A procedure for retrieving the attenuation operator for SH-polarized multiple ScS waves by spectral stacking is outlined. Application of the procedure to 17 multiple ScS phase pairs from 5 western Pacific deep-focus events digitally recorded at Kipapa, Hawaii, and Matsushiro, Japan, yields the following results: (1) Stable estimates of the phase and amplitude response of the attenuation operator are obtained in the frequency interval 6 mHz-60 mHz; (2) Within this band the apparent Q for ScS waves multiply reflected beneath the western Pacific is 156¿13. No significant variation of Q as a function of frequency is observed; (3) Within this band no significant dispersion of multiple ScS waves is observed. However, given the uncertainties in the estimates of the phase response, the existence of the dispersion predicted by linear, causal, constant-Q models is compatible with the observations.