An approximate method is developed for treating problems of electromagnetic scattering, at low frequencies, from a buried object in a lossy ground and excited by a source located in the air region above. The field incident on the object's surface is calculated using the dyadic Green's functions for a half-space. Neglecting the coupling between the air–Earth interface and the object as a first-order approximation at low frequencies, we formulate the scattering problem in terms of the magnetic-field integral equation in conjunction with the impedance boundary conditions. The method of moments is then used to reduce the magnetic-field integral equation to a matrix one in order to determine the induced surface currents. The total scattered field is separated into two terms. One is the direct scattered field, which acts as if no buried inhomogeneity were present. The other term is the anomalous field, which represents the presence of the inhomogeneity. Solutions have been generated, and the numerical results are examined for a few limiting cases to confirm their accuracy. The formulation is then applied for investigating scattering by buried steel spheres. The numerical results show that the method can be used for detecting buried objects.
An Explicit Time Marching Scheme for Efficient Solution of the Magnetic Field Integral Equation at Low Frequencies
