Multidimensional Apparition De-Blending Through Sparse Inversion

Summary We describe a novel multi-dimensional sparse inversion algorithm for apparition de-blending which can handle spatial aliasing and overlapping signal cones. We compose the forward modelling apparition blending operator using radon-like phase shift kernels or atoms. Furthermore, this operator includes the periodic shot-by-shot time delays for each source-line. The source de-blending exploits signal sparsity in the projected domain and relies on a sparse solver to reconstruct each individual source. Windowing in space, time and overlapping frequency bands enhances signal sparsity and isolation from the interfering sources. Synthetic and field data examples show the efficacy of the methodology in presence of spatially aliased apparition seismic data.