Phase Velocities Of Love Waves Research Articles

Love waves in an inhomogeneous interstratum

The propagation of Love waves in an inhomogeneous interstratum, whose rigidity and density follow generalized power law variation, lying between two homogeneous half-spaces has been considered. The characteristic frequency equations have been obtained. The computational results for some special cases are presented in the form of dispersion curves showing the variation of phase and group velocity of Love waves with wave number.

Effect of higher mode contamination on measured Love wave phase velocities

In some circumstances the first higher mode of the Love surface wave can be significantly excited in the period range 30–90 sec by earthquakes and may travel at a group velocity comparable to that of the fundamental mode. This difficult-to-separate contamination will produce a large scatter, but no uniform bias, in phase velocities measured from an ensemble of events. The phase velocities measured from a single event may show a bias over a limited range of periods, but this perturbation may be positive or negative. These results argue against an explanation of observed inconsistencies of Love and Rayleigh wave phase velocities as being due to higher mode contamination. The results are also applicable to the effect of multipath interference of two similar-mode waves traveling at an angle with respect to one another.

Rayleigh wave particle motion and crustal structure

Abstract A feasibility study was made concerning the use of the ellipticity of the Rayleigh wave particle motion for determining earth structures. Variational parameters were computed empirically for both the ellipticity and phase velocity of Rayleigh waves in the period range T = 10-50 seconds. It was found that, in general, the ellipticity and phase velocity are about equally sensitive to structural perturbations, but that near-surface low-velocity sedimentary layers influence the ellipticity much more strongly than they do the phase velocity. Anelasticity has a minor effect on the ellipticity, whereas the presence of interfering waves can have a significant influence. A test of the independence between ellipticity and phase velocity indicated that in our period range ellipticity does contribute independent information, and thus provides an additional constraint toward uniqueness. Using data from LASA, both ellipticity and Rayleigh- and Love-wave phase velocities were measured and the results interpreted in terms of a crustal structure. The ellipticity data proved useful when combined with the phase velocity and some structures that fit the phase velocity data could be rejected on the basis of ellipticity.

Crustal structure of the Mediterranean Sea Part II. Phase velocity and travel times

Abstract A large number of observations of phase velocity of Love and Rayleigh waves have been used in order to determine the crust-mantle structure of the Mediterranean Sea. These velocities have been measured by using records from the Standard Stations located in the Mediterranean borders. The empirical dispersion curves have been compared with those of several models computed for this purpose. Travel-time curves of body waves for paths crossing the Mediterranean region, making use of all possible coastal stations and local earthquakes, have been found to substantiate the results from the surface wave dispersion. Also the value of the Bouguer anomaly in different points of the region was considered in the determination of the crustal thickness, as well as some measurements of group velocity from clear observations of higher modes. The crust-mantle structure under the Mediterranean Sea was found to be formed by two clearly distinct zones which correspond roughly to the areas to the west and east of Italy. The western zone, between Italy and Spain, is of oceanic type with a thin crust (about 14 km) and a low-velocity channel in the Upper Mantle. In the eastern zone, south of Greece, the crust (some 23 km thick) shows a great thickness of the uppermost sedimentary layers, which gives rise to very low velocities of short-period surface waves in that region. Love waves with group velocities smaller than those of Rayleigh have been clearly observed in a large number of earthquakes in this region. The surface wave dispersion as well as the travel-time curves of P and S waves of this zone indicate the existence of a low-velocity channel in the Upper Mantle.

Seismological evidences for the existence of soft thin layers in the upper mantle under Japan

From the seismological data on the crust-mantle structure under Japan, it is impossible to explain the phase velocities of Love and Rayleigh waves by any single model with a weakly heterogeneous, isotropic upper mantle. The significance of the problem is confirmed by the data on S waves from local mantle earthquakes. To explain these observations, a laminated mantle model is proposed, in which soft horizontal layers are interleaved in hard material. The data support a model having 2% soft material with shear velocity as low as 1.1 km/sec.

