Surface Wave Phase Velocity Research Articles

Stability and gravitational effects on surface dust-acoustic waves in self-gravitating semi-bounded dusty plasmas

The stable conditions and gravitational effects on the surface dust-acoustic wave are investigated in self-gravitating semi-bounded dusty plasmas. The dispersion relation of the surface dust-acoustic wave is obtained by the plasma dielectric function with the specular reflection boundary condition. It is shown that the surface dust-acoustic wave become unstable for any values of the wave number when $\tfrac{1}{2}\leq (\omega_{\rm J}/\omega_{\rm pd})^2\leq 1$ . However, when $(\omega_{\rm J}/\omega_{\rm pd})^2 > 1$ or $(\omega_{\rm J}/\omega_{\rm pd})^2 , the Jeans instability does not occur for the domain of the wave number $k_z \lambda_{\rm D} > (\omega_{\rm J}/\omega_{\rm pd})|[(\omega_{\rm J}/\omega_{\rm pd})^2 - 1]/[2(\omega_{\rm J}/\omega_{\rm pd})^2 - 1]|^{1/2}$ . It is also found that the phase velocity of the surface wave decreases with increasing Jeans frequency.

A METHOD TO ESTIMATE PHASE VELOCITIES OF SURFACE WAVES USING ARRAY OBSERVATION RECORDS OF THREE-COMPONENT MICROTREMORS

We propose a method to estimate phase velocities of the Rayleigh and Love waves using array observation records of three-component microtremors. Previous researchers have provided a method on the basis of the spatial auto-correlation (SPAC) method, assuming that the Rayleigh and Love waves are propagated in the same direction. However, this assumption seems to be poorly suited to microtremors, because of the various possible sources and the uncertain nature of microtremors. Thus, we formulate the SPAC coefficients for microtremors in a case where the Rayleigh and Love waves are propagated in different directions. From this, it is shown analytically that the phase velocities of surface waves can be calculated from the SPAC coefficients and that they are independent of the propagation directions of the surface waves.

Effect of roughness on the phase velocity of Rayleigh waves in GaAs crystals

The phase velocity dispersion of the Rayleigh waves on surfaces of GaAs crystals having different roughness has been measured by laser-acoustic wave equipment. Applied model of a rough film with zero elastic moduli explained the effect of roughness on the acoustic surface wave phase velocity and showed good coincidence with the experimental data.

Wave propagation along a cylindrical borehole in an anisotropic poroelastic solid

SUMMARY This paper deals with the propagation of elastic waves along a cylindrical borehole embedded in an anisotropic fluid-saturated porous solid of infinite extent. Biot’s theory is used to derive the Christoffel equation for the propagation of cylindrical waves in an anisotropic fluid-saturated porous material. The saturated fluid is viscous. Waves of axial symmetry are considered here. The frequency equations of surface waves corresponding to the empty and liquid-filled borehole are obtained. The effects of transverse isotropy on the phase velocity of surface waves are studied. The phase velocity of surface waves increases with anisotropy. Surface modes in empty and liquid-filled boreholes in an isotropic poroelastic solid and Rayleigh waves propagating on the free surface of a transversely isotropic fluid-saturated porous solid are obtained as particular cases. The presence or absence of fluid in the borehole affects the phase velocity considerably. The phase velocity increases when the empty borehole is filled with liquid.

Deep structure and seismic anisotropy beneath the East Pacific Rise

Seismic velocities in the upper mantle beneath mid-ocean ridges are known to exhibit anisotropy, especially at depths shallower than 200 km. In this study, we present evidence for deeper anisotropy beneath fast-spreading ridges based on simultaneous inversion of body wave travel times, waveforms, and surface wave phase velocities. The ‘vertical’ (BSV) shear wave speed is systematically faster (by more than 2%) than the ‘horizontal’ (BSH) one at depths of 200–300 km beneath the East Pacific Rise, a result that is consistent with vertical alignment of the fast crystallographic axis of olivine. This anomaly is especially coherent beneath the northern East Pacific Rise, where the observations also support the presence of a modest mantle reflector near 260-km depth. The anisotropy may be associated with deep vertical flow or finite strain, and the presence of this reflector could signal a rheological transition near the bottom of the asthenosphere, reflecting changes in flow direction, development of partial melt, or the persistence of a deep pre-existing strain regime.

