Random noise attenuation by a selective hybrid approach using f-x empirical mode decomposition |

Here, denotes the noise attenuation operator by EMD, denotes the true dipping events, and denotes random noise in the original seismic section.

We can retrieve the useful dipping events by applying another denoising operator onto the noise section,

where denotes a denoising operator which estimate the lost dipping events from the initial noise section, and denotes the estimated dipping events. The final denoised section is given by the summation of the horizontal and dipping signal section:

The denoising operator in equation 5 can be chosen as predictive filtering (Chen and Ma, 2014), wavelet transform (Chen et al., 2012), or curvelet transform (Dong et al., 2013). Thus, equation 5 becomes a general framework for all those EMD based random noise attenuation approaches. To extend its generality, we propose to use SSA (Oropeza and Sacchi, 2011) as in this paper.

The effectiveness of the novel approach can be ascribed to the strong horizontal-preservation ability of EMD. When most of the useful horizontal energy is preserved after EMD, we turn to deal with less number of plane-wave components in the noise section, which is much easier because less signal components usually correspond to a more strict control over the random noise, e.g., smaller prediction length in predictive filtering (Canales, 1984) and lower rank for extracting useful components in SSA (Oropeza and Sacchi, 2011). For example, lower rank corresponds to less-serious rank-mixing problem, that is , less amount of random noise can be leaked into the denoised section.

Random noise attenuation by a selective hybrid approach using f-x empirical mode decomposition |

2015-11-23