The echo formation in the near field of an ultrasonic transducer is strongly influenced by the amplitude distribution of the transducer. In this paper, the velocity amplitude on the face of a plane circular transducer was estimated using on-axis transient radiation of the actual transducer. The velocity amplitude can be obtained by deconvolving the pressure waveform with the electrical characteristics of the transducer and then integrating the result with respect to time. Using the estimated velocity amplitude, the scattering of wideband ultrasonic pulses from a cylindrical rod was then numerically calculated by applying a mathematical description of the echo [Lawu et al., J. Acoust. Soc. Am. 98, 2809--2818 (1995)]. Results of these estimations agree well with those obtained experimentally. The proposed method improves the accuracy of the echo waveforms scattered by an object in the near field of the transducer.