We calculated the ratio of SH wave radiation pattern coefficients for two cases: (1) Epicentral distance (100 km) was the same and azimuthal difference was δθ for a station pair (Fig. 15a) and (2) azimuth from source to stations was the same, and interstation distance caused difference in epicentral distance for a station pair (Fig. 15b).
The coverage of 289,000 ray paths in total, from sources to stations, provides dense sampling over the study area.
where A(f) is the source amplitude, r i is the distance from the source to the station i, S i (f) is the site amplification factor at ith station, and B encompasses the quality factor Q and the average velocity of the medium β such that B=pi f/Qbeta.
The travel-time for surface-wave propagation from a source to a station includes two phase-delay times: one from the source, including the rupture directivity (i.e., finite faulting) and initial phase; the other from the path effect due to propagation from the source through the Earth's structure to the station.
Taking into account the path effect due to the Earth's structure, this study calculates the theoretical Rayleigh wave travel-time (tcal) from the source to the station through a known global surface-wave phasevelocity map derived by Trampert and Woodhouse (2001) (also see Fig. 2 and Appendix A).
For the calculation of ray path from a source to a station and incident angle, we divide the analyzed region into four areas depending on the velocity structure used for the hypocenter determination of local events (Tsukuda et al., 1992; Ito et al., 1995) (Fig. 2 and Fig. 3).
Following Trampert and Woodhouse (1995, 2001) and Zhang and Lay (1996), the travel-time anomaly (Δt) from the source to the station along the great-circle path can be written as: (A.1) where is the reference phase-velocity calculated from the PREM model (Dziewonski and Anderson, 1981), and is the phase-velocity perturbation relative to at position where θ is co-latitude and φ is longitude.
In order to show how Lg wave propagation patterns are drastically modified by interaction with crustal heterogeneities and can be totally blocked by crustal barriers such as the central Sea of Japan, we show a set of snapshots in a vertical section by cutting the FDM model along a profile from the source to a station, together with a record section of synthetic seismograms along the profile.
From these results, we suggest that beating processes in the ionosphere with a spatially distributed ionospheric source can cause pearl structures during the ionospheric duct propagation from high to low latitudes, with long distances from the source to the stations.
Under these conditions, the phase differences of surface waves between two stations are caused by the differential distance (AB′) between a farther station (A) and a point (B′) projected from the nearer station (B) onto the great circle path (AE) from the source to the far station (Fig. 2), so that the measured phase velocities are averages over the differential distance (AB′).
