Reflectivity　inversion　methods　based　on　a　stationary　convolution　model　are　essential　for　seismic　data　processing.　They　compress　the　seismic　wavelet,　and　by　broadening　the　bandwidth　of　seismic　data,　they　assist　the　interpretation　of　seismic　sections.　Unfortunately,　they　do　not　apply　to　realistic　nonstationary　deconvolution　cases　in　which　the　seismic　wavelet　varies　as　it　propagates　in　the　subsurface.　Deep　learning　techniques　have　been　proposed　to　solve　inverse　problems　in　which　networks　can　behave　as　the　regularizer　of　the　inverse　problem.　Our　goal　is　to　adopt　a　semisupervised　deep　learning　approach　to　invert　reflectivity　when　the　propagating　wavelet　is　considered　unknown　and　time-variant.　To　this　end,　we　have　designed　a　prior-engaged　neural　network　by　unrolling　an　alternating　iterative　optimization　algorithm,　in　which　convolutional　neural　networks　are　used　to　solve　two　subproblems.　One　is　to　invert　the　reflectivity,　and　the　other　is　to　estimate　the　time-varying　wavelets.　In　general,　it　is　well　known　that,　when　working　with　geophysical　inverse　problems　such　as　ours,　one　has　limited　access　to　labeled　data　for　training　the　network.　We　circumvent　the　problem　by　training　the　network　via　a　data-consistency　cost　function　in　which　seismic　traces　are　honored.　Reflectivity　estimates　also　are　honored　at　spatial　coordinates　in　which　true　reflectivity　series　derived　from　borehole　data　are　available.　The　cost　function　also　penalizes　time-varying　wavelets　from　varying　abruptly　along　the　spatial　direction.　Experiments　are　conducted　to　find　the　effectiveness　of　our　method.　We　also　compare　our　approach　to　a　nonstationary　blind　deconvolution　algorithm　based　on　regularized　inversion.　Our　findings　reveal　that　the　developed　method　improves　the　vertical　resolution　of　seismic　sections　with　noticeable　correlation　coefficient　improvements　over　the　nonstationary　blind　deconvolution.　In　addition,　our　method　is　less　sensitive　to　initial　estimates　of　nonstationary　wavelets.　Moreover,　it　needs　less　human　intervention　when　setting　parameters　than　regularized　inversion.　©　2023　Society　of　Exploration　Geophysicists.　All　rights　reserved.