Formulation of the acoustically-induced electromagnetic field in a porous formation in terms of Hertz vectors and simulation of the borehole electromagnetic field excited by an acoustic multipole source

The electromagnetic field induced by acoustic waves in a porous formation is investigated. By supposing that the acoustic field is not influenced by its induced electromagnetic field, the governing equations for the coupled acoustic and electromagnetic fields are reduced to a set of Maxwell equations with a propagation current source. The Maxwell equations are then transformed into inhomogeneous vector Helmholtz equations by introducing Hertz vectors. Finally the electromagnetic field is formulated in terms of the solutions to the Helmholtz equations. This method is used to evaluate the electromagnetic field during seism-electric logging in a porous formation. The full waveforms of the acoustic field and the electromagnetic field in the borehole are calculated when the borehole acoustic sources are respectively a monopole, a dipole and a quadrupole.