Study of Scholte wave dispersion curves and modal energy distribution using a wavefield numerical simulation method

The interest of both the scientific community and the professionals towards the MASW method (Multichannel Spectral Analysis of Surface Waves) has been increasing for the last years.cIn the ’90 several researchers have realized that, when dealing with inversely dispersive sites, the MASW method based only on the fundamental mode can really cause erroneous Vs profiles, hence an erroneous seismic site characterization. When dealing with inversely dispersive sites ( i.e. sites where stiffness discontinuities exist, soft layers trapped between stiffer layers or viceversa stiff layers trapped between softer layers) higher modes of Rayleigh waves must be combined together with the fundamental mode to calculate the effective or apparent dispersion curve (Lai 1998, Roma 2001-2002-2006), in order to achieve a reliable Vs profile and a reliable seismic site characterization. It is not sufficient to calculate the numerical higher modes and use them separately for the inversion process, because it is practically impossible to distinguish the experimental higher modes from the field data in the geotechnical scale. It is well known that the apparent experimental dispersion curve that is determined from the field data is the result of a superposition of the several higher modes. In order to obtain a reliable Vs profile and hence a reliable site soil characterization not only the fundamental mode, but also the higher modes of Rayleigh have be combined when calculating the apparent numerical dispersion curve. Consider that it is not sufficient to calculate the higher modes of Rayleigh, because it is necessary to combine the higher modes with the fundamental mode to calculate the numerical apparent dispersion curve, as it is measured in field. This is due to the fact that from field data it is not possible to distinguish and define the higher modes without a large uncertainty. In this article the potentialities of a new algorithm (www.masw.it, Roma 2001) that calculates the apparent dispersion curve using both the fundamental mode and all higher modes are shown into an application to a real case.

SUMMARY Pure shear wave data are only very rarely acquired for offshore site investigations and exploration. Here, we present details of a novel, seabed-coupled, shear wave vibrator and field data recorded by a densely populated, multicomponent ocean-bottom cable, to improve shallow soil characterization. The prototype shear wave vibrator uses vibroseis technology adopted for marine environments through its instalment on top of a suction anchor, assuring seabed coupling in combination with self-weight penetration. The prototype is depth rated to 1500 m water depth, and can be rotated while installed in the seabed. The philosophy is to acquire fully complementary seismic data to conventional P- and P-to-S-converted waves, in particular for 2-D profiling, VSP (vertical seismic profiling) or monitoring purposes, thereby exploiting advantages of shear waves over compressional waves for determining, for example, anisotropy, small-strain shear modulus and excess pore pressures/effective stress. The source was primarily designed for reservoir depths. However, significant energy is emitted as surface waves, which provide detailedgeotechnicalinformationthroughmappingofshearwavevelocitiesinpotentiallyhigh resolution of the upper soil units. To fully utilize pure shear wave content, a proper analysis of surface waves is paramount, due to the proximity of surface wave propagation speed with shear wave velocities. The experiment was carried out in the northern North Sea in 364 m water depth. Cable dragging was necessary to obtain close receiver spacing (2.5 m effective spacing), with total line length of 600 m. Frequency–waveform transforms reveal both Scholte and Love waves. Up to six surface wave modes are identified, that is, fundamental mode and several higher surface wave modes. The occurrence of these two different dispersive surface wave types with well-resolved higher modes allows for a unique analysis and inversion scheme for highresolution mapping of physical properties in the shallow subsurface as well as anisotropy, which is discussed in an accompanying paper. The data presented in this paper are thus a unique (long and densely populated receiver array allows for multimodal Love and Scholte surface waves from the marine environment) but challenging (marine operations) marine data set.

