Surface Wave Phase Research Articles

Interaction of vortices with a progressive surface wave

Interaction of submerged vortices with a progressive surface wave is investigated by the finite-difference numerical solution of Navier-Stokes equations. The progressive wave is the surface gravity water wave in a finite depth. The initial vortex model is Oseen vortex. The numerical computations show that a special pattern of the wave surface may be observed by the interaction from the submerged vortices. The influences of Froude number, the initial geometric configuration of vortices, and the amplitude, initial phase of surface wave on the wave pattern are discussed.

Non-destructive evaluation of TiN films with interface defects by surface acoustic waves

Surface acoustic wave (SAW) measurements are a fast and reliable way to obtain information about the elastic properties of thin film coatings. Measuring the surface wave phase velocity which is dependent on frequency and performing the inverse solution of dispersion relation for surface wave propagation in coated materials enable us to determine the elastic parameters of the film and substrate material. Measuring equipment is used where wide-band surface wave impulses are generated by short laser pulses and received with a piezoelectric transducer. The surface wave phase velocity is obtained by Fourier transforming the impulse form. In this work we are interested in Young's modulus of the film material and its relation to the defects in the interface region of the substrate. Young's modulus is a characteristic material parameter, depending on atomic composition and on the microscopic structure of the material. It is theoretically and experimentally established that, if defects such as flaws are incorporated, Young's modulus is reduced in comparison with that of bulk material. The examined samples were steel pieces (42CrMo4) coated with TiN by ion plating. During the deposition process we have only varied the duration of the ion etching process, while keeping all other technological parameters constant. The ion etching is responsible for the adhesion of the coating by removing residual contamination from the substrate surface. In this way a more or less non-defective interface zone is built up. The procedure of varying only the etching time allows us to obtain different interface properties while leaving film properties constant. Film properties were characterized by means of Auger, X-ray texture and dynamic hardness measurements. It was shown that there is a correlation between Young's modulus and conventional scratch test results. The acoustic emission was used to evaluate the coated material behaviour in the scratch test. From a Weibull diagram of the acoustic emission signals an initial crack load L i was determined. It could be proved that the initial crack load and the Young's modulus correlate with a coefficient R = −0.78.

Non-destructive evaluation of the mechanical behaviour of TiN-coated steels by laser-induced ultrasonic surface waves

Measuring the propagation velocity of ultrasonic surface waves has been used to determine the Young's modulus of TiN films on steel. Wide-band surface-wave pulses are generated by a pulsed nitrogen laser and detected by a piezoelectric PVDF-foil transducer. A spectrum of the surface-wave phase velocity is obtained from the Fourier transformation of the surface-wave signals. The TiN films were deposited after different presputtering times with argon ions to vary the adhesion on the steel substrate. The adhesion behaviour of the films was investigated with the scratch tester. A correlation was found between the Young's modulus of the film material and the acoustic emission activity in the scratch test, which has been shown to be a suitable measure for adhesion.

Source time function complexity of the great 1989 Macquarie Ridge earthquake

The rupture process of the great 1989 Macquarie Ridge (Mw = 8.1) strike‐slip faulting earthquake is examined using an empirical Green function deconvolution method which provides broadband source time functions from both body and surface waves. Recordings from a nearby, much smaller (Mw = 6.4) strike‐slip event provide accurate broadband Green functions for PP, S, SS, Rayleigh, and Love waves, spanning the period range 20–150 s. Body wave deconvolutions indicate that the principle short‐period (<30 s) moment release occurred in the first 25 s of rupture with no resolvable directivity; only minor short‐period energy release occurred over the next 30 s. Surface wave deconvolutions for the usually neglected 20–150 s period range produce source time functions with slightly larger total moment than the body wave deconvolutions and no resolvable directivity from the onset to the peak of moment release in the first 20 s. However, azimuthally dependent broadening of the surface wave source functions, which extend to more than 50‐s duration, indicates a component of northeastward unilateral rupture extension requiring about 30–50 km asymmetry in the overall rupture, compatible with the northeastward asymmetry of the 1‐day aftershock zone. Spectral inversions of long‐period Love and Rayleigh waves indicate a centroid time shift of approximately 25±3 s (50±7s duration trapezoid source) in the period range of 150–280 s, compatible with the deconvolved surface wave source time functions. Deconvolutions using both empirical and theoretical Green functions are optimized to detect any long‐period precursory radiation for periods up to about 250 s, but no convincing evidence for precursory radiation in the passband is found. The long‐period surface wave phase data also do not require a precursor.

