Modeling of the subsurface interface radar

Abstract

Summary form only given. A finite-difference time-domain 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. In general, a source excites all components of the vector wave field; thus, a scalar solution is incomplete. The field is 3-D, while the inhomogeneity is 2-D. This is called a 2-1/2-D problem. Since the current generated by a point source in a plane is an even function of the coordinate perpendicular to that plane, the field components assume even or odd symmetries correspondingly. Using this fact and 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 differential 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 the three-dimensional finite-difference method. A criterion is given to ensure the stability of this finite-difference scheme, which is a generalized form of Courant-Lewy-Friedrichs stability criterion in two dimensions. Two methods are proposed to treat the source region singularity and the inaccuracy caused by rapidly decaying evanescent waves.