Linearized dynamic warping with ℓ₁-norm constraint for multi-component registration

Registration of the travel time of PP waves and PS waves on the same temporal coordinate is critical for joint interpretation of multi-component seismic data. We propose an ℓ₁-norm minimization approach to register the corresponding amplitude of reflection events in the PP waves and PS waves data. The dynamic warping function is linearized in the ℓ₂-norm fitting term, and a sparsity constrained is used to estimate smooth warping functions. The latter is possible by defining the warping function in terms of a cosine basis. Sparsity is used to minimize the number of basis functions that are used to model the warping function. We have also applied a fast iterative soft thresholding algorithm for solving the non-linear registration optimization problem. We apply the linearized dynamic warping approach with ℓ₁-norm regularization to a synthetic example and to a field data set from the Shengli Oilfield, China.