We discuss a TSVD (truncated singular value decomposition) optimization scheme for history matching. We are particularly interested in studying the performance of TSVD under integration of P-wave velocity data. We compare the structure of the main singular value triplets with or without time-lapse seismics. We then analyze the impact of introducing the seismics in a synthetic two-phase model problem. We observe in our experiments a strong regularization of the inversion algorithm due to the seismics. At the same time, we obtain much better reservoir descriptions when 4D seismics is available.