Component wave analysis of borehole seismoelectric wavefields and permeability inversion from seismoelectric logs

Seismoelectric logging is a potential technology in which both the acoustic wave and the converted electric field are recorded in the borehole. The existence of the electric field is due to electrokinetic effect in porous formations. In this study we analyze the component waves of the borehole seismoelectric full-wavefields excited by a point pressure source centered in a fluid-filled borehole surrounded by a porous formation and propose a permeability inversion method of using seismoelectric logs. Frequency-dependent excitation intensities of the mode waves are calculated by using argument principle to search complex poles of borehole seismoelectric characteristic-functions. Excitation intensities of real branch points are also calculated by using the branch cut integral method. From the investigation of the ratio of electric excitation intensity to the pressure field's (REP) with respect to the Stoneley wave, it is found that the REP argument is sensitive to permeability. By using Pride's electrokinetic coupling equations, an approximate formula for the relation between the REP argument and permeability is derived theoretically, based on which the permeability inversion method is proposed. Permeabilities of different sandstones inverted from the simulated seismoelectric logs are given.