Empirical Mode Decomposition Based Instantaneous Spectral Analysis and its Applications to Heterogeneous Petrophysical Model Construction

Spectral analysis is an important step in seismic data processing and interpretation. The frequency contents of seismic traces vary with time due to the fact that the earth is non-stationary medium. Methods were available to improve the temporal and spectral resolution, such as windowed Fourier transform, wavelet transform, S-transform and Matching Pursuit Decomposition, etc. This paper described the Hilbert-Huang Transform (HHT) based on Empirical Mode Decomposition (EMD) that was initially developed to analyze nonlinear and non-stationary water waves. The advantage of HHT-EMD is that it does not require presumed a set of functions as previous methods and allows projection of a non-stationary and non-linear signal onto a time-frequency plane using a set of adaptive Intrinsic Mode Functions (IMF) only determined from the signal itself. The comparisons with wavelet transform and S-transform were made before HHT-EMD was applied to decompose well logs into the wave number-depth (k-z) domain. The depth varying spectrum function was obtained and then used to simulate locally stationary heterogeneous petrophysical models.