Numerical integral operators of convolution type form the basis of most wave-equation-based methods for processing and imaging of seismic data. As several of these methods require the solution of an inverse problem, multiple forward and adjoint passes of the modeling operator are generally required to converge to a satisfactory solution. This work highlights the memory requirements and computational challenges that arise when implementing such operators on 3D seismic datasets and their usage for solving large systems of integral equations. A Python framework is presented that leverages libraries for distributed storage and computing, and provides a high-level symbolic representation of linear operators. A driving goal for our work is not only to offer a widely deployable, ready-to-use high-performance computing (HPC) framework, but to demonstrate that it enables addressing research questions that are otherwise difficult to tackle. To this end, the first example of 3D full-wavefield target-oriented imaging, which comprises of two subsequent steps of seismic redatuming, is presented. The redatumed fields are estimated by means of gradient-based inversion using the full dataset as well as spatially decimated versions of the dataset as a way to investi-gate the robustness of both inverse problems to spatial aliasing in the input dataset. Our numerical example shows that when one spatial direction is finely sampled, satisfactory redatuming and imaging can be accomplished also when the sampling in other direction is coarser than a quarter of the dominant wavelength. While aliasing introduces noise in the redatumed fields, they are less sensitive to well-known spurious artefacts compared to cheaper, adjoint-based redatuming techniques. These observations are shown to hold for a relatively simple geologic structure, and while further testing is needed for more complex scenarios, we expect them to be generally valid while possibly breaking down for extreme cases
Fast wavelet decomposition of linear operators through product-convolution expansions
