Multimode Dispersion Curves Research Articles

Multichannel surface wave analysis of reinforced concrete pipe segments using longitudinal and circumferential waves induced by a point impact

In this paper, we extend the multichannel surface wave (MASW) analysis method for non-destructive testing (NDT) of medium to large diameter concrete pipe segments. In a typical MASW investigation, experimentally obtained surface wave records from an elastic medium are transformed into dispersion curves and compared with the appropriate theory to inversely determine the unknown parameters of the medium. We extend this procedure for the lengthwise and circumferential inspection of an individual concrete pipe segment by employing longitudinal and circumferential waves. These waves are generated by a point impact applied perpendicular to the pipe surface. Using finite element based simulations, it is first shown that the dispersion properties of surface waves traveling along two orthogonal cross-sections of a pipe segment, which intersect the impact point, agrees with the corresponding theoretical properties of longitudinal modes in an infinite hollow cylinder and circumferential Lamb wave modes in a circular annulus. This forms the basis for implementing the MASW method along the lengthwise and angular directions of the pipe, independently. Using the lessons learned from numerical study, an experimental demonstration of the proposed angular MASW implementation is carried out in a reinforced concrete pipe segment held under laboratory conditions. Equations for a cylindrical version of the phase-shift based wavefield transform given in [1] is presented for use in this process and its effectiveness to extract the angular phase velocity spectra from an actual record is demonstrated. Finally, it is shown that multi-modal dispersion curves can be extracted from an actual reinforced concrete pipe segment and its unknown elastic properties can be determined using the proposed method. The numerical models developed in this paper are validated by comparing its results against the measured data.

Dispersion analysis of borehole sonic measurements by Hilbert transform and band-pass filters

Dispersion analysis of waves can reveal important mechanical properties of the formation around the borehole. The traditional dispersion analysis methods are affected by wave modes and aliasing. A new method is developed to perform dispersion analysis of borehole array acoustic logging, which combines the semblance of time-slowness coherence based on differential phase (STC-DP) processing and band-pass filters. Unlike the classic STC method, STC-DP is not sensitive to the window length. Two kinds of band-pass filters, the multiple filter technique and the finite-impulse response filter, are used. The band-pass filters can decompose the waveform signal into a series of waveforms in the frequency-time domain. In contrast to traditional dispersion analysis methods, there is no knowledge of wave modes. The new method can extract multimode dispersion curves, especially for the weak wave mode. For most dispersion analysis methods, the aliasing will appear in the high-frequency band when the scanning range of slowness is large enough. The aliased modes might interfere with other true modes, but the aliased modes are quite different from other true modes in the time-slowness grid. Therefore, aliased modes can be removed in the time-slowness grid based on the modal dispersion curves. Synthetic and field examples are used to verify the advantages of the proposed method over traditional dispersion analysis methods.

Multimodal determination of Rayleigh dispersion and attenuation curves using the circle fit method

In a multi-channel analysis of surface waves (MASW) experiment, inversion of Rayleigh wave dispersion and attenuation curves is used to determine the shear wave velocity and material damping ratio of shallow soil layers. Peak picking and the half-power bandwidth method can be used to determine the dispersion and attenuation curves, respectively. In this paper, the circle fit method is proposed to improve the determination of multi-modal dispersion and attenuationn curves. A numerical MASW experiment is simulated for a layered halfspace, corresponding to a site in Lincent (Belgium). It is shown that the circle fit method results in more accurate estimations of multi-modal dispersion curves than peak picking. Both the circle fit and half-power bandwidth method result in reliable attenuation curves of dominant modes. For other modes an alternative more robust measure of attenuation, based on the circle fit method, is proposed which would enable inversion of these modes.

