Multiplicative random seismic noise caused by small-scale near-surface scattering and its transformation during stacking

Abstract

Even after sophisticated processing, land seismic data in complex areas exhibit weak and distorted prestack reflections with low coherency. Usually, the local stacking methods reveal clear reflections. However, the absolute level of amplitude spectra after such stacking experiences a substantial decline across the entire frequency band, reaching −10 to −25 dB. In addition, stacking leads to a significant and progressive loss of higher frequencies. We describe mathematical and intuitive physical models for multiplicative random noise that could consistently explain these field observations at least semiquantitatively. Multiplicative noise is represented by random timeshifts (residual statics) and random phase perturbations different for each frequency. Residual statics explain the progressive loss of higher frequencies. On the other hand, phase perturbations lead to a severe loss of coherency on prestack gathers and produce a strong downward bias or loss of broadband amplitudes after stacking. We find that both types of multiplicative noise can be physically generated by near-surface scattering layers with small-to-medium-scale geologic heterogeneities. We speculate that such multiplicative distortions can be referred to as seismic speckle noise well established in optics and ultrasonics. Furthermore, we derive the fundamental properties of how random multiplicative noise transforms while stacking. The first essential finding reveals that stacking produces an unbiased estimate of the clean signal phase. The second finding finds the mathematical relationship between the frequency-dependent loss of stacked amplitude and the standard deviation of residual statics and phase perturbations. These findings serve as a theoretical justification for the previously proposed methods of phase substitution and phase corrections and open the way to efficiently address random multiplicative noise in seismic processing.