One dimensional electroseismic modeling using the finite element method

This work presents a finite element procedure for the numerical approximation of the electrosesimic problem at seismic frequencies. The electroseismic equations used are the ones derived by S. Pride, consisting in the coupled Biot’s equations of motion and Maxwell equations where the seismoelectric feeedback is being neglected. The modeled domain comprises two half-spaces, one being air, and the other one a horizontally layered medium. The chosen electromagnetic source is an infinite plane of time dependent electric current located above the surface of the Earth. Under these two assumptions, the electric and magnetic fields and the solid and fluid displacements depend only on one coordinate, namely the one chosen to describe the vertical variations of the Earth; therefore the problem can be considered to be one dimensional. The existence of a unique solution for both the continuous and discrete weak problems is analyzed, considering a finite computational domain by recoursing to absorbing boundary conditions. The finite element procedure is carried out by using C linear functions for the electric field and the solid displacementes, and piecewise constant functions for the magnetic field and fluid displacements, respectively. Examples showing the capabilities of the numerical method are presented.