Phase Velocities Of Love Waves Research Articles

Seismic structure of Precambrian lithosphere: New constraints from broad-band surface-wave dispersion

Depth distributions of seismic velocities and their directional dependence (anisotropy) in the crust and mantle beneath cratons yield essential constraints on processes of their formation and evolution. Despite recent progress in mapping the lateral extent of cratonic roots around the globe, profiles of seismic velocities within them remain uncertain. In this study we employ a novel combination of waveform-analysis techniques and measure inter-station Rayleigh- and Love-wave phase velocities in broad period ranges that enable resolution from the upper crust to deep upper mantle. Sampling a selection of 10 Archean and Proterozoic locations, we derive new constraints on the isotropic and radially anisotropic seismic structure of Precambrian lithosphere. Shear-wave speed V S is consistently higher in the lithosphere of cratons than in the lithosphere of Proterozoic foldbelts. Because known effects of compositional variations in the lithosphere on V S are too small to account for the difference, this implies that temperature in cratonic lithosphere is consistently lower, in spite of sub-lithospheric mantle beneath continents being thermally heterogeneous, with some cratons underlain, as we observe, by a substantially hotter asthenosphere compared to others. Lithospheric geotherms being nearly conductive, this confirms that the stable, buoyant lithosphere beneath cratons must be substantially thicker than beneath younger continental blocks. An increase in V S between the Moho and a 100-150 km depth is consistently preferred by the data in this study and is present in seismic models of continents published previously. We argue that this is largely due to the transition from spinel peridotite to garnet peridotite, proposed previously to give rise to the “Hales discontinuity” within this depth interval. The depth and the width of the phase transformation depend on mantle composition; it is likely to occur deeper and over a broader depth interval beneath cratons than elsewhere because of the high Cr content in the depleted cratonic lithosphere, as evidenced by a number of xenolith studies. Seismic data available at present would be consistent with both a sharp and a gradual increase in V S in the upper lithosphere (a Hales discontinuity or a “Hales gradient”). The V S profile in the upper mantle lithosphere is not shaped by the temperature distribution only; this needs to be considered when relating seismic velocities to lithospheric temperatures. Radial anisotropy in the upper crust is observed repeatedly and indicates vertically oriented anisotropic fabric ( V SH < V SV); this may yield a clue on how cratons grew, lending support to the view that distributed crustal shortening with sub-vertical flow patterns occurred over large scales in hot ancient orogens. In the lower crust and upper lithospheric mantle, radial anisotropy consistently reveals horizontal fabric ( V SH > V SV); the fabric can be interpreted as a record of (sub-)horizontal ductile flow in the lower crust and lithospheric mantle at the time of the formation and stabilisation of the cratons. We also find indications for radial anisotropy below 200 km depth, corroborating recent evidence for anisotropy in the asthenosphere beneath cratons due to current and recent asthenospheric flow.

An alternative method for calculation of Rayleigh and Love wave phase velocities by using three-component records on a single circular array without a central station

SUMMARY A method for the computation of phase velocities of surface waves from microtremor waveforms is shown. The technique starts from simultaneous three-component records obtained in a circular array without a central station. Then, Fourier spectra of vertical, radial and tangential components of motion are calculated for each station and considered as complex-valuated functions of the azimuthal coordinate. A couple of intermediate real physical quantities, B and C, can be defined from the 0- and ±1-order coefficients of the Fourier series expansion of such functions. Finally, phase velocities of Rayleigh and Love waves can be retrieved from B and C by solving respective one-unknown equations. The basic assumption is the possibility of expanding the wavefield as a sum of plane surface waves with Rayleigh and Love wavenumbers being univocal functions of the circular frequency. The method is tested in synthetic ambient noise wavefields confirming its reliability and robustness for passive seismic surveying.

