Rayleigh Surface Wave Velocity Research Articles

The magmatic plumbing system of the Acoculco volcanic complex (Mexico) revealed by ambient noise tomography

The GEMex project is a Mexican-European cooperation in geothermal energy focusing on enhancing the Acoculco geothermal system. The volcanic system belongs to the northeastern part of the Trans-Mexican Volcanic Belt. In this study, we present ambient noise seismic tomographies of the anisotropic shear wave velocities and reveal the magmatic plumbing system. The tomographies result from the joint inversion of the multi-mode Rayleigh and Love surface wave velocities and Horizontal to Vertical Spectral Ratios (HVSR or H/V). We also discuss the advantage of this technique compared to traditional ambient noise tomography methods and underline the importance of considering multiple surface wave modes to correctly reveal velocity anomalies buried a few kilometers in depth. A reservoir is identified at about 5 km depth at the northeast outside of the caldera. This reservoir is linked to the south caldera surface via a conduit that follows the caldera's eastern border, mainly the Chignahuapan graben. An intermediate reservoir is also observed at about 2.5 km depth, just below the three most recent monogenetic volcanoes. Results agree well with geological studies, the caldera collapse, its temporal evolution, and other geophysical studies recently reported.

State space approach to characterize Rayleigh waves in a layer lying over a half-space with nonlocal thermoelasticity

The paper deals with a new model based on Eringen's nonlocal thermoelasticity. The propagation of Rayleigh waves in a nonlocal thermoelastic layer which is lying over a nonlocal thermoelastic half-space is considered in the context of energy dissipation theory. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by state space approach.The frequency equation of Rayleigh surface wave is derived. The effect of the nonlocal parameter on phase velocity, attenuation coefficient, specific loss and penetration depth of Rayleigh surface waves is presented graphically.

Rayleigh wave propagation at the boundary surface of dry sandy ($SiO_2$) thermoelastic solids

PurposeThe purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.Design/methodology/approachThe present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves.FindingsThe dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.Originality/valueRayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.

Surface waves in nonlocal thermoelastic medium with state space approach

In this paper, a new model based on Eringen’s nonlocal thermoelasticity is constructed. The propagation of Rayleigh surface waves in homogeneous isotropic medium is considered under the purview of this new nonlocal thermoelasticity theory in the context of energy dissipation theory. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by state space approach. The frequency equations for different cases are derived. The phase velocity, attenuation coefficients, specific loss and penetration depth of Rayleigh surface waves are computed numerically and presented graphically with respect to frequency and the effects of non-locality on the considered parameters are presented in the figures.

Inverting Rayleigh surface wave velocities for crustal thickness in eastern Tibet and the western Yangtze craton based on deep learning neural networks

Abstract. Crustal thickness is an important factor affecting lithospheric structure and deep geodynamics. In this paper, a deep learning neural network based on a stacked sparse auto-encoder is proposed for the inversion of crustal thickness in eastern Tibet and the western Yangtze craton. First, with the phase velocity of the Rayleigh surface wave as input and the theoretical crustal thickness as output, 12 deep-sSAE neural networks are constructed, which are trained by 380 000 and tested by 120 000 theoretical models. We then invert the observed phase velocities through these 12 neural networks. According to the test error and misfit of other crustal thickness models, the optimal crustal thickness model is selected as the crustal thickness of the study area. Compared with other ways to detect crustal thickness such as seismic wave reflection and receiver function, we adopt a new way for inversion of earth model parameters, and realize that a deep learning neural network based on data driven with the highly non-linear mapping ability can be widely used by geophysicists, and our result has good agreement with high-resolution crustal thickness models. Compared with other methods, our experimental results based on a deep learning neural network and a new Rayleigh wave phase velocity model reveal some details: there is a northward-dipping Moho gradient zone in the Qiangtang block and a relatively shallow north-west–south-east oriented crust at the Songpan–Ganzi block. Crustal thickness around Xi'an and the Ordos basin is shallow, about 35 km. The change in crustal thickness in the Sichuan–Yunnan block is sharp, where crustal thickness is 60 km north-west and 35 km south-east. We conclude that the deep learning neural network is a promising, efficient, and believable geophysical inversion tool.

Characterization of Local Residual Stress at Blade Surfaces by the V(z) Curve Technique

The characterization of residual stress in complicated components is a tough issue. The method of Rayleigh surface wave-based V(z) curve is adopted in this work to evaluate the distribution of residual stresses in aeroengine blades. First, the velocity of Rayleigh surface wave in aeroengine blade was measured by the V(z) curve technique, which can be used to calculate the local residual stress because the change of velocity is thought to be correlated with the contribution from residual stress. Two kinds of plastic-deformed Ti-6Al-4V samples were fabricated by ball-gun shooting to artificially induce distribution of residual stress and then measured by the proposed method. The results indicate that the distribution of the residual stress in both of the samples displays a predictable symmetry. The error of the measured stress is much less than 10% of the yielding stress in Ti-6Al-4V (i.e., about 800 MPa). Finally, the measured residual stresses were verified by X-ray diffraction method, whose results correlate reasonably well with each other. The proposed V(z) curve method and its experimental set-up appear to be a potential in characterizing residual stress at a point-like region, such as in complicated components.

