Phase Velocities Of Love Waves Research Articles

Radially anisotropic structure beneath the Shikoku Basin from broadband surface wave analysis of ocean bottom seismometer records

AbstractWe have analyzed broadband surface wave data from ocean bottom seismometers deployed in the Shikoku Basin in the northeastern Philippine Sea to determine the radially anisotropic uppermost mantle structure beneath this oceanic basin. We first applied noise correlation method to continuous microseismic records to obtain phase velocities for fundamental‐mode and first higher‐mode Rayleigh waves and fundamental‐mode Love waves at periods of 7–29 s. At longer periods, we applied an array analysis method to teleseismic surface waves to obtain phase velocities of fundamental‐mode Rayleigh and Love waves at periods of 29–117 s. Using these broadband phase velocity measurements, we have determined the one‐dimensional radially anisotropic structure from the crust to the low velocity zone (LVZ) beneath the Shikoku Basin without assuming a priori structure in the uppermost mantle. The final structural model (SB‐RA10) has a high‐velocity lid from the Moho to a depth of ∼40 km, with an LVZ at greater depths. S wave velocities decrease by 6%–10% at a depth range of ∼40–70 km. This large decrease in velocity suggests that there is either a large difference in grain size between these layers or indicates the presence of partial melt or water in the LVZ. Furthermore, strong radial anisotropy of 4%–5% (VSH>VSV) is observed in the uppermost mantle, which may be stronger in the LVZ.

The shear wave velocity of the upper mantle beneath the Bay of Bengal, Northeast Indian Ocean from interstation phase velocities of surface waves

SUMMARY The Bay of Bengal evolved along the eastern margin of the Indian subcontinent about 130Ma with the breakup of India from eastern Gondwanaland. Since then the Indian lithospheric Plate has moved northward, along with the Bay of Bengal, and eventually collided with the Eurasian Plate. The age of the lithosphere beneath the central Bay of Bengal is ∼110 Ma. We evaluate the shear wave velocity structure of the upper mantle beneath the central Bay through inversion of phase velocities of fundamental mode Rayleigh and Love waves along two wave paths: (i) between Port Blair (PBA) and VIS (Visakhapatnam) and (ii) between DGPR (Diglipur) and VIS. The seismological observatories PBA and DGPR are located on the Andaman Island and to the east of the Bay and the observatory at VIS in located on the eastern coast of India to the west of the Bay. Using broad-band records of earthquakes, which lie along the great circle arc joining each pair of observatories, we obtain phase velocities between 20 and 240 s periods for Rayleigh waves and between 23 and 170 s for Love waves. These phase velocities are inverted to find the S-wave velocity structure of the upper mantle down to 400km. The crustal structure is based on previous studies of the Bay and kept fixed in the inversion. We obtain a radially anisotropic upper-mantle structure, where the SH-wave velocity (VSH) is greater than the SV-wave velocity (VSV) down to 400km. The S-wave velocity decreases sharply by ∼4.5 per cent for VSV and ∼1.5 per cent for VSH at a depth 110km, which is considered as the Lithosphere–Asthenosphere boundary (LAB), that is, the bottom of the mantle lid. Based on recent studies, such sharp fall of S-wave velocity below the mantle lid appears to indicate a partially molten thin layer (G-discontinuity) at this depth. The thickness of the mantle lid is intermediate between oceanic and continental regions. The lid is also characterized by low radial anisotropy, which decreases to near isotropy at the bottom of the lid. These two characteristics show a ‘continental-like’ mantle lid beneath the Bay. Rapid northward motion of the Indian Plate before its collision with Eurasia might have caused the large radial anisotropy observed below the mantle lid.

Love Wave Propagation in Porous Rigid Layer Lying over an Initially Stressed Half-Space

This paper devotes to study the propagation of Love waves in a fluid saturated, anisotropic, porous rigid layer lying over a prestressed, non-homogeneous, elastic half space. The dispersion equation of phase velocity is obtained. We found that the phase velocity of Love waves is considerably influenced by rigidity, porosity and anisotropy of the porous layer, inhomogeneity of the half-space and prestressing present in the media, the layer and the half-space. As a particular case dispersion equation of Love wave in rigid boundary does not coincides with that of in free bounray. Dispersion curves are plotted for different variation in inhomogeneity parameters and initial stress parameters the effect of the medium characteristics on the propagation of Love waves is discussed.

