistre des sismogrammes avec un interféromètre laser en réception pour étudier les courbes de dispersion de vitesse de phase des ondes de surface. Dans cet article nous décrivons le robot, le protocole expérimental et la procédure de traitement du signal utilisée. La vitesse de phase des ondes de surface est sensible au module d'Young (mesuré par essais destructif) et à la teneur en eau qui peuvent varier avec la profondeur. Des résultats préliminaires obtenus avec un algorithme d'inversion des courbes de dispersion en milieu continument variable (par opposition à un milieu multicouche) en cours de validation sont discutés.
Des ondes ultrasonores de surface (dans la bande de fréquence 60 kHz-180 kHz) sont utilisées pour... more Des ondes ultrasonores de surface (dans la bande de fréquence 60 kHz-180 kHz) sont utilisées pour caractériser les premiers centimètres de dalles de bétons. A ces fréquences, la longueur d'onde est du même ordre de grandeur que la dimension des granulats; le caractère fortement hétérogène du béton perturbe la propagation des ondes qui sont alors en régime de diffusion multiple. Les signaux peuvent être scindés en une partie cohérente (qui résiste au calcul des moyennes) et une partie non cohérente correspondant à la diffusion multiple de l'onde incidente sur une configuration donnée de granulats rencontrés. Il est donc nécessaire de mesurer plusieurs réalisations indépendantes du désordre afin d'évaluer le champ cohérent, qui décrit les propriétés d'un milieu homogène effectif. Pour cela, les mesures sont réalisées en surface à l'aide d'un interféromètre laser. On extrait des mesures les courbes de dispersion en vitesse de phase et d'atténuation pour les ondes de Rayleigh cohérentes. Ces courbes mettent en évidence un gradient de propriétés du béton étudié avec la profondeur.
Earthquake Science/Earthquake science, Feb 1, 2024
• The singularity of critical modes in a horizontally layered medium is investigated when the pha... more • The singularity of critical modes in a horizontally layered medium is investigated when the phase velocity at certain frequency of a mode is equal to the velocity of the P or S wave in a layer. • A method for calculating the eigendisplacements of these critical modes in the classical transfer matrix method is proposed. • It is found that the eigendisplacement of the critical mode whose phase velocity equal to S velocity in the bottom half-space remains constant in the bottom half-space, instead of decaying to zero with depth as normal modes. • An SH critical mode (Love mode) exists in a uniform half-space model with a phase velocity equal to the S velocity, which is similar to the classical Rayleigh mode of P-SV type in the uniform half-space, but the eigenfunction remains constant with depth.
Dense array observation and seismic interferometry have revolutionized the imaging schemes of the... more Dense array observation and seismic interferometry have revolutionized the imaging schemes of the earth structure. It is becoming possible to directly obtain the lateral variation of the ear th&#39;s str ucture b y appl ying array-based methods such as the cross-correlation beamforming (CBF) of the ambient noise to the subsets of the dense array, without tomography. CBF has been prov en to e xtract the azimuth-av eraged multimode surface wav e dispersion curv es. Howev er, the resolution of the dispersion image generated by conventional CBF is low at high frequencies in the frequenc y-v elocity (f-v) domain. Moreov er, the irre gular array geometry and unev en source distribution would bias the result of CBF, especially for the estimation of azimuthdependent velocity. In this paper , tw o beamforming (BF) es are suggested to improve the resolution of multimode dispersion images in the f-v domain. First, the geometrical spreading of the wavefield is corrected to enhance the amplitude at high frequency (or large distance) and thereby improve the resolution of the dispersion image at high frequency. We call this scheme weighted correlation beamforming (WCBF). The azimuth-averaged velocity can be estimated with sufficient resolution using WCBF by stacking the BF output at each azimuth. We show that WCBF is the 2-D Fourier transform of the spatial wavefield from the viewpoint of the wavefield transform. Secondly, a modified beamforming scheme (MCBF) is suggested to reduce the effect of uneven source and/or irregular array geometry. The delay and summation in MCBF are performed only for plane waves incident from the stationary phase region. The azimuth-dependent velocity can therefore be estimated by MCBF with less dependence on the array geometry, as well as on the uneven source distribution. In terms of the estimation of azimuth-averaged phase velocity, we show the F-J method, another array-based method for extracting multimode surface waves from ambient noise using the Fourier-Bessel transform, is the azimuth-averaged version of WCBF. The reliability of WCBF and MCBF is verified based on the synthetic and field data using the array with different geometry. The dispersion image of multimode Rayleigh wave phase velocity at local and regional scales can be generated by WCBF or MCBF with high resolution. In particular, multimode dispersion curves at the local scale can be measured by MCBF with sufficient accuracy using quite short recordings from hours to days. This offers the possibility of a rapid assessment of the media properties.
