Permeability inversion from low-frequency seismoelectric logs in fluid-saturated porous formations

In this paper, a method is proposed to invert permeability from seismoelectric logs in fluid-saturated porous formations. From the analysis of both the amplitude and the phase of simulated seismoelectric logs, we find that the Stoneley wave amplitude of the ratio of the converted electric field to the pressure (REP) is sensitive to porosity rather than permeability while the tangent of the REP's phase is sensitive to permeability. The REP's phase reflects the phase discrepancy between the electric field and the pressure at the same location in the borehole. We theoretically derive the frequency-dependent expression of the REP of the low-frequency Stoneley wave and find that the tangent of the REP's argument is approximately in inverse proportion to permeability. We obtain an inversion formula and present the permeability inversion method by using the tangent of the REP's phase. To test this method, the permeabilities of different sandstones are inverted from the synthetic full-waveform data of seismoelectric logs. A modified inversion process is proposed based on the analysis of inversion errors, by which the relative errors are controlled below 25% and they are smaller than those of the permeability inversion from the Stoneley wave of acoustic logs.