A conductive porous medium excited by a seismic wave is the scene of complex physical phenomena known as seismo-electric effects. Understanding them opens new prospects for imaging geological objects invisible to seismic imaging. Their modeling began with the equations proposed by Pride in the 90s, which are constructed by coupling Maxwell's equations with Biot's wave equations. The coupling terms are written in terms of a frequency-dependent operator, which poses a major difficulty in the time domain, as it is an integral Fourier operator whose discretization is not trivial, especially as it must also consider the co-existence of waves propagating a thousand times faster than seismic waves.