Group velocities were previously determined using the FTAN approach. Phase velocities were determined from the two-station method. The object of the inversions was to obtain the most likely crustal and upper mantle shear velocity structure. Though surface waves are heavily dependent on the shear velocity, they also show a weak dependence on compressional wave velocity and, to a smaller extent, density. Compressional velocity in this study is tied to shear velocity using a Poisson's ratio of 0.27. Densities are assigned to be 2.5 g/cm³ in upper 5km of the crust, 2.8 g/cm³ from 5-70 km depth, and 3.3 g/cm³ below 70 km. We examine errors introduced by these assumptions a posteriori. The crust and upper mantle is treated as a layered 1-D structure with 10 km layers down to 120 km overlying a half space. Two 5 km layers in the shallow Earth, allow for slow near-surface velocities.

Using an arbitrary starting model, a damped least squares inversion is used to suggest optimum model improvements. The process is performed iteratively until the model converges on a solution. While the process typically converges within 2-4 iterations, the solution shows some dependence on the starting model. To account for this, we independently invert 500 randomly generated starting models. These initial models span the range of shear velocities observed in prior studies (figure 1 in Rapine et al). A master model was created to represent the average features of the previous Vs models. (Master Vs model) Each starting model was created by randomly perturbing the layer velocities of the master model by +-0.4 km/s. While there is scatter in the results, the standard deviation of the family of final models is 0.02-0.1 km/s depending on depth (2 std. is shown on plots). The largest variance is observed in the top 10 km. The frequencies associated with these depths are too high to be well-constrained by the 10-70 second surface waves examined here.

Using a wide variety of initial models, a consistent shear velocity structure is identified for each terrain.

Lhasa

The most striking result between the Lhasa and Qiangtang regions is the difference in upper mantle velocity. The velocity transition which presumably exists at the Moho (70-80 km depth) is smeared in both models. At these depths both models have shear velocities of ~4.2 km/s. In the Lhasa terrain, this velocity continues to increase to 4.6 m/s at 110 km depth, while in Qiangtang the upper mantle velocity remains nearly constant below the Moho. Comparison figure of the two velocity structures (.pdf) Both profiles show an increase in velocity at ~40 km depth. The Lhasa profile shows a slight depression of velocities in the mid-crust, however this is minimal. Perhaps more significant is that the Qiangtang region has consisitently slower shear velocities in the lower crust (40-70 km). The group and phase velocities are calculated for each initial and final model. While the surface wave velocities of the initial models vary wildly, they collapse to essentially the same curve after the inversions. The group velocities are fit extremely well while the phase velocities show cannot seem to converge to the exact data points. This implies that the observed data points perhaps have more error than the error bars imply. The errorbars represent only the range of values as observed along the array and not the actual measurement errors which might include location, timing and processing errors (a very hard thing to quantify). LEGEND MODEL PLOT: range of initial models: gray mean final model: black two std. of final models: blue dashed VELOCITY PLOT: Initial group velocity: pale blue Initial phase velocity: pink Final models: black Observed group velocity: blue Observed phase velocity: red Note: Only 10% of the initial velocity curves are shown for clarity.

Qiangtang

Poisson ratio assumption
The assumption of a constant Poisson ratio of 0.27 allows us to treat all compressional wave velocities in terms of shear velocity, thus reducing by half the number of parameters. This is done initially because surface wave velocities have been shown to be significantly more dependent on shear velocity than compressional velocity (see Aki and Richards, for example), and because a near constant Poisson ratio has been observed in many tectonic settings.

Tests of this assumption in the current study show this to be a valid assumption. All final modeling (as shown above) were carried out using a Poisson ratio of 0.27. The results obtained from tests using a constant ratio of 0.25 or 0.29 instead, resulted in shear velocity models which differed by < 0.03 km/s. This is far smaller than the two standard deviation error in the inversion process plotted above. Even if Poisson ratio is assumed to vary as a function of depth, the magnitude of these perturbations would not change the dominant features of the velocity profiles interpreted here.