Crustal and uppermost mantle structure of southern Norway: results from surface wave analysis of ambient seismic noise and earthquake data

SUMMARY We use ambient seismic noise and earthquake recordings on a temporary regional network in southern Norway to produce Rayleigh and Love wave phase velocity maps from 3 to 67 s period. Local dispersion curves are then jointly inverted for a 3-D shear wave velocity model of the region. We perform a two-step inversion approach. First, a direct search, Monte Carlo algorithm is applied to find best fitting isotropic velocity depth profiles. Those profiles are then used as initial models for a linearised inversion which takes into account radial anisotropy in the shear wave structure. Results reveal crustal as well as uppermost mantle structures in the studied region. Velocity anomalies in the upper crust are rather small in amplitude and can in most parts be related to surface geology in terms of rock densities. Old tectonic units like the Oslo Graben (300–240 Ma) and the Caledonian nappes (440–410 Ma) are clearly imaged. Furthermore, we find clear indications for localized crustal anisotropy of about 3 per cent. Despite generally poor resolution of interface depths in surface wave inversion, we find lateral variation of crustal thickness in agreement with previous studies. We are able to confirm and locate the transition from a slow lithospheric upper mantle underneath southern Norway to a fast shield-like mantle towards Sweden.

Advantages of Using Multichannel Analysis of Love Waves (MALW) to Estimate Near-Surface Shear-Wave Velocity

As theory dictates, for a series of horizontal layers, a pure, plane, horizontally polarized shear (SH) wave refracts and reflects only SH waves and does not undergo wave-type conversion as do incident P or Sv waves. This is one reason the shallow SH-wave refraction method is popular. SH-wave refraction method usually works well defining near-surface shear-wave velocities. Only first arrival information is used in the SH-wave refraction method. Most SH-wave data contain a strong component of Love-wave energy. Love waves are surface waves that are formed from the constructive interference of multiple reflections of SH waves in the shallow subsurface. Unlike Rayleigh waves, the dispersive nature of Love waves is independent of P-wave velocity. Love-wave phase velocities of a layered earth model are a function of frequency and three groups of earth properties: SH-wave velocity, density, and thickness of layers. In theory, a fewer parameters make the inversion of Love waves more stable and reduce the degree of nonuniqueness. Approximating SH-wave velocity using Love-wave inversion for near-surface applications may become more appealing than Rayleigh-wave inversion because it possesses the following three advantages. (1) Numerical modeling results suggest the independence of P-wave velocity makes Love-wave dispersion curves simpler than Rayleigh waves. A complication of “Mode kissing” is an undesired and frequently occurring phenomenon in Rayleigh-wave analysis that causes mode misidentification. This phenomenon is less common in dispersion images of Love-wave energy. (2) Real-world examples demonstrated that dispersion images of Love-wave energy have a higher signal-to-noise ratio and more focus than those generated from Rayleigh waves. This advantage is related to the long geophone spreads commonly used for SH-wave refraction surveys, images of Love-wave energy from longer offsets are much cleaner and sharper than for closer offsets, which makes picking phase velocities of Love waves easier and more accurate. (3) Real-world examples demonstrated that inversion of Love-wave dispersion curves is less dependent on initial models and more stable than Rayleigh waves. This is due to Love-wave’s independence of P-wave velocity, which results in fewer unknowns in the MALW method compared to inversion methods of Rayleigh waves. This characteristic not only makes Love-wave dispersion curves simpler but also reduces the degree of nonuniqueness leading to more stable inversion of Love-wave dispersion curves.

The SPAC Method for a Finite M-Station Circular Array Using Horizontally Polarized Ambient Noise

The spatial autocorrelation (SPAC) method is a useful tool for interpreting ambient noise, and several theoretical tools based on this method are available for data collection, processing, and analysis. The method uses the three components of seismic microtremors recorded simultaneously with arrays of different configurations and yields dispersion curves of Rayleigh and Love waves. Existing theories of the SPAC method are based on an idealized circular array with an infinite number of stations (the continuous model). Errors due to the use of a finite number of stations have been derived theoretically for vertically polarized ambient noise. This paper presents an extension of that error theory to horizontally polarized ambient noise so that it is valid for a circular array with M uniformly spaced stations. The quantities that are obtained as the output of the SPAC method, however, depend on the ratio of the power spectral densities (PSDs) of Rayleigh and Love waves, which are difficult to identify beforehand. Instead we introduce a quantity, κ , that does not depend on the PSD ratio and therefore is more convenient for separating the properties of Rayleigh and Love waves. We derive an expression of κ for a finite, M-station circular array ( κ M) and compare it with what it should be in the continuous model ( κ T ). We illustrate κ M and κ T using field data from a site in Tehran and discuss their discrepancies. Finally, we demonstrate how we have estimated Love-wave phase velocities using the calculated κ M.

