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Three-dimensional frequency-domain full waveform inversion of fixed-spread data can be efficiently performed in the viscoacoustic approximation when seismic modeling is based on a sparse direct solver. We present a new algebraic Block Low- Rank (BLR) multifrontal solver which provides an approximate solution of the time-harmonic wave equation with a reduced operation count, memory demand and volume of communication relative to the full-rank solver. We show some preliminary simulations in the 3D SEG/EAGE overthrust model, that give some insights on the memory and time complexities of the low-rank solver for frequencies of interest in fullwaveform inversion (FWI) applications.