FDTD wave propagation in dispersive soil using a single pole conductivity model

In FDTD modeling of lossy, dispersive soil for subsurface imaging and detection applications, the electric flux and the current are convolutions of E(t) with ε(t) and σ(t) respectively. To avoid these memory-intensive computations, the convolutions can often be accurately and simply modelled as second order difference equations. In particular, by matching the corresponding Z-transform of the E-field/current relation to frequency-dependent conductivity results in a ratio of polynomials in Z^-1 (where Z=e^jωΔt ). A good fit to measured soil data over two decades in frequency is possible using only a single pole, two zero conductivity model. Compared to a similarly accurate three-term Debye model, this one-pole model requires one-third the storage of previously computed field values