Polarization anomaly of Love waves caused by lateral heterogeneity

We calculate surface waves propagating in a laterally heterogeneous structure beneath the Kuril trench, where significant Love-wave polarization anomalies, called quasi-Love waves, are generated. Since 3-D wave propagation in the two-dimensionally heterogeneous structure can be assumed, we apply the 2.5-D finite difference method to the surface-wave calculations. The calculations show that a velocity contrast of 7 per cent at depths of less than 210 km beneath the Kuril trench cannot generate quasi-Love waves, and that an unlikely contrast of 20 per cent is required to generate clear quasi-Love waves. The possible cause of the quasi-Love waves inferred from previous studies on coupled free oscillations is a lateral variation in azimuthal anisotropy. The lateral variation in azimuthal anisotropy beneath the Kuril trench suggests a change in the mantle flow induced by the subducting slab.     

Possible mode conversion between Love and Rayleigh waves at a continental margin

Summary. Mode conversion at a continental margin between normal modes of surface waves is investigated by theoretical calculations for oblique incidence for periods longer than 15 s. It is suggested that significant conversion takes place between the various modes of Love waves in the period interval between 15 and 40 s, while there is negligible mode conversion for longer periods. The largest mode conversion involves the lowest modes. In addition the calculations have revealed a small but significant conversion between Love and Rayleigh fundamental modes around 20-s period. Reflections of Love waves are found to be significant only for the continental fundamental mode.     

Seismic body waves in anisotropic media: propagation through a layer

Summary. The square-root energy ratios and pulse shapes are presented for P, SV and SH waves transmitted through a layer of orthorhombic olivine between two isotropic half-spaces. Off incident planes of symmetry, incident P waves generate two small amplitude SH waves (one from each interface), whose amplitudes decrease slowly with increasing period. Incident SV (or SH ) waves can generate large amplitude SH (or SV ) waves which decrease rapidly with increasing period. For incident S waves, many pulses not present in isotropic models are generated, often of large relative amplitude, with many of the transmitted S pulses showing evidence of double arrivals, either in the form of S-wave splitting, or a modification of the shape of the input waveform.     

Global observation of off-great-circle propagation of Long-Period surface waves

In the current generation of global dispersion maps of surface waves, the long-wavelength structure seems to be very well determined. There is general agreement in the patterns of global phase velocity anomalies up to harmonic degree 16. However, the shorter-wavelength structure varies significantly between published maps, and it appears that this part of the models depends strongly on the inversion technique and on the data set of surface-wave dispersion (usually phase measurements). Polarization data depend on the lateral gradient of phase velocity and hence are more sensitive to shorter-wavelength structure than phase data; thus, including these data should enhance resolution. In this paper, I demonstrate that polarization data of long-period surface waves (80 s), as a function of frequency, can be reliably measured using a multitaper technique. the resulting off-great-circle arrival angles of the surface-wave packets are relatively easy to interpret within a ray-theoretical framework. Our data base of three-component recordings is now large enough to provide useful constraints on global dispersion maps, particularly on the shorter-wavelength parts. Apart from the phase velocity model itself, a possible misorientation of the horizontal components at each station is included in a non-linear inversion as an additional independent model parameter. This gives a significant improvement in the fit to the data. Misorientations of more than 3° are probable for at least four of the 37 stations investigated.     

Waveform inversion of mantle Love waves:the Born seismogram approach

Summary. Normal mode theory, extended to the slightly laterally heterogeneous earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love wave (200–500 s) for the Earth's lateral heterogeneity at l = 2 and a spherically symmétric anelasticity ( Q _μ) structure. The data are from the Global Digital Seismograph Network (GDSN). The l =2 pattern is very similar to the results of other studies that used either different méthods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analysed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5 per cent in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range cannot constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.
The calculated modal Q values for the obtained Q _μ model fall within the error bars of the observations. The result demonstrates the discrepancy of Rayleigh wave Q and Love wave Q and indicates that care must be taken when both Rayleigh and Love wave data, including amplitude information, are inverted simultaneously.
Anomalous amplitude inversions of G2 and G3, for example, are observed for some source-receiver pairs. This is due to multipathing effects. One example near the epicentral region, which is modelled by the obtained l = 2 heterogeneity, is shown.     

