On the Role of Priors in Generalized Matching Pursuit to Reconstruct Wavefields from Multicomponent Streamer Data

In conventional single-component data acquisition, a common way to solve the problem of reconstructing aliased seismic data is to use priors that are computed at low frequencies and applied at high frequencies. In contrast, parametric matching pursuit methods such as Generalized Matching Pursuit applied on multicomponent data do not need priors in most conditions to achieve accurate reconstruction under aliasing. In this paper, we examine how and when soft priors can provide further robustness to multichannel matching pursuit algorithms. We illustrate our concepts on synthetic data generated by finite-difference modelling and on data acquired by a 3D-4C towed cable array. We find that multicomponent data allow matching pursuit algorithms to compute and use the priors in ways that are not possible with single-component data. For instance, the priors can be estimated by matching pursuit within an intermediate temporal frequency band, where the signal-to-noise ratios of all the components are high, while the data are already subject to spatial aliasing. The priors generated at these intermediate frequencies can then be used at higher frequencies where the aliasing is stronger, and also at lower frequencies, still aliased and affected by stronger noise.