Electric field of a horizontal antenna above a homogeneous half-space: Implications for GPR

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.