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

Assuming that the seismogram is recording the velocity of the earth's movement (many seismographs are moving magnets inside a coil resulting is a signal proportional to velocity), then the derivative would be proportional to the earth's acceleration and the integral would be proportional to the position.