The formation of a magmatic intrusion at depth is responsible for the formation of various thermohydromechanical (THM) disturbances including the upsurge of shock waves and diffusion of pressure fronts in the volcanic system. We couple electromagnetic theory (Maxwell equations) and thermoporoelasticity (Biot equations) to look at the ground surface electrical signature of these THM disturbances. The nature of this coupling is electrokinetic, i.e., associated with water flow relative to the mineral framework and the drag of the excess of charge located in the vicinity of the pore water/mineral interface (the groundwater flow disturbance being related here to the THM disturbances in drained conditions). A new set of laboratory data shows that the electrokinetic coupling is very substantial in fractured basaltic and volcaniclastic materials, and in scoria with several hundreds of millivolts of electrical potential gradient produced per megapascal of pore fluid pressure variations. Our theoretical analysis predicts the diffusion of electromagnetic disturbances and quasi-static electrical signals. These signals can be used as precursors of a volcanic eruption. Indeed, electromagnetic phenomena recorded at the ground surface of a volcanic system, once properly filtered to remove external contributions, provide a direct and quasi-instantaneous insight into the THM disturbances occurring in the heart of the volcanic structure prior and during a volcanic event. Tomography of the quasi-static electrical field is discussed and applied to self-potential profiles performed at the Piton de la Fournaise volcano during the preparation phase of the March 1998 eruption.