HILBERT TRANSFORM USING THE MOST FREQUENT VALUE METHOD

Abstract

In the study, we present a robust inversion method for calculating Hilbert trans-form, a process that also provides resistance to outlier noise. The inversion-based Fourier transform process combined with the Most Frequent Value method (MFV) developed by Steiner can effectively make the Fourier transform more robust. The resistance of the robust Fourier transform process (IRLS-FT) to outliers and its outstanding noise suppression capability justify the method being tried in the field of seismic data processing. As the first stage, we present the production of the Hilbert transform based on a robust inversion, and as an application example we calculate the absolute value of the analytical signal that can be produced as an attribute gauge (instantaneous amplitude). The new algorithm is based on a dual inversion: we determine the Fourier spectrum of the time signal (channel) by inversion, and the spectrum obtained by the transformation required for the Hilbert transform is transformed into the time range with a robust inversion. The latter operation is carried out using the Steiner weights calculated using the Iterative Reweighting Least Squares (IRLS) method (robust in-verse Fourier transform based on inversion). To discretize the spectrum of the time signal, we use the scaled Hermite functions in a series expansion. The expansion coefficients are the unknowns in the inversion. The new Hilbert transform procedure was tested on a Ricker wavelet loaded with Cauchy post-distribution noise. The results show that the procedure has remarkable resistance to outlier noises and noise suppression an order of magnitude better than that calculated by the conventional (DFT) method.