遺伝的アルゴリズムによる位相速度の逆解析

The applicability of genetic algorithms in an inversion of surface-wave phase velocities to infer an S-wave velocity profile was examined. S-wave velocities and thicknesses are coded to binary strings, and an individual model is generated by connecting all strings for a subsurface structure model. The fitness is defined by squared summation of differences between observed and calculated phase velocities. In addition to three basic genetic processes of selection, crossover, and mutation, the algorithm was improved by the introduction of elite selection rule and dynamic mutation in which the mutation probability varied according to the variety of individuals in a generation. We applied the method to the inversions of synthetic phase velocities and phase velocities from an actual array observation of long-period microtremors. These results indicate that the GA is highly applicable in phase velocity inversion.

Determinations of anisotropic elastic constants using laser-generated surface waves

This paper studied the recovery of elastic constants of anisotropic solids from measured surface wave energy velocities. The calculations of surface wave phase and energy velocities of anisotropic solids were based on an efficient forward formalism. In the experiment, the surface waves were generated by a pulsed laser and detected by using the PS/PR technique, where the source and receiver were located on the same surface of a specimen. The inverse problem was solved successfully by the simplex optimization method. Following the simplex iteration rules, the orientation and the elastic constants can be recovered from the measured surface wave energy velocities. The wave fronts and the caustic effects of the skimming shear waves have also been observed in the laser ultrasound experiment.

Modeling of short-period surface-wave propagation in southern California

Abstract For the 1992 Landers mainshock, the lateral heterogeneity of the lithosphere combined with an extended earthquake source may account for the complexity of the strong-motion observations that cannot be easily interpreted by a simplified point-source model in a laterally homogeneous medium. Both the effect of an extended source and that of lateral heterogeneity are examined using a forward modeling technique that combines distributed nonuniform slip on a fault plane in a 3D medium. Surface-wave synthetics are constructed using surface-wave Gaussian beam method, which allows for a mild degree of lateral heterogeneity. We analyze the amplitude and waveform data of the Landers strong-motion recordings in southern California in order to identify the path effects and the effect of an extended source. The overall source parameters of the Landers earthquake are obtained by comparing synthetics with recordings at near-source stations which lie within relatively homogeneous path structures. This procedure yields a unilateral rupture propagating northwesterly over two distinct rupture segments with somewhat different focal mechanisms. The surface-wave phase velocity map is modified to fit the data recorded at larger hypocentral distances. The final improved model generates a very good agreement between observations and synthetics. In the presence of lateral heterogeneity, the focusing, defocusing, and multipath interference are found to contribute significantly to the strong-motion shaking in a 3D basin.

Microwave backscatter from the sea surface: Bragg scattering by short gravity waves

Resonant Bragg scattering forms the basis for the composite or dual‐scale model for microwave backscatter from the sea surface. The scatterers are short surface waves that are spatially resonant with the incident electromagnetic waves. Bragg scattering is most easily identified when the intrinsic velocity of the scattering agents can be deduced and compared with theoretical surface wave phase velocities. In this paper we present S band (wavelength 10 cm) microwave backscatter data taken at low grazing angles for three situations where the scatterer velocity could be separated from the surface currents. These include a situation where pack ice acts as an additional tracer on the water surface, a wind direction reversal, and an azimuthal scan during low wind speed conditions where two Bragg peaks are visible in the Doppler spectra. These data show that under these conditions the scattering is dominated by propagating 5‐cm resonant waves. Doppler spectra recorded at low grazing angles are interpreted in terms of the angular distribution of the scattering waves, the contributions of wave orbital velocities, and the effects of geometric shadowing.

Born seismograms using coupled free oscillations: the effects of strong coupling and anisotropy

