Love Wave Group Research Articles

Surface wave dispersion, regionalized velocity models, and anisotropy of the Pacific crust and upper mantle

Summary The Rayleigh and Love wave phase and group velocities of Yu & Mitchell (1979) have been inverted after applying anelasticity corrections corresponding to laterally varying Q structures beneath the Pacific Ocean. The derived models indicate that the lithosphere thickens with age at the expense of the asthenosphere, that no resolvable variations of velocity occur in the asthenosphere, and that resolvable variations of velocity in the lithosphere occur only in the younger portions of the Pacific. Azimuthal anisotropy is small (less than 1 per cent) throughout the Pacific. Polarization anisotropy is larger, being resolvable in the lithosphere, but not in the asthenosphere, of all the regions of this study, using data at periods between 20 and 100 s. Limitations of our inversion procedure for anisotropic models were investigated by doing forward calculations assuming that the lithosphere is transversely isotropic with symmetry axes oriented vertically. The results for our models, in which anisotropy is restricted to the lithosphere, indicate that SH and SV velocities in the lithosphere differ only slightly from the velocities derived from our formal inversion procedure. A two-stage model is proposed for the generation of anisotropy in the oceanic lithosphere. Azimuthal anisotropy is generated at the ridges by preferential glide in olivine crystals (Francis 1969) and is thus restricted to the uppermost mantle. As the plates spread and grow older, however, they thicken by the accretion of crystals at their bases which have a preferred vertical orientation. This model is capable of explaining all of the observations of anisotropy presently available from oceanic seismic refraction and surface wave studies.

Shield-like upper mantle structure inferred from long-period Rayleigh- and Love-wave dispersion investigations in the Middle East and southeast Asia

abstract Rayleigh- and Love-wave fundamental-mode group and phase velocities between World Wide Standard Seismograph Network Stations at Chiengmai, Thailand; New Delhi, India; Shiraz, Iran; and Helwan, United Arab Republic, have been obtained from data generated by an earthquake near the New Hebrides Islands. This epicenter and these seismic stations lie practically on one great circle path, the epicenter-to-station directions being confined to the narrow azimuthal window from 294.40° to 297.57°. Application of improved frequency-time analysis to carefully selected subsets of these data makes it possible to obtain results for periods extending to several minutes. The “impulse response” method is introduced for the estimation of interstation dispersion. This method is superior to the usual cross-correlogram method because spectral amplitudes are equalized to a greater degree. These interstation Rayleigh- and Love-wave group- and phase-velocity results are consistent with shield-like upper mantle velocity models. A shear-wave upper mantle low-velocity zone is inferred for the region studied. The observed data support extension of the Indian shield beneath the thick sedimentary cover of the Indogangetic plains.

Shield-like upper mantle velocity structure below the Indo-Gangetic Plains: Inferences drawn from long-period surface wave dispersion studies

Shield-like upper mantle velocity structure has been inferred to exist below the Indo-Gangetic Plains from a study of mantle Rayleigh and Love wave group and phase velocities for periods extending to 200 seconds. The investigations have been carried out for the path between the World Wide Standard Seismic Network Stations at Chiengmai (CHG), Thailand, and New Delhi (NDI), India, for an earthquake with its epicenter in the New Hebrides Islands. Application of improved frequency time analysis has permitted measurement of regional surface wave dispersion for periods extending to several minutes; previous results for this region were for periods no greater than about one minute.

Analysis to Extended Periods of Rayleigh and Love Wave Dispersion across Australia

Group velocities and phase velocities for Rayleigh waves and Love waves have been measured to periods of almost 200 s for nine paths across Australia. This extended range of dispersion data was obtained by the new process of summing cross-correlograms of a large number of seismograms of earthquakes with moderate magnitudes (average mb was 5.8) prior to the non-linear computation of phase. This is an unbiased averaging process that enhances the signal at longer periods. Western-central Australia has the same dispersion as shield areas of other parts of the world; eastern Australia may be catalogued tectonic or ‘aseismic platform’. Group velocity for eastern Australian paths has a pronounced minimum value, possibly less than 3·4 km s−1, between 100- and 200-s period. Smoothed Rayleigh wave phase velocities were obtained by integration of regionally averaged group velocity curves. A usable estimate of fundamental mode Love wave phase velocities was obtained by Fourier analysis of sums of cross-correlograms, but Love wave group velocities could not be resolved by frequency-time analysis.

