Time‐domain simulation of SH-wave‐induced electromagnetic field in heterogeneous porous media: A fast finite‐element algorithm

When a horizontally polarized rotational mechanical wave (SH-wave) travels through a porous rock, acceleration of the rock frame induces a streaming current in the SH particle motion plane. This streaming current is parallel to the particle displacement and has an associated electromagnetic (EM) field. This phenomenon is often described as the electroseismic (EOS) conversion. Numerically, the EOS phenomenon can be simulated in either the frequency or the time domain. Frequency‐domain numerical simulation has huge memory and computational requirements. Traditional time‐domain simulation, on the other hand, must restrict the time steps to be very small to satisfy stability conditions, resulting in large workload. In this paper, we present a fast finite‐element (FE) method simulating the EOS conversion in the time domain. In our method, we decompose the large 2-D FE matrix equations into a set of 1-D matrix equations and solve the problem using the approximate 1-D multistep process. We present numerical examples of 1-D and 2-D models to illustrate the coevolution of the seismic and electromagnetic fields. Our simulation results show that the diffusive electrical field is induced from the spatial variations of mechanical and electrical properties of the porous media due to the imbalance of the induced electric current. Besides the direct SH-wave itself, the transmitted waves, multiple waves, reflected waves, and diffracted waves also induce diffusive electrical fields. The EOS conversion is potentially useful for reservoir characterization, but the EOS data may be difficult to interpret due to the complexity of the superposed wave fields. The diffusive nature of the induced EM fields suggests that antennas should be positioned close to the target of interest in in‐situ measurements. As a result, borehole EOS surveys are likely to be more practical than surface surveys.