Characteristics Of Rayleigh Waves Research Articles

Laser-Generated Rayleigh Waves Propagating in Transparent Viscoelastic Adhesive Coating/Metal Substrate Systems

We have established numerical models for simulating laser-generated Rayleigh waves in coating/substrate systems by a finite element method and investigated the propagation characteristics of Rayleigh waves in systems concerning the viscoelasticity and transparency of adhesive coatings. In this way, we have studied the influence of the mechanical properties of the coating, such as the elastic moduli, viscoelastic moduli, coating thickness, transparency, and coating material, on the propagation characteristics of the Rayleigh waves. The results show that the propagation characteristics of the Rayleigh waves can be divided into low- and high-frequency parts. The high-frequency propagation characteristics of the Rayleigh wave are closely related to the properties of the adhesive coating.

Application of near-surface seismic refraction tomography and multichannel analysis of surface waves for geotechnical site characterizations: A case study

In this case study two geophysical methods based on seismic waves were employed to evaluate the geotechnical properties of the soil deposits at a site for a planned wind farm. Regional geological information shows that the study area is mainly covered by recent alluvium, which is classified as a mixture of fine sand and gravel. Twenty five seismic refraction surveys were carried out in the study area. The acquired shot gathers were processed, from which primary wave (P-wave) and shear wave (S-wave) velocities were derived. The P-wave velocities were obtained by using the Seismic Refraction Tomography method (SRT) while the S-wave velocities were extracted by utilizing the Multichannel Analysis of Surface Waves (MASW) technique, which is established based on the dispersion characteristics of Rayleigh waves. Seismic hazard at the site was evaluated according to the Iranian code using the measured S-wave velocities, and the friction angles of the soil deposits were approximated using an empirical method and by making use of Jaky's formula for earth pressure at rest, which yielded similar values. The deformation properties of the foundation soil were also estimated based on the correlations between seismic wave velocities and elastic properties of soil as well as Janbu's formula for soil modulus. The findings of this study may serve as references for economic and non-destructive geotechnical site characterizations using seismic-wave methods.

Rayleigh wave propagation assessment for transport corridors

Wheel loading from high-speed trains can generate seismic ‘Rayleigh’ waves that propagate in the near surface, causing track and ground displacements. These displacements can increase over low-density, poorly consolidated soils with low wave velocities. Rayleigh wave characteristics were mapped onto soil engineering geological classifications using lithological and density parameters in effective stress-based algorithms that model shear wave velocities with depth. The use of small-scale engineering geological maps and one-dimensional modelling identified low Rayleigh wave velocity profiles associated with alluvial and terrace deposits in river catchments and floodplains along the proposed High Speed 2 route in the UK. Examination of the velocity−depth profiles indicated that sites are especially susceptible to dynamic displacement amplification where train-induced ground motion occurs within an interval of up to half the wavelength of the Rayleigh wave frequency induced by the train load centres. Using the algorithms to attribute density and shear wave velocities to the engineering geological section, a two-dimensional ground model was created for an alluvial-terrace structure at Perivale. Wave propagation modelling using a finite-difference code indicated amplification due to interference effects from wave fronts that propagated along different pathways of up to 2 times on vertical and 2·5 times on the horizontal displacement.

Three dimensional responses of a hill in a layered half-space for obliquely incident Rayleigh waves

An indirect boundary element method (IBEM) is presented to study the three dimensional responses of a hill in a layered half-space for obliquely incident Rayleigh waves. The presented IBEM yields very accurate results and is very convenient to deal with complex boundaries, for the Greens functions of moving distributed loads acting on inclined lines in a layered half-space are used as fundamental solutions to overcome the problem of singularity of the traditional IBEM, and the exact three dimensional dynamic stiffness of layered site is used to avoid discretization of the layer interfaces. The accuracy of the method is verified by comparing its results with published ones. Numerical calculations are performed both in the frequency and time domains by taking a hill in a homogenous and layered half-space as examples, and the effects of the obliquely incident angles, incident frequencies, cross section of the hill, height of the hill, and characteristics of the multi-modal and dispersion of Rayleigh waves propagating in a layered half-space are discussed in detail. Numerical results show that the amplification can be very different between the layered half-space and homogenous half-space for the multi-modal and dispersion characteristics of Rayleigh waves in a layered site. The amplification spectra of the higher modals (second and higher order modes) are very different from those of the first modal, which shows that the amplification spectra are narrowband, the displacement amplitudes near the top of the hill is extremely high at the peak frequencies and the peak frequencies are consistent with those of the effective damping ratio.

