Long-period wave propagation in the upper mantle is investigated by constructing synthetic seismograms for proposed models. A model consisting of spherical layers is assumed. Generalized ray theory and the Cagniard-de Hoop method is used to obtain the transient response. Preliminary calculations on producing the phases P and PP by ray summation out to periods of 50 sec is demonstrated, and synthetic seismograms for the long-period World Wide Standard Seismograph Network (WWSSN) and Long Range Seismic Measurement (LRSM) instruments are constructed.

Models containing prominent transition zones as well as smooth models predict a maximum in the P amplitude near 20°. The LRSM synthetics are quite similar for the various models because the instrument is relatively narrow-band, peaked at 20 sec. The upper mantle appears smooth at wavelengths greater than 200 km. On the other hand, the WWSSN synthetics are very exciting for models containing structure. The triplications are apparent and the various pulses contain different periods.

The amplitude of the P phase at 30° is down to about 25 per cent of its 20° maximum. The amplitude of the PP phase at 35° is comparable to P. Near 37°, the PP phase grows rapidly reaching about twice the P phase amplitude near 40°. Models containing sharp transition zones produce high-frequency interferences at neighboring ranges. A profile of observations is presented for comparison.

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