Effectiveness of Multi-Mode Surface Wave Inversion in Shallow Engineering Site Investigations

Inversion of multi-mode surface-wave phase velocity for shallow engineering site investigation has received much attention in recent years. A sensitivity analysis and inversion of both synthetic and field data demonstrates the greater effectiveness of this method over employing the fundamental mode alone. Perturbation of thickness and shear-wave velocity parameters in multi-modal Rayleigh wave phase velocities revealed that the sensitivities of higher modes: (a) concentrate in different frequency bands, and (b) are greater than the fundamental mode for deeper parameters. These observations suggest that multi-mode phase velocity inversion can provide better parameter discrimination and imaging of deep structure, especially with a velocity reversal, than can inversion of fundamental mode data alone.An inversion of the theoretical phase velocities in a model with a low velocity layer at 20 m depth can only image the soft layer when the first higher mode is incorporated. This is especially important when the lowest measurable frequency is only 6 Hz.Field tests were conducted at sites surveyed by borehole and PS logging. At the first site, an array microtremor survey, often used for deep geological surveying in Japan, was used to survey the soil down to 35 m depth. At the second site, linear multichannel spreads with a sledgehammer source were recorded, for an investigation down to 12 m depth. The f-k power spectrum method was applied for dispersion analysis, and velocities up to the second higher mode were observed in each test. The multi-mode inversion results agree well with PS logs, but models estimated from the fundamental mode alone show a large underestimation of the depth to shallow soft layers below artificial fill.

Effectiveness of multi-mode surface wave inversion in shallow engineering site investigations

Inversion of multi-mode surface-wave phase velocity for shallow engineering site investigation has received much attention in recent years. A sensitivity analysis and inversion of both synthetic and field data demonstrates the greater effectiveness of this method over employing the fundamental mode alone. Perturbation of thickness and shear-wave velocity parameters in multi-modal Rayleigh wave phase velocities revealed that the sensitivities of higher modes: (a) concentrate in different frequency bands, and (b) are greater than the fundamental mode for deeper parameters. These observations suggest that multi-mode phase velocity inversion can provide better parameter discrimination and imaging of deep structure, especially with a velocity reversal, than can inversion of fundamental mode data alone.An inversion of the theoretical phase velocities in a model with a low velocity layer at 20 m depth can only image the soft layer when the first higher mode is incorporated. This is especially important when the lowest measurable frequency is only 6 Hz.Field tests were conducted at sites surveyed by borehole and PS logging. At the first site, an array microtremor survey, often used for deep geological surveying in Japan, was used to survey the soil down to 35 m depth. At the second site, linear multichannel spreads with a sledgehammer source were recorded, for an investigation down to 12 m depth. The f-k power spectrum method was applied for dispersion analysis, and velocities up to the second higher mode were observed in each test. The multi-mode inversion results agree well with PS logs, but models estimated from the fundamental mode alone show a large underestimation of the depth to shallow soft layers below artificial fill.

Using transfer function for estimating dissipative properties of soils from surface‐wave data

ABSTRACTThe quality factor (or damping ratio) can be estimated by analysing the spatial attenuation of surface‐wave data. However, because of the link between geometrical and material dispersion, a coupled analysis of dispersion and attenuation curves is preferable. Using a transfer‐function approach, it is possible to estimate the dispersion and attenuation curves simultaneously, provided the seismic source is known. A formulation based on the deconvolution of seismic traces is used to extend the transfer‐function approach to ordinary seismic gathers in which the source wavelet is not known. The measured transfer function is used in a regression analysis to obtain estimates of the complex wavenumbers, which, in the framework of viscoelasticity, contain all the information relating to phase velocity and attenuation of surface waves for a layered medium. Application of this procedure to experimental data leads to results consistent with those obtained using conventional techniques (e.g. analysis and amplitude regression).

