Random noise attenuation using $f$-$x$ regularized nonstationary autoregression

Conclusions

We have proposed a novel method for random noise attenuation using $f$-$x$ domain regularized nonstationary autoregression. $f$-$x$ RNA uses shaping regularization to constrain the complex nonstationary coefficients to be smooth along space and frequency axes. Contrary to conventional noise-reduction technology, $f$-$x$ domain and $t$-$x$ domain prediction, $f$-$x$ RNA invokes no piecewise-stationary assumption. The parameters used in $f$-$x$ RNA are intuitive because the parameters directly control the smoothness of complex coefficients. The proposed method has two key parameters: filter length and smoothing radius of shaping operator. Filter length is related to the number of events and smoothing radius is related to the smoothness of desired RNA complex coefficients. As the smoothing radius increases, the result of RNA approaches the result of stationary autoregression. This approach does not require breaking the input data into local windows along space axis, although it is conceptually analogous to sliding spatial windows with maximum overlap. Both synthetic and field data examples confirm that the proposed approach can be significantly more effective than other noise-reduction methods in improving signal-to-noise ratio and preserving the signals. A comparison with the recently published $t$-$x$ RNA method has not been attempted, but remains of interest for further investigation. The proposed method is easy to extend to the 3D case ($f$-$x$-$y$ domain). One only needs to add a space dimension in the equation 9 when applied in 3D case. Besides random noise attenuation, $f$-$x$ RNA may have other applications in seismic data processing, such as seismic trace interpolation.

Random noise attenuation using $f$-$x$ regularized nonstationary autoregression