Seismic data acquisition plays a crucial role in identifying potential oil and gas reservoirs during the early phases of exploration.However, obtaining finely sampled seismic data can be costly and physically impossible.Although random sampling improves acquisition efficiency,it shifts the burden from seismic acquisition to data processing. Among the various techniques proposed for wavefield reconstruction, matrix completion methods are computationally efficient and straightforward to implement.These methods exploit the low-rank structure of fully seismic data.However,matrix completion degrades at higher frequencies due to the failure of low-rank structure to accurately approximate higher frequencies. This thesis proposed a recursively weighted matrix completion method and a more efficient method for handling 2D seismic data was also proposed.Compared to 2D seismic data, 3D seismic data can detect reflections outside of the 2D plane but poses a computational challenge due to its large scale.This thesis proposed a parallel weighted reconstruction method to improve the reconstruction of 3D seismic data. Land seismic data presents a greater challenge due to contamination by ground roll, which consists of surface waves with a high spatial frequency content and large amplitude.A practical workflow was proposed in this thesis to improve the recovery of land seismic data.Although matrix completion is an efficient technique for reconstructing fully seismic data, the optimal acquisition design is still being investigated. Recent studies have shown that the spectral gap can be used to predict and characterize the quality of wavefield reconstruction via matrix completion for a given subsampling mask.Based on these findings, a simulation-free seismic survey design for both 2D and 3D seismic data was proposed in this thesis to obtain an improved subsampling survey by minimizing the spectral gap ratio.This concept was extended to the design of a time-lapse seismic survey. A time-lapse seismic survey design that incorporates the joint recovery model with spectral gap was proposed to generate sparse,non-replicated time-lapse acquisition geometries that favor wavefield recovery.