Rayleigh Wave Data Research Articles

High-frequency Rayleigh-Wave method

High-frequency (≥2 Hz) Rayleigh-wave data acquired with a multichannel recording system have been utilized to determine shear (S)-wave velocities in near-surface geophysics since the early 1980s. This overview article discusses the main research results of high-frequency surface-wave techniques achieved by research groups at the Kansas Geological Survey and China University of Geosciences in the last 15 years. The multichannel analysis of surface wave (MASW) method is a non-invasive acoustic approach to estimate near-surface S-wave velocity. The differences between MASW results and direct borehole measurements are approximately 15% or less and random. Studies show that simultaneous inversion with higher modes and the fundamental mode can increase model resolution and an investigation depth. The other important seismic property, quality factor (Q), can also be estimated with the MASW method by inverting attenuation coefficients of Rayleigh waves. An inverted model (S-wave velocity or Q) obtained using a damped least-squares method can be assessed by an optimal damping vector in a vicinity of the inverted model determined by an objective function, which is the trace of a weighted sum of model-resolution and model-covariance matrices. Current developments include modeling high-frequency Rayleigh-waves in near-surface media, which builds a foundation for shallow seismic or Rayleigh-wave inversion in the time-offset domain; imaging dispersive energy with high resolution in the frequency-velocity domain and possibly with data in an arbitrary acquisition geometry, which opens a door for 3D surface-wave techniques; and successfully separating surface-wave modes, which provides a valuable tool to perform S-wave velocity profiling with high-horizontal resolution.

Study of Sediment Nonlinearity Using Explosion Data in the Mississippi Embayment

Strong and weak motion data from the Mississippi Embayment Seismic Excitation Experiment (ESEE) were analyzed for signatures of nonlinear site responses. This experiment was performed jointly by the University of Memphis and U. S. Geological Survey in October 2002, by detonating two explosions of 2500 and 5000 lbs. Intrinsic and scattering Q estimates (QI and QS) from the coda of the strong motion data were found to be very low compared to previously determined Q values of P- and Rayleigh waves of weak motion data from the same explosions. The QI estimates from P-wave late coda of the strong motion data are less by more than 100 at 3 Hz and by more than 200 at 10 Hz, compared to the P-wave Q values determined from the weak motion data by Langston et al (2005). Also, QI determined from the late coda of strong motion Rayleigh-wave data is less by more than 200 at 0.5 Hz and by more than 50 at 3.0 Hz, compared to Q values determined from Rayleigh-wave weak motion data. A resonance peak spectral amplitude of the early part of a strong motion seismogram is shifted to lower frequencies compared to that from a later part of the same seismogram. Spectral amplitude ratios between transverse and vertical components of the strong motion data are degraded between frequencies 2 and 10 Hz for P waves, and less than 4 Hz for Rayleigh waves compared to the weak motion transverse to vertical spectral ratio. All these are signatures of nonlinear site responses during strong ground motion. This study proves the non-transportability of weak motion attenuation results to estimate ground motion from a future large earthquake that may take place in areas like the New Madrid Seismic zone.

Field investigation of Love waves in near-surface seismology

We examine subsurface conditions and survey parameters suitable for successful exploitation of Love waves in near-surface investigations. Love-wave generation requires the existence of a low shear-velocity surface layer. We examined the minimum thickness of the near-surface layer necessary to generate and record usable Love-wave data sets in the frequency range of [Formula: see text]. We acquired field data on a hillside with flat-lying limestone and shale layers that allowed for the direct testing of varying overburden thicknesses as well as varying acquisition geometry. The resulting seismic records and dispersion images were analyzed, and the Love-wave dispersion relation for two layers was examined analytically. We concluded through theoretical and field data analysis that a minimum thickness of [Formula: see text] of low-velocity material is needed to record usable data in the frequency range of interest in near-surface Love-wave surveys. The results of this study indicate that existing guidelines for Rayleigh-wave data acquisition, such as receiver interval and line length, are also applicable to Love-wave data acquisition.