In this paper we are going to show the importance of mode identification in microtremor array analysis. The idea come from four concentric ambient noise array recordings with aperture 100 to 1000 meters, performed in southern urban area of Tehran near the shrine of Imam Khomeini. These measurements were part of a comprehensive research project with the aim of determination of deep shear wave velocity model of Tehran alluvial deposits. Using appropriate signal processing techniques, including array processing methods as well as classical and time-frequency horizontal/vertical spectral ratio, the dispersion curves of surface waves, fundamental resonance frequency and Ellipticity of Rayleigh waves, were extracted. In the final step, the shear wave velocity profile of the site was determined by joint inversion of all of these attributes. The results show 2 different energetic trends in dispersion curves, for arrays of aperture 200 and 400 meters that one of them is coincide with 100m aperture array. For array with aperture 1000m any clear trend of energy could be observed because of deficiency of energy in low frequency. The inversion of data obtained by 100m aperture array alone, assuming the dispersion curve as fundamental mode (a common procedure in urban area) result in shear wave velocity that is not match with existing geological information. Performing the inversion, assuming 2 energetic trends, observed for larger arrays; one as fundamental mode and another as mode 1 of Rayleigh waves, can modify significantly the shear wave velocity profile in accordance with existing geological and geotechnical information. This study show the importance of extracting of correct dispersion curves with detecting fundamental and higher modes, using array measurement with various aperture at one place to obtain more realistic shear wave velocity profile.

<p>It has been widely recognized that the cross-correlation function (CCF) of ambient noise data recorded at two seismic stations approximates to the part of Green’s Function between these two stations. Theoretically, the CCF should include the higher modes, apart from the fundamental mode. However, currently well-known and mature methods that can extract dispersion curves are not pretty proficient in extracting higher modes. Fortunately, our newly proposing method, the Frequency-Bessel Transform Method (F-J Method), has presented its obvious advantage in extracting higher modes. This study applied F-J method to seismic ambient noise data for the east of South China, including Jiangnan Orogen and South China Fold System. We have acquired higher modes, not to mention the fundamental mode with wider frequency than previous studies. Combining both fundamental mode and higher modes, we used L-BFGS inversion method to inverse and acquire more accurate crustal and upper-mantle structure than previous studies only adopting fundamental mode for the east of South China. As shown in this study for the east of South China, we can use F-J method  to conveniently and precisely extract multimodes from ambient noise data and thus add more constrains for inversion results, which can significantly improve the preciseness of imaging crustal and upper-mantle structure.</p>

We present a new inverse method for retrieving the mantle structure, using the fundamental and higher modes surface waves. The fundamental mode is only sensitive to structures down to 400–500 km but higher modes have a depth resolution down to 1000–1500 km. So, they are well suited to the study of the transition zone between 400 and 1000 km depth. A data set of seismograms corresponding to events all located in a small area and recorded at a single station is selected. The inversion of the seismograms is divided into two steps. First, the difference between the real spectra and the sum of the higher modes synthetic spectra is inverted for retrieving the phase velocities of the first higher modes. In a second step, these phase velocities are inverted at depth in order to retrieve the average mantle structure between the receiver and the epicentral area. This structure is modelled as a transversely isotropic medium with a vertical symmetry axis. Because of the non-linearity of the problem, it is necessary to iterate the procedure and to recalculate the Earth eigenfunctions and the new synthetic spectra at each iteration. Numerical tests on synthetic data have been performed and they demonstrate that we have a good resolution at depth down to 1500 km. Some results obtained on real data recorded on GEOSCOPE network are also presented. This method can now be applied systematically to real data.

Use of modal energy distribution in the design of honeycomb sandwich decks

Recent studies have illustrated that the Multichannel Analysis of Surface Waves (MASW) method is an effective geoacoustic parameter inversion tool. This particular tool employs the dispersion property of broadband Scholte-type surface wave signals, which propagate along the interface between the sea water and seafloor. It is of critical importance to establish the theoretical Scholte wave dispersion curve computation model. In this typical study, the stiffness matrix method is introduced to compute the phase speed of the Scholte wave in a layered ocean environment with an elastic bottom. By computing the phase velocity in environments with a typical complexly varying seabed, it is observed that the coupling phenomenon occurs among Scholte waves corresponding to the fundamental mode and the first higher-order mode for the model with a low shear-velocity layer. Afterwards, few differences are highlighted, which should be taken into consideration while applying the MASW method in the seabed. Finally, based on the ingeniously developed nonlinear Bayesian inversion theory, the seafloor shear wave velocity profile in the southern Yellow Sea of China is inverted by employing multi-order Scholte wave dispersion curves. These inversion results illustrate that the shear wave speed is below 700 m/s in the upper layers of bottom sediments. Due to the alternation of argillaceous layers and sandy layers in the experimental area, there are several low-shear-wave-velocity layers in the inversion profile.

