Surface wave focusing effects: Numerical modeling and statistical observations

Most techniques used in seismological practice have been performed under the assumption that surface waves propagate along great circle arcs between the epicenter and the station. However, lateral variations of surface wave phase velocities should result in deviation of the wave paths from great circle arcs and in corresponding anomalies of geometrical spreading (so-called focusing effect). We performed numerical modeling of these effects using the ray approximation on the basis of recent global phase velocity maps for fundamental Rayleigh mode obtained by tomographic inversion in the period range from 60 to 150 s.The aim for such a modeling is to investigate where the conventional methods based on using great circles as paths fail, and to obtain quantitative characteristics for the effects of rays focusing.Predicted and observed focusing effects are analyzed from a statistical point of view on a dataset of real seismic data. Records of earthquakes in a wide magnitude range (6 < Ms < 7) and with epicenters in different seismic regions are used for the analysis (over 3000 measurements). Synthetic and observed Rayleigh wave amplitude spectra are found to be in better agreement when the focusing effect is taken into account: correction of spectra for predicted focusing effect significantly improves the fit of synthetics to observations at periods larger than 75 s.Calculation of focusing effect based on ray theory ignores the effects of wavefront smoothing which increases with increasing period. However, even this approximation gives considerable improvement of synthetics at periods up to 150 s and, therefore, can be used in many applications, such as seismic source studies, magnitude measurements, and Q estimates.We also demonstrated that the discrepancy between real data and synthetics cannot be explained by attenuation effects. It means that there is still large room for improvement of the existing tomographic models which, in order to correctly explain observed amplitudes, must include heterogeneity of anisotropy and anelasticity up to higher degree.