Methods of processing seismic data to remove unwanted noise from meaningful reflection signals are provided for. Assembled seismic data are transformed from the offset-time domain to the time-slowness domain using a Radon transformation. Preferably, the Radon transformation is applied within defined slowness limits pmin and pmax that will preserve coherent noise, and according to an index j of the slowness set and a sampling variable Δp; wherein j = p ma ⁢ ⁢ x - p m ⁢ ⁢ i ⁢ ⁢ n + 1 ⁢ μsec ⁢ / ⁢ m Δ ⁢ ⁢ p , Δp is from about 0.5 to about 4.0 μsec/m. The coherent noise content of the transformed data is then enhanced, and the primary reflection signal content diminished by filtering at least a subset of the transformed data. The filtered data are inverse transformed from the time-slowness domain back to the offset-time domain using an inverse Radon transformation, and, if necessary, an inverse of the offset weighting factor pn is applied to the inverse transformed data, wherein 0