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.
Phase mismatches sometimes occur between final processed seismic sections and zero-phase synthetics based on well logs-despite best efforts for controlled-phase acquisition and processing. Statistical estimation of the phase of a seismic wavelet is feasible using kurtosis maximization by constant phase rotation, even if the phase is nonstationary. After estimation, we achieve space-and-time-varying zero-phasing by phase rotation. We demonstrate how a statistical analysis provides pertinent information about the data that can be used for zerophasing, as a quality control to check deterministic phase corrections, or even as an interpretational tool for highlighting areas of potential interest or areas of potential wavelet instability.
Motivated by the desire for greater resolution in PS data, and an interest in methods designed to produce this, we have explored some fundamental concepts of PS resolution in order to better understand proposed methods. Our study has produced three key results: PS-to-PP mapping using either interval or average velocity ratios yields identical results. Although mapping changes the bandwidth of the PS signal, it does not change its wavelength or resolution. Modest increases in resolution can be realized after mapping if the wavelet is known, but any method designed to increase bandwidth without such knowledge should be treated with caution.
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