Researching on Characteristics of Rayleigh Waves

Rayleigh wave is a secondary wave characterized by low frequency and strong energy, propagating mainly along the interface of medium and rapid attenuation of energy with increase in interface distance. The same as reflected wave and refracted wave, Rayleigh wave also contain subsurface geological information. In this paper, the concept of the Rayleigh wave, wave equation, dispersion equation, the frequency bulk characteristics and the application of the actual data are used to indicate the characteristics of Rayleigh wave and its application.

Study on Characteristics of Rayleigh Waves in Media Containing Shallow Rectangular Cavities

Numerical simulations of Rayleigh wave with a source on the free surface are achieved by using FEM(finite element method). Artificial viscous boundary conditions are used to weaken boundary reflections. Modeling results are proved by comparison between analytic and numerical solutions in homogeneous half-space and layered media. Surface wave field of homogeneous half-space with rectangular cavities are modeled and analyzed. The results show that the velocity of converted wave above cavity is less than which in homogeneous media and energy is concentrated obviously in the area when the depth of cavity is relatively smaller than surface wave length. The cavity can be located by characteristics in time domain and frequency domain of surface wave. Dispersion characteristics of waves above cavity are mainly influenced by the top depth of the cavity instead of bottom depth and consistent with Lamb wave of slab with corresponding height and same media.

Propagation and attenuation of Rayleigh waves in a partially-saturated porous solid with impervious boundary

Abstract Propagation of Rayleigh waves is studied in a three-phase porous solid half-space, which is bounded above by an impervious plane surface. In this dissipative medium, Rayleigh wave propagates as an inhomogeneous wave, which decays with distance from the stress-free plane boundary. The impervious boundary restricts the flow of pore-fluids to the interior of porous solid only. This is ensured by fixing the fluid-pressure gradient in pores at boundary or with the sealing of surface pores. In either case, the existence and propagation of inhomogeneous wave are represented by a dispersion equation, which happens to be complex and irrational. This equation is rationalized into an algebraic equation of degree 24, which is solved for a numerical example. Solutions of the dispersion equation are checked to represent an inhomogeneous wave decaying with depth. Each qualified solution is resolved to define the phase velocity and attenuation coefficient of a Rayleigh wave in the medium. Numerical example compares the velocity and attenuation of Rayleigh wave in porous sandy loam for the two representations of the impervious boundary, one with sealed pores and other with no fluid-pressure gradient. Effects of saturation degree, porosity, capillary pressure, pore-fluids viscosity and frame anelasticity are observed on the propagation characteristics of Rayleigh waves. Existence of second Rayleigh wave is checked numerically. Such a wave is possible only when the porous frame is highly anelastic and saturated enough.

The Deep Structure of the Larderello-travale Geothermal Field (Italy) from Integrated, Passive Seismic Investigations

We report the preliminary results from a project (GAPSS-Geothermal Area Passive Seismic Sources), aimed at testing the resolving capabilities of passive exploration methods on a well-known geothermal area, namely the Larderello-Travale Geothermal Field (LTGF). Located in the western part of Tuscany (Italy), LTGF is the most ancient geothermal power field of the world. GAPSS consisted of up to 20 seismic stations deployed over an area of about 50 x 50 Km. During the first 12 months of measurements, we located more than 2000 earthquakes, with a peak rate of up to 40 shocks/day. Preliminary results from analysis of these signals include: (i) analysis of Shear-Wave-Splitting from local earthquake data, from which we determined the areal distribution of the most anisotropic regions; (ii) local-earthquake travel-time tomography for both P- and S-wave velocities; (iii) telesismic receiver function aimed at determining the high-resolution (<0.5km) S-velocity structure over the 0-20km depth range, and seismic anisotropy using the decomposition of the angular harmonics of the RF data-set; (iv) S-wave velocity profiling through inversion of the dispersive characteristics of Rayleigh waves from earthquakes recorded at regional distances. After presenting results from these different analyses, we eventually discuss their potential application to the characterisation and exploration of the investigated area.