Inhomogeneities in the Earth's Mantle

Using seismic body and surface waves, the velocity structure of the Earth's mantle is determined with the emphasis on regions of anomalous variations (so-called ‘discontinuities’). In the upper mantle, the interpretation of Rayleigh and Love wave dispersion curves yields shear velocity profiles with discontinuities at depths 350 km and 700 km, and a low-velocity zone extending to 350km. In the lower mantle P-velocity profile is determined from dt/dΔ measurements using large aperture seismic array and travel times from Long Shot nuclear explosion for the Japan-Kuriles-Aleutian-Montana path. The velocity structure shows anomalous gradients or ‘discontinuities’ at depths 700, 1200 and 1900km, indicating that the lower mantle is not homogeneous. Lateral variations of the velocity structures are investigated. For the upper mantle studies the Earth is divided into three regions: oceanic areas, continental shields, and tectonic zones. Pure path phase velocities of Love waves are extracted from the composite dispersion data. The pure path shear velocity profiles obtained from these data are characterized by lower velocities under the oceans in the uppermost portion of the mantle. Shields have the highest velocities. These velocity differences are interpreted in terms of temperature variations. At a depth of 110 km the temperature of the oceanic mantle is higher (by 100–500° C depending on the temperature coefficient of the velocity) than that of the mantle under the shields. The presence of lateral heterogeneities in the mantle is demonstrated qualitatively by the differences of dt/dΔ vs Δ curves for two separate paths. Undulations of the geoid as determined from satellite observations are investigated for determining the sources of the anomalies. It is concluded that the main sources of lateral density variations must be in the mantle at depths greater than about 100km.

Phase velocity of surface waves in the transition zone of continental margins: 1. Love waves

The phase velocity of surface waves in the transition zone of a thickening layer is found to be severely influenced by back reflections from the structure beyond the seismic observatory. This feature is more important in producing phase shifts than is the shift in the eigen-value due to the inclined geometry. The effect of an inclined upper surface and an inclined Moho on the phase velocities of Love waves in a single layer are computed. For surface waves traveling from the thinner to the thicker layer, the upper surface produces no calculable effect. For both directions of propagation for an inclined Moho and for propagation from the thicker to the thinner layer for an inclined upper surface, the effect is a maximum in the period range 25 to 45 sec and has a phase shift whose sign is undeterminable in the absence of precise information about the geometry.

Surface wave phase velocities in Finland

Abstract Phase velocities of Rayleigh waves in Finland have been measured by the Fourier analysis method, using records of three stations which are on almost the same great circle as several Greek earthquakes. Phase velocities of Love waves of two of these earthquakes have also been determined. The wave groups were divided by numerical filtering into two frequency channels, which were analyzed separately. The resulting phase velocity curves were then smoothed in order to remove rapid oscillations, and mean values were calculated. The phase velocities were found to be slightly lower than those found for the Canadian Shield (Brune and Dorman, 1963), the maximum deviation for Rayleigh waves being about 0.07 km/sec at a period of 28 seconds and for Love waves about 0.15 km/sec at a period of 32 seconds. At periods shorter than 40 seconds the phase velocities of Rayleigh waves were found to be equal in Northern and Southern Finland within the accuracy of measurement.

Central U.S. crust—Upper mantle structure from Love and Rayleigh wave phase velocity inversion

abstract Fundamental mode Rayleigh and Love wave phase velocities in the period range 5 to 80 seconds have been measured in the central U. S. Using the concept of constant partial derivatives of phase velocity with respect to layer parameters in a least-squares inversion scheme a structural model for the area was determined. Several parameters were constrained on the basis of other available data. It was not possible to fit satisfactorily both Rayleigh and Love data with a simple isotropic model. Conclusions require either anisotropy in the upper mantle or systematic errors in the phase velocity measurements.