SUMMARY We have developed an expression for the first-order Born waveform perturbation for long-period seismic records on an aspherical earth, using an anelastic monopole reference model. We have derived both an explicitly anelastic first-order Born term u’(r, t) and an approximate, but much simpler, expression in which quasi-degenerate modal coupling is represented by secular terms in the time domain. We designate this expression the ‘strong’ Born approximation to identify the presence of ‘strong’ quasi-degenerate coupling. Earlier applications of Born theory to surface wave seismograms have typically neglected the coupling between different modal dispersion branches. The strong Born approximation is linear in the aspherical model, but the secular terms restrict its accuracy to ‘short’ times after event onset, typically fewer than 10 hr. Additional accuracy can be gained by treating the self-coupling of isolated multiplets explicitly by formally summing the Born series using a projection of the aspherical operator 2” onto the multiplet in question. We call this the ‘stronger’ Born approximation, which is a non-linear functional of the aspherical model. The stronger Born approximation is similar to, but formally less accurate than, the subspace projection algorithm. We verified the accuracy of synthetic seismograms calculated with the ‘strong’ and ‘stronger’ Born approximations against Galerkin coupled-mode synthetics using a zonally symmetric, weakly anisotropic upper mantle model. The Born seismograms replicate successfully the ‘quasi-Love’ waveforms that diagnose spheroidal-toroidal coupling, suggesting that the strong Born approximation is adequate to model the interaction of free-oscillation coupling partners that are closely spaced in the frequency domain, at least for short records. We performed a waveform inversion test using three-component synthetic seismograms from 297 source-receiver pairs. Once spheroidal-toroidal coupling is incorporated in the inverse formulation, the waveform perturbations associated with the anisotropic parameters are clearly distinct from waveform perturbations associated with the isotropic parameters. Although the model space used in this experiment is highly restricted compared to the real Earth, these results suggest that the trade off between anisotropy and isotropic lateral structure may be less problematic in a fully-coupled waveform inversion than in a tomographic inversion of surface wave phase delays.

Characterization of thin diamond-like carbon films by ultrasonic surface waves

The method of ultrasonic surface waves is suitable to determine the elastic modulus of thin diamond-like carbon films deposited onto silicon (111) wafers by laser-induced vacuum arc deposition (Laser-Arc) if frequencies in the range up to 100 MHz are used. Surface wave pulses were generated in the thermoelastic regime by an excimer-laser (XeCl, 308 nm). Ultrasonic signals influenced by the film structure were detected by a piezoelectric transducer. The surface wave phase velocity, which is dependent on frequency, was measured using a Fourier transformation technique. To calculate the elastic modulus of the films the inverse problem of surface wave dispersion in coated materials was solved. Carbon films with a thickness of 300 nm deposited at different substrate temperatures in the range between 60 and 500 °C were studied. Young's modulus values up to 230 GPa were obtained for substrate temperatures below 150 °C. The very small modulus for T > 150 °C suggests a drastic decrease in the sp 3-to-sp 2 bonding ratio in the amorphous diamond-like carbon structure. These results correlate with optical studies. High frequency surface waves were demonstrated to be a sensitive indicator for evaluating the structure of the carbon film as dependent on the deposition conditions.

Quantitative electron holography applied to crystal wedges and interfaces

Electron holography is unique among transmission electron microscopy techniques in that it allows retrieval of phase of the electron wave, information which is lost with other imaging techniques. With access to the phase, interactions of the incident electron wave with the electrostatic and magnetic potentials of the specimen can be studied directly with high spatial resolution. Besides resolution enhancement, the original goal for electron holography, applications to wide range of materials problems are currently under investigation. This work will address applications to measurements of mean inner potential of crystals and to epitaxial crystal interfaces.In non-magnetic materials, in the absence of external electrical fields and/or charge layers, the electrostatic potential which alters the phase of the exit surface wave results from the atomic potentials. For amorphous and polycrystalline samples of known thickness, the phase change depends on the volume average of the atomic potentials, i.e. the mean inner potential V0.

Measurement of Velocity of Surface Acoustic Waves on Proton-Exchanged Lithium Tantalate Using Comb Filters

The phase and group velocities of surface waves on z-cut proton-exchanged lithium tantalate were measured. Lithium ions were exchanged for hydrogen ions in heated pyrophosphoric acid. The insertion loss of the filters, which were formed directly on the exchanged layers, was nearly equal to the loss on unexchanged lithium tantalate. The reduction of the phase velocity was proportional to the thickness of the exchanged layers. The reduction was 3.8% for x-propagating surface waves when the layer thickness normalized by the surface wavelength was 0.082. The reduction of the group velocity was 6.4%, which was nearly equal to the reported value of z-cut lithium niobate.

Source phase and amplitude anomalies of long‐period surface waves

In addition to the Fermat phase anomaly and the amplitude anomaly produced by geometric focusing and defocusing along the propagation path, long‐period surface waves on a laterally heterogeneous earth exhibit phase and amplitude variations due to the deviation in takeoff azimuth of the ray at the source. The resulting perturbation in source phase is generally small enough to be ignored; however, the source amplitude anomaly may be comparable to that produced by focusing and defocusing. Adding the source anomaly significantly reduces the variance of amplitude measurements performed on a large suite of synthetic vertical‐component coupled‐mode seismograms. Future tomographic analyses that incorporate amplitude measurements should account for this effect.

