Methods of processing seismic data to remove unwanted noise from meaningful reflection signals are provided for. The methods comprise the steps of assembling seismic data into common geometry gathers in an offset-time domain without correcting the data for normal moveout. The amplitude data are then transformed from the offset-time domain to the time-slowness domain using a Radon transformation. At least of subset of the transformed data is filtered to enhance its coherent noise content and to diminish its primary reflection signal content by defining a slowness high-pass region and, a slowness low-pass region. The low-pass region is defined to enhance the low slowness coherent noise content and to diminish the primary reflection signal content thereof, thereby generating a first subset of said transformed data having enhanced low slowness coherent noise content. The high-pass region is defined to enhance the high slowness coherent noise content and to diminish the primary reflection signal content thereof, thereby generating a second subset of said transformed data having enhanced high slowness coherent noise content. After filtering, the first and second subsets of transformed data are inverse transformed from the time-slowness domain back to the offset-time domain using an inverse Radon transformation to restore the data. The restored signal amplitude data of the first and second subsets of data are then subtracted from the assembled data, thereby enhancing its primary reflection signal content.