Velocities of mantle Love and Rayleigh waves over multiple paths

Abstract Phase velocities of Love waves from five major earthquakes are measured over six great circle paths in the period range of 50 to 400 seconds. For two of the great circle paths the phase velocities of Rayleigh waves are also obtained. The digitized seismograph traces are Fourier analyzed, and the phase spectra are used in determining the phase velocities. Where the great circle paths are close, the phase velocities over these paths are found to be in very good agreement with each other indicating that the measured velocities are accurate and reliable. Phase velocities of Love waves over paths that lie far from each other are different, and this difference is consistent and much greater than the experimental error. From this it is concluded that there are lateral variations in the structure of the earth's mantle. One interpretation of this variation is that the mantle under the continents is different from that under the oceans, since the path with the highest phase velocities is almost completely oceanic. This interpretation, however, is not unique and variations under the oceans and continents are also possible. Group velocities are computed from the phase velocities and are also directly measured from the seismograms. The group-velocity curve of Love waves has a plateau between periods of 100 and 300 seconds with a shallow minimum at about 290 seconds. The sources of error in both Fourier analysis and direct time domain methods of phase velocity measurement are discussed.

A Review of the Investigations into Earth's Crustal Structure from the Dispersion of Seismic Surface Waves

Investigations into continental crustal structure and upper mantle structures of the continents and oceans from the observation of seismic surface waves dispersion are reviewed in this second paper.Part II : Continental Crustal Structure.Up-to-date method, e. g., to determine the crustal structure through the careful fitting of theoretical dispersion curves basing upon the multi-layered crustal models with observed data are quite active in U. S. A. In this continent, Rayleigh waves dispersion due to nuclear explosion under the ground are well utilized. Higher mode surface waves have also been observed and studied. Geographical condition also enables U. S. seismologists to observe phase velocity dispersion over various regions in this continent.In Asia continent, deep Moho in and around Tibet Plateau is evident from the dispersion of Love Waves.Boundary of Antarctic continent is a matter of interesting. This problem, however, has not yet been fully solved from the dispersion of surface waves.Variation of Moho depth beneath Japan has been estimated from phase velocity of both Love and Rayleigh Waves.

Seismic waves and earth structure in the Canadian shield

Abstract Careful measurements of phase velocities in the Canadian shield have been made in the period range 3 to 90 sec for Rayleigh waves and 12 to 60 sec for Love waves by phase correlation of wave trains. The continental Love wave phase velocity data are the first to be reported in the literature. The phase and group velocities are higher than yet found in any other continental area, indicating relatively higher shear velocities in the crust and upper mantle. For paths in the Canadian shield a prominent Lg arrival with a velocity of about 3.65 km/sec is observed and an Sn arrival is recorded clearly to distances of about 4000 km with a velocity of about 4.72 km/sec. A theoretical layered model of the crust and upper mantle consistent with the various types of data has been derived by an inversion method employing least-squares curve-fitting of phase velocity data. This model has a three-layered crust 35.2 km thick with shear velocity increasing to about 3.85 km/sec in the lower crust. The upper mantle has a high speed layer with shear velocity 4.72 km/sec down to about 115 km below which the low velocity channel has a shear velocity of about 4.5 km/sec down to a depth of about 315 km. At greater depths the shear velocity closely follows the Gutenberg model. Higher mode phase velocity dispersion curves computed from the theoretical model are used for computing theoretical seismograms for the Canadian shield. These theoretical seismograms possess many of the features of the observed Lg arrivals, showing that Lg can be explained by normal mode wave propagation in a simple, layered crust. This paper shows that new methods of measuring and interpreting surface wave dispersion, combined with travel time data, can provide detailed and reliable information on shear wave velocity distribution down to depths of a few hundred kilometers in regions of horizontally uniform structure.

A note on Love waves in a homogeneous crust overlying an inhomogeneous substratum

abstract The secular equation is derived, governing the phase velocity of Love waves in a homogeneous elastic crust resting on an inhomogeneous elastic substratum, for a number of variations of shear modulus and density with depth.

A summary of observed seismic surface wave dispersion

Abstract Two sets of curves relating phase and group velocities of Love and Rayleigh waves to periods summarize our present state of knowledge on seismic surface wave dispersion. Periods range from about one second to one hour, and velocities from about one kilometer per second to about eight kilometers per second.

