Seismic data interpolation by greedy local Radon transform

Abstract

We propose a greedy inversion method for a spatially localized, high-resolution Radon transform. The kernel of the method is based on a conventional iterative algorithm, conjugate gradient (CG), but is utilized adaptively in amplitude-prioritized local model spaces. The adaptive inversion introduces a coherence-oriented mechanism to enhance focusing of significant model parameters, and hence increases the model resolution and convergence rate. We adopt the idea in a time-space domain local linear Radon transform for data interpolation. We find that the local Radon transform involves iteratively applying spatially localized forward and adjoint Radon operators to fit the input data. Optimal local Radon panels can be found via a subspace algorithm which promotes sparsity in the model, and the missing data can be predicted using the resulting local Radon panels. The subspacing strategy greatly reduces the cost of computing local Radon coefficients, thereby reducing the total cost for inversion. The method can handle irregular and regular geometries and significant spatial aliasing. We compare the performance of our method using three simple synthetic data sets with a popular interpolation method known as minimum weighted norm Fourier interpolation, and show the advantage of the new algorithm in interpolating spatially aliased data. We also test the algorithm on the 2D synthetic data and a field data set. Both tests show that the algorithm is a robust antialiasing tool, although it cannot completely recover missing strongly curved events.

Localization of marine seismic vibrator based on hyperbolic Radon transform

“…Since the Radon transform processes multichannel data simply, it is frequently applied to seismic data analysis [31][32][33][34][35][36][37].…”

Dreamlet-based interpolation using POCS method

“…Methods for interpolation can be divided into three categories (Gao et al, 2013): First, methods based on mathematical transform and signal analysis Naghizadeh and Innanen, 2011;Naghizadeh and Sacchi, 2010;Trad et al, 2002;Wang et al, 2010); second, prediction filter based methods (Naghizadeh and Sacchi, 2007;Spitz, 1991); third, interpolation methods based on wave equation (Ronen, 1987). In the past several years, rank-reduction method (Gao et al, 2013;Kreimer et al, 2013;Ma, 2013) has also played an important role in seismic data interpolation.…”

The utilization of the double focal transformation for sparse data representation and data reconstruction

“…; Zwartjes and Gisolf ; Zwartjes and Sacchi ; Zwartjes and Gisolf ; Trad ; Naghizadeh ); the linear, parabolic, and hyperbolic Radon transformation (Kabir and Verschuur ; Herrmann et al . ; Trad ; Trad, Ulrych, and Saachi ; Wang, Ng, and Pez ; Verschuur, Vrolijk, and Tsingas ; and the curvelet transformation (Hennenfent and Herrmann ; Hennenfent, Fennelent, and Herrmann ; Naghizadeh and Sacchi ). Often, these methods are better suited to describe the data in the mid‐ and far‐offset ranges.…”