We propose a simple statistical model of random multiplicative noise to describe wavefield distortions caused by small-scale near-surface scattering. We specify two types of multiplicative noise: random phase perturbation and random time shifts (residual statics). We investigate the transformation of amplitude and phase of locally stacked data and demonstrate that the combined action of phase perturbations and residual statics could explain what is observed on real land seismic data from the desert environment. Phase perturbations jumble the coherency of all events and lead to severe amplitude loss during stacking. Residual statics creates additional amplitude loss, progressively increasing with frequency. Remarkably, the phase of the local stack delivers an unbiased estimate of the clean signal phase, justifying the previosuly proposed phase substitution method and paving the way to mitigating multiplicative noise in seismic processing. We also reveal a clear link of the new model to optical and ultrasonic speckle noise, opening opportunities for exploring new methods from other domains.
