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.

We propose a new scheme for high-resolution amplitudevariation-with-ray-parameter ͑AVP͒ imaging that uses nonquadratic regularization. We pose migration as an inverse problem and propose a cost function that uses a priori information about common-image gathers ͑CIGs͒. In particular, we introduce two regularization constraints: smoothness along the offset-ray-parameter axis and sparseness in depth. The two-step regularization yields high-resolution CIGs with robust estimates of AVP. We use an iterative reweighted leastsquares conjugate gradient algorithm to minimize the cost function of the problem. We test the algorithm with synthetic data ͑a wedge model and the Marmousi data set͒ and a real data set ͑Erskine area, Alberta͒. Tests show our method helps to enhance the vertical resolution of CIGs and improves amplitude accuracy along the ray-parameter direction.

This paper presents a 3D least-squares wave-equation migration method that yields regularized common-image gathers (CIGs) for amplitude-versus-angle (AVA) analysis. In least-squares migration, we pose seismic imaging as a linear inverse problem; this provides at least two advantages. First, we are able to incorporate model-space weighting operators that improve the amplitude fidelity of CIGs. Second, the influence of improperly sampled data (footprint noise) can be diminished by incorporating data-space weighting operators. To investigate the viability of this class of methods for oil and gas exploration, we test the algorithm with a real-data example from the Western Canadian Sedimentary Basin. To make our problem computationally feasible, we utilize the 3D common-azimuth approximation in the migration algorithm. The inversion algorithm uses the method of conjugate gradients with the addition of a ray-parameter-dependent smoothing constraint that minimizes sampling and aperture artifacts. We show that more robust AVA attributes can be obtained by properly selecting the model and data-space regularization operators. The algorithm is implemented in conjunction with a preconditioning strategy to accelerate convergence. Posing the migration problem as an inverse problem leads to enhanced event continuity in CIGs and, hence, more reliable AVA estimates. The vertical resolution of the inverted image also improves as a consequence of increased coherence in CIGs and, in addition, by implicitly introducing migration deconvolution in the inversion.

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