Broadband ambient noise surface wave tomography across the United States

This study presents surface wave dispersion maps across the contiguous United States determined using seismic ambient noise. Two years of ambient noise data are used from March 2003 through February 2005 observed at 203 broadband seismic stations in the US, southern Canada, and northern Mexico. Cross‐correlations are computed between all station‐pairs to produce empirical Green functions. At most azimuths across the US, coherent Rayleigh wave signals exist in the empirical Green functions implying that ambient noise in the frequency band of this study (5–100 s period) is sufficiently isotropically distributed in azimuth to yield largely unbiased dispersion measurements. Rayleigh and Love wave group and phase velocity curves are measured together with associated uncertainties determined from the temporal variability of the measurements. A sufficient number of measurements (&gt;2000) is obtained between 8 and 25 s period for Love waves and 8 and 70 s period for Rayleigh waves to produce tomographic dispersion maps. Both phase and group velocity maps are presented in these period bands. Resolution is estimated to be better than 100 km across much of the US from 8–40 s period for Rayleigh waves and 8–20 s period for Love waves, which is unprecedented in a study at this spatial scale. At longer and shorter periods, resolution degrades as the number of coherent signals diminishes. The dispersion maps agree well with each other and with known geological and tectonic features and, in addition, provide new information about structures in the crust and uppermost mantle beneath much of the US.

Effect of Initial Stress on the Behavior of Love Waves in an Elastic Half-Space with a Functionally Graded Layer

The propagation behavior of Love waves in a functionally graded material layered half-space with initial stress is taken into account. The Wentzel-Kramers-Brillouin (WKB) asymptotic technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of mechanical displacement and stress along thickness direction in the layered structure. Firstly, these solutions are used to study effects of the initial stress on the dispersion relations and phase velocities, then influences of the initial stress on the distributions of mechanical displacement and shear stresses along thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of Love wave increases with the increase of the magnitude of the initial tensile stress, while decreases with the increase of the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100MPa. Some other results are shown for distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures.

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

SUMMARY We present the results of Rayleigh wave and Love wave phase velocity tomography in the western United States using ambient seismic noise observed at over 250 broad-band stations from the EarthScope/USArray Transportable Array and regional networks. All available threecomponent time-series for the 12-month span between 2005 November 1 and 2006 October 31 have been cross-correlated to yield estimated empirical Rayleigh and Love wave Green’s functions. The Love wave signals were observed with higher average signal-to-noise ratio (SNR) than Rayleigh wave signals and hence cannot be fully explained by the scattering of Rayleigh waves. Phase velocity dispersion curves for both Rayleigh and Love waves between 5 and 40 speriod were measured for each interstation path by applying frequency‐time analysis. The average uncertainty and systematic bias of the measurements are estimated using a method based on analysing thousands of nearly linearly aligned station-triplets. We find that empirical Green’s functions can be estimated accurately from the negative time derivative of the symmetric component ambient noise cross-correlation without explicit knowledge of the source distribution. The average traveltime uncertainty is less than 1 s at periods shorter than 24 s. We present Rayleigh and Love wave phase speed maps at periods of 8, 12, 16,and 20 s. The maps show clear correlations with major geological structures and qualitative agreement with previous results based on Rayleigh wave group speeds.

Radially anisotropic shear velocity structure of the upper mantle globally and beneath North America

A surface wave dispersion data set of unprecedented size is used to obtain a variable‐resolution model of the radially anisotropic shear wave velocity structure of the upper mantle beneath North America and globally. Love and Rayleigh wave phase velocities for periods in the range 35–150 s constrain a three‐dimensional model of velocity variations on a length scale of a few hundred kilometers within the North American continent and a few thousand kilometers globally. The short‐ and long‐wavelength models are determined simultaneously. Long‐period surface wave phase velocities (200–350 s) are used to help constrain longer‐wavelength and transition zone structure. Laterally varying velocity sensitivity kernels are used to account for the dependence of the velocity sensitivity on lateral variations in crust and mantle velocity structure. The sensitivity kernels are updated in several iterations to avoid nonlinearities associated with the inverse problem for the determination of mantle structure. Variations in isotropic velocity in the uppermost several hundred kilometers of the mantle are found to correlate well with surface tectonic features. Within the North American craton, the locations of strongest radial anisotropy generally correlate with the locations of fastest isotropic velocity. Variations in radial anisotropy show a clear continent‐ocean signature. Strong anisotropy occurs at shallow depths (&lt;100 km) under the continents, with a secondary peak found at a depth of ∼200 km. Maximum anisotropy under the oceans occurs at a depth of ∼125 km, with no secondary maximum. Combined interpretation of isotropic and anisotropic continent‐ocean differences suggests a different role for the low‐velocity zone under continental and oceanic regions.

Upper mantle structure beneath central Western Europe from data on phase velocities of surface waves

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.

