SPECTRAL DECOMPOSITION WITH SPARSITY CONSTRAINT AND ITS APPLICATION

摘要

Spectral decomposition has been widely used in seismic signal processing and interpretation at present because it can reveals lots of valuable information hidden in the broadband seismic response. Unlike the conventional frequency-based methods, spectral decomposition is able to estimate the frequency contents of the signal at the specific time. How to seek an optimal solution is the most significant aspect for Spectral Decomposition with Sparsity Constraints (SDSC). In this paper, the L_1 regularized L_2-norm is employed as the objective function, the Ricker wavelet is chosen to construct a wavelet library and the optimal solution is obtained by the Iterative Soft Thresholding Algorithm (ISTA). We apply SDSC to the synthetic and field examples. The former show that the SDSC method does a better job in both time and frequency resolution than the traditional spectral decomposition technique, namely the continuous wavelet transform (CWT) method, which always suffers from the conflict between time resolution and frequency resolution. Applications to field data further indicate the potential of the SDSC method in identifying the strong anomalies related to hydrocarbon, and detecting the variations in amplitude associated with faulting.