We show that higher modes are an important component of high-frequency Rayleigh waves in the cross-correlations over sedimentary basins. The particle motions provide a good test for distinguishing and separating the fundamental from the first higher mode, with the fundamental mode having retrograde and the first higher mode having prograde motion in the 1–10 s period of interest. The basement depth controls the cut-off period of the first higher mode, which coincides with a rapid increase (over period) in the particle-motion ellipticity or H/V ratio of the fundamental mode. The strong higher mode we observed is not only due to the low-velocity sedimentary layer but also due to the noise sources with significant radial component such as the basin edge scattering. It is important to correctly identify the mode order when inverting the dispersion curves because misidentifying the higher mode as fundamental will lead to an anomalous high V_(SV) velocity.

A full-vectorial numerically efficient Finite Element Method (FEM) based computer code is developed to study complex light-sound interactions in a single mode fiber (SMF). The SBS gain or SBS threshold in a fiber is highly related to the overlap between the optical and acoustic modes. For a typical SMF the acoustic-optic overlap strongly depends on the optical and acoustic mode profiles and it is observed that the acoustic mode is more confined in the core than the optical mode and reported overlap is around 94 % between these fundamental optical and acoustic modes. However, it is shown here that selective co-doping of Aluminum and Germanium in core reduces the acoustic index while keeping the optical index of the same value and thus results in increased acoustic- optic overlap of 99.7%. On the other hand, a design of acoustic anti-guide fiber for high-power transmission systems is also proposed, where the overlap between acoustic and optical modes is reduced. Here, we show that by keeping the optical properties same as a standard SMF and introducing a Boron doped 2ndlayer in the cladding, a very low value of 2.7% overlap is achieved. Boron doping in cladding 2ndlayer results in a high acoustic index and acoustic modes shifts in the cladding from the core, allowing much high power delivery through this SMF.

Research on vibration suppression effect and energy dissipation mechanism of wind turbine piezoelectric blade

Time-domain pulsed broadband laboratory experimental results are presented demonstrating that a thin low velocity fluid layer (thickness <H/10) at the bottom of a floating plate (thickness H) drastically decreases the group velocity of flexural waves on the right side of the dispersion curve maximum Umax. The low Scholte wave velocity of the layer affects the Scholte wave branch dispersion curve and causes it to deviate towards a lower value. Hunkins’ seismic studies of sea-ice [J. Geophys. Res. 65(10) (1960)] revealed two discrepancies between measured and calculated flexural wave group velocity dispersion: (a) sea-ice thickness determined from flexural wave dispersion is generally lower than the actual thickness, and (b) flexural wave components on the right of Umax have considerable lower velocity than predicted. Ultrasonic modeling studies [J. R. Chamuel and G. H. Brooke, J. Acoust. Soc. Am. Suppl. 1 79, S57 (1986)] provided a possible explanation for the first discrepancy namely that the presence of a large number of small cracks in a floating plate reduces U and shifts the corresponding dispersion curves towards an ‘‘effective’’ thinner plate. The current paper provides an explanation for the second discrepancy in Hunkins’ results which cannot be compensated for by changing ‘‘H.’’ Bogorodskii [Sov. Phys. Acoust. 22, 158–159 (1976)] showed the existence of a ‘‘clear-ice’’ layer underneath the ice, during the rapid growth of the ice cover, which has a compressional wave velocity of about 1050 m/s substantially less than the velocity of sound in water. [Work supported by ONR.]