Improved seismic profiling by minimally invasive multimodal surface wave method with standard penetration test source (MMSW-SPT)

Abstract Surface waves propagating in layered media inherently possess multimodal dispersion characteristics. However, traditional surface wave testing methods employing measurements at the free surface usually capture only a single apparent dispersion curve, especially when using short geophone arrays common to near surface and geotechnical-scale investigations. Such single-mode or fragmented multimode apparent dispersion curves contain only a fraction of the possible dispersion information, thus limiting the accuracy of inverted profiles. To enable more robust measurement of higher Rayleigh-wave modes, a recently developed hybrid minimally invasive multimodal surface wave method is combined herein with the widely used geotechnical standard penetration test (SPT), which is employed as a practical and ubiquitous downhole source. Upon superimposing surface wave dispersion data for a range of SPT impact depths within the soil, higher modes can be measured more consistently and reliably relative to traditional non-invasive testing methods. As a result, misidentification of multiple dispersion modes can be practically eliminated, significantly improving the accuracy and certainty of inversion results.

Multichannel processing for dispersion curves extraction of ultrasonic axial-transmission signals: Comparisons and case studies.

Some pioneering studies have shown the clinical feasibility of long bones evaluation using ultrasonic guided waves. Such a strategy is typically designed to determine the dispersion information of the guided modes to infer the elastic and structural characteristics of cortical bone. However, there are still some challenges to extract multimode dispersion curves due to many practical limitations, e.g., high spectral density of modes, limited spectral resolution and poor signal-to-noise ratio. Recently, two representative signal processing methods have been proposed to improve the dispersion curves extraction. The first method is based on singular value decomposition (SVD) with advantages of multi-emitter and multi-receiver configuration for enhanced mode extraction; the second one uses linear Radon transform (LRT) with high-resolution imaging of the dispersion curves. To clarify the pros and cons, a face to face comparison was performed between the two methods. The results suggest that the LRT method is suitable to separate the guided modes at low frequency-thickness-product ( fh) range; for multimode signals in broadband fh range, the SVD-based method shows more robust performances for weak mode enhancement and noise filtering. Different methods are valuable to cover the entire fh range for processing ultrasonic axial transmission signals measured in long cortical bones.

Surface-wave testing of soil sites using multichannel simulation with one-receiver

This paper presents a study on the application of the multichannel simulation with one-receiver (MSOR) surface-wave testing method for geophysical profiling of soil sites. The MSOR method reverses the roles of source and receiver in the widely-used multi-channel analysis of surface waves (MASW) method. To examine the feasibility and accuracy of utilizing MSOR for soil sites, finite element simulations of MSOR testing are performed for three types of soil profiles containing horizontal interfaces, a vertical fault, and a dipping interface, respectively. The effects of variations in the moving impact locations on the uncertainty and repeatability of the dispersion trends are analyzed for the different soil profiles. Real-world case studies are carried out to examine the equivalency of the MSOR and MASW methods for quantifying surface-wave dispersion trends of soil profiles, as well as the advantages of MSOR testing with embedded geophones to obtain more extensive multimodal dispersion data. From the computational simulations and field case studies, MSOR is demonstrated to be equivalent to MASW testing for practical purposes. In addition, MSOR has the advantages of reduced instrumentation cost, improved portability, enhanced ability to measure multi-mode dispersion curves by utilizing borehole geophones, and the potential for improving efficiency of 3-D stiffness profiling.

Resolution equivalence of dispersion-imaging methods for noise-free high-frequency surface-wave data

A key step in high-frequency surface-wave methods is to acquire the dispersion properties of surface waves. To pick dispersion curves, surface-wave data is required to be transformed from the time–space (t–x) domain to the frequency–phase velocity (f–v) domain. In constructing accurate multi-mode dispersion curves, it is necessary to generate a reliable and high-resolution image of dispersion energy in the f–v domain. At present, there are five methods available for imaging dispersion energy: the τ-p transformation, the f-k transformation, the phase shift, the frequency decomposition and slant stacking, and the high-resolution linear Radon transformation. Among them, resolution of the high-resolution linear Radon transformation is the highest. We proposed a processing step to enhance resolution of the other four methods. Resolution of the four enhanced methods and high-resolution linear Radon transformation is compared by imaging dispersion energy of the same synthetic data. As a result, the four enhanced methods generated dispersion images with the same resolution, which revealed that the resolution of the five dispersion-imaging methods is essentially equivalent for noise-free data.

