What do the derivative or the integral of amplitude of a seismogram mean?

Question

I'm doing a project in which I'm analyzing earthquake seismogram waves. I used a program to graph the exact amplitudes and how they changed over the course of a single earthquake. For the project I need to incorporate calculus, so I was wondering, what does finding the derivative of amplitude do? And what does finding the integral get you? The integral is the area under the entire wavelength, but I was wondering if it was equivalent to energy released, or some sort of geology/physics thing I didn't understand. Thank you.

Answer 1

I teach Calculus and my educated guess is that the Integral of the waveform vs time

IS PROPORTIONAL TO

the Energy released by the earthquake.

The 1st Derivative [the rate of change in energy level] should be an indication of how likely

it is that the energy will continue to increase. Above some level determined from empirical past evidence,

it could be used as a warning signal.