Influence of Rigid Boundary and Initial Stress on the Propagation of Love Wave

In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density. The dispersion equation of the phase velocity has been derived. It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space. The velocity of Love waves have been calculated numerically as a function of KH (where K is a wave number H is a thickness of the layer) and are presented in a number of graphs.

An inverse method for determining the elastic properties of thin layers using Love surface waves

Estimation of the mechanical and geometrical parameters of thin coatings and surface layers in materials is of great practical importance in engineering and technology. Indeed, surface properties of many vital engineering components, such as turbine blades, pistons, or bearings, directly affect the longevity and safety of modern machinery. In this article, the authors present a novel inversion procedure for simultaneous determination of thickness, shear elastic constant, and density of thin coating layers in materials. The inversion procedure is based on measurements of the dispersion curve for surface acoustic waves of the Love type. The inverse problem is formulated as an optimization problem with the appropriately designed objective function, depending on the material parameters of the coating layer, ultrasonic frequency, and the experimental data, i.e. measured phase velocity of the surface Love wave. The minimization of the objective function provides three parameters of a thin layer, i.e. its thickness, shear elastic constant, and density. The proposed inverse method was checked experimentally for different layered structures, such as copper layer on steel substrate or ceramics-on-ceramics. The agreement between the results of calculations with the proposed inversion method and the experimental data was good.

SIZE-DEPENDENT BEHAVIOR OF LOVE WAVE PROPAGATION IN A NANOCOATING

The effect of surface/interface stress on mechanical behaviors may become remarkable when the characteristic size of a structure decreases to nanoscale. Various problems have been analyzed to reveal the size-dependent mechanical behaviors of nano structures with curved surfaces/interfaces. In this work, the problem of planar surfaces/interfaces is addressed. The generalized Young–Laplace equation is presented for a planar interface and the propagation behavior of Love wave in a nanocoating is discussed. Parametric studies indicate that if the surface effect of the nanocoating is considered the phase velocity of Love wave shows notable size-dependency on both the nanocoating thickness and the wavelength. When these two sizes are both in nanoscale, the phase velocity further depends on the relative size between them. In addition, increasing the residual surface stress may reduce the phase velocity of Love wave.

Shear wave crustal velocity model of the Western Bohemian Massif from Love wave phase velocity dispersion

We propose a new quantitative determination of shear wave velocities for distinct geological units in the Bohemian Massif, Czech Republic (Central Europe). The phase velocities of fundamental Love wave modes are measured along two long profiles (~200 km) crossing three major geological units and one rift-like structure of the studied region. We have developed a modified version of the classical multiple filtering technique for the frequency-time analysis and we apply it to two-station phase velocity estimation. Tests of both the analysis and inversion are provided. Seismograms of three Aegean Sea earthquakes are analyzed. One of the two profiles is further divided into four shorter sub-profiles. The long profiles yield smooth dispersion curves; while the curves of the sub-profiles have complicated shapes. Dispersion curve undulations are interpreted as period-dependent apparent velocity anomalies caused both by different backazimuths of surface wave propagation and by surface wave mode coupling. An appropriate backazimuth of propagation is found for each period, and the dispersion curves are corrected for this true propagation direction. Both the curves for the long and short profiles are inverted for a 1D shear wave velocity model of the crust. Subsurface shear wave velocities are found to be around 2.9 km/s for all four studied sub-profiles. Two of the profiles crossing the older Moldanubian and Tepla-Barrandian units are characterized by higher velocities of 3.8 km/s in the upper crust while for the Saxothuringian unit we find the velocity slightly lower, around 3.6 km/s at the same depths. We obtain an indication of a shear wave low velocity zone above Moho in the Moldanubian and Tepla-Barrandian units. The area of the Eger Rift (Tepla-Barrandian–Saxothuringian unit contact) is significantly different from all other three units. Low upper crust velocities suggest sedimentary and volcanic filling of the rift as well as fluid activity causing the earthquake swarms. Higher velocities in the lower crust together with weak or even missing Moho implies the upper mantle updoming.

