Time lapse surface seismic experiments have been proposed for monitoring CO2 injection in the subsurface. To monitor the CO2 effect on surface seismic data, precise analysis of 4-D seismic is needed to capture small changes between pre- and post-injection seismic data. We introduce a new technique - Basis Pursuit Inversion (BPI) - to invert for seismic reflection coefficients that has the potential to produce clearer images of subsurface structures than the conventional inversion methods. We demonstrate the application to a pre-injection seismic data volume from Cranfield, which has been a site for carbon sequestration study since 2007. Applications of BPI on the pre-injection seismic data reveal more detailed structure and rock property information and thus has the potential for resolving CO2 plume movement during time-lapse seismic study.