How can I calculate a dispersion curve from an earthquake data ?

Answer 1

You can find the distance to the earthquake from the P-S time difference. Once you have that you can measure the frequency as a function of time from the P or S first arrival and then calculate the travel time as a function of frequency, which you can convert into velocity as a function of frequency because you know the distance from the P-S time difference. You can get dispersion curves for both P and S.