Auto-picking of the first motion arrivals in numerical Green’s functions is often hindered by zero sequences and by numerical modes arising from schemes such as the finite-difference time-domain method. To resolve this problem, we proposed a simple method that adds a random sequence to the numerical Green’s functions and applies a locally stationary autoregressive model for auto-picking. A random sequence around 1% of the maximum body wave amplitude was found to be effective. Use of waveforms for explosive sources composed from diagonal moment-tensor components enables the onset detection more robust for variety of surrounding medium of the hypocenter and the source-station geometry. The proposed method can achieve accuracy comparable to that of manual picking.