Non-linear stacking of signals using generalized average of complex numbers

Stacking repeated records can improve the signal-to-noise ratio (SNR) of seismic, geo-radar, or nuclear magnetic resonance measurements. Stacking usually employs a simple summation of amplitudes, but some procedures are also available based on non-linear stacking. This paper analyses the properties of the PWS (Phase-Weighted Stacks) and GAS (Generalized Average of Signals) methods. The PWS is based on the similarity of instantaneous phases on the corresponding complex signals. The GAS uses the averaging of complex spectra in the frequency domain, employing the Generalized Average of Complex Numbers (GACN).We demonstrate our GAS implementation and present its properties compared to PWS. A new method of averaging using GACN is proposed, where we sum the complex signals in the time domain. All three non-linear methods are applied to synthetic and field data, and the SNR improvement compared to simple summation is analyzed. It is shown that non-linear stacking can improve the SNR by up to the first tens of dB. The advantages of time-domain methods are their lower computational complexity and the fact that they do not depend on the choice of the computation window length compared to GAS.