Surface wave analysis with beamforming

Abstract It is well known that off-great-circle path propagation causes a technical difficulty for surface wave analysis in higher frequency ranges. We propose a new approach that combines a beamforming technique and two-station phase velocity measurement to resolve this problem. Beamforming allows us to determine the correct azimuth of incoming surface waves which can be taken into account in phase velocity measurement. Beamforming results also support that a plane-wave approximation is mostly acceptable for frequencies up to about 50–60 mHz (millihertz), although evidence of multipathing is occasionally recognized in beamforming results as multiple peaks. Application of this correction scheme for Rayleigh-wave data in Southern California seems to make the largest impact on the results of azimuthal anisotropy. Effects are not large for frequencies up to 30 mHz but fast velocity axes in azimuthal anisotropy maps change significantly for higher frequencies.

Anelasticity of the Crust and Upper Mantle beneath the Pacific Ocean from the Inversion of Observed Surface Wave Attenuation

Summary Backus-Gilbert inversion theory is applied to a new set of surface-wave attenuation data to obtain average Qβ−1 models for the crust and upper mantle beneath the Pacific Ocean. The favoured model is obtained from the inversion of Rayleigh-wave data alone. It includes an increase in Q−1 (or decrease in Q) at depths corresponding to the thickness of the litho-sphere as determined from surface-wave velocity studies, a thick zone of high Q−1 (or low Q) in the upper mantle, and decreasing Qβ−1 deeper in the mantle. The mean Q−1 values for the lithosphere are lower than those previously determined for the lower crust beneath continents. Simultaneous inversions of the Love- and Rayleigh-wave data yield models which include thin, alternating regions of high and low Q−1 values. Independent inversions of the Love- and Rayleigh-wave data yield models which differ in their anelastic properties at depths between 20 and 120km. These latter two types of models probably reflect systematic errors in the Love-wave data due to higher mode interference or complexities along the propagation path.

Upper mantle structure beneath continents: New constraints from multi‐mode Rayleigh wave data in western North America and southern Africa

We estimate the averaged 1‐D shear‐wave velocity of the upper mantle beneath western North America and the Kaapvaal region in southern Africa by inverting dispersion measurements of fundamental and higher Rayleigh modes recorded by ∼2000 km aperture broadband arrays. The overtones at periods exceeding 25 s constrain the averaged 1‐D shear‐wave velocity to 650 km depth across the regional arrays. Our overtone analysis confirms the shear‐wave velocity differences observed in global tomographic models with similar horizontal resolution: the western North American mantle features a prominent low velocity zone at depths 50–200 km, while the shear velocity in the upper 180–200 km of the mantle beneath southern Africa is at least 6% higher than in western North America which we interpret as the expression of a cratonic keel. There is no resolvable difference in shear‐wave velocity between southern Africa and western North America below a depth of about 300 km.

Anatolian surface wave evaluated at GEOFON Station ISP Isparta, Turkey

We have studied seismic surface waves of 255 shallow regional earthquakes recently recorded at GEOFON station ISP (Isparta, Turkey) and have selected these 52 recordings with high signal-to-noise ratio for further analysis. An attempt was made by the simultaneous use of the Rayleigh and Love surface wave data to interpret the planar crust and uppermost mantle velocity structure beneath the Anatolian plate using a differential least-square inversion technique. The shear-wave velocities near the surface show a gradational change from approximately 2.2 to 3.6 km s − 1 in the depth range 0–10 km. The mid-crustal depth range indicating a weakly developed low velocity zone has shear-wave velocities around 3.55 km s − 1 . The Moho discontinuity characterizing the crust–mantle velocity transition appears somewhat gradual between the depth range ∼ 25–45 km. The surface waves approaching from the northern Anatolia are estimated to travel a crustal thickness of ∼ 33 km whilst those from the southwestern Anatolia and part of east Mediterranean Sea indicate a thicker crust at ∼ 37 km. The eastern Anatolia events traveled even thicker crust at ∼ 41 km. A low sub-Moho velocity is estimated at ∼ 4.27 km s − 1 , although consistent with other similar studies in the region. The current velocities are considerably slower than indicated by the Preliminary Reference Earth Model (PREM) in almost all depth ranges.

