A method for estimating sonic slowness comprising: obtaining (700) a plurality of sonic waveforms are received by a plurality of receivers of a logging tool after emission of a source sonic wave by a transmitter, obtaining (710) slowness models of the subterranean formation, a slowness model being defined by a at least one cell of constant slowness for at least one wave energy mode, computing (720), for each slowness model, a set of candidate travel times, a candidate travel time of a set of candidate travel times being computed for a wave energy mode and a position of a receiver of the plurality of receivers, computing (730) a relevance indicator for each set of candidate travel times based on the recorded sonic waveforms; searching (740) a match between the sets of candidate travel times and the recorded sonic waveforms by searching a relevance indicator which is optimum, computing (750) a sonic slowness estimate for the subterranean formation from a set of candidate travel times for which the relevance indicator is optimum.