Earth Structure from Free Oscillations and Travel Times

An extensive set of reliable gross Earth data has been inverted to obtain a new estimate of the radial variations of seismic velocities and density in the Earth. The basic data set includes the observed mass and moment of inertia, the average periods of free oscillation (taken mainly from the Dziewonski-Gilbert study), and five new sets of differential travel-time data. The differential travel-time data consists of the times of PcP-P and ScS-S, which contain information about mantle structure, and the times of P′_(AB) - P′_(DF) and P′_(BC)-P′_(DF) which are sensitive to core structure. A simple but realistic starting model was constructed using a number of physical assumptions, such as requiring the Adams-Williamson relation to hold in the lower mantle and core. The data were inverted using an iterative linear estimation algorithm. By using baseline-insensitive differential travel times and averaged eigenperiods, a considerable improvement in both the quality of the fit and the resolving power of the data set has been realized. The spheroidal and toroidal data are fit on the average to 0·04 and 0·08 per cent, respectively. The final model, designated model B1, also agrees with Rayleigh and Love wave phase and group velocity data. The ray-theoretical travel times of P waves computed from model B1 are about 0·8s later than the 1968 Seismological Tables with residuals decreasing with distance, in agreement with Cleary & Hales and other recent studies. The computed PcP, PKP, and PKiKP times are generally within 0·5 s of the times obtained in recent studies. The travel times of S computed from B1 are 5–10 s later than the Jeffreys-Sullen Tables in the distance range 30° to 95°, with residuals increasing with distance. These S times are in general agreement with the more recent data of Kogan, Ibrahim & Nuttli, Lehmann, Cleary, and Bolt et al. Model B1 is characterized by an upper mantle with a high, 4·8 km s^(−1), S_n velocity and a normal, 3·33 g cm^(−3), density. A low-velocity zone for S is required by the data, but a possible low-velocity zone for compressional waves cannot be resolved by the basic data set. The upper mantle transition zone contains two first-order discontinuities at depths of 420 km and 671 km. Between these discontinuities the shear velocity decreases with depth. The radius of the core, fixed by PcP-P times and previous mode inversions, is 3485 km, and the radius of the inner core-outer core boundary is 1215 km. There are no other first-order discontinuities in the core model. The shear velocity in the inner core is about 3·5 km s^(−1).

The azimuthal dependence of Love and Rayleigh wave propagation in a slightly anisotropic medium

Rayleigh's principle is combined with Backus' harmonic tensor decomposition to investigate the effect of a small anisotropy on the propagation of Love and Rayleigh surface waves in an arbitrarily stratified half-space. A slight elastic anisotropy gives rise to an azimuthal dependence of the phase velocities of both Love and Rayleigh waves of the form c(ω, θ) = A1(ω) + A2(ω) cos 2θ + A3(ω) sin 2θ + A4(ω) cos 4θ + A5(ω) sin 4θ where ω is the angular frequency and θ is the azimuth of the wave-number vector. This azimuthal dependence of the Love and Rayleigh wave phase velocities produces, in turn, a similar azimuthal dependence of the Love and Rayleigh wave group velocities. In view of the accumulating evidence from seismic refraction surveys of upper mantle anisotropy under oceans, the theory may be applicable to Love and Rayleigh wave propagation along oceanic paths.

Surface Wave Dispersion and Crust Structure in Greenland

Rayleigh and Love wave group, and phase velocity dispersion has been determined for two profiles crossing the interior of Greenland. It was found that the dispersion is similar on the two profiles. The observed dispersion is only a little different from the Canadian Shield dispersion. The observations have been compared with theoretical model dispersion curves. A model G-62 has been developed for the Greenlandic Shield. It is similar to the model for the Canadian Shield. The depth to the Mohorovičić discontinuity appears to be a little greater than in Canada.

The propagation of short elastic surface waves on a slowly rotating earth

abstract The effects of slow rotation with angular velocity Ω on Love and Rayleigh waves with given horizontal wave vector k on a plane-layered, transversely isotropic half-space have been calculated to first order in Ω. The frequency of Love waves is unaffected by rotation, while the frequency of Rayleigh waves is increased by k−1R(k)Ω · (z^ × k) where z^ is the unit outward normal to the boundary of the half-space and R(k) is a dimensionless function of k, the length of k. R(k) lies between −1 and 1, and vanishes identically for a homogeneous, isotropic halfspace with Poisson ratio 14. The vertical and longitudinal particle motions in a Love wave do not vanish and are neither in phase nor in quadrature with the transverse motion. The transverse particle motion in a Rayleigh wave does not vanish and is neither in phase nor in quadrature with the vertical and longitudinal motions. It has been shown that a group of short, multicomponent waves on an anisotropic curved surface behaves like a classical particle, whose Hamiltonian is generated by the local dispersion relation and the curvilinear coordinates used to describe the surface. This extension of Hamilton's eikonal theory, together with the plane dispersion relations just derived, has been applied to Love and Rayleigh waves of given wave number k on a radially stratified, transversely isotropic sphere of radius a rotating slowly with angular velocity Ω. Correct to first order in Ω and (ak)−1, the trajectory of a Love wave group is unaffected by rotation, while the plane of the great circle trajectory of a Rayleigh wave group maintains its inclination to the axis of rotation and precesses about that axis with angular velocity (ak)−)R(k)Ω. Because of this precession, at a fixed seismograph the direction of arrival of 333 second mantle Rayleigh waves from a point impulsive source changes systematically by about 2R degrees after each circuit of the earth.

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.