Shear velocity structure in the Aegean region obtained by joint inversion of Rayleigh and Love waves

Abstract We present a shear velocity model of the crust and uppermost mantle under the Aegean region by simultaneous inversion of Rayleigh and Love waves. The database consists of regional earthquakes recorded by portable broadband three-component digital stations that were installed for a period of 6 months in the broader Aegean region. For each epicentre–station ray path group velocity dispersion curves are measured using appropriate frequency time analysis (FTAN). The dispersion measurements for more than 600 Love wave paths have been used. We have also incorporated previous results for c . 700 Rayleigh wave paths for the study area. The single-path dispersion curves of both waves were inverted to regional group velocity maps for different values of period (6–32 s) via a tomographic method. The local dispersion curves of discrete grid points for both surface waves were inverted nonlinearly to construct 1D models of shear-wave velocity v. depth. In most cases the joint inversion of Rayleigh and Love waves resulted in a single model (from the multiple models compatible with the data) that could interpret both Rayleigh and Love wave data. Around 60 local dispersion curves for both Rayleigh and Love waves were finally jointly inverted. As expected, because of the complex tectonic environment of the Aegean region the results show strong lateral variations of the S-wave velocities for the crust and uppermost mantle. Our results confirm the presence of a thin crust typically less than 28–30 km in the whole Aegean Sea, which in some parts of the southern and central Aegean Sea becomes significantly thinner (20–22 km). In contrast, a large crustal thickness of about 40–45 km exists in western Greece, and the remaining part of continental Greece is characterized by a mean crustal thickness of about 35 km. A significant sub-Moho upper mantle low-velocity zone (LVLmantle) with velocities as low as 3.7 km s −1 , is clearly identified in the southern and central Aegean Sea, correlated with the high heat flow in the mantle wedge above the subducted slab and the related active volcanism in the region. The results obtained results are compared with independent body-wave tomographic information on the velocity structure of the study area and exhibit a generally good agreement, although significant small-scale differences are also identified.

Improved parameterization to invert Rayleigh-wave data for shallow profiles containing stiff inclusions

Inversion of shear-wave velocity profiles from phase-velocity measurements of Rayleigh-wave energy for sites containing stiff layers can be erroneous if such layers are not characterized in the starting or reference model. Incorporation of a priori knowledge then is key for converging upon a realistic or meaningful solution. Resolving soil profiles in desert regions where stiff layers cemented with calcium carbonate are intermixed with softer, uncemented media is an application for which locating shallow stiff inclusions has important implications. Identification of the stiff layers is critical for foundation design and cost estimating of excavations. A parameterization that seems adequate for this problem is to solve for anticipated high-stiffness layers embedded in a coarser (background) profile that captures the general shear-wave velocity trend of the study area. The optimization is accomplished by using simulated annealing. Uncertainty measures resulting from the inversion are helpful for describing the influence of the parameterization on final model estimates.

Probing the history of the Mathematician paleoplate using surface waves

This paper investigates the shear velocity structure under the northern East Pacific Rise at the latitude range of 9–18°N, using intermediate-period Rayleigh and Love waves. The selected ocean-bottom seismic records provide source–receiver paths that ideally constrain the lithospheric mantle structure beneath the southern Rivera plate and the Mathematician paleoplate. The Rayleigh wave data infer a relatively thin (∼ 30 km) lithosphere under the eastern side of the present-day East Pacific Rise. The associated shear velocities are consistent with existing models of oceanic mantle beneath this region, and the estimated plate age of 2–3 million years agrees with results from magnetic dating. The west of the rise axis is characterized by a thicker and faster lithosphere than the eastern flank, and such structural differences suggest the presence of a relatively old Mathematician paleoplate. The discontinuous change in mantle structure across the East Pacific Rise spreading center are observed in both isotropic and anisotropic velocities. The young oceanic lithosphere east of the rise axis shows strong polarization anisotropy, where the dominant orientation of crystallographic axes roughly parallels the spreading direction. However, the western flank of the rise axis is approximately isotropic, and the lack of anisotropy suggests complex deformation mechanisms associated with earlier episodes of ridge segmentation, propagation and dual-spreading on and around the Mathematician paleoplate.