Long-period surface waves from the Chilean Earthquake of May 22, 1960, recorded on linear strain seismographs

Phase and group velocities of mantle Love and Rayleigh waves obtained from strain seismograph records of the Chilean earthquake are presented. The velocities of mantle Rayleigh waves of period from 300 to 550 seconds agree with those predicted from periods of free spheroidal oscillation of the earth and do not show a flattening of the group velocity curve for periods greater than 380 seconds. Group velocities for mantle Rayleigh waves reach a maximum of 7.8 km/sec at a period of about 1000 sec. Study of initial phases of Rayleigh waves indicates a difference of phase of π between the azimuth to Isabella and the azimuths to Ñaña and Ogdensburg. Determinations of phase and group velocities of Love waves have been extended to periods of 700 seconds. The phase velocity data of Satô [1958] has been corrected for the polar phase shift. The correct curve has been identified from the numerous possible curves which result from a 2π ambiguity in the phase correlation made by Satô. Values of phase velocities are presented for periods in the range of 60 to 700 seconds. The group and phase velocities of both Love waves and Rayleigh waves agree well with those predicted for the Gutenberg-Bullen A model of the earth. It is verified that analysis of seismograms in terms of progressive wave trains is equivalent to analysis in terms of standing waves. In the presence of absorption, as for the earth, the analysis in terms of progressive wave trains has many advantages. Material supplementary to this article has been deposited with the ADI Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D.C. A copy may be secured by citing the document number 6816 and remitting $1.75 for 35-mm microfilm. Advance payment is required. Make check or money order payable to: Chief, Photoduplieation Service, Library of Congress.

The polar phase shift of surface waves on a sphere

Abstract It has been demonstrated by means of a model experiment that elastic surface waves on a sphere advance in phase by π/2 on each crossing of the polar or antipodal region. Comparison of the asymptotic forms of solutions of the wave equation for displacements and dilatation before the polar crossing with those that apply afterward also show the π/2 phase shift. Similarly a π/4 phase advance occurs for waves leaving a point source. Because of the occurrence of the polar phase shift, it is necessary to correct previously published Rayleigh wave and Love wave phase velocities measured by correlation of phases over complete circumferential paths. The corrected Rayleigh wave phase velocity curve is presented here. The polar phase shift is involved in the determination of periods of free oscillation of the earth from surface wave data. Using data from the great Chilean earthquake of May 22, 1960, it is shown that the ratio of the earth's circumference to the wave length at free oscillation periods gives very nearly half integers in accordance with the formula 2 π a λ = n + 1 2 ·

Love waves in a heterogeneous, spherical Earth: 2. Theoretical phase and group velocities

Love wave phase and group velocities have been calculated for the first 14 radial modes for the Jeffreys-Bullen and Lehmann I models. Sphericity, an arbitrary number of discontinuities, gradients within each shell, and a liquid core have been taken into account. A new result is the prediction of maximum values of group velocity of about 7.5 km/sec for all the higher modes and the relation of these maxima and the period cutoffs to travel-time results.

Free oscillations of the Earth: 1. Toroidal oscillations

The free periods of toroidal oscillations of the earth have been computed for two earth models. The lowest period for the Gutenberg model earth is 2651 sec and for the Jeffreys-Bullen model 2732 sec. The surface amplitudes of the oscillations have been computed for three kinds of delta function stress sources—a unit force, a unit couple, and a unit torque—at depths of 600, 250, 100, and 30 km. The amplitudes decrease with increasing depth of the source. For a unit couple at 600 km the maximum amplitude of the lowest period for the Gutenberg model is 1.59×10−25 cm, and for the Jeffreys-Bullen model it is 0.70×10−25 cm. By using the free periods of oscillation we have extended Love wave phase velocity and group velocity dispersion curves to include long-period Love waves. The method used to compute the periods and amplitudes of the free oscillations is an extension of the Thomson-Haskell matrix method used in plane layered media. An example is presented to show the correspondence between the free oscillations and ray theory.