Component Wave Analysis Of Borehole Seismoelectric Wavefields In A Porous Formation

Because of the electric double layer and the fluid flow, propagation of acoustic waves will induce electromagnetic fields in a porous formation. Seismoelectric logging is a method to estimate formation parameters using both the signals of acoustic wavefields and electromagnetic wavefields in the borehole. In this paper, the method of component wave analysis is used to study the seismoelectric wavefields induced by a point acoustic source in a fluid filled borehole embedded in a porous formation.After a short review of the Pride theory and the solutions of axisymmetric seismoelectric wavefields, a process is carried out mathematically to prove that the characteristic wavenumber±ke of the electromagnetic wave in the borehole fluid is not a real branch point of the field functions. Then the single valued definition of field functions on the integration contour is clarified.The paper achieves a method to find complex zero points of the characteristic function using the argument principle. Dispersion curves of the mode waves are obtained with parameters of a typical sandstone formation. These mode waves contains leaky modes and unleaky modes. The cut off frequency, the feature of attenuation and phase velocity and group velocity of mode waves are analyzed. After that the paper calculates the excitation intensity of acoustic wavefields and coupling electric wavefields of mode waves with different source distance, then studies the excitation and the attenuation of mode waves.The excitation intensity of compressional wave, shear wave and electromagnetic wave is obtained by the branch cut integral of the real branch points. After calculating the time domain waveforms of acoustic and electric wavefields of component waves, full waveforms are obtained by superposing them, and are in great agreement with the full waveforms obtained by the method of real axis integration. Then the ratio of the excitation intensity of the electric field to that of the acoustic field (this ratio is defined as Q(ω) in this paper) of each component wave is calculated, so the efficiency of acoustic electric conversion of component waves can be studied in frequency domain.Under different permeability conditions, phase velocity, excitation intensity and time domain waveforms of acoustic and electric fields of the Stoneley wave are calculated. Then the relationship of acoustic and electric fields of the Stoneley wave and permeability is studied. It is found that the argument of Q(ω) is sensitive to permeability, and this sensitivity will decrease if the porosity is increased.