Numerical electroseismic modeling: A finite element approach

JUAN E. SANTOS; FABIO IVÁN ZYSERMAN; PATRICIA M. GAUZELLINO

APPLIED MATHEMATICS AND COMPUTATION

ELSEVIER SCIENCE INC

Lugar: Amsterdam; Año: 2012 vol. 218 p. 6351 - 6374

0096-3003

Electroseismics is a procedure that uses the conversion of electromagnetic to seismic waves in a fluid-saturated porous rock  due to the electrokinetic phenomenom. This work  presents a collection of continuous and discrete time  finite element procedures for  electroseismic modeling in poroelasticfluid-saturated media.  The  model  involves  the simultaneous   solution  of Biot´s equations of motion and Maxwell´s equations in a bounded domain, coupled via an electrokinetic coefficient, with appropiate initial conditions and  employing   absorbing boundary conditions at the artificial boundaries. The 3D case is formulated and analyzed in detail including results on the existence and uniqueness of the solution of the initial boundary value  problem.  Apriori error estimates for a continuous-time finite element procedure based on parallelepiped elements are  derived, with   Maxwell´s  equations discretized in space  using the lowest order mixed finite element spaces of Nédélec,  while for Biot´ s equations  a nonconforming element for  each component of the solid displacement vector and the vector part of the Raviart-Thomas-Nédélec of zero order for the fluid  displacement vector are employed.  A fully implicit discrete-time finite element  method  is also defined and  its stability is demonstrated. The  results are also   extended to the case of tetrahedral elements.    The 2D cases of   compressional and vertically polarized shear waves  coupled with the transverse magnetic polarization  (PSVTM-mode) and  horizontally polarized shear waves coupled with the transverse  electric polarization (SHTE-mode)  are also formulated and     the corresponding finite  element spaces are defined.   The 1D SHTE initial boundary value problem  is also formulated and approximately  solved  using a discrete-time finite element procedure, which was implemented  to obtain   the numerical examples presented.