Application of Hilbert–Huang transform based instantaneous frequency to seismic reflection data

Empirical mode decomposition (EMD) is designed to decompose non-stationary, nonlinear data into a series of intrinsic mode functions (IMFs) adaptively. This procedure is automatic, data-driven and time-variant. And then a Hilbert transform is applied to these IMFs. The combination of EMD with a Hilbert transform is known as Hilbert–Huang transform (HHT). HHT can be used to calculate meaningful multi-resolution instantaneous frequency (HHT based instantaneous frequency). Currently, the application of EMD and HHT to seismic data is performed mainly for noise attenuation. In this paper, we demonstrate new insights of EMD and HHT to seismic data analysis. We first extend the research of Flandrin et al. and analyze how EMD behaves on a Gaussian band-pass signal; we then employ HHT based instantaneous frequency on wedge model and real seismic data to delineate thickness variations. Numerical examples of Gaussian band-pass noise indicate that EMD acts as an adaptive, multi-band overlapping filter bank. The analysis of a wedge model and 2D real seismic data illustrates that HHT based instantaneous frequency is more effective than conventional Hilbert transform based instantaneous frequency in delineating the thickness variation of seismic thin bed.

► We analyze how EMD behaves on Gaussian band-pass signal. ► EMD based instantaneous frequency (IFPs) is used to analyze thickness variation. ► IFPs have a more significant response to thickness variation of layer than IFP. ► IFPs can be used to qualify the thin-bed thickness.