Managing seismic scattering noise in geophysical surveying, especially from near-surface heterogeneity, presents significant challenges. We revisit the role of receiver arrays in mitigating such noise in regions with near-surface meter-scale heterogeneity. Moving beyond traditional approaches that focus on suppressing coherent noise from near-surface arrivals and random ambient noise, our research highlights the substantial impact of speckle scattering noise. This noise, resulting from near-ballistic scattering on small-scale heterogeneities, introduces considerable trace-to-trace variability in phase and amplitude, complicating data processing. By integrating a novel model of random multiplicative noise with sophisticated statistical techniques, we have demonstrated the efficacy of array stacking in significantly reducing this type of noise and decreasing the dispersion of both phase and amplitudes. Our analytical and numerical analyses reveal a notable trend: the reduction in phase and amplitude spread amplifies with the array size. A key finding of our study is the identification of a [Formula: see text] law for phase spread reduction, analogous yet distinct from the well-known [Formula: see text] law observed in amplitude attenuation of additive ambient noise. In our context, this law implies that the standard deviation of residual phase disturbances diminishes in proportion to [Formula: see text], where N denotes the array size. This insight holds particular significance for smaller arrays, such as those with nine receivers commonly used in desert environments.
