Multichannel wavefield reconstruction using smooth slope information from multicomponent data

Local slopes carry useful information about the directionality of the predominant events in a seismic dataset and therefore can be used to steer the reconstruction process of sparsely sampled data. However, in the presence of spatial aliasing (for example, in the crossline direction of streamer data), conventional algorithms fail to provide a reliable estimate of such slopes and only low-frequency, smooth versions of the slope field can be produced. We show that provided the availability of multi-component data, and more precisely the pressure wavefield and its first-order gradient, such slopes are naturally embedded in the data and can be easily obtained by smoothed division of those wavefields. We further show that the estimated slopes can be used as regularization in a multi-channel sparse interpolation problem, providing additional guidance to the reconstruction process compared just using the pressure data and its gradient at the available traces. Numerical examples on 2D and 3D datasets confirm the effectiveness of the proposed two-stage process for multi-channel seismic data reconstruction.