Three-Component Sparse S Transform

In this article, the sparse S transform (ST) is extended to three-component (3C) data and considered in the framework of the sparse inverse theory. The 3C sparse ST is formulated as a constrained optimization where the group sparsity constraint is minimized subject to a data fidelity constraint. Then a fast and efficient algorithm based on the alternative split Bregman technique is employed to solve the optimization. Numerical experiments using synthetic and real seismic data show that the proposed 3C sparse ST automatically generates higher resolution time-frequency (TF) maps compared to single-component sparse decompositions, which has application in phase splitting and earthquake analysis.