In oil and gas exploration, seismic arrays are deployed by geophycisists to image the subsurface. For passive seismic applications, the data recorded by the sensor array may contain velocity and angle information of the propagating seismic wave. This information can be used to infer the properties of material in different earth layers. In order to find the velocity and arrival angle, beamforming algorithms are applied to estimate the wavenumber-frequency spectrum for the seismic signals. The propagating seismic wave field consists of body waves and surface waves. In some applications, surface waves are interpreted as noise, thus filtering is required to remove the surface waves before or during the implemention of beamforming algorithms. In this thesis, we first introduce a data model. Then several beamforming algorithms based on the data model are discussed, and the performance of the different algorithms is evaluated. Capon beamforming as adopted in seismics has limitations. Robust Capon beamforming which can overcome these limitations is explained in the thesis. For filtering of the surface waves, we propose to first reconstruct the irregularly sampled spatial signal into a uniform array, then design a velocity filter to remove the unwanted low-speed noise (surface waves).