A surface wave analysis of seismic anisotropy beneath eastern North America

SUMMARY The nature of upper-mantle seismic anisotropy beneath central and eastern North America has been evaluated using the phase velocities of surface waves traversing the length of the Missouri-to-Massachusetts (MOMA) broad-band array. Frequency-dependent phase delays of fundamental-mode Love and Rayleigh waves, measured across the array using a cross-correlation procedure, require the presence of anisotropy in the upper mantle. 2-D radially anisotropic structures obtained via linearized inversion of these data contain shear anisotropy with a magnitude of ∼3 per cent between the Moho and at least 180-km depth. Models in which the mantle lithosphere is isotropic cannot satisfy the data. This anisotropy is approximately constant across the tectonic transition from the craton to the Atlantic margin. Forward models consisting of a shallow, lithospheric layer of azimuthal anisotropy derived from previous shear wave splitting observations fail to satisfy the surface wave delay times. The combined surface wave and splitting results suggest the presence of two layers of anisotropy: a lithospheric layer that produces the phase-delay differences observed in Love and Rayleigh waves but is transparent to vertically propagating shear body waves; and a deeper (presumably asthenospheric) layer that generates the shear wave splitting. One plausible model is that the lithosphere is characterized by vertically heterogeneous anisotropic fabric, which would produce minimal splitting in vertical shear waves. Such fabric has been hypothesized for regions of weak and complex splitting such as South Africa and Australia; the results here imply that it may be appropriate for North America as well.

Combined Receiver-Function and Surface Wave Phase-Velocity Inversion Using a Niching Genetic Algorithm: Application to Patagonia

A combined inversion of body wave receiver functions and Rayleigh wave phase velocities using a niching genetic algorithm (NGA) increases the unique- ness of the solution over separate inversions and also facilitates explicit parameteri- zation of layer thickness in the model space. This parameterization requires fewer layers and a priori constraints for modeling more complex structures than traditional linearized inversion. NGAs solve for a suite of locally optimal solutions in addition to isolating the globally optimal solution by using an evolutionary paradigm. This nonlinear examination of the error space provides an opportunity to examine trade- off within the model space. The method, when applied to synthetic data, locates interfaces within 2 km of the test structure and identifies appropriate structure and velocity. Applying this method to data from a deployment of five broadband stations in Chilean Patagonia yields a regional model of crustal structure that is consistent with the geological history of the region. Sediment thickness is inversely proportional to crustal thickness, with sediment thicknesses reaching more than 4 km, where the crustal thickness thins to 28 km. This is consistent with previous geological studies, which suggests that the Rocas Verdes basin in western Patagonia formed by crustal thinning, isostatic compensation, and subsequent sedimentation.

Multiple resolution surface wave tomography: the Mediterranean basin

SUMMARY From a large set of fundamental-mode surface wave phase velocity observations, we map the transversely isotropic lateral heterogeneities in the upper-mantle shear velocity structure. We design a multiple resolution inversion procedure, which allows us to parametrize any selected region more finely than the rest of the globe. We choose, as a high-resolution region, the upper mantle underlying the Mediterranean basin. We formulate the inverse problem as in a

CMP cross-correlation analysis of multi-channel surface-wave data

In this paper, we demonstrate that Common Mid-Point (CMP) cross-correlation gathers of multi-channel and multi-shot surface waves give accurate phase-velocity curves, and enable us to reconstruct two-dimensional (2D) velocity structures with high resolution. Data acquisition for CMP cross-correlation analysis is similar to acquisition for a 2D seismic reflection survey. Data processing seems similar to Common Depth-Point (CDP) analysis of 2D seismic reflection survey data, but differs in that the cross-correlation of the original waveform is calculated before making CMP gathers. Data processing in CMP cross-correlation analysis consists of the following four steps: First, cross-correlations are calculated for every pair of traces in each shot gather. Second, correlation traces having a common mid-point are gathered, and those traces that have equal spacing are stacked in the time domain. The resultant cross-correlation gathers resemble shot gathers and are referred to as CMP cross-correlation gathers. Third, a multi-channel analysis is applied to the CMP cross-correlation gathers for calculating phase velocities of surface waves. Finally, a 2D S-wave velocity profile is reconstructed through non-linear least squares inversion. Analyses of waveform data from numerical modelling and field observations indicate that the new method could greatly improve the accuracy and resolution of subsurface S-velocity structure, compared with conventional surface-wave methods.

