Our finite-difference algorithm provides a new method for simulating how seismic waves in arbitrarily heterogeneous porous media generate electric fields through an electrokinetic mechanism called seismoelectric coupling. As the first step in our simulations, we calculate relative pore-fluid/grain-matrix displacement by using existing poroelastic theory. We then calculate the electric current resulting from the grain/fluid displacement by using seismoelectric coupling theory. This electrofiltration current acts as a source term in Poisson's equation, which then allows us to calculate the electric potential distribution. We can safely neglect induction effects in our simulations because the model area is within the electrostatic near field for the depth of investigation (tens to hundreds of meters) and the frequency ranges (10 Hz to 1 kHz) of interest for shallow seismoelectric surveys.We can independently calculate the electric-potential distribution for each time step in the poroelastic simulation without loss of accuracy because electro-osmotic feedback (fluid flow that is perturbed by generated electric fields) is at least 105 times smaller than flow that is driven by fluid-pressure gradients and matrix acceleration, and is therefore negligible. Our simulations demonstrate that, distinct from seismic reflections, the seismoelectric interface response from a thin layer (at least as thin as one-twentieth of the seismic wavelength) is considerably stronger than the response from a single interface. We find that the interface response amplitude decreases as the lateral extent of a layer decreases below the width of the first Fresnel zone. We conclude, on the basis of our modeling results and of field results published elsewhere, that downhole and/or crosswell survey geometries and time-lapse applications are particularly well suited to the seismoelectric method. ?? 2006 Society of Exploration Geophysicists.