Rayleigh wave phase velocities, small‐scale convection, and azimuthal anisotropy beneath southern California

We use Rayleigh waves to invert for shear velocities in the upper mantle beneath southern California. A one‐dimensional shear velocity model reveals a pronounced low‐velocity zone (LVZ) from 90 to 210 km. The pattern of velocity anomalies indicates that there is active small‐scale convection in the asthenosphere and that the dominant form of convection is three‐dimensional (3‐D) lithospheric drips and asthenospheric upwellings, rather than 2‐D sheets or slabs. Several of the features that we observe have been previously detected by body wave tomography: these anomalies have been interpreted as delaminated lithosphere and consequent upwelling of the asthenosphere beneath the eastern edge of the southern Sierra Nevada and Walker Lane region; sinking lithosphere beneath the southern Central Valley; upwelling beneath the Salton Trough; and downwelling beneath the Transverse Ranges. Our new observations provide better constraints on the lateral and vertical extent of these anomalies. In addition, we detect two previously undetected features: a high‐velocity anomaly beneath the northern Peninsular Range and a low‐velocity anomaly beneath the northeastern Mojave block. We also estimate the azimuthal anisotropy from Rayleigh wave data. The strength is ∼1.7% at periods shorter than 100 s and decreases to below 1% at longer periods. The fast direction is nearly E‐W. The anisotropic layer is more than 300 km thick. The E‐W fast directions in the lithosphere and sublithosphere mantle may be caused by distinct deformation mechanisms: pure shear in the lithosphere due to N‐S tectonic shortening and simple shear in sublithosphere mantle due to mantle flow.

Computation of Large Anisotropic Seismic Heterogeneities (CLASH)

SUMMARY A general tomographic technique is designed in order (i) to operate in anisotropic media; (ii) to account for the uneven seismic sampling and (iii) to handle massive data sets in a reasonable computing time. One modus operandi to compute a 3-D body wave velocity model relies on surface wave phase velocity measurements. An intermediate step, shared by other approaches, consists in translating, for each period of a given mode branch, the phase velocities integrated along ray paths into local velocity perturbations. To this end, we develop a method, which accounts for the azimuthal anisotropy in its comprehensive form. The weakly non- linear forward problem allows to use a conjugate gradient optimization. The Earth's surface is regularly discretized and the partial derivatives are assigned to the individual grid points. Possible lack of lateral resolution, due to the inescapable uneven ray path coverage, is taken into account through the a priori covariances on parameters with laterally variable correlation lengths. This method allows to efficiently separate the 2ψ and the 4ψ anisotropic effects from the isotropic perturbations. Fundamental mode and overtone phase velocity maps, derived with real Rayleigh wave data sets, are presented and compared with previous maps. The isotropic models concur well with the results of Trampert & Woodhouse. Large 4ψ heterogeneities are located in the tectonically active regions and over the continental lithospheres such as North America, Antarctica or Australia. At various periods, a significant 4ψ signature is correlated with the Hawaii hotspot track. Finally, concurring with the conclusions of Trampert & Woodhouse, our phase velocity maps show that Rayleigh wave data sets do need both 2ψ and 4ψ anisotropic terms.

Simple equations guide high-frequency surface-wave investigation techniques

We discuss five useful equations related to high-frequency surface-wave techniques and their implications in practice. These equations are theoretical results from published literature regarding source selection, data-acquisition parameters, resolution of a dispersion curve image in the frequency–velocity domain, and the cut-off frequency of high modes. The first equation suggests Rayleigh waves appear in the shortest offset when a source is located on the ground surface, which supports our observations that surface impact sources are the best source for surface-wave techniques. The second and third equations, based on the layered earth model, reveal a relationship between the optimal nearest offset in Rayleigh-wave data acquisition and seismic setting—the observed maximum and minimum phase velocities, and the maximum wavelength. Comparison among data acquired with different offsets at one test site confirms the better data were acquired with the suggested optimal nearest offset. The fourth equation illustrates that resolution of a dispersion curve image at a given frequency is directly proportional to the product of a length of a geophone array and the frequency. We used real-world data to verify the fourth equation. The last equation shows that the cut-off frequency of high modes of Love waves for a two-layer model is determined by shear-wave velocities and the thickness of the top layer. We applied this equation to Rayleigh waves and multi-layer models with the average velocity and obtained encouraging results. This equation not only endows with a criterion to distinguish high modes from numerical artifacts but also provides a straightforward means to resolve the depth to the half space of a layered earth model.

