Theory of ground-penetrating radars III

The governing equations are Maxwell’s. The source of the current is either j = ey δ(z − z0)δ(x)f(t) or eφ δ(z − z0)δ(r − r0)f(t) (straight wire or loop of current, f(t) is a pulse). The conductivity σ(z) and permittivity ε(z) are unknown in the medium (z > 0) and are known in the air (z < 0). The source is in the air: z0 < 0. The μ is a known constant. The data are the values of E(x, y, z, t) and H(x, y, z, t) for all t > 0, all x, y ∈ R on the surface z = 0. For t < 0 the system is at rest: the electromagnetic fields vanish. Given the data, an exact inversion procedure is described to find σ(z) and ε(z).