Impulse excitation scanning acoustic microscopy for local quantification of Rayleigh surface wave velocity using B-scan analysis.

A new technique for performing quantitative scanning acoustic microscopy imaging of Rayleigh surface wave (RSW) velocity was developed based on b-scan processing. In this technique, the focused acoustic beam is moved through many defocus distances over the sample and excited with an impulse excitation, and advanced algorithms based on frequency filtering and the Hilbert transform are used to post-process the b-scans to estimate the Rayleigh surface wave velocity. The new method was used to estimate the RSW velocity on an optically flat E6 glass sample, and the velocity was measured at ±2 m/s and the scanning time per point was on the order of 1.0 s, which are both improvement from the previous two-point defocus method. The new method was also applied to the analysis of two titanium samples, and the velocity was estimated with very low standard deviation in certain large grains on the sample. A new behavior was observed with the b-scan analysis technique where the amplitude of the surface wave decayed dramatically on certain crystallographic orientations. The new technique was also compared with previous results, and the new technique has been found to be much more reliable and to have higher contrast than previously possible with impulse excitation.

A numerical method for predicting Rayleigh surface wave velocity in anisotropic crystals

A numerical method was developed for calculating the Rayleigh Surface Wave (RSW) velocity in arbitrarily oriented single crystals in 360 degrees of propagation. This method relies on the results from modern analysis of RSW behavior with the Stroh formalism to restrict the domain in which to search for velocities by first calculating the limiting velocity. This extension of existing numerical methods also leads to a natural way of determining both the existence of the RSW as well as the possibility of encountering a pseudo-surface wave. Furthermore, the algorithm is applied to the calculation of elastic properties from measurement of the surface wave velocity in multiple different directions on a single crystal sample. The algorithm was tested with crystal symmetries and single crystal elastic moduli from literature. It was found to be very robust and efficient in calculating RSW velocity curves in all cases.

Surface Waves in a Viscoelastic Liquid Half-Space Under Initial Stress in Presence of Thermal and Magnetic Field

In this paper propagation of Rayleigh-type surface waves in a homogeneous, isotropic, perfectly conducting viscoelastic liquid half-space under initial stress in presence of thermal and magnetic field has been discussed, in the context of generalized thermoelasticity using Green–Lindsay model. The frequency equation signifying the velocity of Rayleigh surface waves has been established. The velocity of Rayleigh surface waves is computed numerically for different values of initial stress parameter, magnetic pressure number, thermoelastic coupling parameter and viscosity. The results are shown graphically.

Rayleigh wave dispersion in an irregular sandy Earth's crust over orthotropic mantle

The present paper presents a study of Rayleigh wave propagation in a sandy crustal layer of the Earth lying over an orthotropic mantle with irregular boundary surfaces under the influence of initial stress, gravity field and rigid boundary plane. An attempt has been made to study the dynamics of the individual medium and derive the displacement of the wave for both the media separately. Suitable boundary conditions have been imposed to derive the dispersion equation in closed form. In general, the obtained dispersion equation is complex, which on separating into real and imaginary parts, leads to two different dispersion equations, of which we are neglecting the imaginary part being damping in nature. The real part contains complete information regarding corrugation parameter, wave number, phase velocity, sandy parameter, initial stress and gravity field. The results for irregular boundaries have been obtained in three cases and presented using graphs. It has been found that the initial stress and sandy parameter have a significant effect and remarkable bearing on the phase velocity of Rayleigh surface wave. Corrugation parameters also have a dominant impact on the propagation of Rayleigh wave. This study may be of great help in the field of industrial engineering, submarine structures, civil engineering, aerospace, chemical pipe and metallurgy as well as geophysics.

Hardware and software measurement system for determining the location of inhomogeneities using seismic data

A hardware and software measurement system is developed and implemented based on a high-sensitive accelerometer and a computer with multichannel analog-to-digital converter (ADC). The system makes it possible to detect inhomogeneities of the Earth’s crust using Rayleigh surface waves. The measurement system consists of four universal piezosensors connected to the ADC, the debug stabilization board, the board battery, and the fiberglass base with slots for each sensor. The upper frequency limit of the measurement system is 20000 Hz. Software made by L-Card is used when working with the ADC. This software makes it possible to record data without size restrictions under multimodule operating mode and at any sample rate. All parts of the system are detachable, which ensures its small size and versatility when operating in the field. In this paper, a detailed description of the system is given, and the results of its testing by determining the velocity of Rayleigh surface waves in homogeneous media are presented. A detailed description of the experiments is provided, as well as the results of the use of the system for the detection of near-surface inhomogeneity in order to confirm the effectiveness of and evaluate possible prospects for the microseismic sounding method.