In this paper,finite frequency 3D sensitivity kernel is studied using the mode coupling method un... more In this paper,finite frequency 3D sensitivity kernel is studied using the mode coupling method under the assumption of far field and Born approximation.For the horizontal layered reference media,which is always encountered in the application of Rayleigh waves in geotechnical engineering,3D sensitivity kernel of the perturbed surface wave amplitude and phase caused by the perturbation of the shear wave velocity is computed.The effects of the mode coupling on the kernel are investigated.Studies show that under the JWKB approximation the 3D sensitivity kernel of the perturbed density and wave velocity is reduced to the 2D sensitivity kernel of the perturbed surface wave phase velocity.That means in the first step for the pure path averaged inversion the finite frequency surface wave tomography is similar to the traditional one based on ray theory,just replacing the 1D sensitivity with 2D sensitivity kernel.If the cross-mode coupling is significant,however,the traditional two-step method breaks down and the shear wave velocity should be directly inverted by introducing the 3D sensitivity kernel in finite frequency surface wave tomography.
Noise Cross‐Correlation Function (NCF) is obtained by processing one‐year ambient noise observed ... more Noise Cross‐Correlation Function (NCF) is obtained by processing one‐year ambient noise observed at over 180 broad‐band stations of the North China Array. All available three‐components time series are used to extract Rayleigh and Love waves. The Signal‐to‐Noise Ratio (SNR) at different periods and the azimuth distribution of the inter‐station pairs with high SNR are discussed. The azimuth distributions of the ambient noise sources are investigated by analyzing the beamforming output. Although seasonal variations are observed from the beamforming output, the noise sources at 10~32 s are almost uniformly distributed in all directions, which allows us to perform detailed tomography successfully.
• The singularity of critical modes in a horizontally layered medium is investigated when the pha... more • The singularity of critical modes in a horizontally layered medium is investigated when the phase velocity at certain frequency of a mode is equal to the velocity of the P or S wave in a layer. • A method for calculating the eigendisplacements of these critical modes in the classical transfer matrix method is proposed. • It is found that the eigendisplacement of the critical mode whose phase velocity equal to S velocity in the bottom half-space remains constant in the bottom half-space, instead of decaying to zero with depth as normal modes. • An SH critical mode (Love mode) exists in a uniform half-space model with a phase velocity equal to the S velocity, which is similar to the classical Rayleigh mode of P-SV type in the uniform half-space, but the eigenfunction remains constant with depth.
Dense array observation and seismic interferometry have revolutionized the imaging schemes of the... more Dense array observation and seismic interferometry have revolutionized the imaging schemes of the earth structure. It is becoming possible to directly obtain the lateral variation of the ear th's str ucture b y appl ying array-based methods such as the cross-correlation beamforming (CBF) of the ambient noise to the subsets of the dense array, without tomography. CBF has been prov en to e xtract the azimuth-av eraged multimode surface wav e dispersion curv es. Howev er, the resolution of the dispersion image generated by conventional CBF is low at high frequencies in the frequenc y-v elocity (f-v) domain. Moreov er, the irre gular array geometry and unev en source distribution would bias the result of CBF, especially for the estimation of azimuthdependent velocity. In this paper , tw o beamforming (BF) es are suggested to improve the resolution of multimode dispersion images in the f-v domain. First, the geometrical spreading of the wavefield is corrected to enhance the amplitude at high frequency (or large distance) and thereby improve the resolution of the dispersion image at high frequency. We call this scheme weighted correlation beamforming (WCBF). The azimuth-averaged velocity can be estimated with sufficient resolution using WCBF by stacking the BF output at each azimuth. We show that WCBF is the 2-D Fourier transform of the spatial wavefield from the viewpoint of the wavefield transform. Secondly, a modified beamforming scheme (MCBF) is suggested to reduce the effect of uneven source and/or irregular array geometry. The delay and summation in MCBF are performed only for plane waves incident from the stationary phase region. The azimuth-dependent velocity can therefore be estimated by MCBF with less dependence on the array geometry, as well as on the uneven source distribution. In terms of the estimation of azimuth-averaged phase velocity, we show the F-J method, another array-based method for extracting multimode surface waves from ambient noise using the Fourier-Bessel transform, is the azimuth-averaged version of WCBF. The reliability of WCBF and MCBF is verified based on the synthetic and field data using the array with different geometry. The dispersion image of multimode Rayleigh wave phase velocity at local and regional scales can be generated by WCBF or MCBF with high resolution. In particular, multimode dispersion curves at the local scale can be measured by MCBF with sufficient accuracy using quite short recordings from hours to days. This offers the possibility of a rapid assessment of the media properties.
