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 /spl epsiv/(t) and /spl sigma/(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/sup -1/ (where Z=e/sup j/spl omega//spl Delta/t/). 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.