Crust and upper mantle shear wave structure of the southwest United States: Implications for rifting and support for high elevation

Surface wave phase velocities from 29 earthquakes are used to map the shear velocity structure to ∼350 km depth across the 950‐km‐long Rio Grande Rift Seismic Transect Experiment (LA RISTRA) seismic array in the southwest United States. Events from a range of back azimuths minimize the effects of multipathing. The resulting velocity model reveals a transition in lithospheric thickness from 200 km in the Great Plains to 45–55 km beneath the Rio Grande Rift, thickening beneath the Colorado Plateau to 120–150 km. The upper mantle low‐velocity signature of the rift is roughly twice the width of its surface morphology. An asthenospheric low‐velocity channel underlies the region west of the Great Plains and extends to 300 km depth. This channel is likely the result of warm mantle infill behind the sinking Farallon plate. Buoyant forces within this channel are sufficient to support much of the high elevation of the rift and plateau. No evidence for a deep mantle source is found beneath the rift, implying that present rifting is not driven by deep mantle upwelling. Velocities from 55 to 90 km beneath the rift axis are 10% slower than beneath the Great Plains, consistent with small amounts of partial melt. Low velocities extend to 200–300 km depth on either side of the rift but not directly beneath it, forming an inverted‐U shape. This feature may reflect mantle that has cooled through vertical advection in a subadiabatic environment. Upwelling may be reinforced by small‐scale convection caused by variations in lithospheric thickness and shallow mantle temperatures.

Building and Testing an a priori Geophysical Model for Western Eurasia and North Africa

We construct and evaluate a new three-dimensional model of crust and upper mantle structure in Western Eurasia and North Africa (WENA) extending to 700 km depth and having 1° parameterization. The model is compiled in an a priori fashion entirely from existing geophysical literature, specifically, combining two regionalized crustal models with a high-resolution global sediment model and a global upper mantle model. The resulting WENA1.0 model consists of 24 layers: water, three sediment layers, upper, middle, and lower crust, uppermost mantle, and 16 additional upper mantle layers. Each of the layers is specified by its depth, compressional and shear velocity, density, and attenuation (quality factors, Q P and Q S ). The model is tested by comparing the model predictions with geophysical observations including: crustal thickness, surface wave group and phase velocities, upper mantle n velocities, receiver functions, P-wave travel times, waveform characteristics, regional 1-D velocities, and Bouguer gravity. We find generally good agreement between WENA1.0 model predictions and empirical observations for a wide variety of independent data sets. We believe this model is representative of our current knowledge of crust and upper mantle structure in the WENA region and can successfully be used to model the propagation characteristics of regional seismic waveform data. The WENA1.0 model will continue to evolve as new data are incorporated into future validations and any new deficiencies in the model are identified. Eventually this a priori model will serve as the initial starting model for a multiple data set tomographic inversion for structure of the Eurasian continent.

Measuring surface wave phase velocities beneath small broad-band arrays: tests of an improved algorithm and application to the French Alps