Fully nonlinear inversion of fundamental mode surface waves for a global crustal model

We use neural networks to find 1‐dimensional marginal probability density functions (pdfs) of global crustal parameters. The information content of the full posterior and prior pdfs can quantify the extent to which a parameter is constrained by the data. We inverted fundamental mode Love and Rayleigh wave phase and group velocity maps for pdfs of crustal thickness and independently of vertically averaged crustal shear wave velocity. Using surface wave data with periods T &gt; 35 s for phase velocities and T &gt; 18 s for group velocities, Moho depth and vertically averaged shear wave velocity of continental crust are well constrained, but vertically averaged shear wave velocity of oceanic crust is not resolvable. The latter is a priori constrained by CRUST2.0. We show that the resulting model allows to compute global crustal corrections for surface wave tomography for periods T &gt; 50 s for phase velocities and T &gt; 60 s for group velocities.

Love Waves in Layered Graded Composite Structures with Imperfectly Bonded Interface

AbstractTheoretical analysis and numerical calculations of Love wave propagation in layered graded composites with imperfectly bonded interface are described in this paper. On the basis of WKB method, the approximate analytic solutions for Love waves are obtained. By the interface shear spring model, the dispersion relations for Love waves in layered graded composite structures with rigid, slip, and imperfectly bonded interfaces are given, and the effects of the interface conditions on the phase velocities of Love waves in SiC/Al layered graded composites are discussed. Numerical analysis shows that the phase velocity decreases when the defined flexibility parameter is greater. For the general imperfectly bonded interface, the phase velocity changes in the range of the velocities for the rigid and slip interface conditions.

The inverse dynamic problem of seismic sounding low-frequency regularization

A wave process induced by a plane wave in a vertically inhomogeneous half-space is considered. A traditional geophysical inverse problem is that of recovering the acoustic impedance if the shape of incident wave and the corresponding surface seismogram are known. The classical algorithm for solving this problem based on the reconstruction of the Sturm–Liouville differential operator by using its spectral function is very sensitive to errors in the low-frequency range. We present a regularization method based on approximate reconstruction of the medium with the use of the phase velocities of Love waves.

Seabed property estimation from ambient-noise recordings: Part I — Compliance and Scholte wave phase-velocity measurements

The ability to derive a near-surface shear-velocity profile from ambient-noise records is useful for seismic applications such as shear-wave statics estimation and geohazard prediction. Measurements of seafloor compliance and Scholte wave velocity and amplitude are all related to the near-surface shear-velocity profile. I analyzed a data set of [Formula: see text] of continuous noise records recorded by an ocean bottom cable deployed in [Formula: see text] deep water for seafloor compliance and Scholte waves. I failed to observe seafloor compliance because of limitations in the record length. I have detected Scholte waves on the inline and vertical component geophones and Love waves on the crossline component using [Formula: see text] spectra. Both the Scholte and Love wave phase-velocities can be explained by a simple 1D isotropic near-surface model. The Scholte waves may have been excited by acoustic energy from the recording vessel, while no satisfactory excitation mechanism has been found for the Love waves.

Global Love wave overtone measurements

Love wave phase velocities for fundamental and higher modes are difficult to measure because the different modes cannot easily be separated. Following Yoshizawa and Kennett (2002), we generate suites of path specific one‐dimensional shear wave velocity profiles using the Neighbourhood Algorithm of Sambridge (1999a). From this family of O(104) models both fundamental and higher mode phase velocities with mutually consistent uncertainties are calculated. We have fully automated the method and analysed over forty thousand Love wave seismograms from the GDSN and GEOSCOPE global networks from 1994–2004. Our phase velocity measurements agree remarkably well with previous studies, but we have been able to enlarge the available dataset dramatically. We present global Love wave phase velocity maps (up to the fifth overtone) with unprecedented resolution due to the improved path coverage. Comparing these maps to existing tomographic models, we discern evidence of significant anisotropy in the lower mantle around a depth of 1000 km in the Pacific.

