We have proposed a new method to attenuate random noise in $t-x$ domain, by applying the SDRNAR to each seismic trace and remove the residuals for each trace. SDRNAR can achieve better decomposition than EMD in that no mode mixture exists and no useful energy lays in the noise component. In addition to denoising, the amplitude maps for different frequency components can also be obtained, which can be used to aid in seismic interpretation and help in finding oil & gas related low-frequency anomalies. We use both synthetic and field data examples to demonstrate the implementation and performance of the proposed denoising approach. The proposed approach can not be applied to complex seismic profile, which becomes its main limitation. However, compared with those filters that can be specifically used for horizontal events (e.g. mean filter), the proposed approach can get better result. Because it is applied trace by trace, and thus can preserve spatial discontinuities. Compared with $f$-$x$ deconvolution and mean filter, the proposed approach can obtain higher SNR and preserve more useful energy.