The Application of the Rayleigh Wave in Subgrade Layer Detection

Based on LabVIEW platform, a highway nondestructive detection system was developed to detect highway subgrade layer and strcture characteristic. The integral principle of this system is dispersion characteristics of Rayleigh wave in different medium and the pronounced relationship between propagation velocity of Rayleigh wave and physical-mechanical properties of the medium. Using this test system to conduct a field test on a highway in Henan province and comparing the results with the actual situation, the results validated the practicability and reliability of the system.

Effect of lateral heterogeneity in the soil column on shear-wave velocity estimation by Rayleigh-wave inversion

We conducted elastic-wavefield modeling of shot gathers using soil-column models with vertical and lateral velocity variations to study the dispersive behavior of Rayleigh waves and the effect of lateral heterogeneity on the accuracy of Rayleigh-wave inversion for shear-wave velocity estimation. We also conducted a field experiment over an alluvial valley with soil column that thins out in the direction orthogonal to the valley axis. From the model and field experiments, we found that the dispersion characteristics of Rayleigh waves are greatly influenced by the geometry of and lateral heterogeneities within the soil column. Nevertheless, estimation of shear-wave velocities within a soil column with lateral heterogeneity by Rayleigh-wave inversion is sufficiently robust and accurate for geotechnical applications.

Comment on "Microtremor Measurements in the Nile Delta Basin, Egypt: Response of the Topmost Sedimentary Layer" by E. A. Fergany and S. Bonnefoy-Claudet

“Microtremor Measurements in the Nile Delta Basin, Egypt: Response of the Topmost Sedimentary Layer,” in Seismological Research Letters 80 (4) (Fergany and Bonnefoy-Claudet 2009; hereafter referred to as the FB paper), is a geological investigation of the Nile delta using the H/V spectral ratio (H/V) of microtremor observed at multiple investigation sites. I would like to express my respect for the effort made in spending a long time at each site. However, the authors have misunderstood the interpretation of the H/V technique and make some very important points for the development and application of the H/V technique. As one of the researchers who proposed the H/V technique, I would like to briefly explain the H/V technique and to point out the misunderstandings inherent in the FB paper. Then I will show more-effective results using the data of the FB paper and the correct application of the H/V technique. Many papers including the FB paper describe Nogoshi and Igarashi (1971) (hereafter referred to as the NI paper) as the origin of the H/V technique. However, because the NI paper was written in Japanese, I wonder if foreign researchers can correctly understand the contents. The NI paper says in its abstract that “the amplitude characteristics as the fundamental natures of microtremors are discussed in the present paper” and, as a result, “it was shown that the amplitude characteristics of microtremor was mostly composed of Rayleigh wave.” The H/V of Rayleigh waves had been well known in Japan as the characteristics of Rayleigh waves and has been applied as a tool for distinguishing between the surface wave (Rayleigh wave) and the body wave ( SH wave). Nogoshi and Igarashi compared the H/V between observed microtremor and Rayleigh waves. They describe the above-mentioned result, and they also describe the possibility that the characteristics of …

Study of effects of focal depth on the characteristics of Rayleigh waves using finite difference method

This paper presents a relationship between the focal depth in terms of Rayleigh-wave wavelength and the dominant frequency of Rayleigh waves generated in a homogeneous half-space. Rayleigh waves were simulated using a (2, 4) staggered grid P-SV wave finite difference algorithm with VGR-stress imaging technique as a free surface boundary condition. VGR is an acronym for vertical grid-size reduction. The simulated seismic responses using P-wave and SV-wave sources at different focal depths revealed Rayleigh-wave generation up to certain focal depth only for the considered frequency bandwidth. A shift of normalized spectral shape of Rayleigh wave towards lower frequency with increasing focal depth was inferred. Largest spectral amplitude was obtained in the wavelength for which the ratio of focal depth to the wavelength of Rayleigh wave was around 0.17 in the case of P-wave source and 0.9 in the case of SV-wave source. An exponential decrease of spectral amplitude of Rayleigh wave with the departure of the ratio of focal depth to Rayleigh wave wavelength from the above mentioned values was obtained.