Reappraisal of major African earthquakes, south of 20°N, 1900–1930

We have re-examined those earthquakes in Africa south of 20°N, in the period 1900–1930, that appear from instrumental or macroseismic evidence to have a magnitude of 5 3/4 or greater. We identify more than 50 such events, about twice as many as listed by Gutenberg and Richter (1954). We find that the combined use of early instrumental readings and macroseismic information gleaned from previously untapped sources gives the best control of location. Instrumental relocation is difficult because of the lack of stations in Africa and the very uneven global distribution. For the low-gain, medium-period instruments then in use, the best control often comes from using the maximum Airy phase of surface waves. Similarly, there is a lack of sources of macroseismic information, and the simple building practice makes it difficult to assess intensity. We have recalculated magnitude Ms uniformly using the Prague formula. We discuss these problems and show that it is likely that our list is complete only down to magnitude about 6, and that the seismic record for Africa before this century will probably remain incomplete for events of all magnitudes.

Experiments on the Excitation of Resonances of Elastic Objects by Acoustic Pulses and Theoretical Interpretation

We have carried out tank experiments on the excitation of vibrational resonances of submerged elastic objects by incident short acoustic pulses. We have studied steel spheres, cylinders with hemispherical endcaps, and prolate as well as oblate spheroids. Theoretical interpretations of the resonance positions are provided by the matching of the phases of surface waves excited by the incident pulses, that encircle the object along closed paths. Some results of a French experimental study (G Maze and J Ripoche, University of Le Havre) are interpreted using the same approach.

Surface wave propagation in a half space with a single set of regular joints : J Geophys Res V96, NB3, March 1991, P4173–4186

The dispersion of surface waves is investigated herein for a half-space of a jointed rock medium with a single set of regular joints with an arbitrary angle between the free surface and the joint plane. The intact rock layers are assumed to be linearly elastic, and the joint response is prescribed by linear traction-slip relations. Since the exact surface wave analysis of the jointed half-space is difficult due to a multitude of joints in the domain of the analysis, a high-order homogenization model, proposed by Murakami and Hegemier (1989) is adopted. The model incorporates accurately the harmonic wave dispersion in a jointed full space and is capable of predicting the surface wave propagation down to the wavelength of the order of approximately two intact layer thicknesses. For a jointed half-space with the angle between the joint plane and the free surface less than approximately 30° the surface wave phase velocity spectra is found to exhibit dramatic dispersion. The surface wave velocity increases as much as 87% for the angle 0° and 39% for the angle 30° as the wave number or frequency increases. This dispersion characteristic of the surface wave is due to the dispersion of plane shear waves in a jointed full space in the waveguide direction. The effect of surface wave dispersion in the time domain has been investigated by solving Lamb's problem under plane strain. A jointed half-space with joint planes parallel to the free surface has been analyzed by the finite element method. The time history of velocity and displacement at different observation points exhibits spreading of waves due to dispersion. Surface wave in a half space covered by a solid layer with lower shear wave velocity exhibits the phase velocity reduction with the wave number. It is interesting to note that the surface wave dispersion observed in jointed half-spaces with joint angle between 0° and 30° exhibits the opposite trend.

Pipeline Response to Loma Prieta Earthquake

A field experiment to investigate the response of buried pipelines to lateral offsets and to traveling wave effects is currently being operated at a test site on a trace of the San Andreas Fault in central California. The experiment is located near Parkfield, California, where the U.S. Geological Survey has predicted the recurrence of a moderate earthquake within the next few years. The goal of the experiment is to develop data that can be used to qualify design and analysis methods for pipelines in seismically active areas. Welded steel and ductile iron pipeline segments are buried and instrumented adjacent to an array of survey monuments and strong motion seismographs. Although the predicted moderate earthquake on the Parkfield‐Cholame segment of the San Andreas Fault has not yet occurred, data obtained during low‐intensity shaking from the surface wave phase of the October 1989 Loma Prieta earthquake yields valuable insight into pipeline response. Close correlation is found between ground strains induc...