The nondestructive inspection of components by means of guided waves is an emerging technology in fields like aerospace or pipeline construction and maintenance. The guided waves' capability of propagating many meters in a structure is utilized for swift inspection tasks as well as structural health monitoring. The German Aerospace Center uses Lamb waves for the quality assurance of large-scale aerospace vehicle components made from carbon composites. However, the use of guided waves in NDT requires knowledge of the dispersion curves. DISPERSE is the most renown software for the calculation of dispersion curves. This paper presents the open source Dispersion Calculator (DC). The MATLAB® -based DC is an interactive and fully validated software for the computation of dispersion curves and mode shapes of guided waves in isotropic plates and multilayered anisotropic composites. Damping caused by viscoelasticity and fluid-loading can be considered. DC features the capability of calculating laminates consisting of several hundreds of layers so that even the largest specimens, like rocket booster pressure vessels, can be calculated. This is made possible through the implementation of the stiffness matrix method. DC is also able to distinguish the different mode families, like symmetric, antisymmetric, and nonsymmetric Lamb, shear horizontal, and Scholte waves, depending on the symmetry and coupling properties of a given layup. Lastly, DC features a highly efficient and robust dispersion curve tracing algorithm. DC is available at GitHub, and it has gained many users world-wide since its initial release in 2018.

Properties of a vibrating annular membrane are analyzed mathematically and numerically to investigate the relative harmonicity of the higher-order modes compared with the fundamental mode. The harmonicity depends on the zeros of a cross-product of Bessel functions. For a ratio of external-to-internal diameter up to about 1.2, the higher modes have frequencies which are very nearly exact integer multiples of the fundamental frequency. For circularly symmetric modes, the ratio of all higher radial mode frequencies to exact harmonic values is less than 1.0006 (a logarithmic cent), a ratio imperceptible to a listener. Angle-dependent modes also give good harmonicity, especially if some lower radial modes are suppressed. Thus the modes of an annular membrane whose external-to-internal diameter ratio is less than 1.2 are much more harmonic than those of the full circular membrane of a conventional drum. The theoretical harmonicity is at least as good as reported for stringed melodic instruments (piano, violin). The analysis suggests characteristics for construction of an annular drum-head which is supported on concentric rims of two cylinders; to sound the drum, a braced hoop might be used to excite radial modes, or strikers with grooved faces might be used to excite angular modes without exciting lower radial modes.

