Which component in a 3-component Sp receiver function is the actual Sp RF?
I am not sure I clearly understand the question, but here is a quote from the paper that I looked at a while ago about S Receiver Functions.

From: Yuan, Xiaohui, Rainer Kind, Xueqing Li, and Rongjiang Wang. " The S Receiver Functions: Synthetics and Data Example ." Geophysical Journal International 165.2 (May, 2006): 555-564:

"Here we briefly summarize the processing steps for generating S receiver functions. The ZNE-component seismograms of S and SKS waves are rotated firstly into the ZRT system with the back azimuth determined by locations of the receiver and earthquake. The ZRT components are further ro-tated into the P-SV-SH system with the incidence angle determined by minimizing the amplitudes at time of S/SKS arrival on the P component. Waveforms are visually selected to avoid the confusing of S and SKS phases. Data with strong interference of S and SKS are excluded. A window of S/SKS waves on the SV component is deconvolved from the P component for source equalization. For direct comparison with the P receiver functions, we need to reverse the time axis as well as the amplitudes of the S receiver functions.Move-out correction is then applied for all the PRFs, SRFs and SKSRFs, with a reference slowness of 6.4 s deg−1 and the IASP91 model as reference."

Does this help?