Surface wave propagation in a half‐space with a single set of regular joints

The dispersion of surface waves is investigated herein for a half‐space of a jointed rock medium with a single set of regular joints with an arbitrary angle between the free surface and the joint plane. The intact rock layers are assumed to be linearly elastic, and the joint response is prescribed by linear traction‐slip relations. Since the exact surface wave analysis of the jointed half‐space is difficult due to a multitude of joints in the domain of the analysis, a high‐order homogenization model, proposed by Murakami and Hegemier (1989) is adopted. The model incorporates accurately the harmonic wave dispersion in a jointed full space and is capable of predicting the surface wave propagation down to the wavelength of the order of approximately two intact layer thicknesses. For a jointed half‐space with the angle between the joint plane and the free surface less than approximately 30° the surface wave phase velocity spectra is found to exhibit dramatic dispersion. The surface wave velocity increases as much as 87% for the angle 0° and 39% for the angle 30° as the wave number or frequency increases. This dispersion characteristic of the surface wave is due to the dispersion of plane shear waves in a jointed full space in the waveguide direction. The effect of surface wave dispersion in the time domain has been investigated by solving Lamb's problem under plane strain. A jointed half‐space with joint planes parallel to the free surface has been analyzed by the finite element method. The time history of velocity and displacement at different observation points exhibits spreading of waves due to dispersion. Surface wave in a half space covered by a solid layer with lower shear wave velocity exhibits the phase velocity reduction with the wave number. It is interesting to note that the surface wave dispersion observed in jointed half‐spaces with joint angle between 0° and 30° exhibits the opposite trend.

Reappraisal of major African earthquakes, south of 20�N, 1900?1930

We have re-examined those earthquakes in Africa south of 20°N, in the period 1900–1930, that appear from instrumental or macroseismic evidence to have a magnitude of 5 3/4 or greater. We identify more than 50 such events, about twice as many as listed by Gutenberg and Richter (1954). We find that the combined use of early instrumental readings and macroseismic information gleaned from previously untapped sources gives the best control of location. Instrumental relocation is difficult because of the lack of stations in Africa and the very uneven global distribution. For the low-gain, medium-period instruments then in use, the best control often comes from using the maximum Airy phase of surface waves. Similarly, there is a lack of sources of macroseismic information, and the simple building practice makes it difficult to assess intensity. We have recalculated magnitude Ms uniformly using the Prague formula. We discuss these problems and show that it is likely that our list is complete only down to magnitude about 6, and that the seismic record for Africa before this century will probably remain incomplete for events of all magnitudes.

Recovery of aspherical earth structure from observations of normal mode amplitudes

On an aspherical earth, the normal mode amplitude pattern is perturbed by along-branch coupling. In the geometrical optics approximation, the effect of aspherical earth structure on normal mode amplitudes through along-branch coupling is equivalent to a perturbation Θ in the spatial phase of the amplitude pattern. This observable quantity is related to earth structure through a WKBJ phase integral along the source-receiver minor arc. The amplitude pattern is strongly sensitive to odd-degree earth structure and complements the information contained in the frequency shift pattern, which is sensitive to only even-degree structure. We have developed a method to estimate the amplitudes of unresolvably split multiplets from long-period spectra and have applied it to a large number of IDA and GEOSCOPE recordings to obtain a global data set of normal mode amplitudes for spheroidal modes 0S26−0S43. Normal mode amplitude estimation requires that the first surface wave arrival R1 be available in the seismogram, and coherent amplitude patterns have been obtained for 172 data records. The analysis of normal mode amplitudes affords several advantages not shared by surface wave phase velocity analysis or time-domain waveform fitting. Our method allows the estimation of errors in the model and the ability to cull away modes in the frequency domain, and it makes use of the information contained in the entire seismogram. In addition, our method makes no assumptions concerning the spectral shape of isolated multiplets in the frequency domain. The small data set employed here is only a fraction of the size of previous global data sets, but has the advantage that fewer assumptions are built in to the theory on which the structure inversion is based. Several factors, including uncertainty in the moment tensor scaling and focusing and defocusing effects, prohibit recovery of Θ for individual multiplets and limit us to the recovery of the average Θ over the mode band l = 26−43, for each source-receiver pair. Through a preferential weighting of subsets of this mode band, we may obtain estimates of Θ within narrower mode bands centred, respectively, on l = 31, l = 34, and l = 37. Least squares inversion of Θ within the various mode bands, utilizing approximately 100 source-receiver pairs, yields the geographic distribution of local eigenfrequency perturbation δδlocal(δ, δ) in a truncated spherical harmonic expansion. Inversion is first performed for the best fitting degree-6 earth model using all available modes within the band l = 26-43 with equal weight. The degree-6 earth model is obtained by inverting for degrees 1, 3, and 5 with degrees 2, 4 and 6 fixed according to published results from the frequency studies. Narrower band inversions are performed within l= 26-36, l = 29-39, and l = 31-43. Comparison with model M84A shows that the odd degree-1 and 3 components of aspherical earth structure may be reproduced from the amplitude data set. The degree-5 structure differs significantly from that of model M84A.