Resolution of High-frequency Rayleigh-wave Data

It is essential to understand the potential resolving power of surface wave data in interpreting inverted vertical (layered 1D) and horizontal (‘pseudo-2D’) shear (S)-wave velocity models. The model resolution matrix indicates that the S-wave velocity model of a layered earth model can be perfectly resolved in a least-squares sense if error-free data are inverted. However, we show that errors in real data introduce a smear matrix in the least-squares solution, reducing the resolution of an S-wave velocity model. A field test shows how accurate dispersion curves can resolve a low velocity layer of about 25% contrast at [Formula: see text] depth below a stiff overburden. The horizontal resolution of surface wave surveys is limited to the aperture (length) of the recording array. In phase velocity measurements, the layered model estimate represents an average over this length. Any lateral discontinuities introduce a systematic error into the inversion, leading to acquisition geometry-dependent estimated models. The multichannel analysis of surface waves in roll-along mode allows construction of ‘pseudo 2D-sections’ by aligning 1D models at each spread midpoint. However, images from field data between forward and reverse can be inconsistent. We apply a generalized inversion to these ‘pseudo 2D-sections’ in the horizontal direction, which removes these inconsistencies and provides an improvement in horizontal resolution, allowing a more objective geological appraisal.

3D S-wave velocity pattern in the upper mantle beneath the continent of Asia from Rayleigh wave data

Group velocities of Rayleigh waves in the 10–150 s period range along about 1200 paths across Central Asia and Siberia are used to obtain group velocity maps of the region. To image the lateral variations of group velocities we used the tomography method developed earlier for spherical surface [PEPI 122 (2000) 19]. The method is supplemented by the opportunity to estimate the resolving power of the data. The locally averaged dispersion curves have been then inverted to vertical S-wave velocity profiles up to depth of 500 km at different sites in the region, which thus image a 3D velocity distribution. In order to reduce the number of unknown parameters we assumed the relationships between S-wave and P-wave velocities and densities to be those of the PREM model. The 3D S-wave velocity pattern is displayed in the form of maps at depths from 50 to 350 km with a step of 50 km, and of 2D vertical velocity sections along some profiles crossing different tectonic units. The most remarkable feature of the 3D velocity distribution is the presence of a high-velocity rise at the depths of 250–350 km beneath southern Siberia and western China, which borders upon the low-velocity asthenosphere along the longitude about 105°E. Collision of the high- and low-velocity substances results in pressing-out the viscous asthenosphere material in the weakened zone of the Baikal rift, where the lithosphere is thinned. The rise of the asthenosphere in this zone probably produces mantle upwelling, and leads to uplift of the Khangay Plateau.

Time-domain Pure-state Polarization Analysis of Surface Waves Traversing California

— A time-domain pure-state polarization analysis method is used to characterize surface waves traversing California parallel to the plate boundary. The method is applied to data recorded at four broadband stations in California from twenty-six large, shallow earthquakes which occurred since 1988, yielding polarization parameters such as the ellipticity, Euler angles, instantaneous periods, and wave incident azimuths. The earthquakes are located along the circum-Pacific margin and the ray paths cluster into two groups, with great-circle paths connecting stations MHC and PAS or CMB and GSC. The first path (MHC-PAS) is in the vicinity of the San Andreas Fault System (SAFS), and the second (CMB-GSC) traverses the Sierra Nevada Batholith parallel to and east of the SAFS. Both Rayleigh and Love wave data show refractions due to lateral velocity heterogeneities under the path, indicating that accurate phase velocity and attenuation analysis requires array measurements. T he Rayleigh waves are strongly affected by low velocity anomalies beneath Central California, with ray paths bending eastward as waves travel toward the south, while Love waves are less affected, providing observables to constrain the depth extent of anomalies. Strong lateral gradients in the lithospheric structure between the continent and the ocean are the likely cause of the path deflections.

