Matching Pursuit Fourier Interpolation Research Articles

A comparative study of multidimensional Fourier reconstruction of 2D prestack seismic data

Multidimensional regularization and interpolation methods are an essential component of seismic data processing. Fourier reconstruction algorithms are efficient and straightforward to implement. Minimum Weighted Norm Interpolation (MWNI), Anti-Leakage Fourier Transform (ALFT), and Matching Pursuit Fourier Interpolation (MPFI) are examples of classical Fourier reconstructions techniques for prestack seismic data. MWNI estimates the Fourier coefficients that synthesize spatial data via a regularized inversion method. The MPFI and ALFT algorithms belong to the family of greedy algorithms, which determine Fourier coefficients iteratively. We provide an overview of the three Fourier based reconstruction algorithms mentioned above and compare them to access their strengths and weakness for processing prestack 2D land data. We conduct tests that highlight the capacity of Fourier techniques to reconstruct sparse seismic data and low-quality noisy land seismic data. We pay particular attention to adopting Fourier interpolation for data preconditioning before prestack time migration. We present a processing flow that can be utilized for new and vintage 2D onshore datasets, where preconditioning is essential to obtain high-quality migrated sections. In addition to synthetic examples, we present a real data study that corresponds to a vintage line from the Tacutu Basin, Northern Brazil, which was reprocessed and preconditioned with Fourier interpolation to improve prestack time migration images.

A model‐based data‐driven dictionary learning for seismic data representation

ABSTRACTPlanar waves events recorded in a seismic array can be represented as lines in the Fourier domain. However, in the real world, seismic events usually have curvature or amplitude variability, which means that their Fourier transforms are no longer strictly linear but rather occupy conic regions of the Fourier domain that are narrow at low frequencies but broaden at high frequencies where the effect of curvature becomes more pronounced. One can consider these regions as localised “signal cones”. In this work, we consider a space–time variable signal cone to model the seismic data. The variability of the signal cone is obtained through scaling, slanting, and translation of the kernel for cone‐limited (C‐limited) functions (functions whose Fourier transform lives within a cone) or C‐Gaussian function (a multivariate function whose Fourier transform decays exponentially with respect to slowness and frequency), which constitutes our dictionary. We find a discrete number of scaling, slanting, and translation parameters from a continuum by optimally matching the data. This is a non‐linear optimisation problem, which we address by a fixed‐point method that utilises a variable projection method with ℓ1 constraints on the linear parameters and bound constraints on the non‐linear parameters. We observe that slow decay and oscillatory behaviour of the kernel for C‐limited functions constitute bottlenecks for the optimisation problem, which we partially overcome by the C‐Gaussian function. We demonstrate our method through an interpolation example. We present the interpolation result using the estimated parameters obtained from the proposed method and compare it with those obtained using sparsity‐promoting curvelet decomposition, matching pursuit Fourier interpolation, and sparsity‐promoting plane‐wave decomposition methods.

Dealing with spatial sampling sparseness and irregularity in 3D OBC seismic data offshore Abu Dhabi

Due mainly to commercial and operational constraints, seismic data are often sparsely and irregularly sampled, leading to several challenges in processing of 3D OBC seismic data offshore Abu Dhabi. Conventional linear noise attenuation techniques based on multi-channel filters are not effective with Scholte waves as they are usually aliased with typical sampling intervals in 3D OBC seismic data (e.g., 25 m source and receiver point intervals), and sometimes scattered because of near-surface heterogeneity. To address them, we apply model-based surface wave attenuation, Surface Wave Analysis Modelling and Inversion (SWAMI), which enables an estimate of local near-surface properties by analysing dispersion curves. Thus, both direct and scattered Scholte waves are effectively modelled and attenuated without suffering from under-sampling. A data interpolation and regularization technique called Matching Pursuit Fourier Interpolation (MPFI) is then applied to enhance spatial sampling. MPFI employs an anti-aliasing capability so optimum data reconstruction can be performed for any frequency range. In addition to the regularization aspect, MPFI with a 5D implementation (4 spatial coordinates and time) is targeted to densify receiver line interval and extend source lines, which consequently enhances fold, offset and azimuth distributions of the data.The implementation of the two techniques successfully addresses processing challenges in sparsely and irregularly sampled OBC seismic data.

Innovative Processing Approaches to Overcome Sampling Sparseness and Irregularity in 3D OBC Seismic Data Offshore Abu Dhabi

Due mainly to commercial and operational constraints, seismic data are often sparsely and irregularly sampled, leading to several challenges in processing of 3D OBC seismic data offshore Abu Dhabi. Conventional linear noise attenuation techniques are not effective with Scholte waves as they are usually aliased with typical sampling interval in 3D OBC seismic data, and sometimes scattered because of near-surface heterogeneity. To address this, we apply model-based surface wave attenuation, Surface Wave Analysis Modeling and Inversion (SWAMI), which enables an estimate of local near-surface properties by analysing dispersion curves. Thus, both direct and scattered Scholte waves are effectively modelled and attenuated without suffering a lack of spatial sampling. We also highlight the shortcomings of the application of interferometry to scattered noise attenuation for sparse acquisition geometry. Matching Pursuit Fourier Interpolation (MPFI) is then implemented to deal with insufficient sampling in crossline direction caused by acquisition geometry. MPFI employs anti-aliasing capability so optimum data reconstruction can be performed for any frequency ranges. In addition to regularization aspect, MPFI with 5D implementation (4 spatial coordinates and time) is targeted to densify receiver line interval and extend source lines, which consequently enhances fold, offset and azimuth distributions of the data.