An　adaptive　spectrum-broadening　method　ASBM　is　proposed　in　this　paper　to　improve　the　resolution　of　nonstationary　seismic　data.　We　construct　a　set　of　nonuniform　molecular　windows　by　solving　an　optimization　problem　such　that　in　each　window,　the　seismic　trace　is　approximately　stationary.　These　nonuniform　molecular　windows　are　used　to　produce　a　Molecular-Gabor　frame.　For　the　trace　segment　in　each　window,　the　spectrum-broadening　and　energy　compensation　are　performed　in　Molecular-Gabor　domain.　Subsequently,　a　high-resolution　version　of　the　nonstationary　seismic　data　can　be　obtained　after　inverse　Molecular-Gabor　transform.　Applications　of　this　method　to　both　synthetic　and　real　data　show　that　the　ASBM　can　expand　the　frequency　band　and　recover　the　absorbed　energy　of　the　nonstationary　seismic　trace　effectively,　and　this　method　also　works　well　for　a　general　earth　Q-model　that　varies　with　travel　time.　©　2011　Society　of　Exploration　Geophysicists.