Sparse Spike Deconvolution of Seismic Data Using Trust-Region Based SQP Algorithm

Abstract

A new deconvolution algorithm for retrieving a sparse reflectivity series from noisy seismic traces is proposed. The problem is formulated as a constrained minimization, taking the approximation zero norm of reflectivity as the objective function. The resulting minimization is solved efficiently by the trust-region based sequential quadratic programming (SQP) method, which provides global convergence and local quadratic convergence rates under suitable assumptions. The null space decomposition method and the de-biasing method are employed to reduce computational complexity and further improve the calculation accuracy. Synthetic simulations indicate that the spikes on the reflectivity, both their positions and amplitudes, are recovered effectively by the proposed approach.