SUMMARY We present a discrete representation of strongly heterogeneous poroelastic medium with the JKD-model of the frequency-dependent permeability and resistive friction, and the corresponding finite-difference (FD) scheme for numerical modelling of seismic wave propagation and earthquake ground motion in structurally complex media. The scheme is capable of subcell resolution, that is, allows for an arbitrary shape and position of an interface in the spatial grid. The medium can have either a zero resistive friction or non-zero constant resistive friction or JKD frequency-dependent resistive friction. The scheme has the same computational efficiency as the scheme for a smoothly and weakly heterogeneous medium (medium without material interfaces) because the number of operations for updating wavefield is the same. Several comparisons with a semi-analytical approach proves the efficiency and reliability of the subcell-resolution FD scheme. An illustrative example demonstrates differences between earthquake ground motion in the Biot's and JKD variants of the model of the surface sedimentary basin. The example indicates that it is desirable to perform an extensive parametric study in order to find out when it is necessary to apply relatively complicated and computationally more demanding JKD model and when much simpler Biot's model is sufficient.