Semi-active optimization of 2D wave dispersion into shunted piezo-composite systems for controlling acoustic interaction

Based on recent works on the application of Floquet–Bloch theorem to periodical mechanical systems including frequency-dependent parameters (Collet et al 2011 Int. J. Solids Struct. 48 2837), we propose in this paper an extension to the vibroacoustic behavior analysis of smart structures. The objective is to optimize electronic circuits used to shunt some piezoelectric patches distributed on the structure, in order to minimize the acoustic radiation of the structure. The proposed approach is based on the computation of the multi-modal wave dispersion curves into the whole first Brillouin zone of the structure, and associated propagation characteristics in the acoustic fluid. The impedance of the shunt circuit is then optimized in order to render the acoustic waves evanescent. This work is a collaborative effort supported by the French Research Agency under grant number NT09-617542.

Inversion of shear properties in ocean sediments from numerical Scholte wave

Shear properties in marine environment are important to be measured for the stability of sediments, the tomography of shallow layers, and the conversion of acoustic energy from water-borne into sea bottom. Although surface wave methods are widely used to determine the shear wave velocity profiles at sites, inversion methods of shear attenuation have to be tackled with other difficult problems. So, an inversion method by dispersion curves of surface wave is developed and tested with the numerical Scholte wave data. The method includes three steps: extract of dispersion curves from data, calculation of forward dispersion model, and linear inversion by match of them. To simultaneously estimate dispersion curve of velocity and attenuation, Prony's method is applied for multi-modes of surface wave. Based on the methods of finding complex roots, forward model of dispersion curves is calculated with so accuracy as to get reasonable Jacoby of inversion. Different to inversion of shear velocity, the effect of spread loss is considered and investigated for Scholte wave. The performance of inversion shear wave velocity and attenuation profiles in the upper sediment layers is also examined for multi-mode dispersion curves.

Utilization of multimode Love wave dispersion curve inversion for geotechnical site investigation

Inversion codes based on a modified genetic algorithm (GA) have been developed to invert multimode Love wave dispersion curves. The multimode Love wave dispersion curves were synthesized from the profile representing shear-wave velocity reversal using a full SH (shear horizontal) waveform. In this study, we used a frequency–slowness transform to extract the dispersion curve from the full SH waveform. Dispersion curves overlain in dispersion images were picked manually. These curves were then inverted using the modified GA. To assess the accuracy of the inversion results, differences between the true and inverted shear-wave velocity profile were quantified in terms of shear-wave velocity and thickness errors, ES and EH. Our numerical modeling showed that the inversion of multimode dispersion curves can significantly provide the better assessment of a shear-wave velocity structure, especially with a velocity reversal profile at typical geotechnical site investigations. This approach has been applied on field data acquired at a site in Niigata prefecture, Japan. In these field data, our inversion results show good agreement between the calculated and experimental dispersion curves and accurately detect low velocity layer targets.

Effective dispersion curve and pseudo multimode dispersion curves for Rayleigh wave

The hi-energy bands in the dispersion image are usually interpreted as the true dispersion phase velocities. However, the multiple dispersion modes of Rayleigh wave in layered media stack in space, producing the effective dispersion curve and the pseudo multimode dispersion curves in dispersion image. The effective dispersion curve has the maximum energy with lower phase velocities than pseudo dispersion phase velocities, and thus is often misunderstood as the fundamental mode. Within the tolerable misfit, the effective dispersion curve can approach the true fundamental mode. Different from the true multimode dispersion curves, the pseudo multimode dispersion curves are related to the effective dispersion curve. A numerical model is adapted to simulate the true dispersion curves, effective dispersion curve, and pseudo multimode dispersion curves. Their differences and mutual relations are demonstrated.

