We have developed a complete seismoelectric theory based on the upscaling the Nernst-Planck and Stokes equations in water-saturated porous media. The coupling between the poroelastic deformation of the porous material (described by Biot''s theory) and the low-frequency limit of the Maxwell equation is electrokinetic in nature (due to the relative displacement between a charged mineral and the pore water). The total electrical current density is equal to a conduction term described by Ohm''s law and a source current density associated with the drag of the excess of electrical charge contained in the pore water by the relative velocity between the fluid and solid phases. This excess of electrical charges is due to the presence of the electrical double layer at the interface between the solid phase and the water phase. The complete set of equations is solved with the finite element code Comsol Multiphysics 3.5 in 2D. We consider then a seismic source described by a moment tensor and we compute the electromagnetic disturbances generated by the seismic source. Three types of signals are generated: (i) a signal directly generated by the source. This signal can be described by a multipole expansion and the resulting electrical field decreases therefore as a powerlaw function of the distance. (ii) seismoelectric conversions are generated at heterogenities of the electrical properties. (iii) Finally, co-seismic signals are generated and they propagate at the same speed as the P and S-waves. We will present synthetic seismograms and associated synthetic electrograms and magnetograms. We will discuss the possibility of a joint inversion of the seismic and electromagnetic information to locate the seismic source and to determine its moment tensor. Applications will be discuss about hydrofracturing in oil and gas reservoirs, geothermal systems, and to the monitoring of active volcanoes.
Observations of electric signals in relation with seismic wave propagation have been reported by many authors in the last decade [1-6]. Of most interest are the two seismoelectromagnetic phenomena described in  and [8-9]. The first one, called the direct field, is associated directly with the hydromechanical source. The second interesting effect corresponds to the electromagnetic interface response (also called the seismoelectric conversion) occurring when a compressional wave or a shear wave crosses an interface characterized by a drop in the mechanical or electrical properties. These two effects are created by the relative displacement between the charged solids phase and the pore water. Such a mechanism is one of the so-called electrokinetic effects in petrophysics. Electrokinetic effects are fundamentally related to the existence of the electrical double alyer at the pore water mineral interface. If the material deforms, this surface charge is fixed in a Lagrangian framework attached to the solid phase. This charge is shielded partly by the sorption of counterions in the Stern layer coating the surface of the minerals [10, 11]. Global electroneutrality at the scale of a representative elementary volume requires an excess of electrical charges located in the vicinity of the mineral/water interface, in the so-called electrical diffuse layer [12,13].