We present a full-waveform modeling technique of the coupled seismoelectromagnetic wave propagation in fluid-saturated stratified porous media. Our simulation code uses the macroscopic governing equations derived by Pride <1994>, which couple Biot's theory and Maxwell equations via flux/force transport equations. In this theory the coupling mechanism is explained by electrokinetic effects taking place at the pore level. The synthetic seismoelectrograms and seismomagnetrograms are computed by extending the generalized reflection and transmission matrix method and by using a discrete wave number integration of the global reflectivity obtained in the frequency wave number domain. Synthetic time sections and snapshots of the wave propagation are used to study the seismic, electromagnetic, and seismoelectromagnetic waves properties in fluid-saturated layered porous media. Two wave phenomena are investigated: (1) the electric and magnetic fields induced by the propagation of a seismic perturbation in a homogeneous porous medium and (2) the electromagnetic waves generated at depth when seismic waves propagate through a vertically heterogeneous porous medium. Concentrating on the second effect, we show that the zone which effectively contributes to the generation of EM disturbances along a plane interface coincides with the first Fresnel zone associated with a seismic-to-electromagnetic wave conversion. A numerical sensitivity study shows that the EM waves generated at depth by the passage of seismic waves through an interface are particularly sensitive to contrasts in porosity, permeability, fluid salinity, and fluid viscosity. Our numerical simulations highlight the potential of artificially generated seismoelectromagnetic converted waves for the characterization of the subsurface and its fluid content.