The SPAC (spatial auto-correlation) of the microtremor is widely used to infer a shallow structur... more The SPAC (spatial auto-correlation) of the microtremor is widely used to infer a shallow structure at local scale. On the regional scale, based on the dispersion curves extracted from the interstation NCFs (noise cross correlation functions), the 2D lateral variation of the surface wave velocity is usually established via pure-path inversion. The retrospective study on seismic interferometry shows that the SPAC of the microtremor in the frequency domain is equivalent to the NCFs in the time domain. Therefore, benefitting from the deployment of large and dense networks, the array-based SPAC technique can be used to process the NCFs of the subsets of the network. The lateral variation of the velocity can thereby be obtained directly without pure-path inversion. In this study, an imaging scheme of SPAC with moving subarray is applied successfully to directly obtain the phase velocity maps of Northeastern Tibetan Plateau at regional scale using the interstation NCFs from ChinArray (Phase II). The array is divided into [ 300 subarrays, and the dispersion curves of each subarray are then extracted by SPAC technique. The 2D phase velocity maps between 7 and 35 s are obtained by combining the results of all subarrays. The results are in good agreement with those obtained by classical surface wave tomography. Compared with beamforming method, the velocity at long periods measured by SPAC suffers less bias caused by the array configure at long periods. It is proved that the array-based SPAC technique with moving subarray can be used to image the earth crust structure at regional scale with quite stable measurements.
We have measured radial anisotropy in the crust beneath the northern part of North China by joint... more We have measured radial anisotropy in the crust beneath the northern part of North China by jointly inverting Rayleigh and Love wave phase velocities at periods less than 35 s from 14 months of ambient noise data recorded by 222 broad-band seismic stations. We also estimate the azimuthal anisotropy of phase velocity from Rayleigh wave data. The fast direction of azimuthal anisotropy varies with periods, NE-SW orientation at short and intermediate periods (10-16 s) and NW-SE orientation at periods larger than 20 s. The NE-SW oriented fast direction of azimuthal anisotropy may be related to the fossilized structural fabrics due to the compression during the Indosinian orogeny from late Palaeozoic to middle Mesozoic. The NW-SE trend of anisotropic fabric in the lower crust and uppermost mantle is probably associated with the later lithospheric extension. The observed radial anisotropy also shows a two-layer feature, negative radial anisotropy (Vsh < Vsv) in the upper crust and positive (Vsh > Vsv) in the middle-lower crust. The compressional tectonics from late Palaeozoic to middle Mesozoic may cause crustal materials align vertically throughout the crust. This vertical fabric could make Vsh slower than Vsv. However, the lithospheric extension in the late Mesozoic to Cenozoic time could overprint the older fabric in the middle and lower crust by magma intrusion and underplating. Horizontal alignment of the material or intruded melt sills due to the extension probably produce the observed strong positive radial anisotropy in the middle and lower crust.
The method of spectrum analysis of surface waves (SASW) is discussed briefly. The analysis of the... more The method of spectrum analysis of surface waves (SASW) is discussed briefly. The analysis of the dispersion curves of Rayleigh waves in the frequencywavenumber (fk) domain is suggested due to the problems encountered in SASW. Three models of the layered media are considered according to typical situations in practice. All the modes that can be effectively excited are analyzed. The excitation and propagation characteristics of the Rayleigh waves are investigated by numerical simulation. The effects of some parameters such as number of channels and distance (s) between the source and the first receiver on the dispersion curves are investigated in detail for three models. Some important results about the number of receiver channels, relative error, mode jumping, and other aspects are obtained. It is found that reliable dispersion curves can be obtained by fk analyses when the distance between the first receiver and the source is greater than one half the wavelength (0.5λ).Key words: dispersion curves, Rayleigh waves, SASW, frequencywavenumber domain, mode jumping.