Full SH-wavefield modelling and multiple-mode Love wave inversion

Full SH-wavefield modelling by the reflectivity method is developed for Love wave inversion. The modelling simulates field tests, first by generating time-distance shot gathers, followed by standard plane-wave transform to extract Love wave phase-velocity dispersion. All SH surface wave modes, plus body waves and wavefront spreading are accurately simulated.When a thin low-velocity layer (LVL) is underlain by a much stiffer layer, Love wave modes are well separated and fundamental-mode identification is more straightforward than the equivalent Rayleigh waves. However, when the LVL is thicker and bounded by equally stiff layers, multiple dominant higher modes propagate, and their correct identification and inversion is essential to resolve the soft layer.A first field test shows how multimode Love wave inversion can resolve a 2 m thick clay layer at 1 m depth in the lithological log when only both the fundamental and first higher modes are incorporated. A second field test, where a much thicker LVL, interpreted as a mud plume, is present, shows how several higher modes are required to resolve the soft layer LVL, whereas use of the fundamental or effective mode only fails.

Path-specific Velocity Structure of Western China from Surface-wave Dispersion

We develop one-dimensional (1-D) path-specific velocity models in western China using new Rayleigh and Love wave group and phase velocity dispersion measurements for 20 events in the region. The earthquakes were grouped into three geographic clusters from which we compute the average phase and group velocity dispersion. We invert the average dispersion curves simultaneously for 1-D shear-velocity models appropriate for the three central Asian paths, using three previous shear-velocity models as initial models. The models are validated by forward modeling waveforms of recent events. The crustal thickness beneath western China in the vicinity of the Lop Nor test site is 50–60 km and our velocity models are consistent with major geologic features (e.g., basins and mountain ranges) and previous structural models for this region.

A two-radius circular array method: Inferring phase velocities of Love waves using microtremor records

We present a new method to estimate phase velocities of Love waves from horizontal‐motion seismograms of microtremors, obtained with seismic sensors placed around two circumferences of different radii, under the assumption that the fundamental mode dominates. We applied our new method to field data acquired at a test site where the shallow underground seismic velocity profile is known, and have confirmed that the phase velocities of the fundamental‐mode Love waves could be inferred with sufficient precision within certain wavelength ranges. Outside the wavelength ranges suitable for analysis, the “spectral ratio,” an intermediary quantity calculated from measurement records prior to phase velocity evaluation, deviated from theoretical expectations. The pattern of deviations could satisfactorily be accounted for by considering three factors theoretically: the presence of higher‐mode surface waves, directional aliasing related to the finite number of sensors, and the presence of incoherent noise.

Love Wave Propagation in a Layered Piezoelectric Structure Immersed in a Viscous Fluid

This paper is addressed to the Love wave propagation in a layered piezoelectric structure immersed in a viscous fluid. The layered piezoelectric structure consists of an isotropic layer and a relatively thicker transversely isotropic piezoelectric substrate. The velocity of the Love waves changes due to the presence of the viscous fluid. The exact theory is accurate but not convenient to apply because it is generally difficult to get an explicit relation between the quantities we interest. In this paper, the perturbation approach is applied to obtain the explicit relations for the phase velocity and attenuation of Love waves. The result is useful for the measurement of the viscosity and mass density in Love wave sensors.

Constraints on absoluteSvelocities beneath the Aegean Sea from surface wave analysis

The 3-D structure of the lithosphere beneath the Aegean Sea is investigated through surface wave dispersion analysis. Rayleigh and Love waves recorded by 12 broad-band stations installed for a duration of 6 months in the Aegean region are processed through array analysis and Wiener filtering. Data from three GEOFON stations in the area of Crete were also used. The resulting two-station phase velocities are used to determine lateral variations of Rayleigh wave phase velocities between periods of 20 and 100 s by a 2-D ray tomography method. The obtained phase velocities are inverted to calculate variation of S-wave velocity with depth using a combination of linearized inversion and a Monte Carlo based non-linear inversion. The absolute S-wave velocity is resolved to a depth of approximately 200 km. A high-velocity anomaly of 3 per cent is observed in the southern Aegean attributed to the Hellenic subduction. In the northern part of the Aegean, in the prolongation of the North Anatolian Fault which is influenced by strong extensional movements, we found low absolute S-wave velocities at 50–100 km depth. This supports a model of a distributed deformation of the upper mantle in the area. Separate Rayleigh and Love wave phase velocity inversions along common profiles reveal a strong Love–Rayleigh discrepancy in the northern Aegean down to at least 150 km depth, i.e. most probably including the top of the asthenosphere.

