I am looking to estimate de depth to the lithosphere-asthenosphere boundary and the Vp and Vs structure beneath some stations. I wonder if this can be accomplished by inverting teleseismic receiver function for the station.
Mariano you should read "Fischer, K. M., H.A. Ford, D.L. Abt, and C.A. Rychert (2010), The Lithosphere-Asthenosphere Boundary, Annu. Rev. Earth Planet. Sci., 38(1), 551–575, doi:10.1146/annurev-earth-040809-152438.". She explains how to pick the LAB using different methods.
However estimating the LAB using receiver functions alone is complicated due to the nature of the LAB. It is better to combine your receiver function analysis with other methods, for example shear wave tomography. I did that in my research and is published in EPSL called " Lithospheric Expression of Cenozoic Subduction, Mesozoic Rifting and the Precambrian Shield in Venezuela".
Also in the past during AGU fall meetings I heard several talks indicating how the LAB estimation from receiver functions and other methods can lead to different results unless there is a joint interpretation and they gave some examples. If I remember correctly one of the talks was given by Meghan Miller.