Actually I want to pick the coda window from the seismographs, for which I don't know the OT, But using visual inspection I can pick the P and S wave onset.
If you know the arrival times of waves P and S - i.e. Tp and Ts, it is possible to calculate the difference in arrival times of these waves - i.e. ts-p = Ts-Tp. Using the travel-time curve, you can determine the travel time of the P-wave (tp) for this ts-p value. Then you can find the origin time, t0 = Tp-tp. The closer the hodograph will reflect the velocity structure of the medium, the more accurate obtained value of the origin time will be.