Elastodynamic and electromagnetic processes are coupled together in saturated, porous media, by a phenomenon known as the electrokinetic effect. In horizontally layered media, the seismoelectric system, which contains the coupled elastodynamic and electromagnetic systems, can be separated into two independent modes of propagation: SH-TE and P-SV-TM. The SH-TE mode contains horizontally polarized shear waves coupled with transverse electric polarized electromagnetic waves. In the P-SV-TM mode, both fast and slow compressional waves are coupled with vertically polarized shear waves and transverse magnetic polarized electromagnetic waves. In this thesis, the P-SV-TM mode of the two-dimensional seismoelectric system was expressed in the form of both the two-way and one-way wave equations. The principle of normalizing energy flux across boundaries was applied, improving the matrix amplitude balance of the system and allowing for the implementation of one-way reciprocity theorems. We carried out full-waveform modelling of the flux-normalized P-SV-TM seismoelectric system in a 2-D fluid-saturated, horizontally-stratified, porous media. Both one-way and two-way wavefields were modelled, allowing the composition of one-way wavefields into two-way wavefields to be clearly observed. We investigated both the generation of electromagnetic fields due to the propagation of a seismic pertubation and the generation of seismic waves due to the propagation of a diffusive electromagnetic wave. Reciprocity of the wavefields was verified by applying reciprocity theorems to both one-way and two-way wave vectors. The electromagnetic field that is created when a seismic wave traverses a contrast in medium parameters is rapidly attenuated during propagation. To mitigate the decay in the amplitude of the signal with distance, we modelled a Vertical ElectroSeismic Profiling (VESP) survey, in which receivers could be placed in near proximity to the target layer. In another model, the sensitivity of the seismoelectric method to pore fluid contrasts was tested by simulating the influx of contaminants into an aquifer. It was observed that a small change in the conductivity of the aquifer led to a significant change in the strength of the electromagnetic signal that was generated at the top of the aquifer.