The local measurement of dispersion curves of intermediate-period surface waves is particularly difficult because of the long wavelengths involved. We suggest an improved procedure for measuring dispersion curves using small-aperture broad-band arrays. The method is based on the hypotheses of plane incoming waves and that averaging over a set of events with a good backazimuth distribution will suppress the effects of diffraction outside the array. None of the elements of the processing are new in themselves, but each step is optimized so we can obtain a reliable dispersion curve with a well-defined uncertainty. The method is based on the inversion for the slowness vector at each event and frequency using time delays between pairs of stations, where the time delays Δt are obtained by frequency-domain Wiener filtering. The interstation distance projected on to the slowness vector (D) is then calculated. The final dispersion curve is found by, at each frequency, calculating the inverse of the slope of the best-fitting line of all (D, Δt) points. To test the algorithm, it is applied to synthetic seismograms of fundamental mode Rayleigh waves in different configurations: (1) the sum of several incident waves; (2) an array located next to or above a crustal thickening; and (3) added white noise, using regular and irregular backazimuth distributions. In each case, a circular array of 23 km diameter and composed of six stations is used. The algorithm is stable over a large range of wavelengths (between half and a tenth of the array size), depending on the configuration. The situations of several, simultaneously incoming waves or neighbouring heterogeneities are well handled and the inferred dispersion curve corresponds to that of the underlying medium. Above a strong lateral heterogeneity, the inferred dispersion curve corresponds to that of the underlying medium up to wavelengths of eight times the array size in the configuration considered, but further work is needed to better understand the limits under which the obtained dispersion curve is not biased. In the case of 5 per cent spectral amplitude white noise, the dispersion curve is also stable for wavelengths up to approximately eight times the array size, but this limit depends of course strongly on the noise level. The method is finally applied to data from two arrays in the French Alps located 50 km apart. It is possible to measure the dispersion curves up to wavelengths approximately ten times bigger than the array diameter. The difference in the dispersion curves is compatible with a crustal and lithospheric thickening under the Alps. However, the observed errors are large, which result in severe limits on the interpretation in terms of lithospheric structure. Longer recording periods may help to reduce the errors. Otherwise the algorithm is likely to be of use mainly in areas where the lateral variations outside the array are smaller than those of the French Alps.

Crustal shear velocity structure of the south Indian shield

The south Indian shield is a collage of Precambrian terrains gathered around and in part derived from the Archean‐age Dharwar craton. We operated seven broadband seismographs on the shield along a N‐S corridor from Nanded (NND) to Bangalore (BGL) and used data from these to determine the seismic characteristics of this part of the shield. Surface wave dispersion and receiver function data from these sites and the Geoscope station at Hyderabad (HYB) give the shear wave velocity structure of the crust along this 600 km long transect. Inversion of Rayleigh wave phase velocity measured along the profile shows that the crust has an average thickness of 35 km and consists of a 3.66 km s−1, 12 km thick layer overlying a 3.81 km s−1, 23 km thick lower crust. At all sites, the receiver functions are extremely simple, indicating that the crust beneath each site is also simple with no significant intracrustal discontinuities. Joint inversion of the receiver function and surface wave phase velocity data shows the seismic characteristics of this part of the Dharwar crust to be remarkably uniform throughout and that it varies within fairly narrow bounds: crustal thickness (35 ± 2 km), average shear wave speed (3.79 ± 0.09 km s−1), and Vp/Vs ratio (1.746 ± 0.014). There is no evidence for a high velocity basal layer in the receiver function crustal images of the central Dharwar craton, suggesting that there is no seismically distinct layer of mafic cumulates overlying the Moho and implying that the base of the Dharwar crust has remained fairly refractory since its cratonization.

Circumferential-wave phase velocities for empty, fluid-immersed spherical metal shells.

In earlier studies of acoustic scattering resonances and of the dispersive phase velocities of surface waves that generate them [see, e.g., Talmant et al., J. Acoust. Soc. Am. 86, 278-289 (1989) for spherical aluminum shells] we have demonstrated the effectiveness and accuracy of obtaining phase velocity dispersion curves from the known acoustic resonance frequencies. This possibility is offered through the condition of phase matching after each complete circumnavigation of these waves [Uberall et al., J. Acoust. Soc. Am. 61, 711-715 (1977)], which leads to a very close agreement of resonance results with those calculated from three-dimensional elasticity theory whenever the latter are available. The present investigation is based on the mentioned resonance frequency/elasticity theory connection, and we obtain comparative circumferential-wave dispersion-curve results for water-loaded, evacuated spherical metal shells of aluminum, stainless steel, and tungsten carbide. In particular, the characteristic upturn of the dispersion curves of low-order shell-borne circumferential waves (A or A0 waves) which takes place on spherical shells when the frequency tends towards very low values, is demonstrated here for all cases of the metals under consideration.

