A difficulty encountered in engineering seismic mapping is that reflection events from shallow discontinuities are commonly overlapped with coherent noise such as air wave, direct waves, head waves, and high-amplitude surface waves. Here, the radial trace transform, a simple geometric re-mapping of a trace gather (x-t domain) to another trace gather (v-t domain), is applied to investigate the rejection effect of coherent linear noises. Two different types of data sets were selected as a representative database: good-quality data for intermediate sounding (hundreds of meters) in a sedimentary basin and very noisy data for shallow (${leq}50m$) mapping of the weathered zone and bedrock surface. Results obtained with cascaded application of the radial transform and low-cut filtering proved to be as good as, or better than, those produced using f-k filtering, and were especially effective for air wave and direct wave. This simple transform enables better understanding of the characteristics of various types of noise in the RT domain, and can be generally applied to overcoming diffractions and back-scatterings caused by joints, fractures, and faults commonly that are encountered in geotechnical problems.