Dynamical rupture process on a three-dimensional fault with non-uniform frictions and near-field seismic waves

Summary. Dynamical rupture process on the fault is investigated in a quasi-three-dimensional faulting model with non-uniform distributions of static frictions or the fracture strength under a finite shearing pre-stress. The displacement and stress time functions on the fault are obtained by solving numerically the equations of motion with a finite stress—fracture criterion, using the finite difference method.
If static frictions are homogeneous or weakly non-uniform, the rupture propagates nearly elliptically with a velocity close to that of P waves along the direction of pre-stress and with a nearly S wave velocity in the direction perpendicular to it. The rise time of the source function and the final displacements are larger around the centre of the fault. In the case when the static frictions are heavily non-uniform and depend on the location, the rupture propagation becomes quite irregular with appreciably decreased velocities, indicating remarkable stick-slip phenomena. In some cases, there remain unruptured regions where fault slip does not take place, and high stresses remain concentrated up to the final stage. These regions could be the source of aftershocks at a next stage.
The stick—slip faulting and irregular rupture propagation radiate high-frequency seismic waves, and the near-field spectral amplitudes tend to show an inversely linear frequency dependence over high frequencies for heavily non-uniform frictional faults.     

Numerical simulation of the propagation of P waves in fractured media

We study the propagation of P waves through media containing open fractures by performing numerical simulations. The important parameter in such problems is the ratio between crack length and incident wavelength. When the wavelength of the incident wavefield is close to or shorter than the crack length, the scattered waves are efficiently excited and the attenuation of the primary waves can be observed on synthetic seismograms. On the other hand, when the incident wavelength is greater than the crack length, we can simulate the anisotropic behaviour of fractured media resulting from the scattering of seismic waves by the cracks through the time delay of the arrival of the transmitted wave. The method of calculation used is a boundary element method in which the Green's functions are computed by the discrete wavenumber method. For simplicity, the 2-D elastodynamic diffraction problem is considered. The rock matrix is supposed to be elastic, isotropic and homogeneous, while the cracks are all empty and have the same length and strike direction. An iterative method of calculation of the diffracted wavefield is developed in the case where a large number of cracks are present in order to reduce the computation time. The attenuation factor Q ⁻¹ of the direct waves passing through a fractured zone is measured in several frequency bands. We observe that the attenuation factor Q ⁻¹ of the direct P wave peaks around kd = 2, where k is the incident wavenumber and d the crack length, and decreases proportionally to ( kd ) ⁻¹ in the high-wavenumber range. In the long-wavelength domain, the velocity of the direct P wave measured for two different crack realizations is very close to the value predicted by Hudson's theory on the overall elastic properties of fractured materials.     

Ray asymptotic propagation of the spectra of elastic surface waves in a waveguide with laterally smooth inhomogeneities

Summary. A technique based on ray asymptotics has been developed to propagate complex spectra of elastic normal mode surface waves in a waveguide with material and geometrical properties varying smoothly in the lateral directions. In the technique, the original problem defined in the unstretched coordinates has been transformed into an eiconal equation as well as into a certain number of transport equations defined in stretched coordinates.
The solution of the eiconal equation is equal to the solution of the eigenproblem of the eiconal operator A₀. Due to the self-adjointness of A₀, in each of the relevant local inner product spaces, LIPS, the solution of the eigenproblem, A₀ψ= v ψ results in the set { v _t} of real local eigenvalues and in the orthonormal system {ψ_t} of local eigenvectors.
As the Hamiltonian function of an initial value problem, each eigenvalues gives birth to a bicharacteristic curve as well as to the related ray. The introduction of the rays induces connections between the vertical cross-sections of the waveguide.
Finally, for each asymptotic order j , the LIPS-valued transport equations are reduced to a set of matricial propagation equations in the local spectral amplitude vectors, LSAVs. Consequently, a knowledge of the initial conditions at a vertical cross-section makes it possible to propagate the LSAVs along the rays of the relevant modes. However, to complete the propagation one needs, in addition to the initial values, information about certain additional quantities, non-diagonal terms of order j , diagonal terms of orders lower than j and the auxiliary boundary terms of orders from 1 to j . The treatment has been completed by the propagation of the modal phases along the relevant rays.     

A review of the effects of anisotropic layering on the propagation of seismic waves

Summary. This paper reviews recent work, much of it unpublished, on the effects of anisotropy on seismic waves, and lays the theoretical background for some of the other papers in this number of the Geophysical Journal .
The propagation of both body and surface waves in anisotropic media is fundamentally different from their propagation in isotropic media, although the differences in behaviour may be comparatively subtle and difficult to observe. One of the most diagnostic of these anomalies, which has been observed on some surface-wave trains, and should be evident in body-wave arrivals, is generalized, three-dimensional polarization, where the Rayleigh motion is coupled to the Love, and the P and SV motion is coupled to the SH . This coupling introduces polarization anomalies which may be used to investigate anisotropy within the Earth.