Parametric Matching Pursuit Methods to Reconstruct Seismic Data Acquired with Multichannel Sampling

In marine seismic data acquisition, multichannel sampling can occur in various scenarios, including over/under streamers, multicomponent streamer, and multicomponent ocean-bottom node. In these various multichannel sampling scenarios, each channel outputs samples of a filtered version of a seismic wavefield. These filters are different for each channel; the data are often coarsely and irregularly sampled. The objective is to reconstruct the unknown wavefield from the multichannel samples. In this paper, we discuss how parametric matching pursuit methods can be extended to solve such reconstruction problems. We give two examples based on data that a multicomponent streamer could record and show the form the reconstruction problem takes when two- and three-component data are available.