Fundamental and higher‐mode Rayleigh wave characteristics of ambient seismic noise in New Zealand

In order to use ambient seismic noise for mapping Earth's structure, it is important to understand the spatio‐temporal characteristics of the noise field. This study uses data collected during four austral winter months of 2002 to investigate New Zealand's ambient seismic noise field in the double‐ocean‐wave‐frequency range (0.1–0.3 Hz). It is shown via beamforming analysis that there are two distinct dispersive waves in the data. These waves can be separated. Their estimated phase velocities (2.5–2 and 4–3 km/s in the frequency range 0.14–0.25 Hz) match well with fundamental and higher‐mode Rayleigh dispersion curves. Studies of double‐wave‐frequency microseisms elsewhere generally show the Rayleigh noise fields to be dominated by fundamental mode waves. The reason why higher‐mode signals are observed here may reflect a combination of long ocean wave periods, large waveheights, the direct deep water approach to narrow continental margins, and the proximity of the seismograph array to the source regions.

Numerical simulation of laser-generated Rayleigh wave by finite element method on viscoelastic materials

The propagation of laser-generated Rayleigh wave in the viscoelastic material are studied theoretically. Taking account of the viscosity characteristic of the viscoelastic material, a numerical model for simulating laser-generated Rayleigh wave in the viscoelastic material is developed in the frequency domain. Based on the correctness of the finite element numerical model in the frequency domain, the laser generation of Rayleigh wave in the viscoelastic material is simulated. And then, the propagation characteristics of laser-generated Rayleigh wave are discussed and the difference of Rayleigh waves in the viscoelastic material and the elastic material are compared. The effect of different viscosity modulus to the characteristic of Rayleigh wave is analyzed in detail.

Application of negative velocity dispersion curves to the distinction between layer and substrate Rayleigh waves

This work concerns the investigation of loading layers/substrate structures in order to determine the critical thickness at which Rayleigh wave characteristics of layers can be completely distinguished from those of the substrates. To do so, we first calculate Rayleigh velocity dispersion curves of several thin film materials (about thirty) deposited on different slow and fast substrates (Be, Al 2O 3, AlN, Si, SiO 2, Mg, SiC, TiN, WC and Pyrex). Then, from the beginning of curve saturation (corresponding to the onset of intrinsic layer characteristics) we deduced normalized thickness transition for all layers/substrates combinations. Thus, we were able to deduce an analytical linear expression relating the critical thickness to combined effects of densities and velocities of both layers and substrates. Such a simple relation can be used, as an alternative method, to predict the transition critical thickness for any layer/substrate combination without the usual lengthy calculation of dispersion curves. To cite this article: Z. Hadjoub et al., C. R. Physique 9 (2008).

Three‐dimensional VS profiling using microtremors in Kushiro, Japan

AbstractA practical method is presented for determining three‐dimensional S‐wave velocity (VS) profile from microtremor measurements. Frequency–wave number (f–k) spectral analyses of microtremor array records are combined, for this purpose, with microtremor horizontal‐to‐vertical (H/V) spectral ratio techniques. To demonstrate the effectiveness of the proposed method, microtremor measurements using arrays of sensors were conducted at six sites in the city of Kushiro, Japan. The spectral analyses of the array records yield dispersion characteristics of Rayleigh waves and H/V spectra of surface waves, and joint inversion of these data results in VS profiles down to bedrock at the sites. Conventional microtremor measurements were performed at 230 stations within Kushiro city, resulting in the H/V spectra within the city. Three‐dimensional VS structure is then estimated from inversion of the H/V spectra with the VS values determined from the microtremor array data. This reveals three‐dimensional VS profile of Kushiro city, together with an unknown hidden valley that crosses the central part of the city. The estimated VS profile is consistent with available velocity logs and results of subsequent borings, indicating the effectiveness of the proposed method. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Surface wave tomography of the western United States from ambient seismic noise: Rayleigh wave group velocity maps