Global anisotropic phase velocity maps for fundamental mode surface waves between 40 and 150 s

SUMMARY We constructed global phase velocity maps including azimuthal anisotropy. Azimuthal anisotropy is expanded on a basis of generalized spherical harmonics, which makes the calculation of path integrals of the phase velocity particularly simple. It is generally accepted that the major difficulty in such modelling is determining the strength of the anisotropy relative to the isotropy. We propose a technique which finds the optimum relative weighting of the anisotropic terms prior to inversion. It is clear from our analyses that phase data require azimuthal anisotropy. We further find that Love wave data do not require a 2ψ term, whereas Rayleigh wave data need 2ψ and 4ψ terms. The main effect of azimuthal anisotropy upon the isotropic maps is a loss of power in the highest spherical harmonic degrees, resulting in an overall lower lateral resolution compared with a purely isotropic inversion for the same number of recovered parameters. The correlation of 2ψ and 4ψ components at different periods is relatively high, indicating a shallow source for the azimuthal anisotropy. Overall, fast 2ψ Rayleigh directions agree well with absolute plate motions in the hotspot reference frame.

Inversion of high frequency surface waves with fundamental and higher modes

The phase velocity of Rayleigh-waves of a layered earth model is a function of frequency and four groups of earth parameters: compressional (P)-wave velocity, shear (S)-wave velocity, density, and thickness of layers. For the fundamental mode of Rayleigh waves, analysis of the Jacobian matrix for high frequencies (2–40 Hz) provides a measure of dispersion curve sensitivity to earth model parameters. S-wave velocities are the dominant influence of the four earth model parameters. This thesis is true for higher modes of high frequency Rayleigh waves as well. Our numerical modeling by analysis of the Jacobian matrix supports at least two quite exciting higher mode properties. First, for fundamental and higher mode Rayleigh wave data with the same wavelength, higher modes can “see” deeper than the fundamental mode. Second, higher mode data can increase the resolution of the inverted S-wave velocities. Real world examples show that the inversion process can be stabilized and resolution of the S-wave velocity model can be improved when simultaneously inverting the fundamental and higher mode data.

Rayleigh Wave Dispersion And Three‐Dimensional Velocity Structure in the Continent And Its Margin of Southeastern China

AbstractWith the matched‐filter of using frequency‐time analysis (FTAN) technology, we process the Rayleigh wave data recorded by China seismic stations, and then obtain the dispersion of Rayleigh wave of crossing southeastern China continent and margin belt. We obtain pure path dispersion data of 40 × 40 grid for the southeastern China continent and margin belt by using a stochastic method. Based on the gridding inversion, we obtain the three‐dimensional velocity structure for shear wave velocities by using the surface wave inversion program of Harkrider. The result indicates that: 1. The Moho depth of Southern China continent is 30–40 km and becomes thinner from west to east. At the margin and shallow sea region the Moho depth is 25–28 km and shows a clear zonal pattern. 2. The buried depth of low‐velocity layer in upper mantle lies between 60 to 150 km and exhibits strong lateral variation related to the distribution of deep faults and deep internal dynamic processes. The undulatory variation of the interface in the NS direction is flatter than that in theWE direction. 3. The margin of the southeastern continent is the sea‐continent transition belt of the East Asia continent. The depth of the Moho interface is shallow and the average velocity in the crust is low. The undulation behavior of the deep mantle interface indicates the heterogeneity of the structure and the coupling affect of deep and shallow medium.

The 3-D structure of shear wave in South China and the southward extension of Tanlu fault

By processing the CSND Rayleigh wave data with the matched filter FTAN technique, Rayleigh wave dispersion for southeast China is obtained. The 4∘ × 4∘S wave dispersion of the pure path is calculated using random inversion scheme, and 3-D S wave velocity structure is set up. Incorporating the above-mentioned results with wide angle seismic sounding data, we studied structure framework and the extending of faults in this area, which demonstrates that the depth of Moho in South China varies from 30 to 40 km, shallower from west to east. The depth of Moho varies from 25 to 28 km for the offshore. The depth of the asthenosphere in upper mantle varies from 60 to 100 km. The depth difference of layers at the two sides of Tanlu fault is more than 10 km at the south part of the Yangtze River, and the fault extends downward more than 170 km. The fault exceeds the main land at Hainan Island and slips into the southern China Sea. Both Tanlu fault and the huge bend of gravity gradient anomaly are influenced by deep latent tectonics.