The generalized coherence algorithm on seismic data based on the kernel function

Traditional coherence algorithms most rely on the basic assumption that the relationship between seismic traces is linear and obeys Gaussian distribution. However, in practice, correlation between seismic traces is usually nonlinear, and the seismic traces are non-Gaussian signals. The canonical correlation analysis (CCA) cannot describe the similarity between adjacent seismic traces in detail. To overcome this problem and improve the resolution and robustness of the coherence algorithm, we introduce the kernelized correlation instead of the linear correlation in the C3 algorithm. Note that the kernelized correlation is a generalized correlation with various kernel functions. Then, we discuss how to choose the appropriate kernel function in detail. To demonstrate the validity of the proposed algorithm, we apply it to field data using different kernels. The results demonstrate the effectiveness of the proposed algorithm to describe geological discontinuity and heterogeneity, such as fluvial channels and faults.