Application of the empirical mode decomposition and Hilbert-Huang transform to seismic reflection data

Abstract

Advancements in signal processing may allow for improved imaging and analysis of complex geologic targets found in seismic reflection data. A recent contribution to signal processing is the empirical mode decomposition (EMD) which combines with the Hilbert transform as the Hilbert-Huang transform (HHT). The EMD empirically reduces a time series to several subsignals, each of which is input to the same time-frequency environment via the Hilbert transform. The HHT allows for signals describing stochastic or astochastic processes to be analyzed using instantaneous attributes in the time-frequency domain. The HHT is applied herein to seismic reflection data to: (1) assess the ability of the EMD and HHT to quantify meaningful geologic information in the time and time-frequency domains, and (2) use instantaneous attributes to develop superior filters for improving the signal-to-noise ratio. The objective of this work is to determine whether the HHT allows for empirically-derived characteristics to be used in filter design and application, resulting in better filter performance and enhanced signal-to-noise ratio. Two data sets are used to show successful application of the EMD and HHT to seismic reflection data processing. Nonlinear cable strum is removed from one data set while the other is used to show how the HHT compares to and outperforms Fourier-based processing under certain conditions.