The French national research project SENSO aims at providing a methodology combining several non ... more The French national research project SENSO aims at providing a methodology combining several non destructive testing methods to evaluate indicators required for assessing the durability of concrete cover. A large set of 0.5m x 0.25m x 0.12m slabs has been built for various water/cement ratios, aggregate sizes and type. Those slabs have been subsequently studied under controlled water saturation level, chloride content and carbonation depth. To perform the numerous surface wave phase velocity dispersion curve measurements required for the data base, LCPC has designed a small size portable robot that records seismograms with a laser interferometer as a receiver. In this paper we describe the robot, the experimental protocol together with the signal processing technique used. Surface wave phase velocity is sensitive to shear and Young moduli (controlled by destructive tests) and to water content that are not necessarily uniform with depth and dispersion of surface wave is observed. Preliminary results of dispersion curves inversion illustrate these variations. Résumé Le projet national SENSO a pour objectif de définir une méthodologie qui combine plusieurs méthodes non destructives pour évaluer des indicateurs nécessaires à l'étude de la durabilité des bétons. Un jeu de plus de 100 dalles de 0,5 m x 0, 25 m x 0,12 m a ainsi été réalisé avec différents rapports eau/ciment, tailles et types de granulats. Pour mener à bien les nombreux essais à différentes teneurs en eau, teneurs en Cl-et profondeurs de carbonatation le LCPC a conçu un robot portable qui enregistre des sismogrammes avec un interféromètre laser en réception pour étudier les courbes de dispersion de vitesse de phase des ondes de surface. Dans cet article nous décrivons le robot, le protocole expérimental et la procédure de traitement du signal utilisée. La vitesse de phase des ondes de surface est sensible au module d'Young (mesuré par essais destructif) et à la teneur en eau qui peuvent varier avec la profondeur. Des résultats préliminaires obtenus avec un algorithme d'inversion des courbes de dispersion en milieu continument variable (par opposition à un milieu multicouche) en cours de validation sont discutés.
Des ondes ultrasonores de surface (dans la bande de fréquence 60 kHz-180 kHz) sont utilisées pour... more Des ondes ultrasonores de surface (dans la bande de fréquence 60 kHz-180 kHz) sont utilisées pour caractériser les premiers centimètres de dalles de bétons. A ces fréquences, la longueur d'onde est du même ordre de grandeur que la dimension des granulats; le caractère fortement hétérogène du béton perturbe la propagation des ondes qui sont alors en régime de diffusion multiple. Les signaux peuvent être scindés en une partie cohérente (qui résiste au calcul des moyennes) et une partie non cohérente correspondant à la diffusion multiple de l'onde incidente sur une configuration donnée de granulats rencontrés. Il est donc nécessaire de mesurer plusieurs réalisations indépendantes du désordre afin d'évaluer le champ cohérent, qui décrit les propriétés d'un milieu homogène effectif. Pour cela, les mesures sont réalisées en surface à l'aide d'un interféromètre laser. On extrait des mesures les courbes de dispersion en vitesse de phase et d'atténuation pour les ondes de Rayleigh cohérentes. Ces courbes mettent en évidence un gradient de propriétés du béton étudié avec la profondeur.
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Papers by Laiyu Lu
• A method for calculating the eigendisplacements of these critical modes in the classical transfer matrix method is proposed.
• It is found that the eigendisplacement of the critical mode whose phase velocity equal to S velocity in the bottom half-space remains constant in the bottom half-space, instead of decaying to zero with depth as normal modes.
• An SH critical mode (Love mode) exists in a uniform half-space model with a phase velocity equal to the S velocity, which is similar to the classical Rayleigh mode of P-SV type in the uniform half-space, but the eigenfunction remains constant with depth.
• A method for calculating the eigendisplacements of these critical modes in the classical transfer matrix method is proposed.
• It is found that the eigendisplacement of the critical mode whose phase velocity equal to S velocity in the bottom half-space remains constant in the bottom half-space, instead of decaying to zero with depth as normal modes.
• An SH critical mode (Love mode) exists in a uniform half-space model with a phase velocity equal to the S velocity, which is similar to the classical Rayleigh mode of P-SV type in the uniform half-space, but the eigenfunction remains constant with depth.