Data-Driven Seismic Signal Characterization

High-resolution Radon transform (RT) has been widely developed and used in seismic data processing. However, the sparse representation and perfect data reconstruction cannot be satisfied simultaneously because only the adjoint operator is adopted in the previous proposed inversion-based Radon transform methods. To address this problem, we use a series of generalized atoms (defined by amplitude, traveltime and wavelet) to approximately construct the pseudo-inverse of the adjoint operator based on the separation of amplitude and traveltime. The unknown atoms are constructed by two steps: location and calibration. The location step is based on a greedy algorithm which can select the atom that best explain the input data (residual); and the (amplitude) calibration step is to ensure that the selected atom can approximate the data more accurate. By iteratively applying the location and calibration steps, the locally coherent events in seismic data can be sparsely approximated. Meanwhile, the reconstruction quality is dramatically improved due to the introduction of pseudo-inverse operator. The proposed algorithm is very efficient because no SVD or over-complete system is required. Numerical examples demonstrate that the proposed method is robust to random noises.