Sparse Layer Inversion Using Linear Programming Approach

In this paper, Sparse layer inversion using linear programming (LP) approach is introduced as an improvement to the Basis Pursuit Decomposition (BPD) method. In the BPD method, the seismic trace is represented as a superposition of dictionary patterns. A dictionary is built using the functions of odd and even reflection coefficients which represent a reflectivity series. The seismic data is reconstructed as the convolution of a seismic wavelet and the reflectivity series. For this convolution based model, the model parameters are estimated by minimizing a loss function which consists of the L2 norm of error and an L1 norm of model parameters. However, in this paper, it is suggested to replace the L2 norm of error with that of L1 norm. These L1 norms of error and the model parameters are rewritten as the inequality constrained optimization problems and this is solved using linear programming approach. Application of this method on a real data set from onshore of the Western part of India shows improved resolution of thin layers in seismic sections.