Time-lapse full waveform inversion (FWI) has the potential to reveal high-resolution reservoir production-related velocity changes. However, time-lapse FWI can introduce inversion artifacts, which might mask the true time-lapse signature within the reservoir zone, especially for the inversion of field data examples. We implement sequential bootstrap time-lapse FWI on marine seismic data from North Australia and observe noticeable inversion artifacts. To better understand these time-lapse FWI artifacts, we implement time-lapse FWI using the seismic data with different frequency bands and observe the distribution of the potential true time-lapse signature and inversion artifacts.On the inverted δVp (P wave velocity change) models using data with different frequency bands, the distribution of inversion artifacts exhibits inconsistencies, while the inverted δVp at the reservoir remains consistent. In order to comprehend these observations, we analyze the origin of these time-lapse artifacts from a theoretical perspective and find that a portion of these artifacts may arise from inversion null space and differences in data residuals between baseline and monitoring inversions. Building on these insights, we develop a novel time-lapse FWI method to suppress these inversion artifacts. We use the energy of the inverted δVp utilizing data with a lower dominant frequency band as a gradient-weighting term for time-lapse FWI using data with a higher dominant frequency band. The test of the novel time-lapse FWI method on marine data demonstrates its capability to suppress inversion artifacts effectively. The inverted δVp primarily reflects the 4D response, which is interpreted to be the softening of the reservoir caused by gas coming out of the solution within the oil column due to a pressure drop within the reservoir. To validate this data-driven research solution, we conduct tests on the SEG Advanced Modeling 4D (SEAM4D) model and synthetic 4D data where we know the true underlying earth models and time-lapse reservoir changes.