Time-domain scattering in 2 1/2 dimensions

A finite-difference time-domain (FDTD) method is used to solve the problem of the response of an arbitrary source, in particular, an impulsive point source, in a two-dimensional isotropic inhomogeneous medium. The field is three-dimensional, whereas the inhomogeneity is two-dimensional; hence, this is called a 2-1/2-dimensional problem. Taking advantage of the invariance of the geometry in one dimension, cosine and sine transforms are used to eliminate one of the spatial derivatives in Maxwell's equations, thereby reducing the problem to two dimensions. A rectangular staggered grid is used to discretize the equations. The complete solution is obtained by linearly superimposing several transformed field components. This provides great savings in terms of computer storage and run time over a three-dimensional FDTD method. The subsurface interface radar, in which an impulsive transmitter and an accompanying receiver are used to detect reflections from subsurface objects, is discussed as an example. Effects of increasing conductivity and depth of the buried objects on the quality of the measured signals are studied.