Theoretical study on the amplitude ratio of the seismoelectric field to the stoneley wave and the formation tortuosity estimation from seismoelectric logs

Seismoelectric logging has potential applications in exploring the porous formation characteristics. In this study, we theoretically address how the amplitudes of the Stoneley wave and its accompanying borehole seismoelectric field depend on the porous formation parameters such as porosity, permeability and tortuosity. We calculate the ratio of the electric field amplitude to the pressure amplitude (REP amplitude) for the low-frequency Stoneley wave of different formations and find that the REP amplitude is sensitive to porosity and tortuosity but insensitive to permeability. To confirm this conclusion, we derive the approximate expression of the REP amplitude in the wavenumber-frequency domain which shows that the REP amplitude is dependent on tortuosity but independent of permeability. This contradicts the result concluded by previous researchers from experiments that the REP amplitude is directly proportional to the permeability. The reason is probably attributed to the fact that the rock samples with different permeabilities typically have different tortuosities. Since the REP amplitude is sensitive to tortuosity, we propose a method of estimating formation tortuosity from seismoelectric logs. It is implemented by using the REP amplitude and the wavenumber of the Stoneley wave at a given frequency when the porosity and the pore fluid viscosity and salinity are known. We test the method by estimating the tortuosities from the synthetic seismoelectric waveforms in different formations. The result shows that the errors relative to the input tortuosities are lower than 5.0 per cent without considering the uncertainties of other input parameters.