We apply a recently developed method based on the instantaneous frequency to analyze broadband seismic data recorded by the transportable USArray. We measure in the frequency band [0.018-0.2] Hz about 700 high-quality differential ScS-S anelastic delay times, delta t*(ScS-S), sampling the mantle below Central America and below Alaska that we compare to elastic delay times, delta t(ScS-S), obtained by cross-correlating the S and ScS signals. We confirm that the instantaneous frequency matching method is more robust than the classical spectral ratio method. By a series of careful analyses of the effects of signal-to-noise ratio, source mechanism characteristics and possible phase interferences on measurements of differential anelastic delay times, we demonstrate that in order to obtain accurate values of delta t*(ScS-S) the seismic records must be rigorously selected. In spite of the limited number of data that satisfy our quality criteria, we recover, using an additional stacking procedure, a clear dependence of delta t*(ScS-S) on the epicentral distance in delta the two regions. The absence of correlation between the obtained anelastic and elastic delay-times indicates a complex compositional-thermal origin of the attenuation structure, or effects of scattering by small scale structure, in accordance with possible presence of subducted material. The regional 1-D inversions of our measurements indicate a non-uniform lower mantle attenuation structure: a zone with high attenuation in the mid-lower mantle (Q(mu)approximate to 250) and a low attenuation layer at its base (Q(mu)approximate to 450). A comparison of our results with low-frequency normal-model Q models is consistent with frequency-dependent attenuation with Q(mu)proportional to omega(alpha) and alpha = 0.1-0.2 (i.e. less attenuation at higher frequencies), although possible effects of lateral variations in Q in the deep mantle add some uncertainty to these values.