He, B. and Wu, G., 2015. A slim approximate Hessian for perturbation velocity inversion with incomplete reflection data. Journal of Seismic Exploration, 24: 281-304. A recent velocity model building is the full waveform inversions (FWD that allow to recover the long-scale structures through the refraction waves and diving waves, and the short-scale structures which provide the high-resolution component through the reflection waves. However, incomplete seismic data include non-geological artifacts in the gradient for velocity update. The strong off-diagonal elements of approximate Hessians are important to reflection FWI with incomplete data; however, it is difficult to implement an approximate Hessian using the forward modeling method because of the cost of the computation efficiency. In this study, we investigate the ability of an approximate Hessian to remove artifacts that are caused by incomplete reflection data. In order to reduce the costs associated with calculating the Hessian, the large model is separated into sparse sub-models, and an alternative slim approximate Hessian is implemented sequentially on these sub-models. Afterwards, The complete model is obtained from sub-model using the radial point interpolation method (RPIM). A two-dimensional flat-layers synthetic example provides a reasonable test case for our method. We find that the slim approximate Hessian removes non-geophysical artifacts as effectively as the approximate Hessian, but has the advantages of greater cost-efficiency and lower memory requirements.