Methods of 
processing seismic data to remove unwanted 
noise from meaningful reflection signals are provided for. The seismic data is transformed from the offset-
time domain to the time-slowness domain using a 
high resolution Radon transformation. That is, the 
Radon transformation is performed according to an index j of the slowness set and a sampling variable Δp; wherein j=pmax-pmin+1 µ sec / mΔ p,Δp is from about 0.5 to about 4.0 μsec / m, pmax is a predetermined maximum slowness, and pmin is a predetermined minimum slowness. A corrective filter is then applied to enhance the primary reflection 
signal content of the data and to eliminate unwanted 
noise events. After filtering, the enhanced 
signal content is inverse transformed from the time-slowness domain back to the offset-
time domain using an 
inverse Radon transformation.Suitable forward and reverse 
Radon transformations incorporating an offset weighting factor xn and its inverse pn, where 0<n<1, include the following continuous transform equations, and discrete versions thereof that approximate the continuous transform equations: u(p,τ)= ∫-∞∞ ⅆx∫-∞∞ ⅆt d(x,t)xnδ[f(t,x,τ,p)] (forward transform)d(x,t)= ∫-∞∞ ⅆp∫-∞∞ ⅆ τ pnρ(τ)*u(p,τ)δ[g(t,x,τ,p)] (inverse transform)