The moment tensor inversion method for long-period Rayleigh waves is discussed from the point of view of event-depth resolution. In this method, depth is usually determined by finding the minima in appropriate least squares residuals versus depth curves. We show that depth cannot be resolved if the data are sampled only at one frequency and a choice of frequencies spanning a wide range of values yields better resolution. We also show that the variance reduction at the minimum depends strongly on biases in the data, provided they are not simple &pgr;-periodic functions in azimuth from the source. Since such biases are introduced, in particular, when the propagation corrections are inaccurate, this provides a means by which to study regional trends of phase velocities. This method is then applied to obtain an estimate of lateral heterogeneity in Central Asia. Starting with a reference point in the Pamir mountains and a set of accurately known phase velocities on paths to Eurasian WWSSN stations, we study the Rayleigh waves at these stations, in the period range 30 to 90 s, for eight events located in or near the Tibet Plateau, at increasing distances from the reference point. The scale of heterogeneity in phase velocity is thus found to be about 1000 to 1500 km in this period range. Constraining the source parameters of the most distant events by body wave modeling, we determine new phase velocities on paths to WWSSN stations from the center of the Tibet Plateau. The variation of phase velocity with source location reaches 1 to 2%, and the low velocity within Tibet clearly has a dominant effect. We then discuss the regionalization of phase velocities as a possible way to determine a calibration curve for a given source-to-receiver path. We find that although the regionalized phase velocities in Eurasia are stable to first order, they do not seem accurate enough to be used for moment tensor inversions with arbitrary source locations. This may be due to non ray theoretical effects causing the breakdown of phase velocity additivity when higher order accuracy is needed. On the other hand, reference phase velocities on source-receiver paths can be obtained reasonably fast for events large enough so that body wave modeling is possible to constrain depth and source mechanism. We demonstrate that these phase-velocity curves are accurate enough for the calibration of propagation effects for another event located as much as 400 to 500 km away. This provides an encouraging approach to study both structure and source mechanisms of smaller events within a highly heterogeneous continental region. The only constraint is to find several events with the right magnitude of both long-period body waves and surface waves.