Utilization of multimode surface wave dispersion for characterizing roadbed structure

Accurate measurement of shear (S)-wave velocity in a roadbed subsurface with a velocity reversal is crucial as well as challenging. A high frequency Rayleigh wave survey was carried out on a roadbed site from Henan, China to determine S-wave velocities to approximately 15 m depth. The phase shift approach was used to directly construct a high-resolution image of multimode dispersion curves in the frequency–velocity ( f– v) domain from a multi-channel raw shot gather with a high signal-to-noise (S/N) ratio. The measured fundamental and two higher-mode dispersion curves were then inverted by genetic algorithms to reconstruct the fine structure of the tested roadbed subsurface. Our case study demonstrates that an inversion performed with only fundamental mode data with a limited resolution and a high degree of error may yield an unrealistic model. A better agreement with direct borehole measurements, however, is obtained when the second-mode data are inverted simultaneously with the fundamental mode data, which clearly reveals a 1-m thick softer soil layer between two stiff soil layers in the tested roadbed. A higher accuracy S-wave velocity profile is achieved by simultaneously incorporating the three modes of data into the inversion process. This representative case study highlights advantages of fully exploiting intrinsic multimodal properties of Rayleigh waves and greatly enhances our confidence of accurately imaging and characterizing a complex subsurface.

Experiment and Inversion Studies on Rayleigh Wave Considering Higher Modes

AbstractThe dispersive characteristics of the Rayleigh waves propagating in the layered media are investigated experimentally by ultrasonic detection testing, especially in the presence of a low‐velocity layer. Ultrasonic surface detections are implemented for two layered specimens: Lucite/Steel half‐space and Aluminum/Lucite/Steel half‐space. Characteristics of the multimode dispersion curves are analyzed using the frequency‐wavenumber analysis method. The dispersion curves of the first and second modes are obtained for the first specimen of a slow layer on a fast substrate. The dispersion curves for the second specimen containing a low‐velocity mid‐layer are discontinuous and correspond to different mode branches in different frequency ranges due to the mode jumping. Further analysis based on the experimental data demonstrates that the mode jumping is caused by the different surface displacement distribution with frequency for each mode. This indicates that surface displacement distributions of the modes should be also considered for the inversion problems, especially in the stratified media containing a low‐velocity mid‐layer. Parameters of two specimens are inversed by Genetic Algorithm (GA) using the experimental dispersion curves of surface waves. The displacement distributions of each mode are considered in inversion in the presence of a low‐velocity layer. Mode‐misidentification is avoided by the inversion method presented in this paper and satisfied results are obtained.

Experimental analysis of multimode guided waves in stratified media

The dispersive characteristics of multimode guided waves in stratified media are studied experimentally. Ultrasonic surface detections are performed for two layered specimens: lucite/steel half-space and aluminum/lucite/steel half-space. Characteristics of the multimode dispersion curves are analyzed using the frequency-wave number method. The dispersion curves of two modes are obtained for the first specimen of a low-velocity layer on a fast substrate. The dispersion curves for the second specimen containing a low-velocity midlayer are discontinuous and correspond to different modes branches due to mode jumping. Further analysis demonstrates that the mode jumping is caused by the different surface displacement distribution with frequency for each mode. This indicates that the surface displacement distributions of the modes should be also accounted for in the inversion problems, especially in stratified media with a low-velocity midlayer.

