Seismic surface waves present a characteristic dispersion behavior in which different frequencies travel at different speeds. This characteristic dispersion curve depends on the shear and compressional wave velocity structure of the crust and upper mantle. These physical parameters can be estimated using some inversion method that can be 1D, 2D, or even 3D. 1D inversions are very common for their relative simplicity and speed. However, the dispersion is usually measured between two stations.
So my question is, where do we "place" the resulting 1D estimated model? Is it the average of the crust between the stations (I did the math for this once long ago and it seems that it is not, but I'm not sure)? Or is there no way to place the estimate at a single point?