Characteristic wave speeds in the surface Brillouin scattering measurement of elastic constants of crystals

A simple and robust fitting procedure is presented for determining the three elastic constants of a cubic crystal from surface Brillouin scattering measurements carried out in the $⟨100⟩$ and $⟨110⟩$ directions in a (001) surface. The input data utilized are the Rayleigh surface wave velocity, the Lamb shoulder threshold velocity, and the longitudinal lateral wave velocity measured in the two directions. In fitting these velocities, use of simple closed-form expressions is made for the secular functions determining them. Corresponding expressions for the $⟨010⟩$ and $⟨10\overline{1}⟩$ directions in the (101) plane are also provided. The formulas for the Lamb shoulder threshold, which have not previously been available in the literature, should prove to be particularly useful, as they apply also to thin supported film structures. The procedure is applied to the determination of the elastic constants of the ternary semiconductor alloy ${\text{InAs}}_{0.91}{\text{Sb}}_{0.09}$, yielding ${C}_{11}=74.4\text{ }\text{GPa}$, ${C}_{12}=40.5\text{ }\text{GPa}$, and ${C}_{44}=37.8\text{ }\text{GPa}$.

Fabrication of poly(vinylidene fluoride-trifluoroethylene) ultrasound focusing transducers and measurements of elastic constants of thin plates

This paper investigates a modified method for fabricating focusing ultrasound transducers based on spin-coated poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] copolymer films. The ferroelectric hysteresis loops of the spin-coated P(VDF-TrFE) films are measured to establish the best fabrication parameters. The fabricated transducers are used for high-frequency wave velocity measurements and for non-destructive determination of elastic constants of thin isotropic plates. Both through-thickness longitudinal wave velocities and Rayleigh surface wave velocities of thin-plate samples with thicknesses ranging from 125 to 250 μm are measured, and hence their elastic constants can be determined in a straightforward and accurate way. The obtained results are in good agreement with the data reported by the manufacturers. Limitation of the proposed fabrication method and conventional method is compared and discussed in terms of signal intensity and frequency characteristics.

Evaluation of CVD Diamond Coating Using Back-Reflected Rayleigh Surface Wave

The propagation characteristics of the back-reflected Rayleigh surface wave in chemical vapor deposit (CVD) diamond coated specimens were investigated experimentally using the ultrasonic backward radiation measurement. The deliberated delaminations produced between the coating layer and the substrate decreased Rayleigh surface wave velocity. This initial experimental result obtained in the present study demonstrates the high potential of the backward radiated ultrasound as a tool for nondestructive evaluation of very thin CVD diamond coating layer.

Macroscopic and microscopic examination of the relationship between crack velocity and path and Rayleigh surface wave speed in single crystal silicon

The speed of Rayleigh surface waves, denoted C R, is the accepted upper limit for Mode I crack velocity in monolithic solids. In the current contribution, we discuss several critical issues associated with the velocity of Rayleigh surface waves and crack velocity in single crystal (SC) brittle solids, and the global and local influence of C R on crack path selection in particular. Recent cleavage experiments in SC silicon showed that crack velocity at certain cleavage planes and crystallographic orientations cannot exceed a small fraction of C R, and thereafter the crack deflects to other cleavage planes. Indeed, C R defined by the continuum mechanics ignores atomistic phenomena occurring during rapid crack propagation, and therefore is limited in predicting the crack velocity. Examination of these anomalies shows that this limitation lies in microstructural lattice arrangement and in anisotropic phonon radiation during rapid crack propagation. Globally, C R has no influence on the crack deflection phenomenon. However, the misfit in C R between the original plane of propagation and the deflected plane generates local instabilities along the deflection zone.

