This paper addresses the problem of determining the onset of transient signals such as seismograms, acoustic emissions or ultrasonic signals. Usual manual techniques of onset-time picking are time consuming when numerous measurements are available. This may occur when dealing with (i) anisotropic rocks requiring many elastic wave velocities measurements in the laboratory, (ii) 4-D seismic field data or (iii) laboratory acoustic emissions data. We present a semi-automatic processing technique devoted to the study of case (i). It is based on ultrasonic signal analysis by wavelet transform and an onset-time picking procedure combining Akaike Information Criterion and cross-correlation method. The first step consists in extracting, from the whole experimentally recorded signal, the frequency component corresponding to the perturbation induced by a typical ultrasonic transducer in the laboratory. The second step is dedicated to the onset-time picking of the phase arrival in the extracted signal. The use of this processing technique based on mathematical arguments reduces human subjectivity. Main outcomes are: (i) increase of signal-to-noise ratio; (ii) measurement of elastic wave velocities at prescribed central frequency; (iii) drastic increase of efficiency in wave data processing; and (iv) increase in reliability (repeatability) of wave data acquisition.