Love Wave at a Layer Medium Bounded by Irregular Boundary Surfaces

The problem of the propagation of a Love wave in a corrugated isotropic layer over a homogeneous isotropic half-space has been investigated. The dispersion relation of Love wave propagation in a corrugated layer medium bounded by irregular boundaries is derived. In special cases, the dispersion relation is reduced for the corrugated layers bounded by periodic boundary surfaces, d cos px, d1 cos px and d2 cos px. The dispersion relation is found to be a function of the amplitudes of the corrugation, frequency and position parameters of the corrugated boundary surfaces. The results of Ewing et al. and results similar to Noyer are recovered from our analysis. The phase velocity and group velocity of Love waves are computed numerically and the results are depicted graphically.

10.1007/s11486-008-1008-z

The deep structure of the upper mantle is determined from data on phase velocities of Love and Rayleigh waves measured by a differential method on traces between two stations in central Western Europe. One-dimensional velocity structures are first constructed from data of each pair of stations, after which two-dimensional distributions of SH and SV velocities are calculated by the method of two-dimensional tomography from S wave velocities at fixed depths. The results are presented in the form of 2-D vertical structures of the average S wave velocity (S = (SV + SH)/2) constructed along profiles crossing the region in directions of the best resolution. The main structural features are a higher velocity zone at depths of 60–80 km in the area (48°–50°N, 9°–11°E) and a lower velocity zone in the western part of the region at depths of 100–150 km, probably extending farther beyond the studied area.

Love wave dispersion in central North America determined using absolute displacement seismograms from high‐rate GPS

We use seismic array processing of high‐rate GPS (HRGPS) displacement time series from the Great, 2004, Mw 9+, Sumatra‐Andaman earthquake recorded at over 90 nonuniformly distributed HRGPS stations in central North America to determine the fundamental Love wave phase velocity dispersion curve there. These measurements were performed using frequency domain beam forming, which we show reduces the effects of GPS multipath and common mode noise on the measurement of surface wave phase velocity and azimuth. Our HRGPS based results for surface wave phase velocity agree well with those obtained from 28 broadband seismometers between periods of 20 to 300 s. By separating waves based on their apparent velocity, beam forming supports the simple model for relative displacement HRGPS time series as being the difference between the reference and kinematic station's absolute displacements. Beam forming also demonstrates that for differential GPS processing the infinite apparent velocity beam of an array is composed of the sum of common mode noise and the reference station's absolute displacements, multipath and noise. We show the infinite apparent velocity beam, which we call the generalized spatial filter, is similar to the spatial filter commonly used to remove common mode noise from HRGPS seismograms and can be used to produce absolute displacement time series for the kinematic stations with reduced common mode noise. Beam forming also suggests a filtering method, complimentary to sidereal filtering, to produce GPS multipath reduced HRGPS time series.

Love waves in a fluid-saturated porous layer under a rigid boundary and lying over an elastic half-space under gravity

In this paper, mathematical modeling of the propagation of Love waves in a fluid-saturated porous layer under a rigid boundary and lying over an elastic half-space under gravity has been considered. The equations of motion have been formulated separately for different media under suitable boundary conditions at the interface of porous layer, elastic half-space under gravity and rigid layer. Following Biot, the frequency equation has been derived which contain Whittaker’s function and its derivative that have been expanded asymptotically up to second term (for approximate result) for large argument due to small values of Biot’s gravity parameter (varying from 0 to 1). The effect of porosity and gravity of the layers in the propagation of Love waves has been studied. The effect of hydrostatic initial stress generated due to gravity in the half-space has also been shown in the phase velocity of Love waves. The phase velocity of Love waves for first two modes has been presented graphically. Frequency equations have also been derived for some particular cases, which are in perfect agreement with standard results. Subsequently the lower and upper bounds of Love wave speed have also been discussed.

New Circular-Array Microtremor Techniques to Infer Love-Wave Phase Velocities

We present simple and novel formulas that help to directly infer phase velocities of Love waves ( c L ) using two-component, horizontal-motion, circular-array records of microtremors. Our formulas are analogous to those of the spatial autocorrelation (SPAC) method, a technique of microtremor exploration that is popularly used to infer phase velocities of Rayleigh waves ( c R ). Although the existing theory of the SPAC method does provide the possibility to estimate c L , this can only be done by solving a nonlinear system of equations, wherein the unknowns to be solved for also include c R and the Rayleigh-to-Love power partition ratios. By contrast, c L is the only unknown to appear in our formulas. The field applicability of the c L estimation methods based on the proposed formulas—which we name the SPAC+ L , SPAC- L , and CCA- L (where CCA stands for centerless circular array) methods—is demonstrated by analysis results for two test sites. Among the three techniques proposed, the SPAC+ L method distinguished itself as the best-performing. The valid wavelength ranges of the three methods had lower limits in the area of 2–5 times the array radius r and upper limits in the area of 10–25 r . Similar circular-array microtremor techniques that involve c L alone were proposed in recent years, but the methods we present here are either logistically less expensive or mathematically simpler than any of them.