We have applied ambient noise surface wave tomography to data that have emerged continuously from the EarthScope USArray Transportable Array (TA) between October 2004 and January 2007. Estimated Green's functions result by cross‐correlating noise records between every station‐pair in the network. The 340 stations yield a total of more than 55,000 interstation paths. Within the 5‐ to 50‐s period band, we measure the dispersion characteristics of Rayleigh waves using frequency‐time analysis. High‐resolution group velocity maps at 8‐, 16‐, 24‐, 30‐, and 40‐s periods are presented for the western United States. The footprint of the TA encloses a region with a resolution of about the average interstation spacing (∼70 km). Velocity anomalies in the group velocity maps correlate well with the dominant geological features of the western United States. Coherent velocity anomalies are associated with the Sierra Nevada, Peninsular, and Cascade Ranges, Great Valley, Salton Trough, and Columbia basins, the Columbia River flood basalts, the Snake River Plain and Yellowstone, and mantle wedge features associated with the subducting Juan de Fuca plate.

Rayleigh waves in a double porosity half-space

Based on the governing equations of double-porosity media extended from Biot's theory, the propagation characteristics of Rayleigh waves are discussed in this paper. Characteristic equations of Rayleigh waves in a double porosity half-space with the pervious boundary are derived by assuming that both the coupling mass coefficient ρ 23 and coupling permeability term k (12) are equal to zeros. The dispersion and attenuation properties of Rayleigh waves in a double porosity medium are analyzed numerically. The effects of the porosity and fracture permeability on the behavior of the propagation of Rayleigh waves are investigated. It is found that Rayleigh waves in a double porosity half-space are dispersive and attenuated during propagation. The Rayleigh wave speed is always less than the phase velocity of P1 and shear waves, and always higher than the phase velocity of P3 wave.

Effect of rotation on Rayleigh waves in piezothermoelastic half space

The present paper deals with the study of rotation effect on the characteristics of Rayleigh waves propagating in a homogeneous, transversely isotropic piezothermoelastic half space in the framework of linear theory including Coriolis and Centrifugal forces. The medium is subjected to stress free, thermally insulated, electrically shorted/charge free boundary conditions and is rotating about an axis perpendicular to its plane. Characteristics of surface waves propagating in thermoelastic piezoelectric solids and their dependence upon various geometric and physical parameters are derived. After deriving secular equations in closed form and isolated mathematical conditions, the effect of rotation on dispersion curves and attenuation profiles is studied. The specific loss factor and relative frequency shift are also obtained in case of open and closed circuit electric surface conditions. Finally, in order to illustrate and verify the analytical results, numerical solution of various secular equations and other relevant relations are derived for cadmium selenide (6 mm) class material. The analysis shows that the rotation sensitivity at long wavelengths (in the vicinity of the surface) is substantially greater than those at short wavelengths (deep into the half space). The study is very helpful in the development of rotation sensors and other piezoelectric devices.

Forward Modeling of Steady-State Surface Wave Test

The forward modeling of the dispersion curve of a layered medium calculated from the spectral characteristics of Rayleigh waves requires an efficient algorithm for predicting the surface displacements of the medium under a dynamic load. The usual methods for solving the wave equation are based on matrix methods prone to numerical problem or yielding to the determination of complex modes that are difficult to interpret. A modified linearized stiffness matrix method is proposed in this technical note to solve the discrete stiffness matrix. The developed algorithm is based on a finite element equation associating each surface wave mode to the resonant frequency of a structure with a stiffness depending on the wavelength. The filtering of complex wave modes to keep only suitable surface waves is avoided. Furthermore, the mesh design is based on the actual wavelength of each mode providing a better representation of higher modes. The new algorithm is validated with two irregular stiffness profiles.