<p>We use continuous seismic data from permanent and temporary, broadband and short-period stations that were operating during 2001 and 2008 to investigate the subsurface velocity structure of the Tongariro Volcanic Centre (TgVC) of New Zealand, particularly the highly active but poorly understood Ruapehu and Tongariro Volcanoes. Stacks of cross-correlation of two concurrent ambient noise seismograms can be used to estimate the interstation Green's Function, i.e., the impulse response of the earth between the two receivers. The Green's Functions are used to retrieve the dispersion relation (frequency-dependent velocity) of surface waves at different periods, which reflects the shear-wave velocity structure in the Fresnel volume of the propagating surface waves. Several studies have used dispersion measurements from ambient noise cross-correlations to investigate the shallow subsurface shear-wave velocity structure of active volcanoes around the world. Most use vertical components to retrieve the Rayleigh waves, but it is becoming increasingly common to use the horizontal seismogram components in addition to the vertical, giving further constraints to Rayleigh-wave measurements and introducing data relating to Love waves. We compute 1,048,968 daily cross-correlations for 955 viable station pairs across the two periods, including all nine-components of the cross-correlation tensor where possible. These daily functions are then stacked into 7458 full-stacks, of which we make group velocity dispersion measurements for 2641 RR-, RZ-, TT-, ZR- and ZZ-component stacks. Cross-correlation quality varies across the networks, with some station pairs possibly contaminated with timing errors. We observe both the fundamental and rst higher-order modes within our database of dispersion measurements. However, correctly identifying the mode of some measurements is challenging as the range of group velocities measured reflects both presence of multiple modes and heterogeneity of the local velocity structure. We assign modes to over 1900 measurements, of which we consider 1373 to be high quality. We invert fundamental mode Rayleigh- and Love-wave dispersion curves independently and jointly for one dimensional shear-wave velocity profiles at Ruapehu and Tongariro Volcanoes, using dispersion measurements from two individual station pairs and average dispersion curves from measurements within specifi c areas on/around the volcanoes. Our Ruapehu profiles show little velocity variation with depth, suggesting that volcanic edifice is made of material that is compacting and being hydrothermally altered with depth. At Tongariro, we observe larger increases in velocity with depth, which we interpret as different layers within Tongariro's volcanic system. Slow shear-wave velocities, on the order of 1-2 km/s, are consistent with both P-wave velocities from existing velocity pro files of areas within the TgVC, and the observations of worldwide studies of shallow volcanic systems that used ambient noise cross-correlation. A persistent observation across the majority of our dispersion measurements is that group velocities of the fundamental mode Love-wave group velocity measurements are slower than those of fundamental mode Rayleigh-waves, particularly in the frequency range of 0.25-1 Hz. Similarly, first higher-order mode Love-wave group velocities are slower than first higher-mode Rayleigh-wave velocities. This is inconsistent with the differences between synthetic dispersion curves that were calculated using isotropic, layered velocity models appropriate for Ruapehu and Tongariro. We think the Love-Rayleigh discrepancy is due to structures such as dykes or cracks in the vertical plane having greater influence than horizontal layering on surface-wave propagation. However, several measurements where Love-wave group velocities are faster than Rayleigh-wave group velocities suggests that in some places horizontal layering is the stronger influence. We also observe that the differences between the Love- and Rayleigh-wave dispersion curves vary with the azimuth of the interstation path across Ruapehu and Tongariro Volcanoes. Some significant differences between Rayleigh-wave velocities of measurements with different interstation orientations are also observed, as are differences between Love-wave velocities. This suggests a component of azimuthal anisotropy within the volcanic structures, which coupled with the radial anistropy makes the shear-wave velocity structures of Ruapehu and Tongariro Volcanoes anisotropic with orthorhombic symmetry. We suggest that further work to determine three-dimensional structure should include provisions for anisotropy with orthorhombic or lower symmetry.</p>

The ambient vibration analysis is a non-invasive and low-cost technique used in site characterization studies to reconstruct the subsurface velocity structure. Depending on the goal of the research, the investigated depth ranges from tens to hundreds of meters. In this work, we aimed at investigating the deeper contrasts within the crust and in particular down to the sedimentary-rock basement transition located at thousands of meters of depth. To achieve this goal, three seismic arrays with minimum and maximum interstation distances of 7.9 m and 26.8 km were deployed around the village of Schafisheim. Schafisheim is located in the Swiss Molasse Basin, a sedimentary basin stretching from Lake Constance to Lake Geneva with a thickness ranging from 800 to 900 m in the north to 5 km in the south. To compute the multimodal dispersion curves for Rayleigh and Love waves and the Rayleigh wave ellipticity angles, the data were processed using two single-station and three array processing techniques. A preliminary analysis of the inversion results pointed out a good agreement with the fundamental modes of Rayleigh and Love waves used in the inversion and a quite strong disagreement with the higher modes. The impossibility to explain at the same time most of the dispersion curves was interpreted as the co-existence, within the investigated area, of portions of the subsurface with different geophysical properties. The hypothesis was confirmed by the Horizontal-to-Vertical spectral analysis (H/V) which indicated the presence of two distinguished areas. The observation allowed a new interpretation and the identification of the Rayleigh and Love wave fundamental modes and of the S-wave velocity profiles to be reconstructed for each investigated zone. It results in two S-wave velocity profiles with similar velocities down to 15 km deferring only in their shallow portions due to the occurrence of a low velocity zone at a depth of 50–150 m at the centre of the investigated area.