Foremost in response to Dr. Klemperer's Comment (2008), we wish to emphasize that neither the position nor the origin of a rigid indenter beneath Tibet is the primary object of our research. Rather, the general nature of mechanical layering through the Tibetan lithosphere, and the implications of those properties on vertical coupling, are our fundamental results.
Given that caveat, we acknowledge the spatial discrepancy between the location of the maximum in intermediate-wavelength topography, taken as an indicator of the northward indenter limit, and the limit of Indian crustal material imaged by a variety of seismic methods. There are several possible factors, which both mitigate this discrepancy and decrease our model constraints on complex structures at depth. They are (not in order of importance):
Spatial uncertainty in seismic inversions: Tomographic techniques vary in lateral resolution based on which particular phases are used, azimuthal distribution of arrivals, geometry of the seismometer array, depth of the velocity anomaly, and a variety of other factors. Klemperer (2008) does not provide formal uncertainties on his reported slab positions, although the scatter of positions in his Figure 1 probably reflects an appropriate uncertainty.
Along-strike geometry: Our model consists of a two-dimensional approximation to a strongly three-dimensional problem. This approach suffices to address the questions of mechanical coupling and crustal dynamics that constitute our primary research target, but does not provide an accurate spatial mapping of the indenter in three dimensions. Any change in the position of the indenter front with longitude in our targeted region would result in smearing and flattening of the topographic bulge that we take as a marker for the indenter position. As Klemperer notes, one approximation for the indenter front is parallel to the Himalayan arc itself, implying that the indenter front does have a strongly curved shape not considered in our methodology.
Vertical geometry: The reported model is also fairly insensitive to vertical geometry of the indenter. We find no difference in surface topography or stress coupling for a flat-fronted indenter or a prow-shaped indenter. However, these two different shapes would give very different results for different seismic observations, since the position of the indenter would then vary with depth, such that different seismic arrivals would map different positions for the slab.
Very low topographic slope: One of the most notable characteristics of our modeling results is the relatively low viscosity of the Tibetan middle and lower crust. The very low slope of the topographic bulge associated with flow requires this low viscosity. Although the low slope is critical to our inversion for viscosity, it also means that the position of the bulge maximum is relatively poorly constrained. That is, a stiffer material would produce a narrow, localized bulge given the same dynamics. Such a material would narrowly constrain the position of the indenter front. However, because our primary result is the low viscosity of the Tibetan crust, we inevitably lose spatial resolution of indenter position, especially when combined with factors 2 and 3, above.
Nonlinear dynamic effects: We have modeled the crustal flow dynamics using the simplest possible approximation of a Newtonian fluid. This method does not include any more complicated effects seen in nonlinear fluids, such as asymmetry and forward deflection of a “bow wave” structure, or complicated responses to indenter geometry. Any of these effects might serve to offset the topographic maximum from the actual spatial position of the rigid indenter.
The Lhasa block hypotheses: Our modeling exercise makes absolutely no attempt to explore the genetic origin of the rigid indenter. One possibility proposed by Klemperer is certainly possible, that the indenter front is stiff Tibetan upper and middle crust, rather than Indian upper and middle crust. Because we consider only the mechanical properties of the indenter, and not its history, any origin for the indenter is allowed.
To summarize, we emphasize that the primary result of this work is a mechanical and dynamic model for the central Tibetan Plateau, not a structural or evolutionary model. Dr. Klemperer's observations about the nature of a rigid indenter at depth in the crust beneath Tibet do not change the fundamental results relating to vertical coupling in Tibet determined in our study.