Seismic data decomposition into spectral components using regularized nonstationary autoregression

Discussion

The cost of the proposed decomposition is $O\left(N\,N_t\,N_{iter}\right)$, where $N$ is the number of components, $N_t$ is the number of time samples, and $N_{iter}$ is the number of conjugate-gradient iterations for shaping regularization (typically between 10 and 100). This is significantly faster than the $O\left(N_t^2\,N_{iter}\right)$ cost of time-frequency decomposition for a regularly sampled range of frequencies.

Although the examples of this paper use only 1D analysis, the proposed technique is also directly applicable to analyzing variable slopes of 2D and 3D seismic events, where the analysis applies to different frequency slices in the $f$-$x$ domain (Liu and Chen, 2013; Spitz, 1999; Canales, 1984; Spitz, 2000; Liu et al., 2012).