Constraining seismic properties of the 410- and 660-km discontinuities which delineate the mantle transition zone, is crucial in understanding the mantle composition and convection dynamics. One approach to study the transition zone is to use "triplicated" arrivals of seismic data. One of the challenging components in using triplication data, however, is to identify the three individual phases, since they arrive close in time and overlap with each other. Therefore, we analyze Radon transform of the data, which unwraps the bowtie shape in the original data and separates the three phases. Based on the transformed data, a new methodology to obtain the seismic structure around a discontinuity is introduced that utilizes the fact that spherical ray parameters at the two caustics of the triplication are sensitive to the depth and the velocity jump at the discontinuity.