The memory damped seismograph

This study aims to discuss and quantify the response and the decaying oscillations of a seismograph. The assumption is that instrument recording of the signal is governed by a second order differential equation including a memory formalism. We see that, in general, the response after an impulse is formed by a decaying step variation followed by oscillations with decreasing amplitude. In fact, the singularities of the solutions of the equation in the Laplace transform domain imply the periodic part of the Green function and the decay. We show how the memory stabilizes the system. It is seen theoretically that the classic mathematical model of the seismometer is not very suitable to model the modern version of the seismometer and that the memory model is possibly more appropriate.