Matching Pursuit Methods Applied to Multicomponent Marine Seismic Acquisition – The Issue of Crossline Aliasing

A variational formulation for interpolation of seismic traces with derivative information

“…Most of the ideas however carry over to higher dimensions. Other methods that have been proposed in the literature to address the problem of seismic interpolation are those using sparsity constraints and suitable representations [5,47], alternating projection methods (POCS) [1,18,41], specialized filters [15,39] and matching pursuit methods [31,48,49] to name a few. There are several suggestions in the literature concerning rank minimization formulations, see for instance [6,19,25,26,40,42] that all address higher-dimensional interpolation problems.…”

A Study of Different Greedy Algorithms for Crossline Wavefield Reconstruction Using Multimeasurement Towed Marine Data

“…All methods approximate the measured data ݉ሺ‫ݕ‬ሻ ‫א‬ ԧ ଷே ೞ ൈଵ comprising the total ܸ ௬ , ܸ ௭ and P wavefields by sums of "ghosted" basis functions (BFs). The basis functions are complex exponentials parameterized by the crossline spatial wavenumber (Özbek et al 2010;Vassallo et al 2011). The expansion coefficients appear in each of the three approximating series, but the ghost operators for the different measurements differ.…”

“…The ghost operators define mappings of the upgoing pressure wavefield to different measurements of the total wavefield and provide GMP with a deghosting capability. Vassallo et al (2011) demonstrated that GMP, being a data-dependent technique, can reconstruct data beyond the spatial bandwidth limitations predicted by Papoulis.…”

Directional interpolation of multicomponent data

“…The measurement of the crossline component, on the other hand, has been motivated by the challenge of interpolating data in between sparse measurements in the crossline direction. Popular methods recently developed for using this extra measurement in the interpolation of pressure data are based on Fourier reconstruction and the theory of matching pursuit, for example, as documented in Vassallo et al (2011). Fourier reconstruction/interpolation methods share the assumption that the spectrum of a given signal is sparse; however, they are challenged by spatial aliasing (Naghizadeh 2016).…”