Analyzing and Filtering Surface-Wave Energy By Muting Shot Gathers

Accurate estimation of the fundamental-mode dispersion curve is the most critical processing step of many shallow surface-wave methods. Use of multichannel analysis of surface waves (MASW), has proven very effective in separating different dispersive events that share the same seismic-frequency range. Yet, under certain circumstances, even when using such a data-redundant method, it may not be possible to separate the fundamental mode of the surface waves from higher modes. Dominant higher surface-wave modes, together with body- and guided waves, can impede the estimation of the fundamental mode. This is especially true when relatively short spread lengths are required for the survey for reasons such as higher lateral-resolution demands or presence of noise at the far offsets. A simple multichannel processing technique that mutes the interfering seismic waves in the shot records (offset-time [Formula: see text] domain) can be used to analyze and filter noisy surface-wave modes and thus significantly improve the range and resolution of multimodal dispersion curves in the phase-velocity-frequency domain. This is demonstrated on both synthetic and real shot gathers. One shortcoming of the muting method is the estimation of artificially high phase-velocity values at low frequencies. This artifact can be countered by employing dispersion-curve estimation in the same low-frequency range using the unmuted shot records. The proposed muting technique can be beneficial not only for the evaluation of the fundamental mode of the Rayleigh wave, but also for other types of dispersive seismic energy, such as higher Rayleigh-wave modes, Lamb, guided, and Love waves.

Multi-mode propagation and diffusion in structures through finite elements

The present work addresses the question of guided wave properties in structures. Guided multi-modal dispersion curves and diffusion of waves at singularities are the main concern. A propagative approach, based on a finite element model, is formulated. It provides an effective way to calculate the dispersion curves of complex guided structures. Some properties of guided waves are deduced from the formulation. The question of wave diffusion at substructures coupling locations is also considered. A closed formulation of the problem using Lagrange multipliers is presented. Its numerical implementation is detailed. Ultimately, a numerical test is offered. The case study concerns a thin walled structure.

Possible effects of misidentified mode number on Rayleigh wave inversion

Surface wave dispersion data obtained in field surveys are inherently incomplete. Poorly constrained dispersion curves and inclusion of data from higher-mode dispersion curves can be shown to produce erroneous inversion results. The present study evaluates the effects of cross-mode data mixing, and limited data and frequency range on inversion models. Multimodal dispersion curves were generated from synthetic velocity profiles using the forward modeling method. Subsets of the data points obtained by sampling the resulting dispersion curves using different sample intervals, frequency ranges, and by mixing fundamental-mode data with portion of the data from the higher-mode dispersion curves were inverted. The inversion results show that small sample intervals over a wide frequency range and an unambiguous identification of the fundamental-mode dispersion curve are essential factors for the reconstruction of accurate inversion models. The penetration range and accuracy of the inversion models are particularly sensitive to phase velocities at low frequencies of the dispersion curve. The theoretical results were tested with data from a roadbed survey in northern China. Ground model obtained from dispersion data derived by using the F-K method, which contained many cross-mode data points, was found to deviate substantially from the borehole record. A better agreement with the geotechnical record was obtained by inverse modeling of the dispersion data obtained from the fundamental-mode curve of the MASW spectral image.

Simulated annealing inversion of multimode Rayleigh wave dispersion curves for geological structure

SUMMARY Simulated annealing was used to invert fundamental and higher-mode Rayleigh wave dispersion curves simultaneously for an S-wave velocity profile. The inversion was applied to near-surface seismic data (with a maximum depth of investigation of around 10 m) obtained over a thick lacustrine clay sequence. The geology was described either in terms of discrete layers or by a superposition of Chebyshev polynomials in the inversion and the contrasting results compared. Simulated annealing allows for considerable flexibility in model definition and parametrization and seeks a global rather than a local minimum in a misfit function. It has the added advantage in that it can be used to determine uncertainties in inversion parameters, thereby highlighting features in an inverted profile that should be interpreted with caution. Results show that simulated annealing works well for the inversion of multimodal near-surface Rayleigh wave dispersion curves relative to the same inversion that employs only the fundamental mode.

The ferroelectric domain layer interface wave in multiple domain layered structure

A theoretical analysis is made of the ferroelectric domain layer interface wave in a multiple domain layered structure. The dispersion equation is presented and the dispersion curves are obtained. When domain layer N is large, the multimode dispersion curves form a dispersion band. There are three kinds of dispersion curves corresponding to different field distributions, which describe the different cases of interaction of multiple domains.