This paper describes a method for the fast evaluation of the Sommerfeld integrals for modeling a vertical dipole antenna array in a borehole. When we analyze the antenna inside a medium modeled by multiple cylindrical layers with the Method of Moment (MoM), we need a Green's function including the scattered field from the cylindrical boundaries. We focus on the calculation of Green's functions under the condition that both the detector and the source are situated in the innermost layer, since the Green's functions are used to form the impedance matrix of the antenna. Considering bounds on the location of singularities on a complex wave number plane, a fast convergent integration path where pole tracking is unnecessary is considered for numerical integration. Furthermore, as an approximation of the Sommerfeld integral, we describe an asymptotic expansion of the integrals along the branch cuts. The pole contribution of TM01 and HE11 modes are considered in the asymptotic expansion. To obtain numerical results, we use a fast convergent integration path that always proves to be accurate and efficient. The asymptotic expansion works well under specific conditions. The Sommerfeld integral values calculated with the fast evaluation method is used to model the array antenna in a borehole with the MoM. We compare the MoM data with experimental data, and we show the validity of the fast evaluation method.

In this paper, the time-frequency separation algorithm (TFS) proposed by Belouchrani and Amin is applied to ground penetrating radar (GPR) data to reduce ground clutter, that hides reflected waves from a near-surface planar interface. We formulated the problem with several assumptions so that narrow band signals, whose center frequency and baseband signal depend on propagation paths, are received at the receiver, when a wideband signal is radiated from a transmitter. These phenomena can be clearly seen in time-frequency distribution (TFD) of the received signal. In this paper, we adopted the TFS utilizing the TFD signature as a blind separation technique to separate the ground clutter from the target signals. We show numerical and experimental results in order to verify the validity of the problem formulation and the TFS. We carried out GPR measurements to measure permafrost in Yakutsk, Russia. We found the difference in TFD signatures between the ground clutter and the target signal in the experimental data. We could detect the upper boundary of the permafrost with the TFS in spite of the unstable ground clutter.