Long-period Rayleigh waves from Iranian earthquakes have large amplitude asymmetries between minor arc and major arc arrivals (e.g., R2 and R3) at digital stations in the azimuth range N20¿W to N60¿E. These asymmetries are as large as a factor of 2 at a period of 256 s and persist to periods greater than 300 s. In some cases the entire Rayleigh wave group arrival spanning periods from 100 to 300 s is either uniformly enhanced in amplitude or diminished to such a degree that the group arrival appears to be missing. The amplitude anomalies are generally not accompanied by significant phase anomalies. The irregular azimuthal distribution of the amplitude asymmetries and their occurrence for events with different focal mechanisms and epicentral separations of several hundred kilometers preclude an explanation of these observations by source complexity. Events in the Mediterranean and Nepal do not produce similar amplitude asymmetries at the same stations. The anomalies are thus most likely due to focusing and defocusing propagation effects. As a preliminary investigation of the effects of lateral heterogeneity of upper mantle velocity structure on long-period surface wave amplitudes, surface wave ray-tracing calculations are performed using recently proposed global phase velocity distributions. Dramatic deviations from great circle paths are predicted for long propagation paths (e.g., R3). The particular spatial distribution of lateral velocity gradients around a given source location determines whether substantial amplitude asymmetries will be observed between minor acr and major acr arrivals and whether these will persist for sequential great circle orbits. The 200-s period amplitude asymmetry observed at KIP for the Iranian source region (R2,4≫R3) is well predicted by the ray-tracing results. The absence of this anomaly for the other source regions is also predicted. Other observed anomalies are not all well predicted, but it is clear that geometric effects can contribute significantly to the observed variations of Rayleigh and Love wave amplitudes. This is the probable explanation for the instability of Q estimates made from surface waves. Other source regions producing large surface wave amplitude anomalies include Japan and southeastern Alaska.