Seismic Data Interpolation Via Improved Singular Spectrum Analysis

Seismic exploration mainly contains three parts: data acquisition, dataprocessing and data interpretation. Accurate data interpretation depends on thedensity data collection and accurate data processing. However, due to economicconditions and environmental conditions, the acquired seismic data often appearinsufficient spatial sampling or bad sectors, etc., which is called the missing dataproblem. The center problem of thesis is how to effectively reconstruct the missingdata, namely the seismic data interpolation problem.Seismic wave propagates in the underground media, which should follow thefluctuation law. In other words, the data of some frequency slice is linear dependent.Then the corresponding trajectory matrix should be a low-rank matrix. The missingdata destructs the dependence, and then it will increase the rank of trajectory matrix.So interpolation problem is the reduction of the rank under the conditions ofhigh-fidelity.Recently, the singular spectrum analysis is one kind of rank-reduce algorithms.The algorithm makes full use of the physical meaning of seismic data, and it can geta high signal-to-noise ratio. When the seismic data is large, the algorithm will haslarge computation and slow speed. In addition, choosing a right rank is not adaptive,which needs try and error. In this thesis, LMaFit matrix factorization methodreplaces the singular value decomposition method, which improved singularspectrum analysis. The improved algorithm avoids the singular value decomposition,so it can improve the calculation speed. In addition, the improved algorithmconstraints residual ratio, then it can realize automatic detection and update of therank. At last, the thesis takes an amount of experiments about different types anddifferent sampling rate of the seismic data interpolation problems. Numerical resultsshow that the improved algorithm not only retains the physical meaning of thesingular spectrum analysis, saves calculation time, but also avoids the errordepending on the experience.