The Thermoelasticity of Laser-Based Ultrasonics

ABSTRACT The generation of ultrasound by heat deposition due to laser irradiation has several advantages over conventional generation by piezoelectric transducers. Ultrasound generation by focused laser beam irradiation is a problem of thermoelastodynamics. A mathematical analysis for focused laser beam heating of the surface of an elastic half-space can be carried out by the use of integral transform techniques. It is, however, well known that a point source of heat is mechanically equivalent to a center of expansion. Here we use, therefore, simpler thermoelastic arguments to determine the mechanical loading equivalent to heating by laser irradiation, and then proceed to determine the induced wave motion. This approach has the advantage that the surface center of expansion can be determined for a general class of elastic materials without the necessity of using integral transform techniques. As an example, we consider line-focused laser irradiation of a transversely isotropic material whose axis of symmetry is perpendicular to the free surface of the body. General calculations of ultrasound generated by laser irradiation have shown that by far the most significant part of the generated surface motion is a pulse propagating with the velocity of Rayleigh surface waves. In the approach presented here, the surface-wave pulse is determined for time-harmonic excitation by the use of the reciprocity theorem, whereby the two reciprocal solutions are the actually generated surface waves and a “virtual” surface wave. The technique has general applicability for anisotropic and inhomogeneous materials, as long as the general form of the surface wave is known. Here we consider the case of a transversely isotropic material. In the last part, Fourier superposition of ultrasonic surface wave harmonics is used to obtain the surface wave pulse for arbitrary time dependence of the laser pulse.

Impact breakage of semi-brittle spheres

Quasi-static compression cracking and low-velocity impact cracking of 12.7 mm diameter spheres of acrylic resin and polymethyl methacrylate (PMMA), both types regarded as semi-brittle, has been investigated using postfracture optical microscopy observations and high-speed framing photography at framing rates of 200,000 frames per second. It has been shown that under both quasi-static and dynamic loading conditions the initial necessary step is the plastic deformation of the compressed/impacted sphere to an a/ R value of greater than ∼0.5, where a and R are the radii of contact and sphere, respectively. The high-speed photography has shown that under critical conditions one or two primary meridional cracks initiate at the circle of contact and propagate into the bulk, reaching velocities up to 0.8 of the Rayleigh surface wave velocity of the material of the sphere. From the growing primary meridional cracks, secondary meridional cracks initiate and propagate at high speeds towards the free surface of the sphere, leading to the formation of orange segment-shaped fragments. High-speed photography has also revealed that during impact loading, primary and secondary meridional cracks grow around approximately conical zones at the contact regions. High-speed framing photography at a higher framing rate of 500,000 frames per second has also been used to investigate the response of 600–750 μm diameter PMMA spheres when they impacted a smooth silica flat at 200 m s −1. Although under these impact conditions, the spheres did not break up, information about their rebound energies has been obtained and used to analyse the integrity of the spheres. These microspheres are shown to develop at and beyond the edge of the plastically deformed circular flat meridional cracks, which are very similar to those produced in the 12.7 mm diameter spheres.

Assessment of material degradation due to corrosion-fatigue using a backscattered Rayleigh surface wave

Material degradation due to corrosion-fatigue was evaluated nondestructively using backscattered Rayleigh surface wave. A corrosion-fatigue test was carried out for the specimens made of thermo-mechanically controlled process steel in 3.5 wt.% NaCl solution at 25 °C. The Backscattering profile, which is the amplitude variation of backscattered ultrasound according to the incident angle, of the specimens were measured in water at room temperature after the corrosion-fatigue test. The velocity of Rayleigh surface wave, determined from the incident angle at which the profile of the backscattered ultrasound became maximum, decreased for the specimen that had the large number of cycles to failure in the corrosion-fatigue test. This fact implies that the corrosion degradation occurred at specimen surface in this specific test is dominantly dependant on the time exposed to corrosion environment. The result observed in the present work demonstrates the high potential of backscattered Rayleigh surface wave as a tool for nondestructive evaluation of corrosion degradation of aged materials.

Ionospheric remote sensing of the Denali Earthquake Rayleigh surface waves

Using the Global Positioning System, we have detected ionospheric disturbances associated with the long‐period Rayleigh waves from the 2002 Denali earthquake (Ms = 7.9). The dense California GPS networks allowed us to map the ionospheric perturbations and to compute the group velocity with a high spatial resolution above the Pacific coasts. Due to a low sampling rate, a large error in the velocity determination remains. Nonetheless, it demonstrates that bi‐static remote sensing measurements of seismic waves with GPS networks can be performed. Monostatic measurements with a dedicated satellite could possibly be used to record in the ionosphere surface waves originating from large earthquakes. Such a space‐based remote sensing of the local group velocity of Rayleigh surface waves would effectively complement the seismic networks for high‐resolution global tomography of the Earth's lithosphere.

Surface wave velocity determination by using reflection coefficient method on the liquid-anisotropic-solid interface

Reflection coefficient of a plane wave impinging from liquid onto a liquid–anisotropic–solid interface is useful to theoretically predict the Rayleigh surface wave (RSW) velocity and the pseudo surface wave (PSW) velocity dispersions. In the present letter, several incomplete results proposed by previous investigation are restudied to attempt giving more appropriate physical understanding in theory. It is found that PSW velocity determined by the reflection coefficient analysis is just a nonleaky effect surface wave on the liquid–anisotropic–solid interface but not the leaky one.