Imaging multichannel seismic data for amplitude inversion is a challenging task. The process seeks an inverse for a matrix of very high order that relates the data to a reflectivity model. Due to the irregular coverage of 3D surveys, the matrix is ill-conditioned and its coefficients are badly scaled. In this dissertation, I present a new approach for imaging irregularly sampled 3D data. The strategy is to reduce the size of the full matrix by reducing the size of 3D prestack data before imaging, and to balance the coefficients of the matrix by regularizing the coverage of 3D surveys. I tackle the case of Kirchhoff imaging operators because of their I/O flexibility and computational efficiency. However, after regularization, full-wave extrapolation techniques may become attractive and practical to implement on the regularly sampled prestack volume.
For adequately sampled 3D data with varying surface coverage, I use an asymptotic approximate inverse to obtain a good image. I apply a new partial prestack operator named azimuth moveout (AMO) to reduce the size of the prestack data and regularize its coverage by partial stacking. The effects of irregular coverage and varying illumination at depth are reduced by applying a diagonal transformation to the Kirchhoff operator.
Problems arise in 3D reflection seismology where fine sampling is not possible and the sparse geometry of 3D surveys results in spatial aliasing. I develop a new dealaising technique which I refer to as inversion to common offset (ICO). Posing partial stacking as an optimization process, the inversion improves the stack when the data are spatially aliased. I present two formulations for ICO, namely data-space and model-space inversion and design an efficient implementation of the algorithm in the Log-stretch Fourier domain. To accelerate the convergence of the iterative solution I present a new technique for preconditiong the inversion based on row and column scaling.
Results from field marine and land surveys are presented to demonstrate the application of AMO and ICO for regularizing the coverage of 3D surveys and reducing the costs of 3D prestack imaging. The images obtained by prestack migration after regularization are superior to those obtained by migrating the irregularly sampled data. Furthermore, ICO provides a promising approach for reducing the costs of 3D acquisition.