The origin ofSH-wave resonance frequencies in sedimentary layers

SUMMARY Resonance frequencies are often analysed in geo-engineering studies to evaluate seismic risk and microzonation in urban areas. The Nakamura technique constitutes a popular approach that computes the spectral ratio of horizontal-to-vertical ground motion in ambient noise recordings to reveal the existence of any site resonance frequencies. Its theoretical basis remains however unclear with some authors arguing that the method de-emphasizes any Rayleigh-wave contributions and that the resonance frequencies are solely caused by vertically incident SH waves. Other authors explain the same resonance frequencies by the ellipticity of the fundamental Rayleigh wave. Recent numerical simulations reveal that the magnitude of the peak frequency is proportional to the relative portion of Love waves present. This study demonstrates that Love waves alone can be responsible for any observed resonance frequencies in sedimentary layers. Yet sharp SH-wave resonance frequencies are only excited by a source in the bedrock. These resonance frequencies are caused by inhomogeneous waves excited by the bedrock source that tunnel through the high-velocity bedrock to emerge in the low-velocity sediments with a very reduced range of slownesses. The resulting SH waves are then free to interfere constructively thereby creating the observed resonance frequencies. This general trigger mechanism leads to resonances that are almost offset independent. The resulting resonance frequencies map onto points of maximum curvature in the Lovewave phase–velocity dispersion curves at or just beyond the critical horizontal slowness. They can be analysed with the quarter-wavelength law if a large velocity contrast exists between the unconsolidated sediments and the bedrock. A minor modification of the quarter-wavelength law provides more accurate predictions, also for smaller velocity contrasts. Multisource simulations show that site amplification factors as determined by horizontalover-vertical (H/V) spectral ratios would not only depend on the relative portion of Love waves in the total wavefield but also on the depth distribution and the relative strength of the SH sources inside the bedrock compared with those in the sediments. An accurate interpretation of site amplification factors by means of H/V peak frequencies would thus require in-depth knowledge of the causes and origins of the local microseismic noise field.

Propagation of Love waves in prestressed piezoelectric layered structures loaded with viscous liquid

We investigate analytically the effect of initial stress in piezoelectric layered structures loaded with viscous liquid on the dispersive and attenuated characteristics of Love waves, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of initial stress in the piezoelectric layer and the viscous coefficient of the liquid on the phase velocity of Love waves are analyzed. Numerical results are presented and discussed. The analytical method and the results can be useful for the design of chemical and biosensing liquid sensors.

Transverse surface waves in an FGM layered structure

The existence and propagation behavior of Love waves in a functionally graded material (FGM) layered structure are theoretically investigated in this paper based on the three-dimensional equations of linear electricity. The Wentzel–Kramers–Brillouin (WKB) method is applied to obtain the analytical solutions in the FGM layer. The dispersion equation for a Love surface wave in this kind of structure is obtained in a simple mathematical form, where the material property variation of the FGM layer is arbitrary. First, the solution is used to study the effect of the gradient coefficients on the dispersion curves and the phase velocities of Love waves. Then, the influence of gradient coefficients on the stress and displacement fields is discussed in detail. The reported results are important in the design of surface acoustic wave (SAW) devices with high performance.

Love wave propagation in piezoelectric layered structure with dissipation

We investigate analytically the effect of the viscous dissipation of piezoelectric material on the dispersive and attenuated characteristics of Love wave propagation in a layered structure, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of the viscous coefficient on the phase velocity of Love waves and attenuation are presented and discussed in detail. The analytical method and the results can be useful for the design of the resonators and sensors.

Love waves with a transverse structure

For an arbitrary layered isotropic structure, new exact solutions of the elastodynamic problem for the propagation of surface waves are presented. These solutions describe waves with rectilinear wave fronts propagating at the phase velocities of common SH-polarized Love waves. They linearly depend on a lateral transverse variable and, in addition to being standardly SH-polarized, have a longitudinally polarized anomalous component. The construction uses the assumption of the existence of standard Love waves. It is based on a potential representation of the wavefield and is quite elementary.