FREQUENCY DISPERSION CHARACTERISTICS OF PHASE VELOCITIES IN SURFACE WAVE FOR ROTATIONAL COMPONENTS OF SEISMIC MOTION

When rotational components of ground motion produced by seismic surface waves are computed, the phase velocities must always be dealt with in earthquake engineering. In this paper, appropriate methods are presented to obtain the calculation formulas for the phase velocities of surface waves by applying the theory of elastic wave propagation. Frequency dispersion characteristics of phase velocities are discussed. The rocking component around a horizontal axis and the torsional component around a vertical axis, which are generated, respectively, by the Rayleigh and Love waves, are reasonably given. A procedure is developed to calculate the time histories of these rotational components.

Combined analysis ofSKSsplitting and regionalPtraveltimes in Siberia

SUMMARY Azimuthal anisotropy in the upper mantle of many continental regions is documented by Swave splitting measurements with SKS techniques. Here we present observations of splitting of the SKS seismic phase at seismograph stations in the Siberian platform, where few such data were known previously. The parameters of splitting are coherent: the fast direction everywhere is around 150 ◦ , and the delay of the slow split wave is close to 1.0 s. These observations provide no constraints on the distribution of anisotropy with depth. However, the Siberian platform is remarkable in that it is covered by a network of long-range profiles, where P waves from nuclear explosions are recorded at epicentral distances of 2000 km and more. Depending on epicentral distance these waves sample the upper mantle from the Moho to the transition zone. Two profiles run approximately parallel to the fast direction of the azimuthal anisotropy, whereas the directions of the two others are intermediate between the fast and slow. We examine the observed P traveltimes for their dependence on the azimuth and epicentral distance. With the available data on elastic anisotropy in mantle xenoliths, the values of P-wave anisotropy for horizontal propagation can be used to evaluate S-wave splitting for vertical propagation. It appears that the upper mantle between the Moho and 150 km depth is responsible for not more than about 30 per cent of the large-scale effect in the SKS phase. The major effect is accumulated in a broad low-velocity zone, the top of which is found at a depth of 150 km. Anisotropy within this zone can be caused by recent mantle flow. A similar distribution with depth might explain discrepancies between the estimates of azimuthal anisotropy from phase velocities of surface waves and SKS splitting in North America and South Africa.

Non-linear surface wave phase velocity inversion based on ray theory

Summary The development of temporary and permanent broad-band seismic arrays reinforces the need for advanced interpretation techniques in surface-wave analysis. We present a new method based on 2-D paraxial ray theory of inverting teleseismic surface-wave phase information and constructing phase velocity maps on a regional scale. Measurements of local phase velocities and propagation directions of Rayleigh waves taken from full waveform synthetic seismograms are used to validate the ray theory for smooth structures on a regional scale. Curved wavefronts created by heterogeneous structure outside the study area are taken into account through joint inversion for the phase velocity field and the shape of the incoming wavefronts. In the forward ray tracing procedure, the curved wavefronts are introduced through the boundary conditions by equating the slowness vector of the ray at the edge of the study region with the known gradient of the arrival time of the wave. To make the inverse problem non-singular we constrain the parameters in the inversion primarily by applying a smoothness criteria on the velocity field and on the incoming wave-field. Inversions of synthetic data sets computed by direct ray tracing and by full waveform modelling show that for 100 km spacing between stations the minimum size of structure that we can image is approximately 150 km. Heterogeneities with a size approximately equal to the wavelength are reconstructed by the ray-based inversion even though velocity variations are underestimated due to the wave-field smoothing of the structures. A minimum signal-to-noise ratio of 3.5 is necessary in order to correctly retrieve the phase velocity field. Inversion of a subset of the SVEKALAPKO data for 60 s period demonstrates the applicability of the method on real data.