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Multisource Full Waveform Inversion (FWI) of phase-encoded supergathers has shown great promise in reducing the computational cost of conventional FWI. But for land- or marine-streamer acquisition geometry this approach faces the challenge of erroneous misfit due to the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite-difference modeling method. To tackle this mismatch problem, a key enabling frequency selection strategy is described: At each FWI iteration, we assign a unique frequency band to each shot gather, so that the spectral overlap among those shots-and therefore their crosstallk-is zero. Consequently, each receiver can unambiguously identify and then discount the superfluous sources-those that are not associated with the receiver in the streamer acquisition. This strategy allows significant speedup of FWI.