Random noise is unavoidable in seismic exploration, especially under
complexsurface conditions and in deepexploration environments. The
current problems in random noise attenuation include preserving the
nonstationary characteristics of the signal and reducing
computational cost of broadband, wideazimuth, and highdensity data
acquisition. To obtain highquality images, traditional prediction
filters (PFs) have proved effective for random noise attenuation,
but these methods typically assume that the signal is
stationary. Most nonstationary PFs use an iterative strategy to
calculate the coefficients, which leads to high computational
costs. In this study, we extended the streaming prediction theory to
the frequency domain and proposed the


streaming
prediction filter (SPF) to attenuate random noise. Instead of using
the iterative optimization algorithm, we formulated a constraint
leastsquares problem to calculate the SPF and derived an analytical
solution to this problem. The multidimensional streaming
constraints are used to increase the accuracy of the SPF. We also
modified the recursive algorithm to update the SPF with the snaky
processing path, which takes full advantage of the streaming
structure to improve the effectiveness of the SPF in high
dimensions. In comparison with 2D

SPF and 3D


regularized nonstationary autoregression (RNA), we tested the
practicality of the proposed method in attenuating random
noise. Numerical experiments show that the 3D


SPF is
suitable for largescale seismic data with the advantages of low
computational cost, reasonable nonstationary signal protection, and
effective random noise attenuation.