Ce. Baumann et Ees. Sampaio, Electric field of a horizontal antenna above a homogeneous half-space: Implications for GPR, GEOPHYSICS, 65(3), 2000, pp. 823
Inverse modeling and interpretation of subsurface structures depend on accu
rate knowledge of the undisturbed field. This is especially true in the ana
lysis of radargrams, in which it is difficult to resolve the upper homogene
ous medium from the less shallow scatterers. The available forward models b
ased on plane-wave and ray approximation are not accurate enough for this t
ask. To improve resolution capabilities, we determine the undisturbed field
using exact expressions for the electric held of a sine-shaped ground-pene
trating radar (GPR) signal antenna above a homogeneous half-space. In the f
requency domain it consists of the sum of two improper integrals with compl
ex integrands. Each integrand contains a kernel multiplied by a Bessel func
tion of the first kind and of order zero or one. In the general case these
integrals do not have a solution in closed form, and their integrands are p
oorly convergent. Therefore, to solve the integrals we must use a special f
ormalism involving integrals around branch points. When we assume that both
the transmitter and the receiver are on the boundary of the half-space, th
ere exist analytic solutions for the first integral without further restric
tions and for the second integral for two special cases: free space and hal
f-space, neglecting displacement currents. We check our corresponding numer
ical results against these analytic solutions. In the time domain we repres
ent the electric held as a function of transmitter-receiver offset and time
. For a purely dielectric half-space the backtransformation of the first in
tegral is analytical under the assumed simplification, allowing us to check
the numerical results obtained with a fast Fourier transform (FFT) algorit
hm. These results allowed us to design radargrams for five different models
of a homogeneous earth, and they are fundamental for interpretation and fu
rther research of GPR modeling.