Electroacoustic (E-A) logging describes the acoustic response to an electromagnetic (EM) source in a fluid-filled borehole surrounded by a porous medium. The E-A response is simulated by two different methods in this paper. In the coupled method, the EM field and the acoustic field are modeled using Pride's model, which couples Maxwell's equations and Biot's equations. In the uncoupled method, the EM field is uninfluenced by the converted acoustic field, resulting in separate acoustic formulation with an electrokinetic source term derived from the primary EM field. The difference of the transient full waveforms between the above two methods is remarkably small for all examples, thus confirming the validity of using the computationally simpler uncoupled method. It is shown from the simulated waveforms that an EM-accompanying acoustic field is coupled to the EM field and appears with an apparent phase velocity of the EM wave in the formation. Acoustic waves with the conventional acoustic velocities are also seen in the converted full waveforms. For the sandstone models used in this paper, when permeability is less than 1 Darcy, the E-A Stoneley wave amplitude increases with porosity, which is different from that in conventional acoustic-to-acoustic logging.

A B S T R A C TIn 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.

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Monopole acoustic logs in a homogeneous fluid-saturated porous formation can be simulated by the real-axis integration (RAI) method to analytically solve Biot's equations [(1956a) J. Acoust. Soc. Am. 28, 168-178; (1956b) J. Acoust. Soc. Am. 28, 179-191; (1962) J. Appl. Phys. 33, 1482-1498], which govern the wave propagation in poro-elastic media. Such analytical solution generally is impossible for horizontally stratified formations which are common in reality. In this paper, a velocity-stress finite-difference time-domain (FDTD) algorithm is proposed to solve the problem. This algorithm considers both the low-frequency viscous force and the high-frequency inertial force in poro-elastic media, extending its application to a wider frequency range compared to existing algorithms which are only valid in the low-frequency limit. The perfectly matched layer (PML) is applied as an absorbing boundary condition to truncate the computational region. A PML technique without splitting the fields is extended to the poro-elastic wave problem. The FDTD algorithm is validated by comparisons against the RAI method in a variety of formations with different velocities and permeabilities. The acoustic logs in a horizontally stratified porous formation are simulated with the proposed FDTD algorithm.