Probability density functions for radial anisotropy from fundamental mode surface wave data and the Neighbourhood Algorithm

SUMMARY We applied Sambridge’s Neighbourhood Algorithm (NA) to degree-8 fundamental mode Love and Rayleigh wave phase velocity maps between 40 and 150 s to find models of radial anisotropy in the upper 220 km of the mantle. The NA is a powerful tool to explore a multidimensional model space and retrieve an ensemble of models from which statistical inferences (posterior probability density functions (PPDFs) and trade-offs) can be made. We sought solutions for density anomalies and perturbations in the five elastic coefficients that describe transverse isotropy and obtained independent probability density functions for S-wave anisotropy, P-wave anisotropy, intermediate parameter η, Vp, Vs and density anomalies. We find robust departures from PREM in S-wave anisotropy (ξ ) under cratons and oceans alike, with a clear change of sign in the anomalies with respect to the reference model at approximately 100 km depth. No significant difference is observed between cratons and oceans, both in the amplitude and depth variation of ξ . The signal within continents is clearly age related, with platforms and tectonically active regions characterized by a rapid decrease in ξ with depth, while cratons display a more constant signal. A similar age dependence in S-wave anisotropy is also observed beneath oceans: a strong and rapidly decreasing anisotropy for young oceans and a more constant anisotropy for older oceans. Perturbations in P-wave anisotropy (φ) are small and limited to the shallowest part of the continents. A small age-dependent signal for φ is observed beneath oceans. Anomalies in intermediate parameter η are similar to those in φ (but not globally correlated), but the deviation from PREM is stronger for η than for φ. Cratons appear to be devoid of any η anisotropy in the top 100 km. There is no obvious global correlation between deviations in φ and deviations in ξ , and the ratio between dη and dξ is clearly regionally variable, which cautions against the use of commonly used proportionality factors between these variables in inversions. In all regions, we found a good correlation between the equivalent isotropic P- and S-wave velocity anomalies, with a ratio d ln Vs/d ln Vp close to 1. Density anomalies were not sufficiently well resolved with fundamental mode data alone, but do not influence the results for anisotropy.

微動と地震動の水平アレー観測によるやや長周期帯域地震動の評価

We conducted array measurements of vertical mictrotremors to determine an S-wave velocity structure in Tokyo Metropolitan coastal area in the center of the Kanto district, Japan, for evaluating characteristics of long-period ground motions. Phase velocities of Rayleigh waves were estimated from F-K and SPAC analyses of the array data. We, next, inverted them to S-wave velocity structures of deep sediments from a genetic inversion using existing data on subsurface structure. Furthermore, we investigated characteristics of several earthquake records during shallow earthquakes in the seismic array in the area. Phase velocities of fundamental Love waves and fundamental and first-higher mode Rayleigh waves in a period range from 2 to 7 seconds were determined from semblance analyses of the earthquake array data. The final S-wave profile was selected among the profiles discussed in the microtremor exploration from the constrained condition given from the phase velocities estimated from the earthquake observation. We also discussed on the propagation directions of the surface waves in the earthquake records.

Probability density functions for radial anisotropy: implications for the upper 1200 km of the mantle

The presence of radial anisotropy in the upper mantle, transition zone and top of the lower mantle is investigated by applying a model space search technique to Rayleigh and Love wave phase velocity models. Probability density functions are obtained independently for S-wave anisotropy, P-wave anisotropy, intermediate parameter η, V p, V s and density anomalies. The likelihoods for P-wave and S-wave anisotropy beneath continents cannot be explained by a dry olivine-rich upper mantle at depths larger than 220 km. Indeed, while shear-wave anisotropy tends to disappear below 220 km depth in continental areas, P-wave anisotropy is still present but its sign changes compared to the uppermost mantle. This could be due to an increase with depth of the amount of pyroxene relative to olivine in these regions, although the presence of water, partial melt or a change in the deformation mechanism cannot be ruled out as yet. A similar observation is made for old oceans, but not for young ones where V SH> V SV appears likely down to 670 km depth and V PH> V PV down to 400 km depth. The change of sign in P-wave anisotropy seems to be qualitatively correlated with the presence of the Lehmann discontinuity, generally observed beneath continents and some oceans but not beneath ridges. Parameter η shows a similar age-related depth pattern as shear-wave anisotropy in the uppermost mantle and it undergoes the same change of sign as P-wave anisotropy at 220 km depth. The ratio between dln V s and dln V p suggests that a chemical component is needed to explain the anomalies in most places at depths greater than 220 km. More tests are needed to infer the robustness of the results for density, but they do not affect the results for anisotropy.