Abstract. A new technique for making single-station phase velocity measurements is developed and applied to a large number of globally recorded Rayleigh and Love waves in the period range 35-150 s. The method is based on phase-matched filter theory and iteratively suppresses the effect of interfering overtones by minimizing residual dispersion. The model surface wave signal is described by its amplitude and apparent phase velocity, both of which are parameterized in terms of smooth B-spline functions of frequency. A misfit function is constructed which represents the difference between the model and observed waveforms, and the optimal spline coefficients are estimated in an iterative misfit minimization algorithm. In order to eliminate cycle skips in the measurements of phase at short periods, the waveforms are first matched at long periods, and the frequency range is gradually extended to include higher frequencies. The application of the algorithm to records from the Global Seismographic Network, using earthquakes in the Harvard centroid-moment tensor catalog, results in the determination of more than 50,000 high-quality dispersion curves. The observed variations in measured dispersion for pairwise similar paths are used to estimate realistic uncertainties in the data. Phase delays at discrete periods are inverted for global maps of variations in phase velocity expanded in spherical harmonics up to degree 40. A realistic resolution test indicates that structures are well recovered up to at least degree 20. The new phase velocity maps explain 70-96% of the observed variance in phase residuals, reflecting the high internal consistency of the dispersion measurements.

Ð Measurements of group velocity are derived from phase-velocity dispersion curves and modeled with global laterally-varying isotropic structure. Maps for both Love and Rayleigh waves are created in the period range 35 s to 175 s. The data set of group-velocity measurements includes over 50,000 minor-arc observations and 5,000 major-arc observations. The errors in the measurements are estimated by an empirical method of comparing pairwise-similar paths, resulting in uncertainties which are 20% to 40% of the size of the typical measurement. The models are determined by least-squares inversion for spherical harmonic maps expanded up to degree 40. This parameterization allows for resolution of structures as small as 500 km. The models explain 70±98% of the variance relative to the Preliminary Reference Earth Model (PREM). For the area of Eurasia, the group-velocity maps from this study are compared with those of RITZWOLLER and LEVSHIN (1998). The results of the two studies are in very good agreement, particularly in terms of spatial correlation. The models also agree in amplitude at wavelengths longer than 30 degrees. For shorter wavelengths, the agreement is good only for models at short periods. The global maps are useful for prediction of group arrival times, for revealing tectonic structures, for determination of seismic event locations and source parameters, and as a basis for regional group-velocity studies.

We present a complete ray theory for the calculation of surface‐wave observables from anisotropic phase‐velocity maps. Starting with the surface‐wave dispersion relation in an anisotropic earth model, we derive practical dynamical ray‐tracing equations. These equations allow calculation of the observables phase, arrival‐angle and amplitude in a ray theoretical framework. Using perturbation theory, we also obtain approximate expressions for these observables. We assess the accuracy of the first‐order approximations by using both theories to make predictions on a sample anisotropic phase‐velocity map. A comparison of the two methods illustrates the size and type of errors which are introduced by perturbation theory. Perturbation theory phase and arrival‐angle predictions agree well with the exact calculation, but amplitude predictions are poor. Many previous studies have modelled surface‐wave propagation using only isotropic structure, not allowing for anisotropy. We present hypothetical examples to simulate isotropic modelling of surface waves which pass through anisotropic material. Synthetic data sets of phase and arrival angle are produced by ray tracing with exact ray theory on anisotropic phase‐velocity maps. The isotropic models obtained by inverting synthetic anisotropic phase data sets produce deceptively high variance reductions because the effects of anisotropy are mapped into short‐wavelength isotropic structure. Inversion of synthetic arrival‐angle data sets for isotropic models results in poor variance reductions and poor recovery of the isotropic part of the anisotropic input map. Therefore, successful anisotropic phase‐velocity inversions of real data require the inclusion of both phase and arrival‐angle measurements.

[1] A new method for measuring arrival angles of teleseismic Love and Rayleigh waves is developed. The new method utilizes estimates of surface wave dispersion to create a phase-matched filter to isolate the Love or Rayleigh wave in three-component recordings. The polarization of the filtered wave group is determined in the time domain by application of a variation of the complex polarization method of Vidale [1986]. Orientation, linearity, and ellipticity of particle motion are estimated in several frequency bands to determine the frequency-dependent polarization. The method employs an iterative scheme, by which a predicted Love wave, based on the estimated dispersion and polarization, is subtracted from the three-component data prior to the estimation of Rayleigh wave polarization, and vice versa. The method is applied to an extensive set of Global Seismographic Network data covering the years 1989-1998. Between 4244 and 15,075 measurements are collected for fundamental mode Love and Rayleigh waves at nine different periods (37 to 150 s). Measurement uncertainties are estimated using the statistics of observations for pairwise similar paths and are generally of the order of 15-50% of the total signal, depending on the period and the wave type. Large and azimuthally invariant angle anomalies are documented for several stations and are consistent with misorientation of the horizontal seismometers. Two schemes are employed to determine the misorientations: (1) an azimuthally weighted average at each station, and (2) a joint inversion for seismometer misorientation and globally heterogeneous phase velocities. The determined corrections are robust and correlate well with those reported in earlier studies. Azimuthally varying arrival angle anomalies are shown to agree qualitatively with predictions of wave refraction calculated for recent phase velocity maps, which explain up to 30% of the variance in the new measurements.